Answers
Answer:5
Step-by-step explanation:
it would be 5 because
Related Questions
The temperature on top of Mt. Katahdin dropped 25 degrees over 8 hours. On average, how much did the temperature change each hour? Represent your answer as a rational number.
Answers
Answer: To find the average change in temperature per hour, we need to divide the total change in temperature by the number of hours.
The temperature dropped 25 degrees over 8 hours, so the average change per hour is:
25 degrees / 8 hours = 3.125 degrees per hour
Therefore, the temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.
Step-by-step explanation: The temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.
Make up two data sets. list all the values in each data set and write a story to describe where they come from. The data sets should meet the following conditions:
The data set should come from random samples from a population
The centers of the distribution should be similar
The variabilities of the distributions should be different
Answers
The two data sets that meet the given conditions for in centers, and variability is in the explanations.
What are the two datasets?Data Set 1 - Heights of Adults in a City:
Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62
Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.
Data Set 2 - Salaries of Employees in a Corporation:
Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55
Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.
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PLEASE HELP I NEED TO SUBMIT SOON!!
Answers
The missing measure of the square pyramid and the net would be 11.18 units.
The amount of wood that Dee needs to make the doghouse is 98 square feet of wood.
How to find the net ?The missing measure is the side of the pyramid and this can be found using the Pythagorean Theorem with 11 ft being the height of the triangle and 4/ 2 = 2 being one of the sides and the missing measure being the hypotenuse.
The side length is:
= √ (2 ² + 11²)
= √ ( 4 + 121)
= 11.18 units
To determine the amount of wood needed for Dee's doghouse, we need to calculate the surface area of the square pyramid using its net.
Calculate the area of all four triangular faces:
Total area of triangular faces = 4 x area of one triangular face = 4 x 20.5 = 82 square feet
Calculate the total surface area of the pyramid (net):
Total surface area = area of base + total area of triangular faces = 16 + 82 = 98 square feet
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3. What is the vertex of each quadratic function. a) y = (x + 3)² - 6 b) y = (x-7)² + 2 c) y = (x-4)²
Answers
The vertex of the quadratic functions are (-3, -6), (7, 2) and (4, 0).
Stating the vertex of the quadratic functionsThe vertex of a quadratic function in the form y = a(x - h)² + k is given by the point (h, k).
To find the vertex, we need to rewrite the quadratic function in this form by completing the square.
a) y = (x + 3)² - 6:
We can rewrite this equation as y = (x - (-3))² - 6, which is in the form y = a(x - h)² + k.
Therefore, the vertex is (h, k) = (-3, -6).
b) y = (x-7)² + 2:
We can rewrite this equation as y = (x - 7)² + 2, which is in the form y = a(x - h)² + k.
Therefore, the vertex is (h, k) = (7, 2).
c) y = (x-4)²:
We can rewrite this equation as y = (x - 4)² + 0, which is in the form y = a(x - h)² + k.
Therefore, the vertex is (h, k) = (4, 0).
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I NEED HELP ON THIS ASAP!!!
Answers
1. The numeric values of the function are given as follows:
x = -4, y = 1/16.x = -3, y = 1/8.x = -2, y = 1/4.x = -1, y = 1/2.x = 0, y = 1.2. As x approaches negative infinity, y approaches zero.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The numeric values for this problem are given as follows:
x = -4, y = 1/16, as 2^(-4) = 1/2^4 = 1/16.x = -3, y = 1/8, as 2^(-3) = 1/2^3 = 1/18.x = -2, y = 1/4, as 2^(-2) = 1/2^2 = 1/4.x = -1, y = 1/2, as 2^(-1) = 1/2^1 = 1/2.x = 0, y = 1, as 2^(0) = 1/2^0 = 1.Increasing the negative exponent, the number gets closer to zero.
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Use the trading data for Friday, October 20 and Friday, October 27 to answer the questions. ( in the picture)
A) what was the difference between the high and low prices on October 20?
B) on October 27, what was the actual volume of discovery group shares posted? Write the volume in numerals.
