Answers
An equation that matches the table include the following: y = x + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 5)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1.
At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 1(x - 0)
y - 5 = x
y = x + 5
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Related Questions
If x = 4 units , y = 6 units, and h =5 units, and the area of the rhombus shown above using decomposition
Answers
The total area of the rectangle and the two right-angled triangles is 50 square units.
What is meant by area?
Area refers to the measurement of the size or extent of a two-dimensional surface or shape. It is usually expressed in square units, such as square meters or square feet.
What is meant by a rectangle?
A rectangle is a four-sided polygon with two pairs of parallel sides and four right angles. The opposite sides of a rectangle are equal in length, and the area can be calculated as length x width.
According to the given information
Area of rectangle = h * x
Area of one right-angled triangle = (1/2) * h * y
Total area of two right-angled triangles = 2 * (1/2) * h * y = h * y
Adding the area of the rectangle and the area of the triangles, we get the total area:
Total area = Area of rectangle + Total area of two right-angled triangles
Substituting the given values, we get:
Total area = (5 * 4) + (5 * 6)
Total area = 20 + 30
Total area = 50 square units
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PLEASE HELP ME! I’m not sure how to do this :(
Answers
The distance from Earth to Mercury is approximately 5.7 x 107 miles, which is less than the fuel capacity of Spigot to travel 125% of the distance from Earth to Mars. Therefore, Spigot has enough fuel to travel from Earth to Mercury and return to Earth before refueling. The correct option is D.
What is distance?Distance refers to the amount of space between two points, objects, or locations. It is typically measured in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line or along a curved path, depending on the context.
Distance is often used in conjunction with time to calculate speed and velocity. For example, the distance traveled by a car in a certain amount of time can be used to calculate its speed.
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In this polygon, all angles are right angles.
What is the area of the polygon? Show your work.
Answers
The area of the polygon is solved to be 1044 squared cm
How to find the are of the c]polygonThe area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas
Section 1 has dimensions:
length * width = 46 * 14 = 644
section 2 has dimensions:
length = 46 - 21 = 25
width = 30 - 14 = 16
Area = 25 * 16 = 400
Area of the composite figure
section 1 + section 2
= 644 + 400
= 1044 squared cm
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How can i do parallelogram shown below has an area of
15
1515 units
2
2
Answers
The height of given parallelogram is 5 units.
Given that, the parallelogram shown below has an area of 15 units.
The base is 3 units.
We know that, the area of a parallelogram is Area = Base × Height
Here, Area = 3×Height
15 = 3×Height
Height = 15/3
Height = 5 units
Therefore, the height of given parallelogram is 5 units.
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"Your question is incomplete, probably the complete question/missing part is:"
The parallelogram shown below has an area of 15 units. Find the missing height.
Which is more, 7 yards or 19 feet?
Answers
According to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product.
According to the given information:To compare 7 yards and 19 feet, we need to convert them to the same unit. Since 1 yard is equal to 3 feet, we can convert yards to feet by multiplying by 3, and we can convert feet to yards by dividing by 3.
In the first answer, we converted 7 yards to feet by multiplying by 3, which gave us 21 feet. Then we compared 21 feet to 19 feet, and found that 21 feet is greater than 19 feet. Therefore, we concluded that 7 yards is more than 19 feet.
In the second answer, we converted 19 feet to yards by dividing by 3, which gave us approximately 6.33 yards (rounded to two decimal places). Then we compared 7 yards to 6.33 yards, and found that 7 yards is greater than 6.33 yards. Therefore, we concluded that 7 yards is more than 19 feet.
Therefore, according to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
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The sales department at a certain company consists of two people, the manufacturing department consists of six people, and the accounting department consists of four people. Three people will be selected at random from these people and will be given gift certificates to a local restaurant. Determine the probability that two of those selected will be from the manufacturing department and one will be from the accounting department. Assume that the selection is done without replacement.
Answers
The probability that two of those selected will be from the manufacturing department and one will be from the accounting department is approximately 0.409.
