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3 years ago

If I cut a piece that was 5 centimeters wide and had an area of 20 centimeters. How long was the piece?

Mathematics

2 answers:

Soloha48 [4]3 years ago

6 0

Area= Length x width
So....
Length= Area divided by width.
Plug in equation
20 divided by 5= L
L= 4
Answer is 4 cm

motikmotik3 years ago

4 0

Its length is 4 cm because length multiplied by width = area

so 5x = 20

x = 4

length = 4 centimeters

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14 times a number decreased By eight is 22 Increase by 20 times The same number

kotegsom [21]

Answer:

14x - 8 = 22 + 20x

x = -5

Step-by-step explanation:

Let "the number" be represented by x

Take each part of the statement and translate into algebraic form

"14 times a number" 14x

"decreased By eight" -8

"is" =

"22 Increased by" 22 +

"20 times The same number" 20x

Put the equation together. Solve for x by isolating.

(

14x - 8 = 22 + 20x

14x - 8 - 20x = 22 + 20x - 20x Subtract 20x from both sides

-6x - 8 = 22

-6x - 8 + 8 = 22 + 8 Add 8 to both sides

-6x = 30

-6x ÷ -6 = 30 ÷ -6 Divide both sides by -6

x = -5

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3 years ago

Function or not a Function

Vadim26 [7]

Answer:

Function; Not a function

Step-by-step explanation:

Write the ordered pair in the first set (x, y): (1, 11), (2, 7) , (3, 2)

Write the ordered pair in the second set (x, y): (1, 3), (1, 4), (2, 4) , (3, 2)

The first set in a function because no ordered pair has the same x value.

The second set in not a function because the x value is the same in two of the ordered pairs.

5 0

2 years ago

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

PolarNik [594]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY = $\sqrt{x^2+y^2}$

Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|$

= $=(\frac{1}{2})|-4-6 -8|= 9 units^2$

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

$S_{{\bigtriangleup}ACD'}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2}$ = 10.5 units²

Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

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3 years ago

An aquarium in the shape of a rectangular prism has the volume of 3,758.75 cubic inches, length of 24.25 inches, and width of 12

natulia [17]

You do length times width times you get your area. (I think)

8 0

3 years ago

Need help asap. Simplify the expression 6/c+4/c^2 show work

Zina [86]

By taking a common denominator, we can find out that the simplified expression of the given expression is $\frac{6c+4}{c^{2} }$ .

The given expression is -

$\frac{6}{c}+\frac{4}{c^{2} }$ ---- (1)

We have to simplify the expression.

From equation (1), we have the given expression as -

$\frac{6}{c}+\frac{4}{c^{2} }$

Establishing common denominator $c^{2}$ , we have

$\frac{6c}{c^{2} }+\frac{4}{c^{2}}$

Combining the numerator and common denominator, we have

$\frac{6c+4}{c^{2} }$

Thus, the simplified expression of the given expression is $\frac{6c+4}{c^{2} }$ which is obtained by taking a common denominator.

To learn more about simplified expression visit brainly.com/question/22860327

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1 year ago