C) at what price did discovery group clothes on October 19?
D) use the October 19 closing price from above and the October 20 opening price to find the difference in the prices as a percent increase. Round to the nearest hundredth place.
E) on October 21 discovery group announced that they would close one of their manufacturing plants. This resulted in a drop in their stock price. It closed at $32 express the number change from October 20 to October 21 as a percent rounded to the nearest tenth of a percent.
F) on October 28 discovery group announce that they would not be closing the plant this news cause the price of the stock to rise. It closed at $48.20 express the net change from October 27 to October 28 as a percent, rounded to the nearest tenth of a percent.
G) explain why 52 week high and 52 week low numbers are the same in both charts ?
H) examine the closing price of discover group on October 27 one year earlier one share closed at 30% higher than that amount, what was the closing price one year earlier?
Answers
a. The difference between the high and the low prices on October 20 was $3.33.
b. The actual volume of Discovery Group shares posted on October 27 was 23,600.
c. The closing price for Discovery Group on October 19 was $38.50
What was the percentage decrease?The percentage decrease is calculated below as follows:
closing price on October 19 = $38.50
the opening price on October 20 = $37.22
the percentage decrease in prices = (37.22 - 38.50) / 38.50
the percentage decrease in prices = -3.33% to the nearest hundredth
e. The net change = $32.00 - $38.50
The net change = -$6.50.
The percentage change = (-6.50 / 38.50) * 100
The percentage change = -16.9% to the nearest tenth percent
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given that a test statistic for testing if the true proportion exceeds 0.75 is 1.91. what is the p-value for this test? round to 3 d.p.
Answers
p-value of 0.028 is considered statistically significant at a significance level of 0.05. This suggests that we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis that the true proportion exceeds 0.75.
To calculate the p-value for this test, we need to use the standard normal distribution table or a statistical software.
First, we need to find the area under the standard normal distribution curve to the right of the test statistic of 1.91.
Using a standard normal distribution table, we can find that the area to the right of 1.91 is 0.0287 (rounded to four decimal places).
Since this is a one-tailed test (the alternative hypothesis is that the true proportion is greater than 0.75), the p-value is equal to the area to the right of the test statistic, which is 0.0287.
Therefore, the p-value for this test is 0.028 (rounded to three decimal places). This means that if the null hypothesis (that the true proportion is less than or equal to 0.75) were true, we would expect to see a test statistic as extreme as 1.91 or more extreme in only 0.028 of all possible samples.
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The p-value for the test when the test statistic is 1.91 and we are testing if the true proportion exceeds 0.75 is
approximately 0.028, rounded to 3 decimal places.
Given that the test statistic for testing, if the true proportion exceeds 0.75, is 1.91, we need to find the p-value for this
test and round it to 3 decimal places.
Identify the test statistic
The test statistic provided is 1.91.
Determine the tail of the test
Since we are testing if the true proportion exceeds 0.75, it is a right-tailed test.
Find the p-value
Using a Z-table or statistical software, find the area to the right of the test statistic (1.91) under the standard normal
distribution. This area corresponds to the p-value.
The area to the right of 1.91 in the Z-table is approximately 0.028. Therefore, the p-value for this test is approximately
0.028.
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Match each equation to the value(s) of x that make the equation true. Matching!
choices= (no real solution) (x=9) (x=3) (x= -7) (x-7)
A) 3(x-5) = 2(x-11)
B) 4(3x+7) -5 = 12x +8
C) 3(x+1) -2x = x+3
Answers
Matching of the equation will be:
A) x= -7
B) x= 3
C) x= 9
How to explain the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
A) 3(x-5) = 2(x-11) has x= -7 as the solution.
B) 4(3x+7) -5 = 12x +8 has x= 3 as the solution.
C) 3(x+1) -2x = x+3 has x= 9 as the solution.
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ruby is using the quadratic formula to solve a quadratic equation. which of the following is the next step for simplifying x=−6±85√2 responses
x=−3±8√5
x=−3±√5
x=−3±4√5
this is fully simplified.