To solve the problem, we first need to find the total number of ways to select 3 people out of the 12 people in the company, which is given by the combination formula:
C(12,3) = 12! / (3! * (12-3)!) = 220
Next, we need to find the number of ways to select 2 people from the manufacturing department and 1 person from the accounting department. We can do this by using the combination formula again:
C(6,2) * C(4,1) = (6! / (2! * (6-2)!)) * (4! / (1! * (4-1)!)) = 90
Finally, we can find the probability by dividing the number of desired outcomes by the total number of possible outcomes:
P(2 manufacturing, 1 accounting) = 90 / 220 ≈ 0.409
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Need help completing this
Answers
Answer:
a) What is her GROSS pay for a week? 1,400
b) What is her GROSS pay for a year? 67,200
c) What are her TOTAL DEDUCTIONS for a week? 351.39
d) What is her NET pay for a week? 1,048.61
e) What is her NET pay for a year? 50,333.28
f) What does she pay in Income Tax per YEAR? 13,535.52
g) What does she pay in CPP contributions per YEAR? 2,537.28
h) What does she pay in El contributions per YEAR? 793.92
i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
Step-by-step explanation:
GROSS
without tax or other contributions having been deductedNET
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.There are 4 weeks in a month, 52 weeks in a year.
a) What is her GROSS pay for a week? 1,400
The amount of money she makes per hour × the amount of hours she works per week35 × 401,400b) What is her GROSS pay for a year? 67,200
The amount of money she earns in a month × 12(The amount of money she makes per week × 4) × 12(1,400 × 4) × 125600 × 1267,200c) What are her TOTAL DEDUCTIONS for a week? 351.39
Income Tax + CPP + El281.99 + 52.86 + 16.54334.85 + 16.54351.39d) What is her NET pay for a week? 1,048.61
Her gross pay for a week - Her total deductions for a week1,400 - 351.391,048.61e) What is her NET pay for a year? 50,333.28
Her gross pay for a year - Her total deductions for a yearHer gross pay for a year - ([Her total deductions for a week × 4] × 12)Her gross pay for a year - ([351.39 × 4] × 12)67,200 - ([351.39 × 4] × 12)67,200 - (1,405.56 × 12)67,200 - 16,866.7250,333.28f) What does she pay in Income Tax per YEAR? 13,535.52
Income tax per month × 12(Income tax per week × 4) × 12(281.99 × 4) × 121,127.96 × 1213,535.52g) What does she pay in CPP contributions per YEAR? 2,537.28
CPP per month × 12(CPP per week × 4) × 12(52.86 × 4) × 12211.44 × 122,537.28h) What does she pay in El contributions per YEAR? 793.92
El per month × 12(El per week × 4) × 12(16.54 × 4) × 1266.16 × 12793.92i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
(Her yearly Income Tax ÷ Her yearly Gross Pay) × 100(13,535.52 ÷ 67,200) × 1000.20142... × 10020.142...% or 20.14%According to the U. S. Bureau of the Census, in 2000 there were 35. 3 million residents of Hispanic origin living in the United States. By 2010, the number had increased to 50. 5 million. The exponential growth function A = 35. 3ekt describes the U. S. Hispanic population, A, in millions, t years after 2000. A. Find k, correct to three decimals places. B. Use the resulting model to project the Hispanic resident in population in 2015. C. In which year will the Hispanic resident population reach 70 million?
Answers
The value of k is approximately 0.034. The projected Hispanic resident population in 2015 is approximately 73.9 million. The Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.
To find k, we can use the fact that A = 35.3 million when t = 0 (i.e., in 2000), and A = 50.5 million when t = 10 (i.e., in 2010). Substituting these values into the exponential growth function, we get
35.3 = 35.3e^0k
50.5 = 35.3e^(10k)
Dividing the second equation by the first equation, we get
50.5/35.3 = e^(10k)
Taking the natural logarithm of both sides, we get
ln(50.5/35.3) = 10k
Solving for k, we get
k ≈ 0.034
Therefore, the exponential growth function is A = 35.3e^(0.034t).
To project the Hispanic resident population in 2015, we need to find A when t = 15 (i.e., 15 years after 2000). Substituting t = 15 into the exponential growth function, we get
A = 35.3e^(0.034*15) ≈ 73.9 million
Therefore, the projected Hispanic resident population in 2015 is approximately 73.9 million.
To find the year in which the Hispanic resident population reaches 70 million, we need to solve the exponential growth function for t when A = 70. Substituting A = 70 into the exponential growth function, we get
70 = 35.3e^(0.034t)
Dividing both sides by 35.3, we get
e^(0.034t) = 70/35.3
Taking the natural logarithm of both sides, we get
0.034t = ln(70/35.3)
Solving for t, we get
t ≈ 24.7
Therefore, the Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.
