10. Which of the following functions is the inverse of the function {(1,2).(3,4).(6,8)) ? (1 point)
A. {(6,8).(3,4),(1,2))
B. {(2,1),(4,3).(6,8)}
C. {(2,1),(4,3), (8,6)
D. {(2,1),(3,4).(8.6)]

Answer:

So if you're having difficulty visualizing the differences, you can rewrite them so they all have the same denominator

7/12 = 35/60

1/2 = 30/60

2/3 = 40/60

4/10 = 24/60

1/6 = 10/60

So now it's easier to see how they compare to each other.

10/60, 24/60, 30/60, 35/60, 40/60

And then simplify them or just refer to what they were before

1/6, 4/10, 1/2, 7/12, 2/3

I hope this helps!

Answer:

44 quarts of paint

Step-by-step explanation:

Given,

75-foot fence needs = 4 quarts.

We have to use the unitary method to determine how many quarts will be needed for the fencing system. Hence,

75-foot fence needs         = 4 quarts of paint

1-feet fence needs            = (4/75) quarts of paint

825-foot fence needs      = (4 x 825)/75 quarts of paint

                                          = 3,300/75 quarts of paint

                                          = 44 quarts of paint

Therefore, we need 44 quarts of paint for 825-foot fence.

To determine how many quarts of paint are needed for an 825-foot fence, we can set up a proportion and solve for the unknown quantity.

To determine how many quarts of paint are needed for an 825-foot fence, we can use the concept of ratios. Since we know that 4 quarts of paint are needed for a 75-foot fence, we can set up a proportion:

To solve for the unknown quantity, we can cross-multiply and solve for the missing value:

Dividing both sides of the equation by 75, we get:

By performing the calculation, we find that quarts of paint is approximately 44 quarts. Therefore, 44 quarts of paint are needed for an 825-foot fence.

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Answer:

[tex]0.5a[/tex]

Step-by-step explanation:

We have been given a trigonometric function [tex]g(a)=7.6\text{ cos}(0.5a)[/tex]. We are asked to find the argument of the cosine function.

We know that a trigonometric equation is solved for an unknown angle and that unknown angle is known as the argument of the trigonometric function. For example: [tex]\text{cos}(\theta)=0[/tex]. In this equation [tex]\theta[/tex] is the argument of the equation.

Upon looking at our given function, we can see that [tex]0.5a[/tex] is the argument.

Answer:

[tex]\large\boxed{\dfrac{1}{8}\%=\dfrac{1}{800}}[/tex]

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\\dfrac{1}{8}\%=\dfrac{\frac{1}{8}}{100}=\dfrac{1}{8}\cdot\dfrac{1}{100}=\dfrac{1}{800}\\\\\text{other method}\\\\\text{Convert the fraction to the decimal:}\\\\\dfrac{1}{8}=0.125\to\dfrac{1}{8}\%=0.125\%\\\\0.125\%=\dfrac{0.125}{100}=\dfrac{0.125\cdot1000}{100\cdot1000}=\dfrac{125}{100000}=\dfrac{125:125}{100000:125}=\dfrac{1}{800}[/tex]

The solution to the system of equations is (3,1)

Step-by-step explanation:

The system of equations represented by graph are:

[tex]y=4-x\\y=x-2[/tex]

Solving the system of equations

Let:

[tex]y=4-x\,\,\,eq(1)\\y=x-2\,\,\,eq(2)[/tex]

Putting value of y from eq(2) into eq(1):

[tex]x-2=4-x\\Simplifying:\\x+x=4+2\\2x=6\\x=6/2\\x=3[/tex]

So, Value of x = 3

Putting value of x into eq(2)

[tex]y=x-2\\y=3-2\\y=1[/tex]

So, value of y= 1

So, The solution to the system of equations is (3,1)

Keywords: System of equations

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Answer:

slope = - 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 3)

m = [tex]\frac{-3-5}{6+2}[/tex] = [tex]\frac{-8}{8}[/tex] = - 1

Answer:

