Given that 4 is a zero of the polynomial function f(x), find the remaining zeros.f(x) = x³ - 6x² + 25x - 68List the remaining zeros (other than 4).4(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a cc

Given:

Ben, Claire, and Devon are swimming one mile.

Ben swam 0.77 of the mile before stopping.

So, the distance Ben swam = 0.77 x 1 = 0.77 mile

Claire swam 3/5 of the mile.

So, the distance Claire swam = 3/5 x 1 = 3/5 = 0.6 miles

Devon swam 82% of the mile before stopping.

So, the distance Devon swam = 82% of 1 mile = 0.82 x 1 = 0.82 miles

Arrange the distances in order from the largest to the least:

0.82, 0.77, 0.6

So, the answer will be:

The farthest distance is for Devon = 0.82 miles

The shortest distance is for Claire = 0.6 miles

Answer: g(f(5)) = 352

Step-by-step explanation:

The question being asked is the same as finding g(f(5)).

What this means is to find f(5), and then plug that value into g(x) as x and solve.

f(5) = 4(5) + 1 = 20 + 1 = 21

g(f(5)) = g(21) = 21^2 - 4(21) - 5 = 441 - 84 - 5 = 357 - 5 = 352

Note: You could also find g(f(x)), and then plug 5 in as x and solve.

Start by plugging f(x) into g(x) such that you get g(x = f(x))

g(f(x)) = (4x + 1)^2 - 4(4x + 1) - 5

Now, replace x with 5 and solve to get g(f(5)).

g(f(5)) = (4(5) + 1)^2 - 4(4(5) + 1) - 5 = 352

we can see the interval is between -2 and 1. but the -2 isn't included (you can notice by the white circle) and the 1 is included, so in interval notation you get:

(-2,1]

Answer:

Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)

Has the same slope, m but a different y intercept (0,b)

So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b

y = mx + b

m = -2

1 = -2(1) + b

1 = -2 + b

Add 2 to both sides of the equation to solve for b

1 + 2 = b

3 = b

The line is

y = -2x + 3

The form of the linear equation is

m is the slope

b is the y-intercept

The given equation is

Let us compare the given equation with the form above, then

and the value of b is

The slope of the line is the coefficient of x

The y-intercept is the numerical term

The slope = -2/3

The y-intercept = 1

The right answer is D the last answer

In any question like that, put the equation in the form

y = m x + b

m is the slope

b is the y-intercept

Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome of credit.

Step 1

Loan Amount(p)= 3600

Number of Payments per year(n)= 12

Time in Years (t)=4

Installment Payment (m)=83.81

Total amount paid in 48 installments= 4022.88

Amount Paid - Amount Financed = 4022.88 - 3500 = 522.88 in finance charges.

To determine the annual percentage rate. Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome.

Finance Charge​/ Amount financed × 100= 522.88/ 3600× 100= 14.5

To use Table , look for 48 in the far left-hand column under the heading Number of Payments. Then move across to the right until you find the value closest to 14.5. In this case, 14.5 is in the table. The value 7 is at the top of this column. The yearly percentage rate is therefore around 7. Monthly payments are 83.81. After 12 payments have been made, 30 payments remain. Therefore, P = 83.81 and n = 30. Use the APR table to calculate V . In the Number of Payments column, find the number of remaining payments, 30, and then look to the right until you reach the column headed by 7%, the APR. intersect at 9.30. Thus, V = 9.30.

:[tex]u=nPV/100+V\\u=30*83.81*9.30/100+9.30=213[/tex]

Total due amount = Total remaining payment including interest- saving on interest + 12th monthly payment= 2514.3- 213.934+ 83.81= 2384.17

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We want to know if (x-sqroot(6)) is a factor of (x^4 - 36)

That's mean:

Where P(X) is a polinomial.

In this case, if x = sqroot(6) the polinomail (x^4 - 36) must be zero, that's mean sqroot(6) is a root (or a zero) of (x^4-36).