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How could you mathematically prove that the elevation on ramp B is steeper than ramp A? (without using logic)
Answers
Elevation on ramp B is more steep than ramp A.
What is elevation?"Elevation" typically refers to the height of a location above sea level. It is often used in geography and topography to describe the height of a mountain or the altitude of a city or other location. Elevation is usually measured in feet or meters, and it can have a significant impact on climate, weather patterns, and other environmental factors.
What is steep?"Steep" can have a few different meanings depending on the context. It can refer to a steep slope or incline, such as a steep hill or mountain. It can also mean a high price or cost, as in "the price is too steep for me." Additionally, "steep" can refer to the act of soaking something in hot water in order to extract flavor, as in steeping a tea bag in hot water.
For RampA:
tanα=36/30
tanα=1.2
For Ramp B:
tanβ=36/20
tanβ=1.8
Therefore for Ramp B angle is more than Ramp A and incase of tangent function value of angle increases with the angle measures.
So β>α.
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Graph the data set. {(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)} Which kind of model best describes the data?
Answers
Answer:
linear
Step-by-step explanation:
i js took the test
The kind of model that best describes the data is a linear relation
Calculating the kind of model best describes the data?From the question, we have the following parameters that can be used in our computation:
{(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)}
In the above dataset, we can see that
As x increases by -1The values of y increases by -3Using the above as a guide, we have the following:
The relation has a constant rate of -3/-1
Evaluate
The relation has a constant rate of 3
Only linear relations have constant rates
Hence, the kind of model that best describes the data is a linear relation
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help what do i put in the box
Answers
The value of x, obtained using the property of bisected angles is 10
What are bisected angles?Bisected angles are angles that are split by a line segment in two to create two angles of the same measure.
The specified information indicates;
[tex]\overrightarrow{GI}[/tex] bisects ∠DGH
m∠DGI = x - 3
m∠IGH = 2·x - 13
The angle addition postulate indicates that we get;
m∠DGH = m∠DGI + m∠IGH
The definition of the bisected angle ∠DGH indicates that we get;
∠DGI = ∠IGH
Therefore;
x - 3 = 2·x - 13
2·x - 13 = x - 3
2·x - x = 13 - 3 = 10
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There are 56 people at the party. Only 14
of them are wearing red. What percent of
people are NOT wearing red?
Answers
Answer: 75%
have a good day/night and crush that homework/class!! you are loved
brainliest??
Answer: 75%
Step-by-step explanation: 56 - 14 = 42. So, 42 people are not wearing red. 42/56 is .75, which is the decimal form for 75%. Also, if you simplify 42/56, you get 3/4 which is also 75%
Read this excerpt from "A Visit from the Goon Squad."
Whatever the reason, a swell of approval palpable as rain lifted from the center of the crowd and rolled out toward its edges, where it crashed against buildings and water wall and rolled back at Scotty with redoubled force, lifting him off his stool, onto his feet (the roadies quickly adjusting the microphones), exploding the quavering husk Scotty had appeared to be just moments before and unleashing something strong, charismatic, and fierce. Anyone who was there that day will tell you the concert really started when Scotty stood up.
How does the author portray Scotty in this excerpt?
His confidence is transformed by the crowd’s response.
His musical ability is improving as he performs.
His anger is unleashed by the chaos of the crowd.
His excitement is shown by his moves on stage.
Answers
Answer:
His confidence is transformed by the crowd’s response.
Step-by-step explanation:
Scotty is described as being a "quavering husk...just moments before." This shows his lack of confidence and anxiety about being on stage.
Solve for length of segment a.
a
3 cm
4 cm
6 cm
a = [?] cm
If two segments intersect inside
or outside a circle: ab = cd
Enter
Answers
The length of segment a in the given chords is determined as 2.
What is the length of segment a?The measure of length a is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
a x 6 = 3 x 4
6a = 12
divide both sides of the equation by 6;
6a/6 = 12/6
a = 2
Thus, the value of a in the given chords is determined by applying chord theorem.
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Determine whether the triangles are similar. If so, write a similarity statement. Explain ur reasoning.
Answers
Answer:
Both 2B and 2A are not similar.
Step-by-step explanation:
----------------------------------------
Let me be helpful!
Let's start with 2B. It is easier to understand the subject that way.
->for a triangle to be similar, it's angles and sides must be the same.
-2B's triangle shows that line TW got scaled by x2.2 (22/10)
-Line ZW got scaled by 1.18
-2b are not similar.
Now on it 2A!
