Explain what defines direct variation. Then, check which of the following tables include directly proportional quantities x and y x 1 2 3 4 y 7 14 21 28

Answers

Answer 1

Direct variation in mathematics is when two numbers are written in an equation where one of the numbers multiplied by a constant term to equal the other.

In the table in the equation, we see direct variation.

X Y
1 7
2 14
3 21
4 28

We can find the constant of the variation by dividing y by x. This constant should remain the same for all terms of x in the table with their corresponding y values.

y/x
7/1=7
14/2=7
21/3=7
28/4=7

As we can see, the values in the table all share a direct variation between x and y with the value 7.

This can be expressed in an equation: y = 7x.

Related Questions

Which is an example of the associative property?
A) x + 5 = 5 + x
B) (x + 3) + 7 = x + (3 + 7)
C) 3 • (x + 5) = 3 • x + 15
D) If x = a, and a = 7, then x =

Answers

The first thing we are going to do to solve the problem is to define what associative property is:
Associative property Property that is fulfilled if, given any three elements of a given set, it is verified that there is an operation that verifies equality
An expression that meets the definition is:
(x + 3) + 7 = x + (3 + 7)
We observe that both members of equality are identical, but written in different ways.
Answer:
B) (x + 3) + 7 = x + (3 + 7)

Which of the following values are zeros of
x(x+5)(x-3)?
SELECT ALL THAT APPLY.

A. -5
B. -3
C. 0
D. 3
E. 5

Answers

Zeros are values of x that make any of the factors be zero: 0, -5, 3.

Selections A, C, D apply.

John bikes for 2 hours at a speed of 15 miles per hour. How many hours will it take Shannon to cover the same distance at a speed of 10 mi/h?

Answers

if john bikes for two hours 15 miles per hour two hours is thirty miles of biking
D=RT
Distance= 30 miles
Rate= 10 miles per hour
Time= t
plug numbers in
30 = 10t
divide each side by ten to get t by itself
t= 3
time = 3
3 hours to travel 30 miles biking at 10mph

Answer:

3 hours to travel 30 miles biking at 10mph

Step-by-step explanation:

hope this helps... :)

What is another way to write this number 300+70+5/10+8/100

Answers

Hello!

Your answer is 370 [tex] \frac{29}{50} [/tex]

Another way to write that number would be 370 58/100.
I hope this helped! :-)

A little help pwease :o ? A group of 45 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. O.o

Answers

45= 2(a) + a
45= 2a + a
45= 3a
15= a

30. Since there are twice as many children as adults, let's say the number of adults is x. That means the amount of children is 2x. You know that in total there are 45 people. This means that the number of adults plus the number of children is 45. So we can set up x + 2x = 45. We can solve for x. 3x = 45 so x = 15. Remember, as we stated before, x is the number of adults. 2x is the number of children. Since x = 15, 2x = 30 so there are 30 children in the group.

AAAAAAAAAAAAAASSSSSSSSSSAAAAPPPPPPPPP.........

Answers

The y-intercept is the base pay.
Choice A).

identify a counterexample for the following conditional: if you live in Springfield, then you Iive in Illinois.

Answers

You could live in Springfield, MO. Then you would not be living in Illinois.

The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4 What are the possible dimensions of the classroom? Use Factoring.

Answers

Answer: The expression factors to (2x - 1)(5x + 4)

In a rectangle the area is L x W. So if we know the area is 10x^2 + 3x - 4, then all we have to do is factor it to find possible values for the L and W.

If you factor the expression by grouping, you will get (2x - 1) and (5x + 4).

Your questions asks for possible dimensions, you could give the two expressions as dimensions.

If you wanted to select a value for x, you could plug it in and get values that could be dimensions.

For example if you let x = 10, you would have a rectangle that has a width of 19 and a length of 54.