So, if we evaluate (x^4 - 36) in x=sqroot(6):

So, the answer is true.

Answer:

-3x-6=-9

Step-by-step explanation:

[tex]-3x-6=-9[/tex]

       [tex]+6[/tex]     [tex]+6[/tex]

[tex]-3x = -3[/tex]

[tex]-3x/-3 = -3/-3[/tex]

[tex]x=1[/tex]

Answer:

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

A square with dimensions:

Square has all sides equal:

Each side is:

Perimeter:

The perimeter of the square is found as 64 units.

For the given question,

The dimension of the square are given as;

For square, as all sides are equal.

Then,

Width = Length

Put the values.

4x = 36 – 5x

9x = 36

x = 4

Put in dimensions.

The perimeter of square is;

Perimeter = 4 × side

Perimeter = 4 × 16

Perimeter = 64 units.

Thus, the perimeter of the square is found as 64 units.

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Total Sales = 14910

8% on 5000

10% on 5500

15% on

14910 - 10500 = 4410

So,

15% on 4410 [this is the excess of 10,500]

Converting percentages to decimal:

8% = 8/100 = 0.08

10% = 10/100 = 0.1

15% = 15/100 = 0.15

Total Commission

10 more than d is the same as d plus 10, so the algebraic expression is:

d + 10

Answer: d + 10

The height of the building is 38.85 ft.

Given;

length of the ladder, x = 39 ft

the angle between the ground and the ladder, θ = 85°

let the height of the building be h.

Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.

Apply the following trig ratio to determine the height of the triangle;

sin(θ) = opposite/hypotenuse

sin(85°) = h/39

h = 39sin(85°)

h = 38.85 ft

Therefore, the height of the building is 38.85 ft (approx.).

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you can find the slope taking two points of a graph or function,

identify the rightmost point and apply this equation

where (x2,y2) is the rightmost point and (x1,y1) is the other point

If i have two points (3,4) and (6,2)

the rigthmost point is (6,2) because 6 is greater than 3 and these two numbers are x, the place where I can locate myself horizontally or left or right

so, apply the equation

So, the slope is

The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"

The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:

We know that:

P=26m

w=x

l=1.5x

Then, replace the measurements on the formula:

From this expression, you can calculate x, first, add the like terms:

Second, divide both sides by 5 to determine the value of x:

The width is x= 5.2m

The length is 1.5x= 1.5*5.2= 7.8m

Given the function:

Where A is the amount of money (in dollars) Diane has left in her account after t trips on the toll roads.

(a)

After 8 trips on the toll roads (t = 8):

(b)

If her account is empty:

Solving the equation for t:

Solution

- Let the length of the rectangle be x

- Let the width of the rectangle be y.

- Thus, we can interpret the lines of the question as follows:

- Now, let us solve these two equations simultaneously.

- We shall proceed by solving the system of equations graphically.

- Wherever the graphs of Equation 1 and Equation 2 intersect represents the solution to the system of equations

- The plot of the equations is given below

- Observe that the graphs cross at two points. The first point is positive and the other, negative.

- Since we cannot have negative lengths (x) or width (y), we can discard the negative coordinates.

- Thus, the length (x) and width (y) are given below:

Final Answer

The length of the rectangle is 156 feet

Answer : 1500 miles

According to the distance time relationship

Distance = Rate x time

From the figure given, the hawk flies 500 miles in 5 days

We can find our rate using the above parameters

Since, distance = rate x time

Rate = distance / time

Rate = 500 / 5

Rate = 100 miles / day

Since, the rate remains constant

How far the hawk can fly in 15 days can be calculated as follows

Time = 15 days

Rate = 100

Distance = ?

Disatnce = rate x time

Distance = 100 x 15

Distance = 1500 miles

The Hawk can fly 1500 miles in 15 days

From the question, we have the given information.

We will use the formula below to solve the question

Therefore;

Since the Amount = 13797.71, we can get the interest by using the formula below.