- line JK got scaled by 0.75
- Line JL got scaled by 0.5
-they are not similar
Let me know if I am incorrect!
-A friendly 8th grader :)
If a sphere has a volume of 36π cubic inches, what is its radius?
radius = ___ inches
Answers
The radius of the sphere is approximately 3.634 inches.
We have,
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume of the sphere and r is its radius.
We know that the volume of the sphere is 36π cubic inches.
Substituting this value into the formula, we get:
36π = (4/3)πr³
Multiplying both sides by 3/4π, we get:
r³ = (36π)/(3/4π) = 48
Taking the cube root of both sides.
r = (48)^(1/3)
r = 3.634 inches (rounded to three decimal places)
Therefore,
The radius of the sphere is approximately 3.634 inches.
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The National Junior Honor Society made $238at their cake sale. They sold circular Shaped cakes for $7 and heart shaped cakes for $5. If they Sold twice as many heart cakes as circular ones. how many heart cakes did they sell?
Answers
The number of heart cakes that were sold at the cake sale was 28
According to the question,
Cost of circular-shaped cake = $7
Cost of heart shaped cake = $5
Total sale = $238
Let the number of circular cakes shaped be x
Since the number of heart cakes was sold twice as many as the circular cake, the number of heart cakes will be 2x
Cost of x circular-shaped cake = $7 * x
Cost of 2x heart shaped cake = $5 * 2x
Total sale = Cost of x circular cake + Cost of 2x heart cake
Thus, we get the following equation,
238 = 7x + 10x
238 = 17x
x = 14
Thus, the number of heart cakes sold was 2x that is 28.
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Calvin has a gift card which he is using to buy candy (x), and he has been tracking how much money (y) he spends. He noted that after buying 4 pieces of candy (in all) he has $28.00 left on his card and then after buying 10 pieces of candy (in all) he has $25.00 left on his card. Write the equation of the line that represents his spending on candy
Answers
Answer:
To write the equation of the line that represents Calvin’s spending on candy, we need to first find the slope and the y-intercept of the line.
We can use the two points given in the problem: (4, 28) and (10, 25)
Slope (m) = (y2 - y1) / (x2 - x1)
= (25 - 28) / (10 - 4)
= -3/6
= -1/2
The slope represents the rate at which Calvin is spending money on candy.
Now, we can use the point-slope form of the equation of a line to find the equation of the line.
y - y1 = m(x - x1)
y - 28 = (-1/2)(x - 4)
y - 28 = (-1/2)x + 2
y = (-1/2)x + 30
Therefore, the equation of the line that represents Calvin’s spending on candy is y = (-1/2)x + 30.
Answer: Equation that represents his spending on candy- y = (³⁄₁₀) x
X = number of candy
Step-by-step explanation:
y = money spend x = number of candy
y = (m)x
cost for 10 pieces of candy = $(28 - 25) = $3
⇛ 3 = (m)x10 (x = 10 & y = 3)
⇛m=(³⁄₁₀)
Therefore the equation representing his spending on candy is
⇛ y = (³⁄₁₀) x
2.
(05.02 MC)
Given ΔABC, what is the measure of b? (2 points)
Triangle ABC with angle A measuring 54 degrees and angle C measuring 59 degrees and side BC measuring 11
b = 9.668
b = 11.655
b = 12.516
b = 16.841
Answers
The measure of side ‘b’ in the given triangle ABC, with angle A measuring 54 degrees and angle C measuring 59 degrees and side BC measuring 11 is option-c:12.516, which is found using Sine-law.
What is Sine-law?In a scalene or oblique triangle (a non-right triangle), the law of sine describes the relationship between the sides and angles. Trigonometric laws such as the law of sines and law of cosines are crucial when "solving a triangle" by calculating the unknown angles or sides. The ratio of a triangle's side lengths to the sine of each of its opposite angles must be equal in order for the sine rule to apply. Triangle side length ratios to their corresponding opposite angles are connected by the law of sines. All three sides and the diagonal angles maintain the same ratio.
Given that ∠A= 54° ,∠C= 59° & side BC=a=11
We know that ∠A + ∠B + ∠C = 180° {angle sum property}
Consider △ABC,
54° + 59° + ∠B = 180°
113° + ∠B = 180°
∠B = 180°- 113°
∠B = 67°
Applying Sine-Law,
[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B} = \frac{C}{sin\ C}[/tex]
By using,
[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B}[/tex] , we get:
[tex]\frac{11}{sin\ 54} =\frac{B}{sin\ 67}\\ \\\frac{11}{0.80901} =\frac{B}{0.92050} \\\\B=\frac{11}{0.80901} \times 0.92050[/tex]
B = 13.59686 x 0.92050
B = 12.5159
B = 12.516
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Refer to the attachment for the complete question.
