The graphs below are both quadratic functions. The equation of the red graph
is fx) = ». Which of these is the equation of the blue graph, g(x)?

Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)

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Explanation Section:

It is false

If f(x) is a function , then for each value of x there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

Bye! - SunnyBunny <3

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

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The distance travelled by Jim in 24 step is 9 miles by unitary method.

According to the given question.

The number of steps travelled by Jim = 24

Also, it is given that "Carly takes three steps to walk the same distance as Jim walks in four steps".

Therefore, by unitary mehod we can say that

The number of steps walked by Carly = 3 × (24/4) = 3 × 6  = 18

So, the distance travelled by Carly in 18 steps

= 18 × 0.5miles

= 9 miles

Since, the Carly's 18 steps is equals to Jim's 24 steps.

Therefore, the distance travelled by Jim in 24 step is 9 miles.

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The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Parent functions are the basic function that represents the entire family of that function family

The function is given as;

g(x) = 3cos (x + 180°) + 1

As a general rule, the parent function of any function is the basic equation of the function family

The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

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By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

In this problem we have three ordered pairs to be checked on a given function by direct evaluation, a ordered pair lines on the curve of function if and only if the x-value of the ordered pair leads to the y-value by evaluating in the function. Now we proceed to evaluate each of the three points at the function presented in the statement:

(x, y) = (1, 4)

h(1) = - 2 · 1²

h(1) = - 2

By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

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Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(6,~-7)[/tex]

[tex](x_2,~y_2)=(4,~3)[/tex]

Given the midpoint formula

[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]

Substitute values into the given formula

[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]

Simplify values on the numerator

[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]

Simplify the fractions

[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

2r + t + r

3r + t

The correct answer is C - None of the Above.

When we combine like terms, we combine terms that have the same variables but different coefficients. We cannot add 2r and t because r and t are not the same variables.

Hope this helps!

Answer:

None of the above

Step-by-step explanation:

Because the answer is 3r + t

Considering the given box plots, it is found that:

a) They had the same IQR.

b) Athlete A went on the shortest training ride.

c) Athlete B went on more rides longer than 35 miles.

d) Athlete B had a greater median distance.

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

Hence, for Athlete A, we have that:

For Athlete B, we have that:

Hence:

a) They had the same IQR.

b) Athlete A went on the shortest training ride.

c) Athlete B went on more rides longer than 35 miles(as it is less than his median).

d) Athlete B had a greater median distance.

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Answer:

A

Step-by-step explanation:

f(-3) = 2^-3

to get rid of a negative in an exponent, move the whole thing to the denominator.

1/(2^3)

2^3 = 2×2×2

1/(2×2×2)

1/8

The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

A rectangular prism is a three-dimensional shape, having six faces, where all the faces are rectangles.

The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.

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The minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(8) - f(3).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:

[tex]\int_{3}^{8}4dx \leq \int_{3}^{8}f'(x)dx \leq \int_{3}^{8}5dx\\\Rightarrow [4x]_{3}^{8} \leq [f(x)]_{3}^{8} \leq [5x]_{3}^{8}\\\Rightarrow 4*8 - 4*3 \leq f(8)-f(3) \leq 5*8 - 5*3\\\Rightarrow 20 \leq f(8) -f(3) \leq 25[/tex]

Thus, the minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

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Answer:177

Step-by-step explanation:so for short, you need to multiply the 300 miles with the 59 precent we have and divide it to 100 this provides us the answer of miles he slept through the road trip

The number of miles they had travelled when Bentley fell asleep is 177 miles.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Bentley fell asleep 59% of the way through the trip.

The total length of the trip was 300 miles.

The number of miles

= 59% of 300

= 59/100 ×300

= 59×3

= 177 miles

Therefore, the number of miles they had travelled when Bentley fell asleep is 177 miles.

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The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.

The given expression according to the task content is; a³b⁵/a⁴b.

It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;

a^(3-4)b^(5-1)

Consequently we have;

b⁴/a.

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The forces have a magnitude of 59 pounds, and their direction angles are zero.

Two forces of 17 and 42 pounds act horizontally on an object.

i.e

F1 = 17 pounds

F2 = 42 pounds

As the magnitude of the force represents the sum of all the forces

The direction is the same

Magnitude : 17 + 42 = 59 pounds

The Direction angles : 0

As they have the same direction so angle will be 0.

The forces have a magnitude of 59 pounds, and their direction angles are zero.

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Answer:59 and 0

Step-by-step explanation:

EDGE

Using a proportional relationship, it is found that the unit rate of change is of 9.

The relation d = 9t is graphed at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, we have d as a function of t, hence the relationship is:

d = kt.

When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:

k = d/t = 1.8/0.2 = 9

The relation d = 9t is graphed at the end of the answer.

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The rate of change in the plant's height in terms of inches per week will be 1 2/3 inches.

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.

The calculation for the rate of change is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.

The change in y (y being the height of the plant) over 4 weeks was 6 2/3 inches and there are four weeks. Therefore, the average height will be:

= 6 2/3 ÷ 4

= 1 2/3 inches

The average rate of change of the plant growth per week was 1 2/3 inches.  

