The graph of the fourth-degree polynomial function f (x) is shown in the coordinate plane below. Based on the graph, which of the following are linear factors of f (x). Select all that apply. A. (x - 2) B. (x - 3) C. (x + 2) D. (x - 5) E. (x + 1)

The linear equation that gives the height on the x-th month is:

y = 2.5*x + 74.5

This will be modeled with a linear equation of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.

So the slope is:

[tex]a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5[/tex]

Then the linear equation is:

y = 2.5*x + b

To get the value of b, we use the fact that when x = 3, we have y = 82,

82 = 2.5*3 + b

82 = 7.5 + b

82 - 7.5 = b = 74.5

Then the linear equation is:

y = 2.5*x + 74.5

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

The compound interest when $7300 when interest is compounded semi annually is $2482.70.

The compound interest when $7300 when interest is compounded monthly is $1972.73.

An investment earns compound interest when both the amount invested and the interest accrued increases in value at predetermined time intervals.

The formula to represent compound interest is :

FV - amount invested

FV = P (1 + r)^nm

a. 7300 x [1 + (0.1/2)]^(3 x 2) = 9782.70

Compound interest = 9782.70 = 7300 = $2482.70

b. 7300 x [1 + (0.08/12)]^(12 x 3) = 9272.73

9272.73 - 7300 = $1972.73

To learn more about compound interest, please check: https://brainly.com/question/26367706

#SPJ1

Answer:

D

Step-by-step explanation:

it shows the correct one

Answer:

First, multiply 5 and 8. That equals 40. Then you take the square root of 40, which doesn't result in a whole number, so you factor 40 and removing perfect squares. In which case the answer would be 2√10

Answer:

y = 130

Step-by-step explanation:

given that y varies directly with x and z then the equation relating them is

y = kxz ← k is the constant of variation

to find k use the condition y = 150 when x = 2.5 and z = 12 , then

150 = k × 2.5 × 12 = 30k ( divide both sides by 30 )

5 = k

y = 5xz ← equation of variation

when x = 4 and z = 6.5 , then

y = 5 × 4 × 6.5 = 20 × 6.5 = 130

Answer:

-13/20

Step-by-step explanation:

-0.65 can be written as -65/100. To simplify, divide both numerator and denominator with 5. 65/5=13.  100/5=20

And you get -13/20 for your answer.

The domain and range of the functions sin x, cos x, and tan x will be (-∞, ∞) and [-1, 1], (-∞, ∞) and [-1, 1], and R - (2n + 1)π/2 and (-∞, ∞) respectively.

The domain means all the possible values of x and the range means all the possible values of y.

The three restricted functions are given below.

f(x) = sin (x)

f(x) = cos (x)

f(x) = tan (x)

Then the domain of the three restricted functions will be

The domain of sin x will be (-∞, ∞).

The domain of cos x will be (-∞, ∞).

The domain of tan x will be R - (2n + 1)π/2.

Then the range of the three restricted functions will be

The range of sin x will be [-1, 1].

The range of cos x will be [-1, 1].

The range of tan x will be (-∞, ∞).

The graph is given below.

More about the domain and range link is given below.

https://brainly.com/question/12208715

#SPJ1

Answer: Hope this helps you.

-2

Step-by-step explanation:

y = mx+b (B is y-int)

y = 4^x-2

-2 is clearly replacing the b (y-int) meaning b, the y-int, is -2

[tex]y = {4}^{x} - 2 \\ for \: y \: intercept \: x \: s \\ is \: 0 \\ y = {4}^{0} - 2 \\ y = 1 - 2 \\ y = - 1 \\ [/tex]

Y intercept : (0,-1)

Hope it helps

please give brainliest

Answer:

a

b

b

:)

Step-by-step explanation:

hi brother i have got the answer hope its correct

Answer:

The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the formula for the volume of the cylinder is given by:

We have r = 10 inches and h = 5 inches

V = 500π cubic inches

Percent change in volume from cylinder A to cylinder B:

= 50%

Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

Learn more about the cylinder here:

brainly.com/question/3216899

Step-by-step explanation:

Answer: (0,-1)

Step-by-step explanation:

Let's start with the first inequality, [tex]y < -x^{2}+x[/tex]. To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.

Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).

Therefore, the answer is (A) (0, -1).

Answer:

w + 10 = 40

Step-by-step explanation:

10 more than w is w + 10 is equal to 40 is =40

w + 10 = 40

Please mark as brainliest.

Answer:

Step-by-step explanation:

10 more than w is equal to 40 what is the expression

10 + w = 40                 is the expression

w = 40 - 10

w = 30                        is the solution

[tex]\textbf{Notation one:}~~ \dfrac 76\\\\\textbf{Notation two:} ~ \text{7 to 6}[/tex]

Answer:

-3x

Step-by-step explanation:

its just like regular subtraction, 2-5= -3, and just add an X at the end and you get -3x.