The correct answer is A. f(x)= 2(3^x)

Step-by-step explanation:

The exponential function y = 2(3)ˣ, has an initial value of 2

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplicative rate of change

Given the exponential function y = 2(3)ˣ, has an initial value of 2

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Answer:

Ratio = [tex]\frac{Perfect.squares}{non.Perfect.squares}[/tex] = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

The perfect squares from 1-30 are:

1, 4, 9, 16, 25

Total no. of perfect squares = five =5

Total no. of non perfect squares = 30-5 = 25

Ratio =[tex]\frac{Perfect.squares}{non.Perfect.squares}[/tex] = 5 / 25 = [tex]\frac{1}{5}[/tex]

The ratio of perfect squares to non-perfect squares for the numbers 1 to 30 is 1:5.

A perfect square is a number that is the square of an integer. For the numbers 1 to 30, the perfect squares are 1, 4, 9, 16, 25, as these numbers are squares of integers 1, 2, 3, 4, 5 respectively. The number of perfect squares is 5.

The total number of tiles is 30. So the number of non-perfect squares is 30 - 5 = 25.

The ratio of perfect squares to non-perfect squares in simplest form, then, is 5 : 25. Simplified, this ratio is 1 : 5.

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Answer:

Train b is moving faster than a by 45 units an hour

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

9+2=1/3x

11=1/3x

x=11/(1/3)=(11/1)(3/1)=33/1=33

Answer:

The answer is undetermined

Step-by-step explanation:

i'm not joking the when the line is parallel to the y axis it has no slope because it runs vertically but if the line was horizontal the slope would be 0

Answer:

multiply all together

Step-by-step explanation

Answer:

it's D

Step-by-step explanation:

y= .05x+20

x=50

y=.05(50)+20

2.5+20

y=22.5

y=.25x+10

x=50

y=.25(50)+10

12.5+10

y=22.5

Answer: 17

================================

How I got that answer:

(2,3) and (3,1) have '3' in common in that the y value of the first pairs with the x value of the second.

If you picture a chain, then you start with x = 2, move to y = 3, then move to x = 3 and then y = 1

2 ---> 3 ---> 3 ---> 1

So f(f(2)) = f(3) = 1

If g(x) = f(f(x)), then we know (2,1) is on the graph of g(x)

-------------------------

Repeat for (3,1) and (1,5)

3 ---> 1 ---> 1 ---> 5

f(3) = 1

g(x) = f(f(x)) = f(f(3)) = f(1) = 5

We know that (3,5) is on the graph of g(x)

-------------------------

The two points on g(x) are: (2,1) and (3,5)

Comparing that to (a,b) and (c,d) we can see

a = 2, b = 1, c = 3, d = 5

a*b + c*d = 2*1 + 3*5 = 2 + 15 = 17

Answer:

=3

Step-by-step explanation:

Okay so you 1/2 divided by 1/6

Answer:

3

Step-by-step explanation:

1/2÷ 1/6

=  

1/2×6/1

=  

1 × 6

2 × 1

=  

6/2

=  

6 ÷ 2

2 ÷ 2

=  3

Just Divide 1/6 by 1/2

Answer:

Step-by-step explanation:

10/25=20/50=40/100

6/8=3/4=12/16

3/5=6/10=60/100

1/10=10/100

Answer:M=24

Step-by-step explanation:

There are 2 ways to do this

---------------------------------------------------

Method 1) Divide both sides by 25, then add 2 to both sides

25(M-2) = 650

M-2 = 650/25

M-2 = 26

M = 26+2

M = 28

---------------------------------------------------

Method 2) Distribute the 25 through to each term inside the parenthesis. Then isolate for M by adding 50 to both sides, and then dividing both sides by 2.

25(M-2) = 650

25M - 50 = 650

25M = 650+50

25M = 700

M = 700/25

M = 28

---------------------------------------------------

The questions pertain to the analysis of linear relationships between variables using scatter plots, lines of best fit through linear regression, and understanding correlation coefficients to identify the strength and direction of relationships in data.