Answer:

(5x + 4) and (2x – 1)

Step-by-step explanation:

If ED = 10 and DB = 3x-8, what is the length of EB

1. 32
2. 22
3. 10
4. 20

Answers

Based on the picture, we know that ED is equal to DB. Therefore:

2 times ED=EB
2(10)=20

EB is 20

Answer:
EB = 20 units

Explanation:
This question can be solved using two methods:
Method #1:
From the image, we can note that D is the midpoint of EB, therefore, ED = DB
This means that:
EB = 2*10 = 20 units

Method #2:
From the image, we know that ED = DB
We are given that ED = 10 units
Therefore:
DB = 3x - 8 = 10
3x = 18
x = 6
DB = 3(6) - 8 = 18 - 8 = 10 units
EB = EB + DB = 10 + 10 = 20 units

Hope this helps :)

Write the equation, in slope-intercept form, of the line passing through the origin and the point $(-4,3)$.

Answers

If the equation is passing trough the origin, it will be passing trough the point (0,0). We now for our problem that the equations is also passing trough the point (-4,3). So, our line is passing trough the points (0,0) and (-4,3). To write the equation in slope-intercept form, first, we need to find its slope [tex]m[/tex]. To do that we are going to use the slope formula: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex].
From our two points we can infer that [tex]x_{1}=0[/tex], [tex]y_{1}=0[/tex], [tex]x_{2}=-4[/tex], [tex]y_{2}=3[/tex]. Lets replace those values in the slope formula:
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex]m= \frac{3-0}{-4-0} [/tex]
[tex]m= \frac{3}{-4} [/tex]
[tex]m=- \frac{3}{4} [/tex]

Now that we have our slope, we can use the slope-intercept formula:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-0=- \frac{3}{4} (x-0)[/tex]
[tex]y=- \frac{3}{4} x[/tex]

We can conclude that the equation of the line passing trough the points (0,0) and (-4,3) is [tex]y=- \frac{3}{4} x[/tex].

The radius of a circle is equal to half of its diameter. What is the RADIUS of this circle?

Answers

If the diameter is 18, the radius would be nine. Someone please tell me if I missed something.

9 are you looking for area or circumference A= 3.14 x (9x9) c= 3.14 x 9 x2

If △STU ~ △XYZ, which statements must be true? Check all that apply. ∠S ≅ ∠X ∠T ≅ ∠Y ST = XY SU = XZ

Answers

Answer:

A.) ST/XY = TU/YZ
C.) <S congruent to <X
D.) <T congruent to <Y

Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal. Triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex].

Given :

[tex]\rm \Delta STU \sim \Delta XYZ[/tex]

Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal.

Now, it is given that triangle STU is similar to triangle XYZ. This condition is only true when:

[tex]\rm \angle S \cong \angle X[/tex]

[tex]\rm \angle T \cong \angle Y[/tex]

[tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex]

It can be conclude that if triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex] . Therefore, the correct option is A), C) and D).

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simplify 8v + W + 7 - 8v + 2w

Answers

8v + w + 7 - 8v + 2w
= 3w + 7

The answer is 3w +7.
8v +-8v is just 0. That is why it is not included in the equation.

In 2004, the world's largest carousel was located at the House on the Rock, in Spring Green, Wisconsin. Suppose that the center of the carousel is at the origin and that one of the animals on the circumference of the carousel has coordinates (24, 32). If one unit of the coordinate plane equals 1 foot, what is the diameter of the carousel

Answers

1. You have that the Standard form for the equation of a circle when its center is at the origin, is:

x²+y²=r²

2. You must calculate the radius. Then:

r=√(x²+y²)

x=24
y=32

3. When you substitute the values of "x" and "y" into the equation r=√(x²+y²), you obtain:

r=√(x²+y²)
r=√(24²+32²)
r=√(576+1024)
r=√1600
r=40 feet

4. Therefore, the diameter (D) of the circle, is:

D=2r
D=2(40 feet)
D=80 feet

Please help!!! Thank you!!!

Answers

To find the total area of this figure, it would be easiest to find the area of the left part (rectangle) and then find the area of the right part (triangle), and then add the two area values together.

First, we will find the area of the rectangle, using the formula A = lw, where l is the length of the rectangle and w is the width of the rectangle.
The length of the rectangle is 13 cm and the width is 9 cm. If we substitute in these values into our equation, we get:
A = (13cm)(9cm)
A= 117 cm^2

Next, let’s find the area of the triangle, using the formula A=(1/2)bh, where b is the base of the triangle and h is the height.
The base of the triangle is 11 cm and the height of the triangle is 5 cm (found by subtracting 13-8 as seen in the figure). If we substitute in these values and simplify, we get:
A=1/2(11cm)(5cm)
A=1/2(55cm^2)
A=27.5 cm^2.