Answers
After evaluating −6±85√2, you will obtain two solutions for x, which can be simplified further. To simplify the solutions, you can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
Multiplying by the conjugate of the denominator, we get:
x=−6±85√2
x=−6±85√2 * (85√2 ± 6) / (85√2 ± 6)
Simplifying this expression, we get:
x=−3±4√5
Therefore, the answer is x=−3±4√5.
(c) explain, in a few sentences, what causes a graph of a function in polar coordinates to pass through the origin. how is this different from what makes a graph of a function in rectangular coordinates pass through the origin?
Answers
the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.
How to solve the question?
In polar coordinates, a graph of a function passes through the origin if and only if the function's value at θ=0 is equal to zero. This is because the origin in polar coordinates represents the point (r=0, θ), where r is the distance from the origin and θ is the angle of the point with respect to the positive x-axis. When a function's value at θ=0 is equal to zero, it means that the point on the graph at θ=0 lies on the positive x-axis and has a distance of r=0 from the origin, which is the origin itself.
In contrast, a graph of a function in rectangular coordinates passes through the origin if and only if the function's value at (0,0) is equal to zero. This is because the origin in rectangular coordinates represents the point where the x and y axes intersect, and a point on the graph with coordinates (x,y) passes through the origin if and only if x=0 and y=0, which means the function's value at (0,0) is equal to zero.
In summary, the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.
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There are 3 classes of 22 students making
Ice cream sundaes. A sundae can be
made using one of 3 syrups and one of 3
candy toppings. Each student makes one
sundae. Which expression can be used to
find the total number of sundaes made by
the students?
A 3x22
B 3 x 22
C 3x3x22
D 3³x9x22
Answers
The expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.
What is expression?In mathematics, an expression is a combination of variables, numbers, and mathematical operations that can be evaluated to produce a value. It can be as simple as a single number or variable, or it can be more complex and involve multiple variables and operations. Expressions can be used to represent a wide variety of mathematical concepts and relationships, and are an essential part of algebra, calculus, and other branches of mathematics.
According to given information:The number of sundaes that can be made by one student is 3 x 3 = 9 (since each student chooses one of 3 syrups and one of 3 candy toppings).
Since there are 22 students in each class, the total number of sundaes made by one class is 22 x 9 = 198. Since there are 3 classes, the total number of sundaes made by all the students is 3 x 198 = 594.
Therefore, the expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.
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How many green apples would james have if he ate 1 red apple and 2 green apples out of the 50 green apples he had got.
Answers
Answer:
48
Step-by-step explanation:
50 (total green apples) - 2 (green apples eaten) = 48 (green apples left)
A small can of beans is 3 in. high with a 1 in. radius and sells for $1.49. Which can of beans is a better deal?
a. 9 in. high; 3 in. radius; sells for $39.95
b. 3 in. high; 2. in. radius; sells for $5.96
c. 3 in. high; 3 in. radius; sells for $13.41
Answers
Therefore, can b and c are the same better deal since they have the same price per cubic inch using the volume of a cylinder.
Volume of a cylinder calculation.
To compare which can of beans is a better deal, we need to calculate the volume of each can and divide it by the price. The can with the highest volume per dollar is the better deal.
a) The volume of the can is V=πr²h=(3.14)(3²)(9)=254.34 cubic inches. The price per cubic inch is $39.95/254.34 = $0.157, rounded to three decimal places.
b) The volume of the can is V=πr²h=(3.14)(2²)(3)=37.68 cubic inches. The price per cubic inch is $5.96/37.68 = $0.158, rounded to three decimal places.
c) The volume of the can is V=πr²h=(3.14)(3²)(3)=84.78 cubic inches. The price per cubic inch is $13.41/84.78 = $0.158, rounded to three decimal places.
Therefore, can b and c are the same better deal since they have the same price per cubic inch.