Find the value of x and y 45 5
Answers
answer is : x 25. y = 20 both y's will cancel . 2x =50.=x=25
What would be the appropriate hypotheses for a research company who wants to see if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multivitamin
Answers
The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.
To examine if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multi-vitamin, the appropriate hypotheses for the research company would be as follows:
Null Hypothesis (H0): There is no significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. In other words, the mean amount of vitamin D in both types of multi-vitamins is equal.
Alternative Hypothesis (H1): There is a significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. This means that the mean amount of vitamin D in one type of multi-vitamin is not equal to the other.
The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.
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4.a) Increase £75 by 5%
Please help me and explain this to me.
Answers
Answer:
£78.75
Step-by-step explanation:
An easy way step but longer way to do this is
10% of 75 is 7.5 ((75/10= 7.5))
divide by 2 on both sides
5% = 3.75
then just add it, its increasing 75 by 5%
so 75 + 3.75 = 78.75
100/100 × £75 = £75 .
increasing it by 5% means +5%
so
100% + 5% = 105%
105% of £75 is
105/100 × £75 = £78.75
hope this helps :)
Select the correct answer.
Henry's bread recipe calls for 3 cups of flour, with a variation of up to 4 tablespoons depending on the humidity level. There are 16 tablespoons
in 1 cup. Which inequality could be used to find the number of tablespoons of flour actually used in a recipe?
A.
|t+4|<=48
B.
|t+48|<=4
C.
|t-4|>=48
D.
|t-48|<=54
Answers
The inequality to find the number of tablespoons of flour actually used in a recipe is |t - 48| <= 4. The correct answer is D.
Since the recipe calls for 3 cups of flour with a variation of up to 4 tablespoons, the total amount of flour used can vary between 3 cups - 4 tablespoons and 3 cups + 4 tablespoons. Converting tablespoons to cups, this becomes 3 cups - 1/4 cup and 3 cups + 1/4 cup.
Thus, the range of cups of flour used is [3 - 1/4, 3 + 1/4], which is [2.75, 3.25]. Multiplying by 16 to convert back to tablespoons, we get the range [44, 52].
So, the inequality that could be used to find the number of tablespoons of flour actually used in the recipe is
|t - 48| <= 4
where t is the number of tablespoons of flour used. So, the correct option is D).
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How do you find the hypotenuse of a 45-45-90 triangle if you know the length of the legs?
Answers
The length of the hypotenuse of a 45-45-90 triangle is √2x units.
To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:
Leg 1 = Leg 2 = x
To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:
x² + x² = h²
Simplifying this equation, we get:
2x² = h²
To solve for h, we need to take the square root of both sides of the equation:
√(2x²) = √(h²)
√2 * x = h
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Do you want to use a Square section of your yard for a garden. Do you have a most 52 feet of fencing to surround the garden. Right and solve inequality to represent the possible length of each side of the garden
Answers
The possible lengths of each side of the garden is given by the inequality relation 0 ≤ x ≤ 12
Given data ,
Let's assume that the square garden has sides of length x.
To surround the garden, we will need fencing of length equal to the perimeter of the square, which is 4x
The total amount of fencing is at most 52 feet
So , the inequality is
4x ≤ 52
Dividing both sides by 4, we get:
x ≤ 13
Therefore, the possible length of each side of the garden is less than or equal to 13 feet
And , each side of garden should be more than 0 , so
x > 0
Hence , the full inequality representing the possible length of each side of the garden would be 0 < x ≤ 13
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a cathedral ceiling shown in the figure below is 8 feet high at the west wall of a room. as you go from the west wall toward the east wall, the ceiling slants upward. three feet from the west wall, the ceiling is 10.5 feet high. exercise (a) what is the slope of the ceiling? step 1 the slope is the rise over the run. when we move 3 feet east from the west wall the run is incorrect: your answer is incorrect. feet. the corresponding rise is the difference in ceiling heights. rise
Answers
The slope of the cathedral ceiling is 0.83.
To calculate the slope of the cathedral ceiling, we need to find the rise over the run. The rise is the difference in ceiling heights between the two points. The run is the horizontal distance between the two points.