The equivalent expression of [tex]\frac{7^5}{7^2}[/tex] is [tex]\frac{7*7*7*7*7}{7*7}[/tex]

The expression is given as:

[tex]\frac{7^5}{7^2}[/tex]

Expand the numerator and the denominator

[tex]\frac{7^5}{7^2} = \frac{7*7*7*7*7}{7*7}[/tex]

The above expression is represented by option (d)

Hence, the equivalent expression of [tex]\frac{7^5}{7^2}[/tex] is [tex]\frac{7*7*7*7*7}{7*7}[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ1

Answer:

StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction

Step-by-step explanation:

Edge

A triangle is a 2-D shape that has 3 sides and angles. The area of the triangle below is 27 square units

A triangle is a 2-D shape that has 3 sides and angles

In order to determine the area of the shape, we will determine the area of the square circumscribing it first;

Area of the square = 10 * 9 =90 square units

Find the area of the two right triangles

Area of the right triangles = 0.5(10 * 9) + 0.5(9 * 4)

Area of the right triangles = 45 + 18

Area of the right triangles = 63 square units

Take the difference

Area of the given triangle  = 90 - 63 = 27 square units

Hence the area of the triangle below is 27 square units

Learn more on area of triangle here: https://brainly.com/question/17335144

#SPJ1

The approximate original price of the car is $23032

The given parameters are:

Rate, r = 8%

Price at 4 years old = 16,500

An exponential function is represented as:

y = a(1 - r)^x

Where a represents the initial value

This gives

y = a(1 - 8%)^x

Evaluate

y = a(0.92)^x

At 4 years old, we have:

16500 = a(0.92)^4

Divide both sides by (0.92)^4

a = 23032

Hence, the approximate original price of the car is $23032

Read more about exponential function at:

https://brainly.com/question/11464095

#SPJ1

Answer: 15 inches

Step-by-step explanation:

Answer:

In a right triangle, the hypotenuse, 2x, is equal to twice the length of the shortest leg, x, and the longer leg is equal to the product of the length of the shortest leg, x, and the square root of 3.

Hypotenuse: 10 in.

Shortest Leg:2x=10 , so x=5 in,

Longer Leg:   x sq rt 3 5 sq rt 3 in

area- 1/2 bh, 1/2 5*5 sq rt 3=

25t sq rt 3=21.65 sq inches

Marcella won't be able to win the competition because the length of the rope is less than 162 feet.

How to find the sides of a right angle triangle?

The situation forms a right angle triangle.

The kite released rope is the hypotenuse side of the triangle formed.

The opposite side of the triangle is the height of the kite from the ground.

Therefore,

sin 28 = opposite / hypotenuse

sin 28 = 75 / h

h = 75 / sin 28

h = 75 / 0.46947156278

h = 159.754085116

h ≈ 160 feet

Therefore, she won't be able to win the competition because the length of the rope is less than 162 feet.

learn more on right triangle here: https://brainly.com/question/26774610?

#SPJ1

The y-intercept is 3.75, and the equation of the line of best fit is

y = 1.5x + 3.75, and after 13 months, 23 matches could be won.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

Part A:

As we can see in the graph, the line crosses the y-axis at a certain point between 3 and 4.5.

So the y-intercept lies between 3 and 4.5

We can take the middle of these two values to get the approximate value of the y-intercept.

b = (3+4.5)/2 = 3.75

We know the line of the best fit is:

y = mx + b

y = mx + 3.75

b is the y-intercept and m is the slope of a line

Plug the point (9, 18) in the equation to get the value of m:

18 = 9m + 3.75

m = 1.5

y = 1.5x + 3.75

Plug x = 13 months in the above equation:

y = 1.5(13) + 3.75

y = 23.25 ≈ 23 number of matches that could be won

Thus, the y-intercept is 3.75, and the equation of the line of best fit is

y = 1.5x + 3.75, and after 13 months, 23 matches could be won.

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ1

Answer:

Step-by-step explanation:

x divided by the sum of x and 5

x : (x + 5) =

x × (1/1x^-1 + 1/5) =

1 + 1/5x

Answer:

y = -x - 5

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

Since you have been given the slope and y-intercept, you can substitute these values into the equation to find the answer.

m = -1                  

b = -5

y = mx + b

y = (-1)x + (-5)

y = -x - 5

Answer:

y = -x -5

Step-by-step explanation:

We can use y = mx + c to find the equation of the line.

Here,

m ⇒ slope of the line

c ⇒ y - intercept

They have already given that,

m ⇒ -1

c ⇒ -5

So, now we can write the equation of the line like this.

To write the equation of the line you can replace m and c with -1 & -5 respectively.

Let us write now.

y = m x + c

y = -1x - 5

Answer:

The LCM of 16x^2 and 40x^2 is 80x^5

:) Good Luck

Step-by-step explanation:

The length of the band in terms of π is given by the expression:

L = 40mm + π*10mm

Remember that for a circle of diameter D, the circumference is:

C = π*D.

Now, if you look at the image, you can see that the length of the band will be equal to 4 times the diameter of the pencils (one time for each side). Plus 4 times one-fourth of the circumference of each pencil (for the four corners).

because the diameter is 10mm, the length of the band will be:

L = 4*10mm + 4*(π*10mm/4)

L = 40mm + π*10mm

This is the length of the band in terms of π.

If you want to learn more about circles:

https://brainly.com/question/14283575

#SPJ1

Answer: B

Step-by-step explanation:

Angles that measure 90 degrees, angles that measure 90 degrees are right angles, and perpendicular lines form right angles.

Since angle EAB is a right angle, and it is formed by segments EA and AB, B is the answer.

Answer:

$46.272

Step-by-step explanation:

i beleive the answer is 2610.4109589