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2 years ago

Find the value of x, y, z in the rhombus below

Mathematics

1 answer:

galben [10]2 years ago

5 0

Answers:

x = -28
y = -12
z = -11

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Explanation:

Any rhombus is a parallelogram, but not the other way around.

For any parallelogram, the opposite angles are congruent.

-8y-8 = 88

-8y = 88+8

-8y = 96

y = 96/(-8)

y = -12

Also, for any parallelogram, the adjacent angles are supplementary (meaning they add to 180).

(-3x+8) + (88) = 180

-3x+96 = 180

-3x = 180-96

-3x = 84

x = 84/(-3)

x = -28

And we can also say,

88 + (-9z-7) = 180

-9z+81 = 180

-9z = 180-81

-9z = 99

z = 99/(-9)

z = -11

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A container in the shape of a rectangular prism is shown. What is the volume, in cubic inches, of the container? V = lwh

Gala2k [10]

Answer:

$V=2551.5\ in^3$

Step-by-step explanation:

Given that,

Length of the prism, $l = 20\dfrac{1}{4}\ in$

The breadth of the prism, $b = 10\dfrac{1}{2}\ in$

The height of the prism, h = 12 in

We need to find the volume of the prism. The formula for the volume of a rectangular prism is given by :

$V=lwh$

Put all the values,

$V= 20\dfrac{1}{4}\times 10\dfrac{1}{2}\times 12\\\\V=2551.5\ in^3$

So, the volume of the rectangular prism is equal to $2551.5\ in^3$ .

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3 years ago

A principal of $2600is invested at 6.75% interest, compounded annually. How much will the investment be worth after 14 years

dedylja [7]

Answer:

$6488.19

Step-by-step explanation:

To solve this problem we use the compounded interest formula:

$amount = principal(1 + (r \n))^({n}{t})$

a = $2600(1+(0.0675/1))¹*¹⁴

a = $6488.19

8 0

4 years ago

The larger of two consecutive integers is 10 more than 4 times the smaller. Find the integers.

nevsk [136]

Answer:

-2 and -3

Step-by-step explanation:

Let L represent the large integer and S represent the smaller integer

Given Large Integer = 10 + 4 times Smaller Integer

Mathematically:

L = 10 + 4S -------eq 1

It is also given that the integers are consecutive,

hence L = S + 1------ eq2

Now we can solve a system of equations by substitution.

Substitute eq 2 into eq 1

S + 1 = 10 + 4S (subtract 1 from both sides)

S = 10 - 1 + 4S

S = 9 + 4S (subtract 4S from both sides)

S - 4S = 9

-3S = 9 (divide both sides by -3)

S = 9 / (-3) = -3 (answer)

form equation 2,

L = S + 1

L = -3 + 1

L = -2 (answer)

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3 years ago

Find the volume of a<br> cylinder with a radius of<br> 8 feet and a height of 7<br> feet

AveGali [126]

The answer to your question is 56

5 0

3 years ago

Profit is always calculated as revenue minus expenses. If a company’s expenses were $10 million, write an equation that expresse

ivann1987 [24]

The equation that expresses profit, P, (in millions of dollars) in terms of revenue, R, (in millions of dollars) is P = R - 10

The profit is $15 million when revenue is $25 million

Step-by-step explanation:

The formula of the profit is P = R - E, where

R is the revenue
E is the expenses

If a company’s expenses were $10 million, wee need to write an equation that expresses profit, P, (in millions of dollars) in terms of revenue, R, (in millions of dollars) and then find the profit when revenue is $25 million

∵ P is the profit in millions of dollars

∵ R is the revenue in millions of dollars

∵ The expenses E were $10 million

∵ Profit = Revenue - Expenses

∴ P = R - 10

The equation that expresses profit, P, (in millions of dollars) in terms of revenue, R, (in millions of dollars) is P = R - 10

∵ The revenue R = $25 million

∵ P = R - 10

- Substitute the value of R in the equation

∴ P = 25 - 10

∴ P = 15

∴ The profit is $15 million

The profit is $15 million when revenue is $25 million

Learn more:

You can earn more about the word problems in brainly.com/question/10557938

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3 years ago