When we add together the area of the rectangle with the area of the triangle, we will get the total area of the figure.

117 cm^2 + 27.5 cm^2 = 144.5 cm^2
Your answer is 144.5 cm^2 or the first option.

Hope this helps!

The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.

The numbers are: ___ ,___ or ____,___

Answers

Answer: The smaller number is 9 and 5/42. The larger number is 53 and 13/21.

To find these answer you have to write the following two equations.

x - y = 44 and 1/2
7y - x = 10 and 3/14

Then, you can use the substitution method to solve them. Change the first equation to: x = 44 + y. Substitute that into the second equation and solve for y. Once you have that, plug it back into the first equation and solve for x.

The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].

Let's denote the two numbers as x and y, where x is the smaller number. We're given that [tex]y - x = 44 \frac{1}{2}[/tex] and [tex]7x - y = 10 \frac{3}{14}[/tex].

To solve this system of equations, we can use substitution or elimination. Let's use elimination:

1. Multiply the second equation by 2 to clear fractions: [tex]14x - 2y = 20 \frac{6}{14}[/tex].

2. Add the modified second equation to the first equation:

[tex](y - x) + (14x - 2y) = 44 \frac{1}{2} + 20 \frac{6}{14}[/tex]

[tex]13x - y = 64 \frac{11}{14}[/tex]

Now, we have a simpler equation: [tex]13x - y = 64 \frac{11}{14}[/tex].

3. Add this equation to the original second equation to find x:

[tex]7x - y + 13x - y = 10 \frac{3}{14} + 64 \frac{11}{14}[/tex]

[tex]20x - 2y = 75[/tex]

4. Now, we can solve this equation along with the first equation to find x and y.

After solving, we get x = 11 and [tex]y = 55 \frac{1}{2}[/tex].

The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].

Thus, the numbers are [tex]{11 \text{ and } 55 \frac{1}{2}}[/tex].

Correct Question:

The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.

A circle of radius 1 centered at (4, 0) is rotated about the y-axus. Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis. In two or more complete sentences, describe the three-dimensional shape. Upload both parts A and B as your final answer.

Answers

Answer: The three-dimensional shape that would result would be in the shape of a donut.

Imagine taking a knife and cutting a slice in a donut. The cross-section of where you cut would be a circle. This is what would happen if you rotated the circle around the y-axis. It would be like that cross-section of the donut going around the entire circle.

Final answer:

When a circle rotates around the y-axis, it forms a three-dimensional object known as a cylinder. The cylinder will have a radius of 1 and height equal to the diameter of the circle, which is 2.

Explanation:

When a circle of radius 1 centered at (4,0) is rotated about the y-axis, the three-dimensional shape that is produced is known as a cylinder.

This cylinder would have a radius of 1, and its height would be equal to the length of the diameter of the original circle, which is 2 units (from -1 to 1 along the x-axis).

In terms of the visual representation, imagine a circle on a piece of paper, now pick up the paper and rotate it about the line that is the y-axis. The paper, on which the circle is drawn, forms a cylindrical shape when rotated. The edges of the paper represent the bases of the cylinder and the surface of the paper forms the curved surface of the cylinder.

Learn more about 3D Shapes after Rotation here:

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jack lease a car for $159\month for 39 months. the amount due when he signed the lease was 2399. how much did jack pay during the first year of the lease.

Answers

The answer is $4,307. If he is paying 159 a month for 39 months, then you take 159 and muliply it by 12 for the year. That gives you 1908. You then add the 2399 that you paid when he signed the lease and it gives you the 4307.

When the town of Bradyville first started its voluntary recycling program, 1500 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 15% each year.

Which explicit rule can be used to determine the number of people participating in the program in the fifth year?

an=1500(1.15)^n−1

an=1500(0.15)^n

an=1500(1.15)n

an=1500(0.15)^n−1

Answers

Answer: an = 1500(1.15)^n (It looks like you have a typo in the third choice)

This is an example of an exponential equation.
These types of equations are in the form: y = ab^x

A is the starting amount, b is the rate and x is the number of years.