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What is the approximate solution to the equation 6e^4x — 3 = 21? a) 0.7945 b) 0 c) 0.1505 d) 0.3466
Answers
Answer: the answer is d) 0.3466.
Step-by-step explanation:
Starting with the equation:
6e^(4x) - 3 = 21
Add 3 to both sides:
6e^(4x) = 24
Divide both sides by 6:
e^(4x) = 4
Take the natural logarithm of both sides:
ln(e^(4x)) = ln(4)
Use the property of logarithms that ln(e^y) = y:
4x ln(e) = ln(4)
Simplify:
4x = ln(4)
Solve for x by dividing both sides by 4:
x = (1/4) ln(4)
Using a calculator, we get:
x ≈ 0.3466
Therefore, the answer is d) 0.3466.
Given parallelogram ABCD, which statements would allow you to conclude that the parallelogram is a rhombus? Select all that apply.
~a.) Line Segment AD ≅ Line Segment AB
~b.) ∠DCE ≅ ∠BCE
~c.) Line Segment BC ⊥ Line Segment DC
~d.) Line Segment AC ⊥ Line Segment BD
~e.) Line Segment AB ≅ Line Segment DC
~f.) ∠ABC ≅ ∠CDA
Answers
The correct statements to conclude that a parallelogram is a rhombus are: a.) Segment AD ≅ Segment AB e.) Segment AB ≅ Segment DC
f.) ∠ABC ≅ ∠CDA
What is a parallelogram and its properties?In two dimensions, a parallelogram is a geometric figure with parallel sides. It has two parallel sides that are the same length, making it a four-sided polygon (sometimes called a quadrilateral). The sum of the adjacent angles of a parallelogram is 180 degrees. Parallelograms are a unique class of polygons.
To conclude that a parallelogram is a rhombus, we must show that all four sides are congruent (of equal length). Therefore, statements that provide information about the sides of a parallelogram can help us make this conclusion.
The correct statements to conclude that a parallelogram is a rhombus are:
a.) Segment AD ≅ Segment AB
e.) Segment AB ≅ Segment DC
f.) ∠ABC ≅ ∠CDA
These statements tell us that opposite sides are congruent and opposite angles are congruent, which are properties of a rhombus. However, the expressions b, c and d do not give information about the sides, so it cannot be concluded from them that the parallelogram is a rhombus.
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10. A cone has a Volume of 94.25cm ^ 3 If the radius of the cone is 3 cm, what is the height of the cone?
Answers
Answer:
10 cm
Step-by-step explanation:
V =1/3 x π x r² x h
94.25 =1/3 x π x 3² x h
94.25 ÷ 3π =h
so, h= 10 cm
Please answer asap
It is due today
It would be helpful
Answers
The calculated volume of the figure is 761.97 cubic inches
Calculating the volume of the figureFrom the question, we have the following parameters that can be used in our computation:
CylinderConeHollow cylinderThe volume of the figure is calculated as
Volume = Cylinder + Cone - Hollow cylinder
So, we have
Volume = 3.14 * (8/2)^2 * 18 + 1/3 * 3.14 * (8/2)^2 * 5 - 3.14 * (2)^2 * 18
Evaluate
Volume = 761.97
Hence, the volume is 761.97 cubic inches
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The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides. 5,2. 2360679775,5. 47722557505
Answers
An equation that expresses the relationship between the lengths of the three sides is a^2 + b^2 = c^2.
In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.
The relationship between the lengths of the three sides in a right triangle is described by the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
Mathematically, this can be represented as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
For the given right triangle with lengths 5, 2.2360679775, and 5.47722557505, we can plug in the values of a, b, and c to get:
5^2 + 2.2360679775^2 = 5.47722557505^2
which simplifies to:
25 + 5 = 30
This equation is true, indicating that the given lengths do indeed form a right triangle according to the Pythagorean Theorem.
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Write the equation of the parabola that has its x-intercepts
at (5, 0) and (-6, 0) and its
at (0, -1).
