find the surface area of the prism

Hello,

Perimeter of a rectangle : 2 * (length + width)

Area of a rectangle : length * width

We know that the perimeter of the rectangle is equal to 10 feet and its area is equal to 6 square feet.

Let's call x the length of the rectangle and y the width of the rectangle. The pair (x ; y) verifies the following system :

2 (x + y) = 10 ⇔ x + y = 5 ⇔ x = 5 - y

x * y = 6 ⇔ (5 - y) * y = 6 ⇔ 5y - y² - 6 = 0 ⇔ y² - 5y + 6 = 0

⇔ y² - 3y - 2y + 6 = 0 ⇔ y(y - 3) - 2(y - 3) = 0 ⇔ (y - 2)(y - 3) = 0

⇔ y = 2 ou y = 3

x = 5 - y ⇔ x = 5 - 2 or x = 3 - 2 ⇔ x = 3 or y = 2

S = {(3 ; 2) ; (2 ; 3)}

The width of the rectangle is 2 or 3 feet.

:-)

Answer:

x² + 7x - 4 = 0

Step-by-step explanation:

A quadratic equation in standard form is

ax² + bx + c = 0 ( a ≠ 0 )

Given

- 7x + 4 = x² ( subtract - 7x + 4 from both sides )

0 = x² + 7x - 4 , that is

x² + 7x - 4 = 0 ← in standard form

Answer:

y=-1/2x-4

Step-by-step explanation:

Hi there!

We're given the equation x+2y=14 and we want to find a line that is parallel to it and passes through (-8,0)

Parallel lines have the same slopes, but different y intercepts.

So let's find the slope of x+2y=14

we do this by converting x+2y=14 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).

for x+2y=14, to convert to slope-intercept form, start by subtracting x from both sides

2y=-x+14

divide both sides by 2

y=-1/2x+7

so the slope of x+2y=14 is -1/2

The slope of the new line (the one parallel to x+2y=14 and passes through (-8,0) will also have a slope of -1/2).

Here's the equation of that line so far:

y=-1/2x+b

we need to find b (y intercept)

as the equation will pass through (-8,0), we can use it to solve for b

substitute -8 as x and 0 as y

0=-1/2(-8)+b

multiply

0=4+b

subtract 4 from both sides

-4=b

substitute into the equation

y=-1/2x-4

Hope this helps! :)

Answer:

True

Step-by-step explanation:

Smoking damages your entire cardiovascular system. Speaking of this Nicotine causes blood vessels to tighten, which restricts the flow of blood. Over time, the ongoing narrowing, along with damage to the blood vessels, can cause *peripheral artery disease*. Smoking also raises blood pressure, weakens blood vessel walls, and increases blood clots.

* Peripheral artery disease is a common circulatory problem in which narrowed arteries reduce blood flow to your limbs

Hope this helps :) Brainliest would be appreciated XD

Answer:

B

Step-by-step explanation:

y=e^x+3

Answer:

5P5 × 20P15

Step-by-step explanation:

i think...

sorry if im wrong

good luck

Answer: A, B, C

Step-by-step explanation:

AC is half of AB, so AB = 2AC

1/2 of AB will be AC, and AB

AC = CB

Answer:

The solution is (5, 3)

Step-by-step explanation:

To solve this system of linear equations, let's use elimination by addition and subtraction.  This approach is particularly easy because one equation already has +y and the other -y, summing up to zero:

4x+y=23

3x-y=12

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

7x   = 35

Then x must be 5.  

Substituting 5 for x in the first equation, we get

4(5) + y = 23.  Then 20 + y = 23, or y = 3.

The solution is (5, 3)

Answer:

the 9th term would be  -15

Step-by-step explanation:

Answer:

The correct value is t* = 2.492.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.492, which is the answer to this question.

Answer:

63 inches tall.

Step-by-step explanation:

60 + 3 = 63.

Answer:

130°

Step-by-step explanation:

angle TFM + angle MFD = 180° (being a linear pair)

or, 4m + 142° +2m + 56°= 180°

or, 6m= 180°- 198°

or, m= -18°/6

so, m= -3°

now, angle TFM = 4m +142°= -12°+142°= 130°

(4a³+6a²-10a-4)+(6a²+a²+a+7)

(4a³+6a³)+(6a²+a²)+(-10a+a) + (-4+7)

10a³+7a²-9a+3

OPTION D is the correct answer

Answer:

option d is the correct answer

I hope it helped U

stay safe stay happy

The system of linear inequalities is represented by the graph is y < x – 2 and y > x + 1

The equation of a line is expressed as y = mx + b

For the blue line;

m = 1

Since the line cuts the line at y = 1, hence the y-intercept is 1

The required equation of the red line will be y > x + 1

For the red line;

m = 1

Since the line cuts the line at y = -2, hence the y-intercept is -2

The required equation of the red line will be y < x - 2

Hence the system of linear inequalities is represented by the graph is y < x – 2 and y > x + 1

Learn more on inequality graph here: https://brainly.com/question/9774970

Answer:

B Or y < x – 2 and y > x + 1

Step-by-step explanation:

y < x – 2 and y > x + 1

Answer:

What is the number of boys? I think you forgot to add the number in.