From the problem statement, we know that the ceiling is 8 feet high at the west wall and 10.5 feet high three feet from the west wall. So the rise is:
rise = 10.5 - 8 = 2.5 feet
The run is the horizontal distance between the two points, which is:
run = 3 feet
Now we can calculate the slope:
slope = rise/run = 2.5/3 = 0.83
Therefore, the slope of the cathedral ceiling is 0.83.
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Please help me.
Giving 40 points
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a) i) The pressure on the ground by snowshoe hare is 0.07 N/cm².
ii) The pressure on the ground by European hare is 0.15 N/cm².
b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet.
a) The pressure on the ground can be calculated by dividing the force on the ground due to weight by the total surface area of the feet.
i) For the snowshoe hare, the pressure on the ground is:
Pressure = Force on ground / Total surface area of feet
Pressure = 14 N / 200 cm²
Pressure = 0.07 N/cm²
ii) For the European hare, the pressure on the ground is:
Pressure = Force on ground / Total surface area of feet
Pressure = 38 N / 250 cm²
Pressure = 0.15 N/cm²
b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet than the European hare and exerts less pressure on the ground. This allows the snowshoe hare to move more easily over the snow without sinking.
Additionally, the snowshoe hare has fur on the soles of its feet, which provides additional insulation against the cold snow. These adaptations help the snowshoe hare survive in its snowy environment by allowing it to move and find food more easily.
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Use inverse operations to solve each of the following quadratic equations. Put each of your responses in the simplest radical form possible.
Answers
The given quadratic equations by solving using inverse operations gives,
(a) x = ±2√2, (b) x = ±3√2 + 5, (c) x = ±4√2, (d) x = ±√90 - 2 and (e) x = 4 ±3√3.
Given are some quadratic equations.
We have to solve this using the inverse operations.
Inverse operations are operations which undo the operation which is done to the equation.
(a) 1/2 x² - 4 = 0
Adding both sides by 4,
1/2 x² = 4
Multiplying both sides by 2,
x² = 8
Taking the square root on both sides,
x = ±√8 = ±2√2
(b) (x - 5)² = 18
Taking the square root on both sides,
x - 5 = ±√18
x - 5 = ±3√2
Adding 5 on both sides,
x = ±3√2 + 5
(c) 2x² + 7 = 71
Subtracting by 7 on both sides,
2x² = 64
Dividing by 2 on both sides,
x² = 32
Taking the square root on both sides,
x = ±4√2
(d) 5 (x + 2)² + 37 = 487
Subtracting by 37 on both sides,
5 (x + 2)² = 450
Dividing by 5 on both sides,
(x + 2)² = 90
Taking the square root on both sides,
x + 2 = ±√90
Subtracting by 2 on both sides,
x = ±√90 - 2
(e) (x - 4)² /3 + 8 = 17
Subtracting by 8 on both sides,
(x - 4)² /3 = 9
Multiplying both sides by 3,
(x - 4)² = 27
Taking the square root on both sides,
x - 4 = ±3√3
Adding both sides by 4,
x = 4 ±3√3
Hence the values are found.
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3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors. (True or False)
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Given statement "3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors." is true. Because the rise and run of a gable roof allows you to calculate the slope factor, which can then be used to calculate the rake length and area of the roof.
If you know the rise and run of a gable roof, you can calculate the rake length and area using slope factors. The slope factor is a ratio that relates the length of the roof to the height of the roof.
The slope factor is calculated by dividing the rise of the roof by the run of the roof. Once you have the slope factor, you can use it to calculate the rake length and area of the roof.
The rake length is the length of the diagonal edge of the roof, and it can be calculated by multiplying the slope factor by the run of the roof.
For example, if the run of the roof is 10 feet and the slope factor is 0.5 (which corresponds to a 6:12 pitch), then the rake length would be 5 feet (0.5 x 10).
The area of the roof can be calculated by multiplying the rake length by the width of the roof.
For example, if the width of the roof is 20 feet and the rake length is 5 feet, then the area of the roof would be 100 square feet.
Statment is true.
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How do you calculate the distance traveled by an object by first calculating when it is stopped?
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To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms
2. Use the given information
3. Determine when the object is stopped
4. Calculate the distance traveled
Identify the terms:
For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:
Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:
To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.
Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:
Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.
We can use the equation s = ut + 0.5at²,
where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.
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