The a. Perimeter = 22√7 - 2√3 meters. The Area = 4√12 - 3√7 square meters
How to Find the Area and Perimeter of a Rectangle?Area = length * width
Perimeter = 2(length + width)
Given the following:
Length of the rectangle = 5√7 + 2√3 meters
Width of the rectangle = 6√7 - 3√3 meters
a. Perimeter = 2(5√7 + 2√3) + 2(6√7 - 3√3)
10√7 + 4√3 + 12√7 - 6√3
22√7 - 2√3 meters
b. Area = (5√7 + 2√3)(6√7 - 3√3)
= 5√7(6√7 - 3√3) + 2√3(6√7 - 3√3)
= 210 - 15√21 + 12√21 - 18
= 192 - 3√7
= 4√12 - 3√7 square meters
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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).
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
Help it a screenshot
The equation will be w = 40b
How do you formulate an equation for the scenario provided?To find the total weight (w) of the soil in pounds when Yuki stacks b bags, you can use a simple linear equation. Each bag weighs 40 pounds, so the equation will be: w = 40b
This equation shows that the total weight (w) of the soil in pounds is equal to the number of bags (b) multiplied by the weight of each bag (40 pounds).
The above answer is based on the information below as seen in the picture;
Yuki works at a garden store. She is stacking 40 pounds bags of soil.
write an equation that gives the total weight, w, of the soil in pounds when Yuki stacks b bags.
+ - . = b, w, 40
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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
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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(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?
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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PLS HELP I WILL GIVE YOU 50 PTS BUT IF FOOL ANSWERS WILL GET REPORTED AND GOOD ANSWERS WILL GET BRAINLYEST
Answer: Ok so first you would take the 86 and multiply it by .2 or 20% and that would get you 17.2 for blank 2
then you would take 86 and subtract 17.2 to get 68.8 for blank 3
sooo... he would pay 68 dollars and 80 cents with the coupon
Step-by-step explanation:
im really smart and good at math : )
The sales tax is 4%. The cost of lunch is 6. 50. What is the amount of the sales tax?
The amount of the sales tax is 0.26
How to calculate the amount of sales tax?Convert tax percentage into a decimal by moving the decimal point two spaces to the left.Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.Add the sales tax value to the pre-tax value to calculate the total cost.Now, The sales tax is 4%.
The cost of lunch is 6. 50.
=> 4% of 6.50
4/ 100 × 6.50
0.04 × 6.50
=> 0.26
Hence, The amount of the sales tax is 0.26
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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
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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. 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
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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Find the volume of the cone that has a height of 12 and diameter of 12. Use 3.14 for pi.
Round your answer to the nearest tenths place.
TYPE ONLY THE NUMBER DO NOT INCLUDE THE UNIT
Answer:
425.2
Step-by-step explanation:
v = 1/3[tex]\pi r^{2} h[/tex] If the diameter is 12, then the radius is 6
v = [tex]\frac{3.14(6^{2})12 }{3}[/tex]
v = [tex]\frac{3.14(36)(12)}{3}[/tex]
v = 452.16
Helping in the name of Jesus.
(ASAP) Tell whether the transformation appears to be a rigid motion. Explain.
Yes, the transformation is a rigid motion because the angle measures and the distances between the vertices of the image are the same as the corresponding angle measures and distances in the preimage.
Why is the transformation a rigid motion?Since the shape and size are the same in both the preimage and the image, and only the position has changed, this transformation is considered a rigid motion. Rigid motions, such as translations, rotations, and reflections, preserve the shape and size of the original figure.
Assuming the shape has been bent, it means that the angle measures and distances between the vertices have been altered. But this is not the case.
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9) Find m/B
В
22 mi
A
110°
23 mi
ec
с
The measure of angle ∠B in triangle ABC will be 35.89°.
Given that:
Sides, AC = 23 miles and AB = 22 miles
Angle, ∠A = 110°
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = AC / sin B
23 / sin C = BC / sin 110° = 23 / sin B
The value of BC is calculated as,
BC² = AB² + AC² - 2 AB·AC cos A
BC² = 22² + 23² - 2 x 22 x 23 x cos 110°
BC² = 1359.124
BC = 36.87 miles
The value of angle B is calculated as,
36.87 / sin 110° = 23 / sin B
sin B = 0.586
∠B = 35.89°
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PLEASE HELP I NEED TO SUBMIT SOON!!