Answer: Interest =$1497.71

Given:

Required:

to show which graph is correct for the inequality.

Explanation:

Given graph is correct for the equation.

Required answer:

The given graph is correct.

Step 1

Find the resultant of the vectors

Given a right angle triangle

As shown:

Given ∠58

the opposite side to the angle = 22

The adjacent side to the angle = x

So,

solve for x:

round to the nearest whole number

So, the answer will be x = 14

According to the given graph, we have the following:

1) The graph represents a plane descending.

2) The line is slanting downwards and therefore has a negative slope.

3) It takes the plane 15 seconds to touch the ground.

4) The plane starts at 3 kilometers in the sky.

5) Graph does not touch the origin (0,0).

The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.

Hello there. To answer this question, we need to remember some properties in simple and coumpound interests investments.

For simple interest, the balance will be equal to P(1 + rt), in which P is the amount invested, r is the interest rate in years and t is the time (can be either years of months).

For compound interest, the balance will be equal to P(1 + r)^t.

So, using the values P = $19,000.00 and the time is equal to 30 years, we have for:

a) 7% simple interest

It means that r = 7% and then we can use the first formula

19000(1 + 0.07*30)

We converted the rate to decimals above

Multiplying the values, we have:

19000(1 + 2.1)

19000*3.1

$58.900

b) 7% compounded monthly

First, we need to convert the time from years to months, multiplying by 12

30*12 = 360 months

Using the second formula, we have:

19000(1 + 0.07)^(360)

Sum the values into parenthesis

19000*1.07^(360)

The height reached by the projectile is 784 feet.

The projectile experiments an uniformly accelerated motion due to gravity, whose height is represented by the quadratic equation:

h(t) = - 16 · t² + 224 · t

Where t is the time, in seconds.

In this problem we need to find the maximum height reached by the projectile, which can be found by finding the vertex form of the quadratic equation:

h(t) = - 16 · (t² - 14 · t)

h(t) - 16 · 49 = - 16 · (t² - 14 · t + 49)

h(t) - 784 = - 16 · (t - 7)²

The maximum height of the projectile is 784 feet.

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We want to find the value for

To do that, first let's rewrite this expression as

Using the following property

We can rewrite our expression as

Using the given value on the text, we get our answer

Rotation 90° about the origin.

First, choose a point from triangle A.

For example: (-2,2)

For any point (x,y) rotated 90° =(-y,x)

So:

(-2,2) becames = (-2,-2)

Triangle D

All the options are correct

A quick and smart way is to substitute a value for x in each of the options and verify if the right hand side equals the left hand side

Let x = 30

A) (sin x + cos x)² = 1 + sin 2x

(sin 30 + cos 30)² = 1.866

1 + sin 2(30) = 1.866

Therefore (sin x + cos x)² = 1 + sin 2x

B)

Therefore:

C) sin 6x = 2 sin3x cos3x

sin 6(30) = 0

2 sin3(30) cos3(30) = 0

Therefore sin 6x = 2 sin3x cos3x

This can also be justified by sin2A = 2sinAcosA

D.

Options A to D are correct

The Solution:

Let the outcomes when two dice are tossed be as summarized in the picture attached below:

The inequality representing the amount of money, m. Derrick's football team needs to raise is D. m>$520

In mathematics, Inequality is part of equations solved with the use of the some special type of equality signs. The signs used inequality calculations are

Given that:

Derrick's football team needs to raise at least $1,000

The team collected 480

To solve the given problem we have the inequality in the form

at least $1,000 ≡ greater than or equal to 1000

m > $1000

having collected $480 so far. The amount collected is subtracted from the $1000

m > $1000 - $480

m > $520

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Answer:

2/13

Step-by-step explanation:

Out of a total 13 marbles , 2 are yellow     2 out of 13 = 2/13

Answer:

2/13

Step-by-step explanation:

6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble = 13 marbles

P( yellow) = number yellow / total

                 = 2/13