Gary painted some shapes. Select one number from each column to show a fraction greater than 1 that names the parts Gary painted

The average rate of change for any function f(x) is the ratio of change in its y-values to change in its x-values for any two particular points on the curve of the function f(x). Mathematically, we can write it as follows :-

Average rate of change = [tex] \frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} [/tex]

It says to find the average rate of change from x = 0 to x = 10.

From the given table, x = 0 corresponds to y = f(0) = -6 and x = 10 corresponds to y = f(10) = 204.

So we have two points A(0, -6) and B(10, 204).

Using the above formula, we can find average rate of change from A to B.

Average rate of change from (0, -6) to (10, 204) = [tex] \frac{204-(-6)}{10-0} =\frac{204+6}{10} = \frac{210}{10} =21 [/tex]

Hence, the final answer is 21.

The fraction that goes in the middle to make the comparison true is 7/10.

5/8 < 7/10 < 8/10

Option C is the correct answer.

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

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

We have,

5/8 < x < 8/10

The value for x is greater than 5/8 but less than 8/10.

1/2 is less than 5/8.

1/3 is less than 5/8.

7/10 is greater than 5/8 and less than 8/10.

1/4 is less than 5/8.

Thus,

5/8 < 7/10 < 8/10

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Final answer:

The hyperbolas' equations are analyzed to find the values of a² and b². For the first equation, a² is 9 and b² is 16; for the second, a² is 4 and b² is 16; and for the third, a² is 3 and b² is 2.

Explanation:

To identify the required elements for each of the hyperbolas, we need to look at the equations of the hyperbolas and determine the values of a and b, which are the square roots of the denominators of the x-squared and y-squared terms when they are in the standard form for a hyperbola, x²/a² - y²/b² = 1 for horizontal hyperbolas, and y²/a² - x²/b² = 1 for vertical hyperbolas.

1. For the hyperbola x²/9 - y²/16 = 1, the required elements are a² and b². Hence, a² = 9 and b² = 16, leading to the answers being c and d respectively.

2. The hyperbola 4x² - y² = 16 can be rearranged to x²/4 - y²/16 = 1. Here, a² = 4 and b² = 16, making the answers c and d respectively.

3. For hyperbola 2y² - 3x² = 6, it rearranges to y²/3 - x²/2 = 1. In this case, a² = 3 and b² = 2, so the answers are d and a respectively, since we are looking for a and b, not a² and b².

Answer:

its 2 feet and 11 inches

Step-by-step explanation:

The total time for two game is 32 minutes. The time for each game can be determine using system equation.

The time for game is 10 minute and 22 minute respectively.

Given:

Total time to complete two game is 32 minutes.

Let [tex]x[/tex] is the time took to complete one game.

Write the system equation for the given condition.

[tex]\begin{aligned}\\ x+x+12=32\\2x=32-12\\x=10 \:\rm min\\\end{aligned}[/tex]

As per the question, one game took 12 minutes longer than other. So the time for second game is,

[tex]x+12=10+12=22 \:\rm minutes[/tex]

Thus, the time took to complete game is [tex]10\:\rm minutes[/tex] and [tex]22\:\rm minutes[/tex] respectively.

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Answer:

it is 100%

Step-by-step explanation:

i did it on usa test prep

Answer:

500 x 0.7 = 350 I hope it helps

Step-by-step explanation:

The product of (6x - y)(2x - y + 2) is 12x² + y² -8xy + 12x -2y

The required table to multiply (6x - y)(2x - y + 2) is shown below.

"It is a mathematical statement that consists of constants, variables and some mathematical operations."

For given question,

We have been given an expression (6x - y)(2x - y + 2)

The product of above expression is,

(6x - y)(2x - y + 2)

= 6x(2x - y + 2) - y(2x - y + 2)

= 12x² - 6xy +12x - 2xy + y² - 2y

= 12x² + y² -8xy + 12x -2y

The required table to multiply (6x - y)(2x - y + 2) is shown below.

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Use formula for the length of the arc:

[tex] \text{Arc Length} = (\theta\cdot \dfrac{\pi}{180^{\circ}}) \cdot r [/tex], where [tex] \theta [/tex] is central angle.

Substitute [tex] \theta [/tex] and r=3 into formula:

[tex] \text{Arc Length} = (\theta\cdot \dfrac{\pi}{180^{\circ}}) \cdot r=(70^{\circ}\cdot \dfrac{\pi}{180^{\circ}})\cdot 3=\dfrac{7}{6}\pi [/tex].

Answer: [tex] \text{Arc Length} =\dfrac{7}{6}\pi [/tex].

Answer:

its 3.7

Step-by-step explanation:

Leon has $47 and Kim has $64. We solved the problem by setting up an equation with the given information and solving for each person's amount.

The question presents a typical algebraic problem. Let's denote Leon's amount of money as L and Kim's amount as K. According to the problem, Kim has $17 more than Leon, so we can write this as K = L + $17.

Since the total amount of money they have together is $111, we can formulate the following equation: L + K = $111. By substituting the first equation into the second, we get L + (L + $17) = $111.

Simplifying by combining like terms, we get 2L + $17 = $111. To find the value of L, we subtract $17 from both sides, resulting in 2L = $94. Dividing by 2 gives us L = $47.

Since K = L + $17, we substitute the value of Leon's money to find Kim's: K = $47 + $17 = $64. So Leon has $47 and Kim has $64.

Answer:

a. P’(-4, 7), Q’(-6, 7) , R’(-7, -1) and S’(-3, -1)

Step-by-step explanation:

Answer:

The equation of line is y=x+3.

Step-by-step explanation:

Consider the provided graph.

The slope intercept form of a line is:

y=mx+c

Where m is the slope and c is the y intercept.

y-intercept is a point where the value of x is 0.

From the provided graph we can identify the y intercept of the line is 3. Because at (0,3) the value of x is 0.

Now find the slope of line as shown

[tex]m = \frac{Rise}{Run}[/tex]

Here for 1 unit of run the graph rise 1 unit, thus the slope of the line is:

[tex]m = \frac{1}{1}=1[/tex]

Now substitute the value of m and c in the slope intercept form.

y=x+3

Hence, the equation of line is y=x+3.

answer : y=6(1/3)^x, option C

Decay curve means when x value increases the y value will decrease.

We plug in 3 values for x and check the y value

Lets start with first option

[tex] y=2(4)^x [/tex]

x=0 , y= 2

x=1, y= 8

x=2, y=32

when x value increases the y value also increases. so option A is not a decay curve

[tex] y=3^x -4 [/tex]

x=0 , y= -4

x=1 , y= -1

x=2 , y = 5

when x value increases the y value also increases. so option B is not a decay curve.

[tex] y= 6(\frac{1}{3})^x [/tex]

x=0, y = 6

x=1, y = 2

x=2 , y= 0.67

when x value increases the y value decreases. so option C is a decay curve

The equation that will produce a decay curve is y = 6(1/3)^x.

The equation that will produce a decay curve is y = 6(1/3)x.

A decay curve is characterized by exponential decay, where the base of the exponent is less than 1. In this equation, the base is 1/3, which is less than 1. As x increases, the value of (1/3)x decreases, resulting in a decay curve.

For example, if we substitute x = 0 into the equation, we have y = 6(1/3)0 = 6(1) = 6. As x increases, the value of y decreases exponentially.