Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.

surface area = 2(wl +hl+hw)

w=3

l=8

h=5

wl=3*8 =24

hl=5*8 =40

hw=5*3 =15

24+40+15 = 79

2*79 = 158 feet^2

The surface area of the rectangular prism is 158 square feet.

The surface area of any given object is the area or region occupied by the surface of the object.

Surface Area = 2{(h × l) + (h × w) +(l × w)]

Where,

l is the length of the rectangular prism

h is the  height of the rectangular prism

w is the width of the rectangular prism

According to the given question

Length of the rectangular prism = 8 feet

width of the rectangular prism = 3feet

height of the rectangular prism = 5 feet.

Therefore,

the surface area of the rectangular prism = 2[(8 × 5)+ ( 5 × 3) + ( 8 × 3)]

surface area of rectangular prism = 2[ 40 +15 +24} = 158 square feet.

Hence, the surface area of the rectangular prism is 158 square feet.

Learn more about the surface area of rectangular prism here:

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The conjugate of the given zero 2 - 4i is 2 + 4i, which must also be a zero of the polynomial f(x) due to the Complex Conjugate Root Theorem.

Given the zero 2 - 4i of the polynomial function f(x) = [tex]x^4 - 4x^3 + 21x^2 - 4x + 20,[/tex] we know by the Complex Conjugate Root Theorem that if a polynomial has real coefficients, then any complex zeros must occur in conjugate pairs. Therefore, the conjugate of 2 - 4i, which is 2 + 4i, must also be a zero of the polynomial function.

As a result, the polynomial can be factored to include the factors (x - (2 - 4i)) and (x - (2 + 4i)). When these factors are multiplied out, they will give you a quadratic factor of the polynomial, which when multiplied with the remaining factors, will result in the original polynomial f(x). The two factors, when multiplied together, yield a quadratic with real coefficients, which means any remaining zeros must also satisfy this quadratic equation.

The remainder theorem states that the answer when d + 4 is substituted into the whole equation, the remainder would be the answer divided by d + 4. Therefore:

d + 4 = 0

d = -4

Evaluating when d = -4:

d^4 + 2 * d^2 + 5 * d − 10

= (- 4)^4 + 2 * (- 4)^2 + 5 * (- 4) – 10

= 256 + 2 * 16 – 20 – 10

= 256 + 32 – 30

= 258

Therefore basing on the remainder theorem, the remainder would then be:

Remainder = 258 / (d + 4)                             ---> Answer

Answer:

Brett should buy a ladder of minimum 30 ft length.

Step-by-step explanation:

Brett wants to paint his exterior of a double story home.

Height of the roof of the second story from the ground = 29 feet

Maximum angle between the ground and the ladder should be = 80°

Now from the figure,

sin 80° = [tex]\frac{AB}{AC}[/tex]

0.9848 = [tex]\frac{29}{AC}[/tex]

AC = [tex]\frac{29}{0.9848}[/tex]

AC = 29.45

     ≈ 30 ft

Therefore, Brett should buy a ladder of minimum 30 ft length.

Answer:  y=3x

Step-by-step explanation:

Final answer:

To find the number of different line-ups a team can make, we use permutations. Using the formula for permutations, we arrive at the answer of 437,760 different line-ups.

Explanation:

To find the number of different line-ups a team can make, we need to use the concept of permutations. Since there are 9 positions on a baseball team and 18 players, we can arrange the players in a line-up using the formula for permutations:

P(n, r) = n! / (n-r)!

Where n is the total number of players (18) and r is the number of positions (9). Substituting the values, we get:

P(18, 9) = 18! / (18-9)! = 18!/9! = 437,760.

Therefore, there are 437,760 different line-ups that the team can make.

Answer:

Given the functions: [tex]f(x)= -x^2 +3x+5[/tex] and [tex]g(x) = x^2+2x[/tex]

Now, calculate first [tex](f+g)(x)[/tex] ;

[tex](f+g)(x) = f(x) + g(x)[/tex]

Substitute the given values we have;

[tex](f+g)(x) = -x^2+3x+5+x^2+2x[/tex]

Combine like terms;

[tex](f+g)(x) =5x+5[/tex]

Let y = [tex](f+g)(x)[/tex]

Then, we have y = 5x+5

Now, Graph the equation of the line y =5x +5

Using slope intercept form: An equation of line is given by :

y = mx +b ; where m is the slope of the line and b is the y-intercept.

On comparing we get;

m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)

Now, find the intercepts of the equation: y=5x+5;

x-intercepts: The graph or line crosses the x-axis i.,e

Substitute y = 0 and solve for x;

0 = 5x +5

Subtract 5 on both sides we get;

-5 = 5x

Divide both sides by 5 we get;

x = -1

x-intercepts= = (-1, 0)

Similarly for y-intercept:

Substitute the value of x= 0 and solve for y;

y = 5(0)+5

y = 5

y-intercepts = (0, 5)

Now, using these point we can draw a graph of function [tex](f+g)(x) =5x+5[/tex] as shown below in the attachment.