All you have to do is put the pieces in place. Since it is a 15% increase, we are using 1.15 for the rate. And the starting value (a) is 1500.

Answer:

Here you go. :)

Cara muffin recipe calls for 1 1/2 cups of flour for the muffins and 1/4 cup flour for the topping.If she makes 1/2 of the original recipe.How much flour will she use.

Answers

The amount of flour she is using all together is 7/8.
The amount of flour she is using for the muffins is 6/8,
and the amount of flour she is using for the topping is 1/8.

Hope this helps

The amount of cups of flour needed to make 1/2 of the original recipe is 7/8 cups.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Recipe:

Amount of flour for muffins = [tex]1\frac{1}{2}[/tex] = 3/2 cups

Amount of flour for toppings = [tex]\frac{1}{4}[/tex] = 1/4 cups

The total amount of flour:

= 3/2 + 1/4

= (12 + 2) / 8

= 14 / 8

= 7/4 cups

We see that the total amount of flour needed to make one Cara muffin recipe is 7/4 cup of flour.

To make 1/2 of the original recipe.

The amount of flour needed:

1 recipe = 7/4 cups

Divide both sides by 2.

1/2 recipe = 1/2 x 7/4 cups

1/2 recipe = 7/8 cups

Thus,

The amount of cups of flour needed to make 1/2 of the original recipe is 7/8 cups.

Learn more about fractions here:

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Find the inverse function for the function f(x) = mx + b?

Answers

y = mx + b
The inverse is created by interchanging x and y like this.
x = my + b and solving for y
(x - b) = my Now divide by m
(1/m) * (x - b) = y

Most flat screen TVs today are made with an aspect ratio (ratio of the length to the height) of 16:9. Xenock Electronics' top selling TV is their 28-inch model, whose viewing area has a length of 24 inches and a height of 13.5 inches. This TV costs $226.99. They have three main competitors that claim to offer a better deal per viewing area. Phil's Supercenter claims their 18-inch model, whose viewing area length is of the length of Xenock's 28-inch model, is a better deal per viewing area at $152.99. Tyler's Electronics claims their 33-inch model, whose viewing area height is 20% taller than Xenock's 28-inch model, is a better deal per viewing area at $276.99. Beltre's Superstore claims their 82-inch model, whose viewing area dimensions are 300% as large as Xenock's 28-inch model, is a better deal per viewing area at $2,079.99. List the TV's in order of best deal per viewing area. Assume all TV's have the same aspect ratio.

Answers

List of the TV's according to best deal per viewing area.
1. Phil's Supercenter: 24 inches in length x 13.5 inches in height = 324 inches in viewing area for $152.99 or $0.47/inch

2. Tyler's Electronics: 28.8 inches in length x 16.2 inches in height = 466.56 inches in viewing area for $276.99 or $0.59/inch

3. Xenock Electronics: 24 inches in length x 13.5 inches in height = 324 inches in viewing area for $226.99 or $0.70/inch

4. Beltre's Superstore: 72 inches in length x 40.5 inches in height = 2,916 inches in viewing area for $2,079.99 or $0.71/inch

Tyler's, Xenock's, Beltre's, Phil's

Which of the following statements is true about the given function?

Answers

I think the answer is c

The quadratic formula is:

x = (-b plus or minus √b² - 4ac)/2a

Therefore, the other answer would be √7 - 5i

Each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 feet. If there are four blades on the windmill, what is the total area of the blades 1.56 ft2 2.14 ft2 3.28 ft2 or 4.96 ft2 im unsure of this one but im going with 2.,

Answers

The area of a blade with rectangular shape = 1/2 * b * h where b is the base and h, the height. Here b = 7 and height = 4 So the area of the blade = 1/2 * 7 * 4 = 14ft^2 If the are four blades the total area is the summation of individual blade. So area = 14 + 14 + 14 + 14 = 56ft^2. Hence none of the option satisfies the answer.

How would you factor

4x^3 + 2x^2 + 2x?

Please explain in steps not just give me the straight answer.

