The algebraic expression 6x² + 9x + 3 represents the area of a rectangle. What is the area of the
rectangle when x = 3 feet?
a. 51 square feet
b. 60 square feet
c. 66 square feet
d. 84 square feet

Answer:

The percentage change is 140%

Step-by-step explanation:

Given

[tex]L= 3W_1[/tex] ---- initial dimension

[tex]W_2 = 6m[/tex] --- new width

[tex]A_2 = 45m^2[/tex] --- new dimension

Required

The percentage increment

The length remains constant because only the width is extended.

The new area is:

[tex]Area =Length * Width[/tex]

[tex]A_2=L * W_2[/tex]

Make L the subject

[tex]L = \frac{A_2}{ W_2}[/tex]

Substitute values for A and W

[tex]L = \frac{45m^2}{6m}[/tex]

[tex]L = \frac{45m}{6}[/tex]

[tex]L = 7.5m[/tex] --- this is the length of the garden

Calculate the initial width:

[tex]L= 3W_1[/tex]

Make W1 the subject

[tex]W_1 = \frac{1}{3} * L[/tex]

[tex]W_1 = \frac{1}{3} * 7.5[/tex]

[tex]W_1 = 2.5[/tex]

So, the initial area is:

[tex]A_1 = L_1 * W_1[/tex]

[tex]A_1 = 2.5 * 7.5[/tex]

[tex]A_1 = 18.75[/tex]

The percentage change in area is:

[tex]\%A = \frac{A_2 - A_1}{A_1}[/tex]

[tex]\%A = \frac{45 - 18.75}{18.75}[/tex]

[tex]\%A = \frac{26.25}{18.75}[/tex]

[tex]\%A = 1.4[/tex]

Express as percentage

[tex]\%A = 1.4*100\%[/tex]

[tex]\%A = 140\%[/tex]

Answer:

use the slope formula to find the slope of a line given the coordinates of two points on the line and the slope formula is m=( y2- y1)/ (x2 - x1) or the change in the y values over the change in x values.The coordinates of the point represent x1 and y1. The coordinates of the second points are x2, y2.

Answers:

Blank 1 = p and q

Blank 2 = Consecutive interior angles converse

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

Explanation:

There's a lot of visual noise here, meaning there's a lot of lines and angles to potentially distract. I recommend redrawing things but only drawing lines p and q, and the transversal cut line t. Furthermore, I would mark only angle 8 and angle 13. See the diagram below.

The diagram is optional, but hopefully you can see that the angles are same side interior angles, aka consecutive interior angles. That's why we go with the consecutive interior angles converse

If we drop the "converse" portion, then that theorem says parallel lines lead to supplementary consecutive interior angles. The converse just reverses the flow of the logic.

Answer:

1,800$

Step-by-step explanation:

25% is 1/4th of the total amount. So...

Divide 2,400$ by 4 and get 600

Now, subtract 600 from 2,400.

Note:

Pls notify me if my answer is incorrect for the other users that will see this response. Thank you.

-kiniwih426

Answer:

30°

Step-by-step explanation:

it is the alternating angle.

Answer:

Top row, third one from left to right

Step-by-step explanation:

Use test points:

when x = 0 , y = 2(0) - 4 = 0 - 4 = -4

(0, -4)

when y = 0, 0 = 2x - 4, 4 = 2x, 2 = x

(2, 0)

Top row, third one from left to right

Answer:

3r(1 + 2r)

Step-by-step explanation:

3r + 6r^2

take common

3r(1 + 2r)

Answer:

3r(1+2r2)

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

1) the area of the given circle is: A=π*r²=256π (in²).

2) the part of the shaded sector is 110/360=11/36, it means that the required area of the shaded sector is: 11/36 * A = 256* π * 11 / 36≈246 (in²).

