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3 years ago

Solve using elimination -x+4y=-19 -3x+3y=6

Mathematics

1 answer:

Liula [17]3 years ago

5 0

Answer:x = -9, y = -7

Step-by-step explanation:

Equation 1) -x + 4y = -19

Equation 2) -3x + 3y = 6

Multiply ALL of equation 1 by 3 so that both equations include -3x in it.

1) 3(-x + 4y = -19)

Simplify.-3x + 12y = -57 → equation 3

Now, subtract equation 3 from equation 2.

-3x + 12y = -57

(-)-3x + 3y = 6

Simplify.

9y = -63

Divide both sides by 9.

9y ÷ 9 = -63 ÷ 9

Simplify.

y = -7

Now that we have the value for y, simply plug in -7 for y into equation 1.

1) -x + 4y = -19-x + 4(-7) = -19

Simplify.-x - 28 = -19

Add 28 to both sides of the equal sign.

-x - 28 + 28 = -19 + 28

Simplify.-x = 9

Divide both sides by -1.x = -9

Now we know that : x = -9, y = -7

To check our work, simply plug in -9 for x and -7 for y into equation 1.

1) -x + 4y = -19-(-9) + 4(-7) = -19

Simplify.

9 - 28 = -19-19 = -19

Therefore, x = -9, y = -7

Hope this helped! :)

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3 years ago

Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 363636 feet^3 3 cubed. Syrus isn't sure if

stealth61 [152]

Answer:

The height of the tent = 3 feet

Step-by-step explanation:

Question

Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 36 feet^3. Syrus isn't sure if the tent will be tall enough for him to sit up inside. The tent is the shape of triangular prism whose length is 6 feet and width is 4 feet. What is the height of the tent?

Given:

Length of the tent = 6 feet

Width of the tent = 4 feet

Volume of the tent = 36 $feet^3$

To find the height of the tent.

Solution:

Since the ten is in shape of triangular prism, so the volume of traingular prism is given as:

$V=\frac{1}{2}\times l\times w\times h$

where $l$ represents length, $w$ represents width and $h$ represents height of the prism.

Plugging in the know values of the dimension of the tent and the volume to find the height of the tent.

$36=\frac{1}{2}\times 6\times 4\times h$

Simplifying.

$36=12h$

Dividing both sides by 12.

$\frac{36}{12}=\frac{12h}{12}$

$3=h$

∴ $h=3$

Thus, the height of the tent = 3 feet

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4 years ago

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4 years ago

ace bike rentals rents bikes for $28 per day. Renters can keep the bike for 8 hours. Bart's bikes rents bikes for $30 per day. R

lyudmila [28]

Bart company charges a lower rate. It is lower by rate $ 0.5 per hour

<h3>Solution:</h3>

Given that Ace bike rentals rents bikes for $28 per day. Renters can keep the bike for 8 hours

Also given that Bart's bikes rents bikes for $30 per day. Renters can keep the bike for 10 hours

To find: company that charges lower rate

Let us find the hourly rate of Ace and Bart

$\text {hourly rate }=\frac{\text { Rental price }}{\text { total time in a day }}$

Hourly rate of Ace company:

Rental price = $28

total time in a day 8 hours

$\text {hourly rate }=\frac{28}{8}=3.5$

So the hourly rate of Ace company is $ 3.5 per hour

Hourly rate of Bart company:

Rental price = $ 30

total time in a day 10 hours

$\text {hourly rate }=\frac{30}{10}=3$

So the hourly rate of Bart company is $ 3 per hour

Comparing hourly rate of both companies

Ace company is $ 3.5 per hour

Bart company is $ 3 per hour

Bart company < Ace company

3 < 3.5

Thus bart company charges a lower rate

<h3>How much lower?</h3>

hourly rate of Ace company - hourly rate of Bart company = 3.5 - 3 = 0.5

So, it is lower by rate $0.5 per hour

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3 years ago

Use radical notation to rewrite each expression and simplify 9 3/2

scoundrel [369]

Answer:

$9^{\frac{3}{2}}=\sqrt{9^3}=27$

Step-by-step explanation:

The fractional exponent m/n is often translated to radical form as ...

$x^{\frac{m}{n}}=\sqrt[n]{x^m}$

In this case, I find it easier to evaluate as ...

$x^{\frac{m}{n}}=(\sqrt[n]{x})^m=\boxed{(\sqrt{9})^3=3^3=27}$

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3 years ago