Answer:  Option 'D' is correct.

Step-by-step explanation:

Since we have given 4 trapeziums with parallel sides :

[tex]a=8\ km\\b=4\ km[/tex]

For height 'h'. we will consider the right angled triangle with

Perpendicular = 4.3 km and base = 2 km ,

We need to find the hypotenuse:

[tex]H^2=B^2+P^2\\\\H^2=2^2+4.3^2\\\\H^2=4+18.49\\\\H=\sqrt{22.49}\\\\H=4.742\ km[/tex]

Now, Lateral surface area of the figure = 4 × Area of trapezium

[tex]4\times \frac{1}{2}\times (8+4)\times 4.742\\\\=113.81\ km^2\\\\=114\ km^2[/tex]

Hence, Option 'D' is correct.

The standard form for rate equation is:

F = P (1 + r)^n

or

F = P b^n

So b = 1 + r

In this case, r is given as 9.5% or 0.095. Therefore:

b = 1 + 0.095

b = 1.095

The growth factor is 1.095.

52 weeks per year

 biweekly means she gets paid every 2 weeks

 so 52/2 = 27

22500/27 = 833.33 each paycheck

17 + x = 26

17 +n = 26

n + 17 = 26

 something like those, you didn't give options to choose from.

Answer:

x + 17 = 26

Step-by-step explanation:

mathematical statement represents “17 more than a number is 26”

Let x be the unknown number

17 more means we add 17 with the unknown number x

so it becomes x+17

'is' represents an = sign

So the equation for the mathematical statement  “17 more than a number is 26” becomes  x + 17 = 26

Answer:

option c)10

Step-by-step explanation:

Given is a least integer function as

[tex]f(x) =-2[x]+8[/tex]

We are to find out the function value when x = -1.8

Substitute for x the value -1.8

we have

[tex]f(x) =-2[-1.8]+8\\[/tex]

-1.8 has the integer -1 to the left of it.

Hence we get

[tex]f(x) =-2[-1]+8=10[/tex]

Hence answer is option c)10

Answer:

Refer graph attached below

Step-by-step explanation:

Given equation  [tex]x^2-4=5[/tex]

We have to  Solve the given equation  [tex]x^2-4=5[/tex] graphically.

We first solve the given equation [tex]x^2-4=5[/tex]

Consider the given equation [tex]x^2-4=5[/tex]

Adding 4 both sides, we have

[tex]\Rightarrow x^2-4+4=5+4[/tex]

Simplify, we get,

[tex]\Rightarrow x^2=9[/tex]

[tex]\Rightarrow x^2-9=0[/tex]

To plot the graph let [tex]x^2-9=y[/tex] be the equation

It will be a parabola with vertex (0,9).

Refer graph attached below

Answer:

What was the answer?!?!!?!? >-<

Final Answer:

The rectangular coordinates of the point[tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex], where [tex]$(r, \theta)$[/tex] corresponds to the polar coordinates (7, 5), are approximately (-13.59, 11.54).

Step-by-step explanation:

In polar coordinates, a point is represented as [tex]$(r, \theta)$[/tex] , where [tex]$r$[/tex] is the distance from the origin, and $\theta$ is the angle with respect to the positive x-axis. In rectangular coordinates, the point is represented as (x, y).

Given that the point [tex]$(r, \theta)$[/tex]  in polar coordinates is equivalent to the point (7, 5) in rectangular coordinates, we can express this relationship as:

[tex]\[ x = r \cos(\theta) \][/tex]

[tex]\[ y = r \sin(\theta) \][/tex]

For the given point $(7, 5)$, we have:

[tex]\[ x = 7 \cos(5) \][/tex]

[tex]\[ y = 7 \sin(5) \][/tex]

Now, you want to find the point [tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex] in rectangular coordinates. This can be expressed as:

[tex]\[ x' = 2r \cos\left(\theta + \frac{\pi}{2}\right) \][/tex]

[tex]\[ y' = 2r \sin\left(\theta + \frac{\pi}{2}\right) \][/tex]

We know that [tex]$\cos\left(\theta + \frac{\pi}{2}\right) = -\sin(\theta)$[/tex] and [tex]$\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)$[/tex]. Substituting these into the equations:

[tex]\[ x' = -2r \sin(\theta) \][/tex]

[tex]\[ y' = 2r \cos(\theta) \][/tex]

Now, if we substitute the values of [tex]$r$[/tex]  and [tex]$\theta$[/tex] from the given point (7, 5):

[tex]\[ x' = -2 \times 7 \times \sin(5) \][/tex]

[tex]\[ y' = 2 \times 7 \times \cos(5) \][/tex]

Calculating these values will give you the rectangular coordinates of the point $\left( 2r, \theta + \frac{\pi}{2} \right)$.