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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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?
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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What is the length of the diagonal from P to Q?
The length of the diagonal from the given shape above would be = 12
How to calculate the length of the diagonal?To calculate the length of the diagonal from P to Q, the Pythagorean theorem should be used such as;
C² = a² + b²
The Pythagorean theorem states that the the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Therefore;
C = ?
a = 8
b = 9
C² = 8²+9²
C² = 64+81
C² = 145
C = √145
= 12.
Therefore, the length of the diagonal P to Q of the given shape above is 12.
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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?
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
Show that the four points (2,1), (-1,-5), (1,5) and (-2,-1) are the vertices of a parallelogram
They form a parallelogram because opposite sides of the given points have an equal slope.
What is the slope?The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
According to the given information:To prove that the four points (2,1), (-1,-5), (1,5), and (-2,-1) are the vertices of a parallelogram, we need to show that opposite sides are parallel.
First, we can find the slope of the line connecting (2,1) and (-1,-5):
m1 = (1 - (-5)) / (2 - (-1)) = 6/3 = 2
Next, we can find the slope of the line connecting (1,5) and (-2,-1):
m2 = (5 - (-1)) / (1 - (-2)) = 6/3 = 2
Since the slopes are the same, the line segments connecting these points are parallel.
Now, we can find the slope of the line connecting (2,1) and (1,5):
m3 = (5 - 1) / (1 - 2) = -4
Next, we can find the slope of the line connecting (-1,-5) and (-2,-1):
m4 = (-1 - (-5)) / (-2 - (-1)) = 4/3
Since the slopes are different, the line segments connecting these points are not parallel.
However, we can also see that the line connecting (1,5) and (-1,-5) has the same slope as the line connecting (-2,-1) and (2,1), which is:
m5 = (5 - (-5)) / (1 - (-1)) = 10/2 = 5
Therefore, the line segments connecting (1,5) and (-1,-5), and (-2,-1) and (2,1) are parallel.
Since opposite sides are parallel, the four points (2,1), (-1,-5), (1,5), and (-2,-1) form a parallelogram.
Therefore, they form a parallelogram because opposite sides of the given points have an equal slope.
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Simplify: 4 3/5x3=??
Answer:
69/5 or 13.8
Step-by-step explanation:
..…........
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
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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A laptop computer sells for $2,149.99 and has a mail-in rebate for $200. What is
the cost after the rebate if an envelope costs 15¢ and a stamp costs 39¢?
The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.
What is cost?
Cost" is the amount of money or resources that are required to produce, acquire, or obtain something. In other words, cost refers to the expenses that are incurred in the process of acquiring or producing a good or service.
For example, the cost of producing a product may include the cost of raw materials, labor, overhead expenses, and other related costs. Similarly, the cost of acquiring a product may include the purchase price, taxes, shipping costs, and any other fees or expenses associated with the purchase. Overall, cost is a crucial factor in business and economics, as it determines the profitability of a venture and helps to make informed decisions regarding investments and pricing strategies
To find the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp, we can follow these steps:
Subtract the mail-in rebate from the original price of the laptop:
$2,149.99 - $200 = $1,949.99
Add the cost of the envelope and stamp to the cost of the laptop after the mail-in rebate:
$1,949.99 + $0.15 + $0.39 = $2,090.53
Therefore, the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp is $2,090.53.
To explain this calculation, we first subtract the mail-in rebate of $200 from the original price of the laptop, which gives us the price of the laptop after the rebate. Then, we add the cost of the envelope and the stamp to this price to get the total cost of the laptop after the rebate and the cost of the envelope and stamp.
Therefore, The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.
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a rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 720 feet of fencing is used. find the dimensions of the playground that will enclose the greatest total area.
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
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
Which of these is something I can pay for with the money in a savings account?
Answer:
what are the options?
Step-by-step explanation:
Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
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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write 3.6*10^5+4.8*10^4 in scientific notation
Answer: 3.610^5+4.810^4 in scientific notation is 4.08*10^5.