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Complete question:

Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of 6 2/3 inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.

a.+1 2/3B)-1 2/3C)+3/5D)-5/2

The value of the product expression 6 * 330 is 1980

The product expression is given as:

6 * 330

Express 330 as the product of 33 and 10

6 * 330 = 6 * 33 * 10

Express 33 as the product of 3 and 11

6 * 330 = 6 * 3 * 11 * 10

Evaluate the product of 6 and 3

6 * 330 = 18 * 11 * 10

Evaluate the product of 11 and 10

6 * 330 = 18 * 110

Evaluate the product of 18 and 110

6 * 330 = 1980

Hence, the value of the product expression 6 * 330 is 1980

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invest in each bond = $7000

An income statement, also known as a profit and loss account, is one of a company's financial statements and displays the company's receipts and outlays for a specific time period. It explains how revenues are converted into net income or net profit.

According to the given data:

Let n be the amount invested at 8%

the amount invested at 12% would be : 14000-n

so,

8n+12(14000-n) = 1400

8n + 168000 - 12n = 1400 * 100

4n + 168000 = 140000

n = 28000/4

   =  7000

Therefore,

At 12% amount invested

= 14000 - 7000

= $7000

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[tex]y = mx + b \\ y = nx + c \\ for \: the \: two \: lines \: to \: be \: perpendicular \\ m.n = - 1[/tex]

[tex]m = 3 \\ \\ 3n = - 1 \\ n = \frac{ - 1}{3} [/tex]

[tex]y = \frac{ - x}{3} + 2[/tex]

Answer:

The slope is -3.

Step-by-step explanation:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

The correct graph is in the attached image.

Answer:

  B.  A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)

Step-by-step explanation:

The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.

When the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.

When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.

The given inequality

  y ≤ 2x -4

includes the "or equal to" case, so the boundary line is solid.

The equation of the boundary line is written in slope-intercept form:

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.

This tells you that the boundary line intercepts the y-axis at the point (0, -4).

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

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The height of the basketball at 0.5 seconds will be = 26.5

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.

Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.

According to the given equation if we put value in it we will follow the following steps -

[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]

Therefore, the height of the basketball at 0.5 s will be 26.5

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Answer:

Is the question supposed to be (1.5), if so then the answer would be 21.5

Step-by-step explanation:

ht=-16t^2+35t+5

h(1.5)=-16(1.5)^2+35(1.5)+5

=21.5

Answer:

angle l = 115

angle k = 115

angle j = 114

angle i = 66

Step-by-step explanation:

angle l = it is opposite to 115 so its the same

angle k = opposite opposing angles with angle l

angle j = 180-66=114 (between 2 parallel lines the sum of 2 angles is 180)

andle i = 180-114=66 (straight line = 180 degrees so subtract angle j to get i)

Answer:

k = 33

Step-by-step explanation:

Terminating decimal numbers:  Decimals that have a finite number of decimal places.

For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5.  As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.

Prime factorization of 660:

⇒ 660 = 2 × 2 × 3 × 5 × 11

⇒ 660 = 2² × 3 × 5 × 11

Therefore:

[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]

The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out.  To do this, their lowest common multiple must be the numerator:

⇒ LCM of 3 and 11 = 3 × 11 = 33

[tex]\implies \sf \dfrac{33}{660}[/tex]

[tex]\implies \sf k=33[/tex]

Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.

Answer:

33

Step-by-step explanation:

The number of rectangles of different sizes can be formed from 36 identical rectangles is 5

From the question, we have proofs of;

Total number of identical squares = 36

Now, let the measurement of the side of each square be 1 unit

We have that the formula for area of a square is;

Area of a square = Side × Side square units

We have the area of the square to be;

Area of each square = 1×1 = 1 square units

This is so because the rectangles are identical both in length and width

Let's find the area of the identical squares

Area of total 36 identical squares

=  36×1 square units

=  36 square units

So Area of the rectangle = length × breadth square units

if the rectangles are formed from 36 identical squares then their areas are the same

Total area of required rectangles = 36 square units

It can be written as;

36 = length × breadth

(1,36) , (2,18),(3,12),(4,9),(6,6) are the different rectangles formed from 36 identical squares

Total rectangles = 5

Thus, the number of rectangles of different sizes can be formed from 36 identical rectangles is 5

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The line that is not another name for Q is RL

For a line to represent the point Q, the following must be true:

Using the above highlights,

Hence, the line that is not another name for Q is RL

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In the case above:

(a) If there is an increased from 64 to 196, then the variance decreases.

(b) If there is a decreased from 784 to 49, then the variance increases.

Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.

Since the standard error takes place in the denominator, hence, if the standard error increases, the variance goes up.

Therefore, In the case above:

(a) If there is an increased from 64 to 196, then the variance decreases.

(b) If there is a decreased from 784 to 49, then the variance increases.

See full question below

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?

What is the variance about?

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Answer:

4/7

Step-by-step explanation:

[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12

7x3=21

[tex]\frac{12}{21} = \frac{4}{7}[/tex]