The questions provided are centered around the concepts of linear equations, scatter plots, correlation, and regression analysis in the realm of mathematics. Scatter plots are graphical representations showing the relationship between two variables. In these types of questions, the independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis. To analyze the relationship, one can use linear regression to find the line of best fit, which is a straight line that best represents the data on a scatter plot. The correlation coefficient, often denoted as r, indicates the strength and direction of the linear relationship between two variables.

The line of best fit can be found by calculating the least-squares line, which minimizes the sum of the squares of the vertical distances of the points from the line. The equation of this line is typically in the form y = a + bx, where 'a' is the y-intercept and 'b' is the slope. The slope indicates how much the dependent variable changes for a one-unit change in the independent variable. The y-intercept is the value of the dependent variable when the independent variable is zero. A correlation coefficient of zero implies no linear relationship between the variables.

When looking at data such as stock market trends or health-related measurements like BMI and cholesterol, understanding the strength and type of correlation is essential for making predictions. For example, a positive correlation indicates that as one variable increases, the other variable tends to increase, while a negative correlation indicates the opposite. It's important to note that correlation does not imply causation; just because two variables are correlated does not mean that one causes the other.

The series will be:

[tex]4+16+64+.......+2^{50}[/tex]

Hence, Option A is the right answer

Step-by-step explanation:

The series can be fount out by putting the values of i in the expression written with the summation

The expression is:

[tex]2^{2i}[/tex]

while i = 1 to 25

Putting i = 1

[tex]2^{2(1)}\\= 2^2\\= 4[/tex]

Putting i = 2

[tex]2^{2(2)}\\= 2^4\\= 16[/tex]

Putting i = 3

[tex]2^{2(3)}\\= 2^6\\= 64[/tex]

....

Putting i = 25

[tex]2^{2(25)}\\= 2^{50}[/tex]

The series will be:

[tex]4+16+64+.......+2^{50}[/tex]

Hence, Option A is the right answer

Keywords: Summation, Series

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Answer:

y = c/z²  

Step-by-step explanation:

(1) y ∝ 1/x²or

   y = a/x² where a is a constant

   x ∝ z or x = bz, where b is a constant

Substitute x into (1)

y ∝ a/(bz)² = a/(b²z²) = (a/b²)/z²

a is a constant and b is a constant, so a/b² is a constant.

Let c = a/b². Then

y = c/z²

Answer:

2.8

Step-by-step explanation:

.8*2=1.6  1.2

1.6+1.2=2.8

Answer:

2.8

Step-by-step explanation:

Simply Substitute for X:

[tex]0.8(2) + 1.2\\1.6+1.2\\2.8[/tex]

You would get 2.8 as the answer.

Answer:

40%

Step-by-step explanation:

125 - 75= 50

50 ÷ 125 = 0.4

0.4 = 40%

it is d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

First find how many bottles Ginger will need.

15 mL x 365 day = 5475 mL for 1 yr

5475 mL / 350mL = 16 bottles

Then find the price for the 16 bottles.

16 bottles x $4.85 = $77.60

Answer:

The price of a senior ticket is $12.

Step-by-step explanation:

Given:

Mr. Smith purchased 8 senior tickets and 5 child tickets for $136. Mr. Jackson purchased 4 senior tickets and 6 child tickets for $96.

Now, to get what is the price of a senior ticket.

Let the senior ticket be [tex]x[/tex] and the child ticket be [tex]y[/tex]:

So, according to question

[tex]8x+5y=136[/tex].........(1)

[tex]4x+6y=96[/tex]...........(2)

Now, we have system of equations:

Multiplying the equation (2) by -2 we get:

[tex]-8x-12y=-192[/tex].......(3)

Now, adding the equation (3) and (1) the variables and the numbers:

[tex]-8x-12y+8x+5y=-192+136[/tex]

[tex]-7y=-56[/tex]

Dividing both sides by -7 we get:

[tex]y=8[/tex]

Putting the value of y in equation (2) we get:

[tex]4x+6(8)=96[/tex]

[tex]4x+48=96[/tex]

On solving the equation we get:

[tex]x=12[/tex].

