The length of a rectangle is 3 ft longer than its width.
If the perimeter of the rectangle is 70 ft, find its length and width.

Answer:

A)

6x - y = 8

3x + 2y = 9

(Graph is attached for you⤴⤴⤴)

Step-by-step explanation:

Line m ordered pairs = (-4,-32), (2,4),

(5, 22)

Line n ordered pairs = (-5,12), (1,3), (5,-3)

Use this formula⤵⤵⤵

[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]

For line m, we'll use (2,4) and (5,22):

22 - 4 = 18

5 - 2 = 3

18 ÷ 3 = 6

Slope of line m = 6

For line n, we'll use (1,3) and (5,-3):

-3 - 3 = -6

5 - 1 = 4

Slope of line n = -6/4 or -3/2

We'll turn all the options to slope-intercept form, so we can tell which has the slopes we need.

A) - Subtract 6x on both sides to get

-y = -6x + 8, then flip all the signs to get y = 6x - 8.

- Subtract 3x on both sides to get 2y = -3x + 9, then divide 2 on both sides to get y = -3/2 x + 9/2.

B)

- Subtract 6x on both sides to get

y = -6x - 8.

- Subtract 3x on both sides to get

-2y = -3x + 9, then divide -2 on both sides to get y = -3/2 x - 9/2.

C)

- Add 6x on both sides to get -y = 6x - 8, then flip all signs to get y = -6x + 8.

- Add 3x on both sides to get 2y = 3x + 9, then divide 2 on both sides to get

y = 3/2 x + 9/2.

D)

- Subtract 6x on both sides to get

-y = -6x - 8, then flip all signs to get

y = 6x + 8.

- Add 3x on both sides to get -2y = 3x + 9, then divide -2 on both sides to get

y = -3/2 x - 9/2.

Hope this helps :)

Answer:

[tex]a=60\\b=44\\c=76[/tex]

Step-by-step explanation:

You can write these equations to represent the problem:

[tex]a+b+c=180\\b+c=2a\\b=c-32[/tex]

Now, just solve it as a system of equations. I'll solve by substitution, starting from the bottom as b is already defined there.

[tex]b=c-32\\b+c=2a\\(c-32)+c=2a\\c+c-32=2a\\2c-32=2a\\a=c-16[/tex]

That's the middle equation done, now I'll do the top one:

[tex]b=c-32\\a+b+c=180\\a+(c-32)+c=180\\a+2c-32=180\\a+2c=212\\a=-2c+212[/tex]

Now we have just 2 equations with 2 variables. That's another system of equations, but this one is much easier to solve. Using substitution again:

[tex]a=c-16\\a=-2c+212\\c-16=-2c+212\\3c-16=212\\3c=228\\c=76[/tex]

Finally, we have one variable solved. Using the value of C, now we can solve for A:

[tex]c=76\\a=c-16\\a=76-16\\a=60[/tex]

Thats 2 done. Now, pick any equation that has all 3 variables and solve for B:

[tex]a=60\\c=76\\a+b+c=180\\60+b+76=180\\b+136=180\\b=44[/tex]

All 3 variables done.

[tex]a=60\\b=44\\c=76[/tex]

Now, we can confirm that they're correct by checking with the original equations:

[tex]a+b+c=180\\60+44+76=180\\180=180\\\\b+c=2a\\44+76=2(60)\\120=120\\\\b=c-32\\44=76-32\\44=44[/tex]

They all work fine.

Answer:

-4/9

Step-by-step explanation:

Answer:

9a+18=9

9a=-9

a=-1

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

The 2 given angles are adjacent on a straight line and sum to 180° , then

123 + 2x + 17 = 180

140 + 2x = 180 ( subtract 140 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Y-intercept - 4

Slope - 3

Slope intercept form - y=3x + 4

Hope it's correct and it helped:)

Answer:

what is it

Step-by-step explanation:

We know that f(x) = 12x + 12

f(1) = 12 * 1 + 12= 24

f(0) = 12*0 + 12 = 12

The formula of the average rate of change is : f(1) - f(0)  /  (1 - 0)

(24 - 12) / 1 = 12/1 = 12

So the average rate of change is 12

Good Luck

Answer:

around 5 books

Step-by-step explanation:

hope this helpsss :D

Answer:

C: 16 is a constant

B:3

A: 4

Answer: C: 16 is a constant

B:3

A: 4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Well since 11 of the pirates had eyepatches, and 11 is greater than 9, all 9 of the pirates that had cutlasses had eyepatches as well. I don't know if this is completely correct but it's the only thing that makes sense to me.

Answer:

2b + 3n = £15.50

4b + 1n = £13.50

2 ( 2b + 3n =  15.50 )

4b + 6n = 31.00

    4b + 6n =  31.00

-    4b +  1n = 15.50

            5n  = 15.50

              n  =  3.1

subtitue n in to the equation

2b + 9.3 = £15.50

2b          = £6.20

b             = 3.10p

Step-by-step explanation:

both the bracelets and necklace cost £3.10

The cost of one bracelet is $2.50

b = cost of the bracelet

n = costs of necklace

⇒ 2b + 3n = 15.50

⇒ 4b+1n = 13.50

Multiply the first equation by -2

⇒ -4b - 6n = -31

⇒ 4b + n = 13.50

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

-5n = -17.50

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

Divide each side by -5

⇒ -5n / -5 = -17.5 / -5

⇒ n = 3.50

Now we can find b

⇒ 4b + n = 13.50

⇒ 4b + 3.50 = 13.50

⇒ 4b + 3.50 - 3.50 = 13.50 -3.50

⇒ 4b = 10

Divide by 4

⇒ 4b / 4 = 10/4

⇒ b = 2.50

The cost of one bracelet is $2.50.