Step-by-step explanation:

Don't worry, I'll still help you! I'll be here waiting! :)

Answer:

[tex]Q_3 = 64[/tex]

Step-by-step explanation:

Given

Box of a box plot with the range: 60 - 64

Required

The upper quartile

To do this, we simply identify the endpoint of the range

Given that the range of the box is 60 to 64.

We have:

[tex]Start = 60[/tex]

[tex]End = 64[/tex]

Hence:

[tex]Q_3 = 64[/tex]

Answer:

Answer 3.0/528 claudiasai 88-2n + 2927,25,23,21,19- 2 difference- 2n + 29-2 x (1 ) + 29 =27-2 x (3) +29 =23

Step-by-step explanation:

Write a recursive formula for each sequence. 3. 1, 6, 11, 16, ... SOLUTION: ... Check for a common ratio by dividing each term by the term that precedes it. = 3 ;. = 3 ; ... 19. 100, 80, 64, 51.2, ... SOLUTION: Subtract each term from the term that follows it. ... Patrick thinks that the sequence can be written as a recursive formula​.

Answer:

[tex]a_{n}[/tex] = 27 - 8n

Step-by-step explanation:

There is a common difference between consecutive terms, that is

11 - 19 = 3 - 11 = - 8

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 19 and d = - 8 , then

[tex]a_{n}[/tex] = 19 - 8(n - 1) = 19 - 8n + 8 = 27 - 8n ← general rule

Answer:

see explanation

Step-by-step explanation:

(a)

The consecutive angles are supplementary, sum to 180° , then

3y + 2y - 5 = 180

5y - 5 = 180 ( add 5 to both sides )

5y = 185 ( divide both sides by 5 )

y = 37

Then ∠ A = 3y = 3 × 37 = 111

The opposite angles are congruent , then

3x + 3 = 111 ( subtract 3 from both sides )

3x = 108 ( divide both sides by 3 )

x = 36

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

(b)

The diagonals bisect each other , so

x + 8 = 16 - x ( add x to both sides )

2x + 8 = 16 ( subtract 8 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

and

5y + 4 = 2y + 13 ( subtract 2y from both sides )

3y + 4 = 13 ( subtract 4 from both sides )

3y = 9 ( divide both sides by 3 )

y = 3

Answer:

D

Step-by-step explanation:

Have a great summer :)

Answer:

C

Step-by-step explanation:

The slope is negative, so we can exclude the graph A and D

If we substitute y with 2 and x with -3 we have

2 = -4/3 (-3) -2

2 = 4 - 2

2 = 2

the equality is verified so C is the answer

Answer:

2) is not proportional, 3) is not proportional, 5) is proportional, 6) is not proportional.

Step-by-step explanation:

Number 2 is not proportional since it doesn't go through the origin on the graph and the line is not a straight line.

Number 3 does not go through the origin, so number 3 is also not proportional.

Number 5 is proportional since when you divide y by x, it is always 7.

Number 6 is not proportional because when you divide y by x or x by y there are not the same answers.

Answer:

AB: 3

BC: 5

CD: 3

DA: 5

Step-by-step explanation:

You’re welcome

Answer:

y>2/1+-4

Step-by-step explanation:

y> because it's shaded over and since it's not dashes it needs the underline

2/1 because it's goes to the left twice and up once

-4 because that's where it starts

Answer:

a

Step-by-step explanation:

1/2 of 10 is 5

Answer: b

Step-by-step explanation:

there are 6 numbers on a regular dice. 3 even, 3 odd

Answer:

slope = [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (4, 4)

m = [tex]\frac{4-2}{4-(-3)}[/tex] = [tex]\frac{2}{4+3}[/tex] = [tex]\frac{2}{7}[/tex]

Answer:

= 2

7

Step-by-step explanation:

slope = y2 - y1

x2 - x1

=4 - 2

4 - -3

= 2

7

y - 4 = 2

x - 4 7

7(y - 4) = 2(x - 4)

7y - 28 = 2x - 8

7y = 2x - 8 + 28

7y = 2x + 20

7 7 7

Gradient = 2

7