Ask question

Ask question

All categories

3 years ago

10

If a = -12/5, then 5x + 2y = 6 and 3x - ay = 4 are parallel.

1 answer:

Lemur [1.5K]3 years ago

3 0

<span><span><span><span>5x </span>+<span>2y </span></span></span>=<span>6

</span></span>Add -2y to both sides

<span><span>5x</span>=<span><span>−<span>2y</span></span>+6

</span></span><span><span><span>‌</span></span></span>Divide both sides by 5

<span>x=<span><span><span>‌<span><span>−2/</span>5</span></span>‌y </span>+<span><span>‌ <span>6/5</span></span>‌

</span></span></span><span><span><span>that into the second equation:

</span></span></span>
<span><span><span>3<span>(<span><span><span>‌<span><span>−2/</span>5</span></span>‌y</span>+<span><span>‌<span>6/5</span></span>‌</span></span>)</span></span>+<span><span>‌<span>12/5</span></span>‌y </span></span>=4

simplify

</span><span><span><span><span>‌<span>6/5</span></span>‌y</span>+<span><span>‌<span>18/5</span></span>‌ </span></span>=4

</span>Add (-18)/5 to both sides

<span><span><span>‌<span>6/5</span></span>‌y</span>=<span>‌<span>2/<span>5

divide both sides by 6/5

y = 1/3

substitute 1/3 for y in x = -2/5y +6/5 to solve for x

x = -2/5(1/3) +6/5

x = 16/15

so x = 16/15 and y = 1/3
now replace both x and Y in each of the original equations to check the answers:

5(16/15) +2(1/3) = 5 1/3 + 2/3 = 6 true

3(16/15) - -12/5(1/3) = 4 true
so they are parallel

</span></span></span></span><span><span><span><span>
</span></span></span></span>

You might be interested in

Need help with these table what do I do?

Greeley [361]

Answer:

just ask it again

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

To convert from gallons to liters, multiply by?

-Dominant- [34]

In order to convert gallons to liters you must multiply by 3.7853
I hope this helped

5 0

3 years ago

John bikes at a speed of 10 miles per hour

mihalych1998 [28]

Answer:

15 miles

Step-by-step explanation:

10x1.5=15

3 0

2 years ago

Read 2 more answers

Ryan rode his bike of a mile. James rode his bike of a mile. Who rode farther? Exactly how much farther? Use the rectangles belo

34kurt

Answer:

Stewhapt

rectangles-by-step explanation:

5 0

3 years ago

An experiment was conducted to investigate whether there is a difference in mean bag strengths for two different brands of paper

Elanso [62]

Answer:

A two-sample t-test for a difference between sample means

Step-by-step explanation:

<u>Explanation</u>:-

A random sample of 50 bags from each of Brand X and Brand Y was selected

Given two sample sizes n₁ and n₂

Each bag was held from its rim, and one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped

mean of ounces the first sample = x⁻

mean of the second sample =y⁻

Given data one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped

Standard deviation of the first sample = S₁

Standard deviation of the second sample = S₂

Now we use t - distribution for a difference between the means

$t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }$

where

$S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2}S_{2} ^{2} }{n_{1} +n_{2} -2 }$

Degrees of freedom γ = n₁ +n₂ -2

3 0

3 years ago