A system of equations comprises two or more equations and seeks common solutions to the equations.

Learn more the system of equations about here: brainly.com/question/14323743

#SPJ2

Answer:

Step-by-step explanation:

given A(-1, 2), B(-3, 4), C(-2, 5)

after translating by (4, 4)

points are A(-1 + 4, 2 + 4),  B(-3 + 4, 4 + 4), C(-2 + 4, 5 + 4)

A(3, 6), B(1, 8), C(2, 9)

to rotate 90° counter clockwise (x, y) ----> (-y, x)

now it is rotated around point A(3, 6).That means A remains same and we need to find new coordinates of B and C.  To find B and C let us make origin as A and find B ,C coordinates from it.

B'(1 - 3, 8 - 6) = (-2, 2)

C'(2 - 3, 9 - 6) = (-1, 3)

now it becomes (-y, x)

B'(-2, -2)

C'(-3, -1)

now we have to move origin from (3,6) to (0,0) again.

so B'(-2 + 3, -2 + 6) = (1, 4)

C'(-3 + 3 , -1 + 6) = (0, 5)

now reflection over y axis means (x, y) --> (-x, y)

A'(-3, 6)

B'(-1, 4)

C'(0, 5)

it is different from the options

but this is the process, tell me if you find any step different from the question

see the figure below

Answer:

12.64

Step-by-step explanation:

cos 53 = Adjacent side/Hypotenuse

cos 53 = Adjacent side/21

21 * cos 53 = (Adjacent side/21) * 21

21 cos 53 = Adjacent side

Adjacent side (AB) ≈ 12.64

Answer:

317 is the finally awnser

Answer:

g(x) = (x - 1)³

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

Here g(x) is the graph of f(x) shifted 1 unit to the right , then

g(x) = (x - 1)³

Answer:

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

Step-by-step explanation:

First make points out of the number!

(5,0), (-2,0), and (0,-20)

Plug it into this, p and q being the roots

y=a(x-p)(x-q) ---> y=a(x-5)(x+2)

Now plug in x and y from our y-intercept

-20 = a(0-5)(0+2) --> -20 = -10a ---> 2 = a

Now plug in "a" in orginal equation

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

Answer:

5/16

Step-by-step explanation:

Answer:

18 = 2 x 3²

Step-by-step explanation:

Factors of 18: 1, 2, 3, 6, 9, 18

Prime factorization: 18 = 2 x 3 x 3

Adjacent angles will be same

[tex]\\ \sf\longmapsto <N=<P[/tex]

[tex]\\ \sf\longmapsto 6y=8y-16[/tex]

[tex]\\ \sf\longmapsto 8y-6y=16[/tex]

[tex]\\ \sf\longmapsto 2y=16[/tex]

[tex]\\ \sf\longmapsto y=8[/tex]

Answer:

[tex]y = 8[/tex]

Step-by-step explanation:

If two sides of a triangle is equal the opposite interior angles are also equal.

Therefore,

[tex]6y = 8y - 16 \\ 16 = 8y - 6y \\ 16 = 2y \\ \frac{16}{2} = \frac{2y}{2} \\ 8 \degree = y[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

hot dog= $2.25

juice= $1.50

Step-by-step explanation:

Let the price of a hot dog be $H and that of a juice be $J.

H +J= 3.75 -----(1)

2H +3J= 9 -----(2)

(1) ×2:

2H +2J= 7.5 -----(3)

(2) -(3):

2H +3J -(2H +2J)= 9 -7.5

Expand:

2H +3J -2H -2J= 1.5

J= 1.5

Substitute J= 1.5 into (1):

H +1.5= 3.75

H= 3.75 -1.5

H= 2.25

∴ The price of a hot dog and a juice is $2.25 and $1.50 respectively.

Answer:

56

Step-by-step explanation:

Let the angle be " x ".

Complement of the angle = ( x - 22 )

To find : x = ?

x + x - 22 = 90

2x - 22 = 90

2x = 90 + 22

2x = 112

x = 112 / 2

x = 56

Therefore, the angle is 56.

Answer:

55

Step-by-step explanation:

You multiply 5 on both sides of the ratio, and you get 40 children : 15 adults. Adding that up, you would get 55 people.

Answer:

Step-by-step explanation:

Write and solve an equation of ratios.  The given ratio is 8:3.  The number of children is 40 and that of adults is 40 - c.  Note that c + (40 - c) = 40.

Solve the following equation of ratios for c:         8        40

                                                                               ---- = ----------

                                                                                3          a

Cross multiplying, we get 8a = 120, of 15.  Then a = number of adults = 24.

Here a = 15 and c = 40.  Check the ratio 40/15; does it equal 8/3?  YES

The total number of people at the pool is 40 + 24, or 64

Answer:

Step-by-step explanation:

g(3)= (3+1)/(3-1)= 4/2= 2

f(2)= 3(2)-7 = 6 - 7 = -1

answer is a. -1

Answer:

kikjnknj

Step-by-step explanation:

9514 1404 393

Answer:

  n = 3

Step-by-step explanation:

In order for 3 × 3 = 9 to be a factor of both numbers, we must have ...

  n = 3

Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation: