What is 2/3 to the power of 2

Work out the area of the shaded shape.

Step2247 [10]

Answer:

Step-by-step explanation:

A = 8(14) - 9(8 - 4) = 76 m²

4 0

2 years ago

The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.

lorasvet [3.4K]

$p = 2w + 2l$ $p = 42$
$a = l * w$ $a = 108$

You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:

Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
$2's$ $cancel$ $out$
$\frac{p}{2} = w + l$

Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
$\frac{p}{2} - l = w + l - l$
$l's$ $cancel$ $out$
p/2 - l = w

$a = l * w$

You replace w with the equation above p/2 - l = w
$a = l( \frac{p}{2} - l)$

Multiply out the L.
$a = \frac{p}{2}l - l^{2}$

Plug in all your numbers a = 110 and p = 42
$110 = \frac{42}{2}l - l^{2}$
$110 = 21l - l^{2$

Move everything to the left side so $l^{2}$ would be positive (makes the equation easier when $l^{2}$ is positive).
$l^{2} - 21l + 110 = 0$

Factor.
$(l -10)(l-11) = 0$

Make each parenthesis set equal to 0.
$l-11=0$ $l-10=0$

Add.
$l = 11$ $l = 10$

By doing this you solve for both the width and length so the answer is:
w = 11 L = 10

8 0

2 years ago

Denzel and three friends go to the movies. each person buys a movie ticket for $8, a snack for $4, and a drink for $2. which num

swat32

8(4) + 4(4) + 4(2)
32 + 16 + 8

^^ Either one of these two expressions can be written down and they'd both be right.

6 0

2 years ago

An equation that involves a multiplication addition, contains a variable, and has a solution of 8.

yulyashka [42]

A variable is an unknown like x so

first we start with
x=8
then we subtract (because you must add to reverse subtraction)
x-2=8-2
x-2=6
then we divide ( because you must multiply to reverse division)
(x-2)/3=6/3
(x-2)/3=2

find x

7 0

2 years ago

Can someone please help me with 21-24 and explain/ show how you got the answer?

oksano4ka [1.4K]

The solution (x,y) needs to work in both equations. With multiple choice you can do guess and test method. Otherwise you need to combine the two equations into one by substitution or elimination methods.

21. substitution works well here since one equation is y= x+3. you can easily substitute the (x+3) for y in the other equation.
2x + (x+3) = -6
3x + 3 = -6
3x = -9
x = -3
use this in either equation to find y.
y = (-3)+3
solution: (-3,0)

22. these both equal y so they equal each other.
4x - 1 = 3x +6
4x - 3x = 6 + 1
x = 7
use this in either equation to find y
y = 4(7) - 1
y = 28 - 1
y = 27
solution: (7,27)

23. one equation is y = 2x - 3. So substitute (2x -3) for y in the other equation.
4x = 2(2x - 3) + 6
4x = 4x - 6 + 6
4x = 4x
x = x
any solution will work, infinitely many.

24. infinitely many solutions means the two equations are the same equation. Like the previous one they didn't look the same but if you put them both in terms of y...
y= 2x-3
4x = 2y + 6
4x - 6 = 2y
(4x - 6)/2 = y
2x - 3 = y
same equation.

from the image, I can't see all options but A & C do not look like the same equations. It's got to be either B or D.

3 0

2 years ago