Answers
Answer:
y = (1/25)x^2 - 1
Step-by-step explanation:
To begin, we can use the fact that the x-intercepts of the parabola are at (5, 0) and (-6, 0) to determine the x-intercepts form of the equation. The x-intercepts form of a parabola is given by:
(x - r)(x - s) = 0,
where r and s are the x-coordinates of the x-intercepts.
Using this form, we can write:
(x - 5)(x + 6) = 0
Expanding this equation gives:
x^2 + x - 30 = 0
Next, we use the fact that the vertex of the parabola is at (0, -1) to determine the y-intercept form of the equation. The y-intercept form of a parabola is given by:
y = a(x - h)^2 + k,
where (h, k) is the vertex.
Substituting (0, -1) into this equation gives:
y = a(x - 0)^2 - 1
Simplifying gives:
y = ax^2 - 1
Now we can use the fact that the parabola passes through the point (5, 30) to determine the value of a. Substituting x = 5 and y = 0 into the equation above gives:
0 = a(5)^2 - 1
Solving for a gives:
a = 1/25
Substituting this value of a into the equation above gives the final equation of the parabola:
y = (1/25)x^2 - 1
5/0-6/0-41=
hope that helps okay :) if not really really sorry
Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
Answers
By using slope intercept , These were the two points on the line: (0,-2) and (7,2).
Define slope intercept?A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.
We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.
These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.
We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).
So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.
Graph given below:
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Javier design a mosaic wall Mural using a 100 tiles in three different colors yellow blue and red if 64 of the tiles are yellow what percent of the tires are either red or blue
Answers
To find the percentage of tiles that are either red or blue, you can divide the number of red or blue tiles by the total number of tiles and then multiply by 100.
So, the percentage of tiles that are either red or blue is (36/100) x 100 = 36%.
An electrician is running wire from the electric box on a house to a utility pole 85 feet away. The angle of elevation to the connection on the pole is 17°. How much wire does the electrician need? (Round your answer to two decimal places.)
ft
Answers
The electrician needs approximately 296.26 feet of wire.
What is trigonometry?The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).
According to question:The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.
Using trigonometry, we can write:
sin(17°) = opposite / hypotenuse
where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:
hypotenuse = opposite / sin(17°)
To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:
tan(17°) = opposite / 85
Solving for the opposite side, we get:
opposite = 85 tan(17°)
Substituting this into the formula for the hypotenuse, we get:
hypotenuse = (85 tan(17°)) / sin(17°)
hypotenuse ≈ 296.26 feet
Therefore, the electrician needs approximately 296.26 feet of wire.
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Question 6(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Answers
After comparing the data, a measure of variability for both sets of data to be utilised to find the place with the most stable temperature: C. Range, because Sunny Town is skewed.
What exactly is skewness?Skewness is a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram in mathematics, and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.
We may rationally establish that Sunny Town's box plot (box-and-whisker plot) is distorted by closely inspecting it.
Conversely, the Desert Landing box plot (box-and-whisker plot) is symmetrical (vertical line dividing the box into two equal halves), which simply means that both whiskers on either side of the box plot (box-and-whisker plot) are roughly equal and symmetric.
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On the coordinate plane, rectangle JKLM has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2). What is the perimeter of rectangle JKLM? If necessary, round your answer to the nearest tenth
Answers
The perimeter of rectangle JKLM which has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2) On the coordinate plane is 30 units.
By applying the Pythagorean distance formula we calculate the length of each side of the rectangle as,
Distance, d = √{(x₁ - x₂)² + (y₁ - y₂)²} (units)
where (x₁, y₁ ) and ( x₂, y₂) are the coordinates of both the end of a side of the rectangle.
The coordinates of the rectangle JKLM are given as J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2).
Thus,
| JK | = √{(-2 - 6)² + (2 +4)²} = 10 units
| JM | = √{( -2 +5)² + (2 +2)²} = 5 units
| KL | =√{(6-3 )² + (-4+8 )²} = 5 units
| LM | = √{(3+5)² + (-8+2)²} = 10 units
Therefore, JK and LM are sides opposite to each other (and let it be length) and JM and Kl are the other pair (and let it be the breadth) in the rectangle.