Step-by-step explanation: The initial step to convert 3.610^5+4.810^4 into scientific notation is to combine the two values.
The sum of 3610 multiplied by 10 to the power of 5 and 4810 multiplied by 10 to the power of 4 is equal to adding 3610 multiplied by 10 to the power of 4 and 4810 multiplied by 10 to the power of 4, resulting in 40.8 multiplied by 10 to the power of 4.
We can convert 40.8*10^4 to scientific notation by shifting the decimal point to the left until there is only one non-zero digit to the left of the decimal, and denoting the number of decimal places moved with a 10 exponent.
Rewording: When you raise 40.810 to the power of 4, the result is 4.0810 to the power of 5 when you add 1 to the exponent. This is equivalent to multiplying 4.08 by 10 and raising it to the power of 5.
(15 POINTS) Help pls ty
When does the graph of a quadratic function have a minimum value?
(this is a recorded answer so make it short and simple please thanks!)
The graph of a quadratic function in the form of y = ax² + bx + c, where "a" is not equal to zero, has a minimum value when "a" is positive.
what is quadratic function ?
A quadratic function is a second-degree polynomial function of the form f(x) = ax² + bx + c, where "a", "b", and "c" are constants, and "a" is not equal to zero. The graph of a quadratic function is a U-shaped curve called a parabola.
In the given question,
The graph of a quadratic function in the form of y = ax² + bx + c, where "a" is not equal to zero, has a minimum value when "a" is positive. This is because the parabola opens upward, and the vertex of the parabola, which represents the minimum point of the function, is located at the point (-b/2a, c - b²/4a).
On the other hand, if "a" is negative, the graph of the quadratic function will have a maximum value. This is because the parabola opens downward, and the vertex of the parabola represents the maximum point of the function.
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solve by substitution
-8y=5x+17
-7y=-2x-17
Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = -10.51 and y = 6.26.
Define equation.In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics of the above x + 7 suggestions. improving in this case provides b + 7 while constructing y + 7 before integrating.
Here,
Let's apply these steps to the provided equation system:
=> -8y = 5x + 17 ...(1)
=> -7y = -2x - 17 ...(2)
Solve equation (1) for x in terms of y in step 1:
=> -8y = 5x + 17
=> 5x = -8y - 17
=> x = (-8y - 17)/5
Step 2: Replace the value of x in equation (2) with the expression from step 1:
=> -7y = -2((-8y - 17)/5) - 17
Step 3: Address the equation that results for y.
=> -7y = (-16y - 34)/5 - 17
=> -35y = -16y - 34 - 85
=> -35y + 16y = -119
=> -19y = -119
=> y = (-119)/(-19)
=> y = 6.26
Step 4: Replace the formula for x from step 1 with the value of y obtained in step 3:
=> x = (-8(6.26) - 17)/5
=> x = -10.51
Consequently, the system of equations has an answer of x = -10.51 and y = 6.26.
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I NEED HELP ON THIS ASAP!!!
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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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.
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.
Austin Corp. reported the following information for 2013 and 2014.Interest receivable, December 31, 2013 $1,100Interest receivable, December 31, 2014 1,400Interest income--2014 3,200How much cash was received for interest during 2014?A. $2,900B. $3,200C. $3,500D. $3,800
Cash received for interest during 2014 was $3,500 .The following equation can be used to determine the amount of money received as interest in 2014:
Amount received as interest equals Interest Income for 2014 plus the decline in Interest Receivable
The difference between the balance of interest receivable at December 31, 2013, and at December 31, 2014, can be used to calculate the decline in interest receivable:
Reduced interest due = Interest due at December 31, 2013, minus Interest due at December 31, 2014, which equals $1,100 minus $1,400, or -$300.
The fact that the balance of interest receivable increased from 2013 to 2014 indicates that the company produced more interest money during the year than it received. In light of this, the money earned on interest in 2014 is:
Interest income from 2014 plus a decrease in interest receivable equals $3,200 minus (-$300) to $3,500 in interest payments received.
Hence, $3,500 is the correct response (C).
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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
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.