Answers

[tex]\bf 4x^3+2x^2+2x\implies 2x(2x^2+x+1)[/tex]

so in short, the only factoring doable to it, without any complex factors, is that of taking the common factor of 2x.

now, the trinomial of 2x²+x+1, will not give us any "real roots", just complex or "imaginary" ones.

if you have already covered the quadratic formula, you could test with that, or you can also check that trinomial's discriminant, and notice that it will give you a negative value.

[tex]\bf \begin{array}{llcccll} & 2 x^2& +1 x& +1\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \qquad 1^2-4(2)(1) \\\\\\ discriminant\implies b^2-4ac= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

Answer:

[tex]2x(2x^2+x+1)[/tex]

Step-by-step explanation:

We have been given an expression and we are asked to find factor out our given expression.

[tex]4x^3+2x^2+2x[/tex]

To factor our given expression we need to factor out the greatest common factor of each term of our given expression.

We can rewrite our given expression as:

[tex](2\cdot 2\cdot x\cdot x\cdot x)+(2x\cdot x)+2x[/tex]

We can see that the greatest common factor of our given expression is 2x.

Upon factoring out 2x from our given expression we will get,

[tex]2x(2\cdot x\cdot x+x+1)[/tex]

[tex]2x(2x^2+x+1)[/tex]

Therefore, the factored form of our given expression is [tex]2x(2x^2+x+1)[/tex] .

The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary.

Answers

By definition, the volume of a sphere is:
[tex]V = \frac{4}{3} (\pi) (r ^ 3) [/tex]
Where,
r: sphere radio
Substituting values we have:
[tex] V = \frac{4}{3}(3.14)(( \frac{21.6}{2} ) ^ 3) [/tex]
[tex]V = 5273.99424 [/tex] Rounding the result to the nearest tenth:
[tex]V = 5274.0 cm ^ 3 [/tex] Answer:
the sphere's volume is:
[tex]V = 5274.0 cm ^ 3 [/tex]

want 100p and brainiest answer first, ((((please))))

what is 2 1
1__ - 2__ = ?
3 3

Answers

I believe it’s -2 over 3

When a number is divided by -3, the result is 12 more than the number what is the number?

Answers

Final answer:

To find the number that, when divided by -3, the result is 12 more than the number, we set up an equation and solve it to get the answer, which is -9.

Explanation:

When a number is divided by -3, and the result is 12 more than the number itself, we can set up the following equation to find the number: number / -3 = number + 12. Following division and multiplication rules for signs, and executing proper algebraic manipulations, we can solve this equation.

First, we multiply both sides by -3 to get rid of the fraction:
-3 * (number / -3) = -3 * (number + 12),
which simplifies to:
number = -3(number) - 36.
Next, we add 3(number) to both sides to get:
4(number) = -36.
Finally, we divide both sides by 4 to isolate the 'number':
number = -36 / 4
number = -9.

Therefore, the number in question is -9.

The following is the correct way to begin solving for the quotient of 39.538 divided by 5.3 using the standard method:

True
False

ILL GIVE BRAINLIEST IF U GET IT RIGHT!!

Answers

The standard method is correct but it shows 53 instead of 5.3
so it is False. Hope it helps

Answer:the answer is false

In july in seattle, the grass grows 1/2 inch a day on a sunny day and 1/4 inch a day on a cloudy day. in seattle, in july, 75% of the days are sunny and 25% of the days are cloudy.
a.find the expected value of grass growth for the day
b.find the expected value of grass growth for the month of july ( 31 days ) -- round both to 2 decimal placees

Answers

expected value equals sum of the product of each value and its possibility.
a.
1/2×75％＋1/4×25％=0.4375
the expected value of grass growth for the day is 0.4375
b.
0.4375×31=13.5625
the expected value of grass growth for the month of july is 13.5625

Final answer:

Calculate the expected grass growth in Seattle based on the daily growth rates for sunny and cloudy days, then find the expected growth for the month of July.

Explanation:

a. Expected value of grass growth for the day:

Expected growth = (0.75 x 0.5) + (0.25 x 0.25) = 0.4375 inches

b. Expected value of grass growth for the month of July:

Expected growth for July = 31 days x Expected growth per day = 31 x 0.4375 = 13.56 inches

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