Thus, perimeter of a rectangle can be found with the formula,
Perimeter of JKLM = 2( length + breadth) in units
= 2(10+ 5) units
= 30 units
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3) In a triangle ABC, [AM] is the median relative to [BC] and O is the midpoint of [AM]. (BO) cuts [AC] at D. Let E be the midpoint of [DC]. 1º) Prove that BMED is a trapezoid. 2º) Prove that D is the midpoint of [AE]; deduce that CD = 2AD. 3º) Prove that OD = 4 BD.
Answers
1) The lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.
2) CD = 2AD.
Trapezoid and mid point1) To prove that BMED is a trapezoid, we need to show that BM || ED.
Since O is the midpoint of AM, we have OB || MD (as OB and MD are both perpendicular to AM).
Also, since E is the midpoint of DC, we have DE || AC (as DE and AC are both perpendicular to BC).
Therefore, to show that BM || ED, it is enough to show that AC || OB.
We know that OB is a transversal to the parallel lines BM and AM, so we have:
∠OBD = ∠MBC (corresponding angles)
Similarly, we have:
∠OAD = ∠ABC (corresponding angles)
Since ∠MBC = ∠ABC (because [AM] is the median), we have:
∠OBD = ∠OAD
Therefore, the lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.
2) To prove that D is the midpoint of [AE], we need to show that AD = DE.
Since [AM] is the median, we have:
AD = MC
Also, since E is the midpoint of DC, we have:
DE = EC
So it is enough to show that MC = EC.
Since O is the midpoint of AM, we have:
OM = MA/2
But MA = MC + AC/2 (because [AM] is the median), so we have:
OM = (MC + AC/2)/2
= MC/2 + AC/4
Also, since E is the midpoint of DC, we have:
OE = EC/2
But AC = 2DC (because [AM] is the median), so we have:
OE = EC/2 = AC/4
Therefore, we have:
OM = OE
So triangle OME is isosceles, and we have:
∠OEM = ∠OME
But ∠OED = ∠OEM (because DE || AC), so we have:
∠OED = ∠OME
Therefore, triangles ODE and OME are similar, so we have:
OD/OM = OE/OE
= 1
Therefore, OD = OM.
But we also have:
OM = MA/2 = MC/2 + AC/4
= AD/2 + AC/4 (because [AM] is the median)
So we have:
OD = OM = AD/2 + AC/4
= AD/2 + DC/2 (because AC = 2DC)
= (AD + DC)/2
= AE/2 (because E is the midpoint of DC)
Therefore, we have shown that D is the midpoint of [AE].
Moreover, we have:
CD = AE/2 = AD + DC/2 = AD + AC/4 (because AC = 2DC)
= AD + MC/2 (because [AM] is the median)
= AD + AD/2 (because AD = MC)
= 3AD/2
So we have CD = 2AD.
3) To prove that OD = 4BD, we need to show that BD = (1/4)OM.
Since [AM] is the median, we have:
BM = MC
Also, since O is the midpoint of AM, we have:
OM = BM/2 + AM/2
= BM/2 + 2BM/2 (because [AM] is the median)
= 3BM/2
Therefore, we have:
BD = BM - MD
= MC - MD
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I NEED HELP ON THIS ASAP!!!
Answers
The table for the function f(x) = 2ˣ should be completed as follows;
x -4 -3 -2 -1 0
f(x) 1/16 1/8 1/4 1/2 1
As x approaches negative infinity, f(x) decreases.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the negative power rule to the function based on each of the x-values, we have the following:
f(x) = 2⁰ = 1
f(x) = 2⁻¹ = 1/2
f(x) = 2⁻² = 1/2² = 1/4
f(x) = 2⁻³ = 1/2³ = 1/8
f(x) = 2⁻⁴ = 1/2⁴ = 1/16
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find out the perimeter of the semicircle
take pie to be 3.142 and write down all the digits in the calculator
the radius of the semicircle is 11cm
Answers
Answer:
P = 11 + (1/2)π(11) = 11 + 5.5π = 28.279 cm
Letting π = 3.142:
P = 11 + (1/2)(3.142)(11) = 28.281 cm
In the xy-plane, how many horizontal or vertical tangent lines does the curve xy2=2+xy have?