Answer:

Rs 12,500

Step-by-step explanation:

the price before VAT = 100/10 × Rs 5000 =

Rs 50,000

the price before discount = 50,000 / 80%

= 50,000/0.8 = 62,500

so the discount amount = 62,500-50,000

= Rs 12,500

Answer:

180(n-2) or B

Step-by-step explanation:

Answer:

4*4=16+7=23

Step-by-step explanation:

4 inches x 4 weeks is 16 inches

7 + 16 = 23

Answer:

8,654,210 and 1,024,568

Step-by-step explanation:

biggest number to smallest

Answer:

top answer, domain and range have no restrictions

Step-by-step explanation:

Answer:

1.58feet

Step-by-step explanation:

Given data

Total lenght of rope= 5 feet

She cuts 2 feet

Remainder= 5-2= 3feet

Now let us convert 17inches to feet

from tables, 17inches is 1.41667feet

Hence the amount of rope now left is

=3-1.41667

=1.58feet

Answer:

I think it would be 36, if you use Area=Length×Width×Height

Answer:

10 to the 9th power

Step-by-step explanation:

Answer:

16.

Step-by-step explanation:

n - 7 = 9

Add 7 to both sides

n = 9 + 7 = 16.

Answer:

16

Step-by-step explanation:

Given

n - 7 = 9 ( add 7 to both sides )

n = 16

Answer:

[tex]cos(\alpha)=\frac{3}{5}=0.6[/tex]

[tex]cosec(\alpha)=\frac{5}{4}=1.25[/tex]

Step-by-step explanation:

El cos(α) se define como el cociente entre el cateto adyacente y la hipotenusa.

El valor del cateto adyacente en nuestgro caso es CA = 3.

La hipotenusa se calcual de la siguiente manera:

[tex]h=\sqrt{3^2+4^2}=5[/tex]

Por lo tanto, el cos(α) sera:

[tex]cos(\alpha)=\frac{3}{5}=0.6[/tex]

El cosec(α)=h/CO.

El cateto opuesto CO = 4 y la hipotenusa h = 5

Por lo tanto, el cosec(α) sera:

[tex]cosec(\alpha)=\frac{5}{4}=1.25[/tex]

Espero te haya sido de ayuda!

Answer:

A

Step-by-step explanation:

Marginal cost is the change in total cost as a result of increasing output by one unit

Marginal cost  = Δcost / Δquantity

0.2 / 0.25 = 0.8

The marginal cost would decrease because the change in output is higher than the change in total cost

Marginal benefit would increase

Opportunity cost is the cost of the opportunity forgone when one alternative is chosen over other alternatives. There is no enough information given to determine the impact on opportunity cost

Answer:

[tex] \sqrt{2} =1.41421356237...[/tex]

Answer:

The proof that √2 is indeed irrational is usually found in college level math texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead is a "proof by contradiction": if √2 WERE a rational number, we'd get a contradiction.

...

A proof that the square root of 2 is irrational.

2 = (2k)2/b2

b2 = 2k2

Answer:

x² + 13x + 42 = 0

Step-by-step explanation:

(x + 6)(x + 7) = x² + 7x + 6x + 42 = x² + 13x + 42

Answer:

huh???

Step-by-step explanation:

it should be

9x+1y+8

      ^it could be just y instead of 1y

Answer:

the answer is = 9x+y+8

Step-by-step explanation:

...

Answer:

Step-by-step explanation:

╭═══════ღ❦ღ══╮

[tex]\boxed{ \sf{Answer}}[/tex]

⏩ Substitute the value of 'f' in the equation.

[tex]4 - 2f \\ = 4 - 2(1) \\ = 4 - 2 \\ = 2[/tex]

⏩ The answer will be 2.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

╰══ღ❦ღ═══════╯

Answer:

2

Step-by-step explanation:

If you multiply 2 by 1, you get 2. Then subtract 2 from 4 to get 2.

Hope that this helps!

Answer:

Here we do not have the options, so I will answer in a general way.

We have two statements:

p = A number is greater than 25

q = A number is less than 35

We want to have:

p ^ q is true

This means:

p and q are true.

So, we need to find a number such that both conditions are meet, so we need to find a number N such that

The number N is greater than 25  (from p)

The number N is less than 35 (from q)

So N can be any number between 25 and 35

So, some of the possible values of N are:

N = 26

N = 27

N = 28.6

N = 33

N = 34

Concluding, any number N ∈ (25, 35) can be a solution.

(Note that N = 25 and N = 35 are not solutions)