Consider the function graphed at right.
The function has a maximum
of 3
The function is increasing on the interval(s):
The function is decreasing on the interval(s):
at x =
-4
4
-32
-5--
3 4 5
1 2 3 4 5

Option A is correct. The value of function (f/g)(x) is found to be  [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that  x ≠  -2/3.

In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

The new function obtained by performing f first and then g is the combination of two functions g and f.

Given:

f(x) = [tex]\sqrt[3]{3x}[/tex]

g(x) = 3x + 2

(f/g)(x) =  [tex]\sqrt[3]{3x}[/tex]/(3x+2)

Also, the denominator should not be equal to 0.

So, 3x + 2 ≠ 0

     x ≠  -2/3

Therefore, the value of function  is found to be  [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that  x ≠  -2/3. So, Option A is correct

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Based on the definition of perpendicular bisector, the value of b = 5.

A perpendicular bisector can be described as any line that bisects another line segment at right angles.

This means, the measure of the angles at the point of bisection are right angles (90 degrees).

Therefore:

12b + 30 = 90 [definition of perpendicular bisector]

Solve for b

12b + 30 - 30 = 90 - 30

12b = 60

Divide both sides by 12

12b/12 = 60/12

b = 5

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Answer: if you multiply you will end up with 675

Step-by-step explanation:

The width of the river to the nearest foot will be 45 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Paula remains on a waterway and sights the contrary bank at a point of the wretchedness of 7 degrees.

If Paula is 5.5 feet tall.

Let 'w' be the width of the river. Then the width of the river will be given as,

tan 7° = 5.5 / w

0.12278 = 5.5 / w

w = 44.79

w ≈ 45 feet

The width of the river to the nearest foot will be 45 feet.

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The total change in the cats weight for all 3 months is -0.5 pounds.

Since we have 3 months which is from April to June, Now let add up the change in weight in pounds so as to find the total change

Let x represent the total change

x = -0.7 + 0.5 + (- 0.3 )

x = -0.5 pounds

Therefore the -0.5 pound is the change in weight.

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By the concept of basic arithmetic, it is $3.64 more expensive per pound, to buy salmon at Super Grocery A than at Super Grocery B.

The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.

At Super grocery B, 3 pounds of Salmon cost = $ 24.63

So, 1 pound will cost = $ 24.63/ 3

= $ 8.21

At Super grocery A, 2 pounds of Salmon cost = $ 23.70

So, 1 pound will cost = $23.70/ 2

= $ 11. 85

To buy salmon at SuperGrocery A than at SuperGrocery B expense per pound is given by

= $11.85 - $ 8.21

$ 3.64

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Answer: C

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

The equation of the parabola that has one real solution with the line y = x - 5 is y = x² + 7·x + 4

The standard form of the equation of a parabola is y = a·x² + b·x + c

The equation of the line is; y = x - 5

The parabola that has one real solution with the line is given by the parabola that is equal to both (x - 5) and the equation for the parabola;

Analyzing the quadratic equations of the parabolas with the equation y = x - 5, gives;

x² + x - 4 - x + 5 = 0

x² + 1 = 0

x² = -1

x = ±√(-1) (Complex solution)

x² + x + 4 = 0

The discriminant, b² - 4·a·c is 1² - 4 × 1 × 4 = -15 < 0 (Complex solution)

x² + 5·x + 14 = 0

The discriminant, b² - 4·a·c is 5² - 4 × 1 × 14 = -31 < 0 (Complex solution)

x² + 6·x + 9 = 0

The quadratic equation that gives one real solution with the equation y = x - 5 is therefore;

y = x² + 7·x + 4

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Answer: 4.00

Step-by-step explanation:

If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.

Answer:

Step-by-step explanation:

Given is a parallelogram.

One of the properties of a parallelogram is its diagonals bisect each other.

It gives us:

The surface area of the largest size sphere that can fit in this box is 400π

What is the surface area of the sphere?

The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.

Here, we have

The diameter of the biggest sphere will be equal to the side of the sphere.

radius = 20/2

​ = 10

The surface area of the sphere = 4πr²

=4π(10)²

= 400π

Hence, the surface area of the largest size sphere that can fit in this box is 400π.

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A total of 9 workers are needed to finish the same task in 4 days

From the question, we understand that:

3 workers can complete a certain task in 12 days

This means that

3 workers = 12 days

The proportionality constant is then calculated as

Proportionality constant = Number of workers x Number of days

Substitute the known values in the above equation So, we have the following equation

Proportionality constant = 3 * 12

Evaluate

Proportionality constant = 36

When the number of days is 4, we have

Days = 4

So, we have

Proportionality constant = Number of workers x Number of days

This gives

36 = Number of workers x 4

Divide both sides by 4

Number of workers = 9

Hence, the number of workers is 9

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Answer:95

step by step explanation

The length of wall in real life is 4 feet.

Given that on an architect's blueprint, 1 inch corresponds to 4 feet.

In this architect's plan, a wall represented by a line 1 inches long on the blue print.

So, the length of wall in real life is = 4 feet.