Answers
The curve xy²=2+xy has two horizontal or vertical tangent lines, namely x = 2/3 and y = -1/3, and x = -1/3 and y = 1/3.
To find the horizontal or vertical tangent lines of the curve xy²=2+xy, we need to take the derivative with respect to x and y and solve for when the derivative equals zero.
Taking the derivative with respect to x, we get:
y^2 + 2xy(dy/dx) = y(dy/dx) + 2x
Simplifying, we get
(dy/dx)(y^2 - y) = 2x - y^2
Taking the derivative with respect to y, we get
2xy + x(dy/dy)(2y) = dy/dy + x
Simplifying, we get
(dy/dy)(x-2y) = 1-x
Setting both derivatives equal to zero, we have
(dy/dx)(y^2 - y) = 2x - y^2 ...(1)
(dy/dy)(x-2y) = 1-x ...(2)
From (2), we get
dy/dy = (1-x)/(x-2y)
Substituting into (1), we get
(1-x)/(x-2y)(y^2 - y) = 2x - y^2
Simplifying, we get
y^3 - 3xy^2 + (2x^2-1)y + x = 0
This is a cubic equation in y, which can have up to three solutions. To find the horizontal or vertical tangent lines, we need to set dy/dx = 0 or dy/dy = 0.
Setting dy/dx = 0, we get
2x - y^2 = 0
Setting dy/dy = 0, we get
x - 2y = 1
Solving these equations simultaneously, we get
x = 2/3 and y = -1/3 or x = -1/3 and y = 1/3
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The given question is incomplete, the complete question is:
In the xy-plane, how many horizontal or vertical tangent lines does the curve xy²=2+xy have?
. A middle school teacher conducted a survey of the 8th grade class and found that 43 students were athletes and 19 of those students drink soda. There were 33 students that were not athletes, but drank soda. Last, they found that 22 students were not athletes and did not drink soda. Given this information, how many students don't drink soda
Answers
There are 46 students don't drink soda.
Let's use a Venn diagram to represent the information given in the problem:
Athletes
/ \
/ \
Soda / \ No Soda
/ \
/ \
/ \
----------------------------------------------
| |
| |
| |
Drink No Drink
| |
| |
| |
----------------------------------------------
| |
| |
| |
19 24
| |
| |
|
----------------------------------------------
| |
| |
| |
33 10
| |
| |
| |
----------------------------------------------
| |
| |
| |
24 22
| |
| |
| |
----------------------------------------------
The diagram, we can see that there are 24 students who drink soda and are athletes, 19 who drink soda but are not athletes, 33 who are not athletes but drink soda, and 22 who are neither athletes nor soda drinkers.
The number of students do not drink soda, we need to add the number of students who are athletes but do not drink soda to the number of students who are neither athletes nor soda drinkers:
Number of students who don't drink soda
= Number of athletes who don't drink soda + Number of students who are neither athletes nor soda drinkers
Number of athletes who don't drink soda = Total number of athletes - Number of athletes who drink soda = 43 - 19 = 24
Number of students who are neither athletes nor soda drinkers = 22
The number of students who don't drink soda is:
Number of students who don't drink soda = 24 + 22 = 46.
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Please simplify the sum and show work and answer the questions in the picture below
Answers
The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.
These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc
From the information given, we have that;
x -2/x + 3 + 10x/x² - 9
Find the lowest common denominator and simplify
(x-2)(x² - 9) + (x-3)(10x) /(x²- 9)(x+ 3)
Now, expand the bracket, we get;
x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)
collect the like terms of the denominator and that of the numerator, we get;
11x³ - 39x -2x²/(x²- 9)(x+ 3)
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