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olga2289 [7]
2 years ago
7

A rectangular piece of paper has an area of 117 square inches and a perimeter of 44 inches. What are the dimensions of the paper

?
Mathematics
1 answer:
-Dominant- [34]2 years ago
3 0

Answer:

13x9

Step-by-step explanation:

half of perimeret of  rectangle L+W

half of perimeter of  rectangle = 44/2 = 22

L+W=22

LxW=117

  Think of 2 numbers that added =22 and multiplied =117

       13+9 =22

    13x9 =117

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What is the solution of the following system of linear equations? −21 + 15x = 6y −5x + 2y = −8 Select one: A. (15, -7) B. (4, 11
quester [9]

Answer:

C. No solution

Step-by-step explanation:

System of Equations:

A) -21+15x=6y

B) -5x+2y=-8

Simplifying and rearranging equation A.

Dividing each term by 3 (common factor for each term) in equation A.

\frac{-21}{3}+\frac{15x}{3}=\frac{6y}{2}

-7+5x=2y

Subtracting both sides by 2y

-7+5x-2y=2y-2y

-7+5x-2y=0

Adding 7 both sides.

-7+7+5x-2y=0+7

5x-2y=7  

Adding the above equation to equation B.

   5x-2y=7  

+ -5x+2y=-8

We have 0=-1

which is not true.

Hence the system has no solution. (Answer)

3 0
3 years ago
Exit
krok68 [10]
B because you have to add 30 to 60
8 0
3 years ago
if a cylinder has a volume of approximately 125.6 cubic cm and has a height of 10cm what is the length of the radius
Elina [12.6K]

Answer:

radius = 4 cm

Step-by-step explanation:

To find the length of the radius, we will follow the step below;

First, write down the formula for finding the volume of a cylinder

v=πr²h

where v is the volume of a cylinder

r is the radius      and

h is the height of the cylinder

from the question given,

v=125.6    and h = 10 cm

we can now proceed to insert the values into the formula and solve for r

note that π is a constant which is equal to 3.14

v=πr²h

125.6 =3.14×r×10

125.6 =31.4 r

Divide both-side of the equation by 31.4

125.6/31.4 =31.4 r/31.4

4 = r

r =4 cm

The length of the radius = 4 cm

4 0
3 years ago
The hemisphere of radius r is made from a stack of very thin plates such that the density varies with height, r = kz, where k is
Papessa [141]

Answer:

M = ¼ k π R⁴

zG = 8/15 R

Step-by-step explanation:

Note: I'm using lower case r as the radius of each plate and upper case R as the radius of the hemisphere.

The mass of each plate is density times volume:

dm = ρ dV

Each plate has a radius r and a thickness dz.  So the volume of each plate is:

dV = π r² dz

Substituting:

dm = ρ π r² dz

We're told that ρ = kz.  Substituting:

dm = kz π r² dz

Next, we need to write the radius r in terms of the height z.  To do that, we need to look at the cross section (see image below).

The height z and the radius r form a right triangle, where the hypotenuse is the radius of the hemisphere R.

Using Pythagorean theorem:

z² + r² = R²

r² = R² − z²

Substituting:

dm = kπ z (R² − z²) dz

We now have the mass of each plate as a function of its height.  To find the total mass, we integrate between z=0 and z=R.

M = ∫ dm

M = ∫₀ᴿ  kπ z (R² − z²) dz

M = kπ ∫₀ᴿ (R² z − z³) dz

M = kπ (½ R² z² − ¼ z⁴) |₀ᴿ

M = kπ (½ R⁴ − ¼ R⁴)

M = ¼ k π R⁴

Next, to find the center of gravity, we use the weighted average:

zG = (∫ z dm) / (∫ dm)

zG = (∫ z dm) / M

We already found M, we just have to evaluate the other integral:

∫ z dm

∫₀ᴿ kπ z² (R² − z²) dz

kπ ∫₀ᴿ (R² z² − z⁴) dz

kπ (⅓ R² z³ − ⅕ z⁵) |₀ᴿ

kπ (⅓ R⁵ − ⅕ R⁵)

²/₁₅ k π R⁵

Plugging in:

zG = (²/₁₅ k π R⁵) / (¼ k π R⁴)

zG = ⁸/₁₅ R

5 0
3 years ago
Use the distributive property to rewrite the expression 5(4x. + 7)
LUCKY_DIMON [66]

Answer: The answer is 20x + 35

Step-by-step explanation: 5(4x+7) You multiply 5 in both numbers and you get 20x+35

5 0
3 years ago
Read 2 more answers
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