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Answer:

4ft

Step-by-step explanation:

If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.

a) $149911.84 can be afforded

b) $39600 is the total money you will pay the loan company

c) $246088.16 is the interested amount

Calculation

Given,

d=$1100

N= 30 years

r = 8% or 0.08

a) Loan amount that can be afforded

[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]

[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]

= $149911.84

b) Total money you pay = d×N×k

=1100×30×12

=$39600

c) Interest paid = Total money paid – loan amount

⇒39600–14911.84 = $246088.16

Hence,

a) $149911.84 can be afforded

b) $39600 is the total money you will pay the loan company

c) $246088.16 is the interested amount

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Answer:

Step-by-step explanation:

Distance is the total length covered by an object.

Displacement is the distance between the final point and the initial point.

The distance of the helicopter's flight is 150 m

The displacement of the helicopter's flight is zero.

Displacement is the distance between the final point and the initial point.

We have,

A helicopter lifts 75m vertically into the air and then comes back down to the ground.

Distance is the total length covered by an object.

Distance of the helicopter's flight.

= 75m + 75m

= 150 m

Displacement of the helicopter's flight.

= Final point - Initial point

= 0 - 0

= 0  

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Answer: 56 minutes

Step-by-step explanation:

7 = 7, 14, 28, 35, 42, 49, 56

8 = 8, 16, 24, 32, 40, 48, 56

7 and 8 have 56 in common so it would take them 56 minutes

Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.

In order for us to find out the total possible combinations, we will use the formula as:

Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons

We are given that;

Number of possible chairpersons = 16

Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)

Thus, we can say that;

Total possible combinations = 16 * 15

Total possible combinations = 240 combinations

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

Explanation:

Unfortunately the U from "universal set" and the union symbol look almost identical.

What I'll do to avoid confusion is to let E represent the set of everything we care about, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Feel free to use other notation if it makes better sense to you.

From this set, we'll erase items that are found inside set A = {f, g, p, q}

So we go from this

E = {f, g, h, p, q, r, x, y, z}

to this

A' = {h, r, x, y, z}

Everything found in here is guaranteed to not be inside set A.

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

The next step is to union set A' with set B. This is where we combine those two sets into a larger set of items. Toss out any duplicates. Each unique letter is to be listed once.

A' u B = {h, r, x, y, z}  U  {g, h, q, x, y}

A' u B = {h, r, x, y, z,        g, h, q, x, y}

A' u B = {g, h, q, r, x, y, z}

It's recommended you sort the items in a consistent fashion.

Set this result aside for now, and come back to it later.

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

Go back to the set of everything, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Cross off stuff found in set C, so we guarantee to form the opposite or complement set C'

C' = set of everything NOT found in C

C' = erase "p,q,x,y,z" from set E

C' = {f, g, h, r}

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

To recap we found

Intersect those sets by looking at what they have in common. This is the overlapped region between the sets.

The three items in common are: {g, h, r}  which forms the final answer.

The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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Answer:

5 yds

Step-by-step explanation:

i am assuming that 4 yd and 3 yd are the legs

so

to find the hypotenuse you square both legs add them and then take the square root of that

so

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

the final side is 5

Using the given table, the y-values are 36, 54, 81, 121.5, and 182.25.

We are given a table. Mathematical tables are collections of numbers that represent the outcome of a computation with varied arguments. The table has two columns and five rows. The first column shows the x-values. The second column shows the f(x) values. We know that y = f(x). So, the second column shows the y-values. The y-value is the vertical value in a pair of coordinates. It denotes how high or low the point is. In an ordered pair of coordinates, the y-coordinate is always written second (x, y). The five rows show the data points with corresponding x-values and y-values.

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The probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3% is 0.9968

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 9% = 0.09

sample size, n = 789

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.09(1 - 0.09)) / 789}

= √{(0.09 * 0.91) / 789}

= 0.0102

The probability

differ from the population proportion by less than 3%

|X - 0.09| < 0.03

X < 0.12 OR X > 0.06

0.06 < X < 0.12

P(z < 0.12) - P(z < 0.06 )

z score for z < 0.06

z = (0.06 - 0.09) / 0.0102

= -2.9412

p value for z < -2.9412 = 0.0016

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9984

The probability required = 0.9984 - 0.0016 = 0.9968

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The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3

An exponential equation is an equation that has exponents that consists of variables.

The given equation is y = 2ˣ

The equation for the transformation is; y = A·2ˣ + k

The points on the graphs are;

(0, 1), (1, -1) and (2, -5)

Plugging the x and y-values to find the value A and k gives  the following simultaneous equations;

When x = 0, y = 1, therefore;

1 = A·2⁰ + k = A + k

1 = A + k...(1)

When x = 1, y = -1, which gives;

-1 = A·2¹ + k

-1 = 2·A + k...(2)

Subtracting equation (1) from equation (2) gives;

-1 - 1 = 2·A - A + k - k

-2 = A

1 = A + k, therefore;

1 = -2 + k

k = 2 + 1 = 3

k = 3

Which gives;

y = -2·2ˣ + 3 = 3 - 2·2ˣ

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Answer:

y=-1/4x+4

Step-by-step explanation:

The graph starts on 4 so that is your y-intercept

Use slope formula to get the slop (y2-y1 over x2-x1)

Use 2 coordinates for formuls (In your case (0,4) and (4,3))

3-4=-1 4-0=4

slope is -1/4

y= -1/4x+4

Answer:

yes

Step-by-step explanation:

because 4

Answer:

Step-by-step explanation:

average rate of change

[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]