Therefore, the price of a senior ticket is $12.

Answer:

x = 90°

Step-by-step explanation:

We are given a trigonometric function of x from which we have to a solution for x.

The function is [tex]\cos^{2} x + 2\sin x - 2 = 0[/tex]

⇒ [tex]1 - \sin^{2} x + 2\sin x - 2 = 0[/tex]  

{Since we know the identity [tex]\sin^{2} \alpha + \cos^{2} \alpha = 1[/tex]}

⇒ [tex]\sin^{2} x - 2 \sin x + 1 = 0[/tex]

⇒ [tex](\sin x - 1)^{2} = 0[/tex]

{Since we know the formula (a - b)² = a² - 2ab + b²}

⇒ [tex](\sin x  - 1) = 0[/tex]

⇒ [tex]\sin x = 1 = \sin 90[/tex]

⇒ x = 90° (Answer)

To solve cos^2 x + 2sin x - 2 = 0, we convert cos^2 x to 1 - sin^2 x and solve the quadratic equation sin^2 x - 2sin x + 1 = 0, finding that sin x equals 1. Thus, the numerical value of the trigonometric function is sin x = 1.

To find a numerical value of one trigonometric function of x for the equation cos2x + 2sin x - 2 = 0, let's start by expressing everything in terms of sin x:

Using the Pythagorean identity, we know that cos2x = 1 - sin2x. So, we can write:

(1 - sin2x) + 2sin x - 2 = 0

Simplifying, we get:

1 - sin2x + 2sin x - 2 = 0

-sin2x + 2sin x - 1 = 0

This is a quadratic equation in terms of sin x. Let's solve it:

sin2x - 2sin x + 1 = 0

We recognize this as a perfect square trinomial:

(sin x - 1)2 = 0

So, we have:

sin x - 1 = 0

Therefore:

sin x = 1

So, the numerical value of one trigonometric function of x from the given equation is sin x = 1.

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

in this problem

For x=-14, y=-7

Find the value of the constant of proportionality k

[tex]k=y/x[/tex]

substitute

[tex]k=-7/-14=0.5[/tex]

so

The linear equation is

[tex]y=0.5x[/tex]

Find x when the value of y=10

substitute the value of y in the equation

[tex]10=0.5x[/tex]

solve for x

Multiply by 2 both sides

[tex]x=20[/tex]

Final answer:

In direct variation relationship 'y = kx', using the given y = -7 when x = -14, the constant of variation 'k' is found to be 0.5. To find x when y = 10, we use 'y = kx' to get x = 20.

Explanation:

The student's question revolves around the concept of a direct variation, which is a fundamental topic in algebra. The direct variation relationship between two variables 'x' and 'y' can be expressed as 'y = kx', where 'k' is the constant of variation. To determine the constant 'k', we can use the given condition, which states that when x = -14, y = -7. This equation simplifies to 'k = y/x', so 'k = (-7)/(-14)' which equals 0.5.

Now, we need to find 'x' when y is 10. Using the direct variation equation 'y = kx' and our calculated 'k' value of 0.5, we can set up the equation '10 = 0.5x'. Solving for 'x', we get 'x = 10/0.5' which simplifies to 'x = 20'. Thus, when y equals 10, the corresponding value of x is 20.

Answer:

6

Step-by-step explanation:

8-2=6

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

                 [tex]500=x^2y[/tex]

Therefore, [tex]y=\dfrac{500}{x^2}[/tex]

It is open box. The surface area of box, S .

[tex]S=x^2+4xy[/tex]

Put  [tex]y=\dfrac{500}{x^2}[/tex]

[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]

For critical point, S'(x)=0

[tex]2x-\dfrac{2000}{x^2}=0[/tex]

[tex]x^3=1000[/tex]

[tex]x=10[/tex]

Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]

y = 5

Double derivative of S(x)

[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10

[tex]S''(10) > 0[/tex]

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²