When a polygon reflects across the y-axis, how do the coordinates of the points change?

9x+3y-4z=37<br>4x+3y +7z =16<br>x-5y +8z=-31

Evgen [1.6K]

Answer:

x = 2 , y = 5 , z = -1

Step-by-step explanation:

Solve the following system:

{9 x + 3 y - 4 z = 37 | (equation 1)

4 x + 3 y + 7 z = 16 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 4/9 × (equation 1) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+(5 y)/3 + (79 z)/9 = -4/9 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Multiply equation 2 by 9:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 1/9 × (equation 1) from equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - (16 y)/3 + (76 z)/9 = -316/9 | (equation 3)

Multiply equation 3 by 9/4:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - 12 y + 19 z = -79 | (equation 3)

Add 4/5 × (equation 2) to equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+(411 z)/5 = -411/5 | (equation 3)

Multiply equation 3 by 5/411:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 79 × (equation 3) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y+0 z = 75 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 2 by 15:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 3 × (equation 2) from equation 1:

{9 x + 0 y - 4 z = 22 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Add 4 × (equation 3) to equation 1:

{9 x+0 y+0 z = 18 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 1 by 9:

{x+0 y+0 z = 2 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Collect results:

Answer: {x = 2 , y = 5 , z = -1

4 0

3 years ago

A study found that out of 300 people 60% of them prefer to eat hamburgers rather than hot dogs. Find the 95% confidence interval

Lerok [7]

Answer:

(0.5446, 0.6554)

Step-by-step explanation:

As the sample is sufficiently large, the formula is used to estimate the proportion shown in the attached image.

Where:

P: sample proportion = 0.6

n: Sample size = 300

$1-\alpha$ : Confidence level = 0.95

α: Significance = 0.05

$Z_{\alpha / 2} = 1.96$ *

* Obtained from the normal standard table.

When introducing these values in the formula shown in the image we obtain:

$0.6 + 1.96 *\sqrt {\frac{0.6*0.4}{300}}$

$0.6 - 1.96 *\sqrt{\frac{0.6*0.4}{300}}$

Finally, the confidence interval is:

(0.5446, 0.6554)

8 0

3 years ago

For f(x) = x3 − 10, identify the rule for g(x) = f(x) + 14 and its graph.

MAVERICK [17]

Answer:

I need help with this one too!

Step-by-step explanation:

7 0

2 years ago

I NEED SOME HELP!!! IT'S REALLY URGENT!!!

Ksenya-84 [330]

10) M^2 + M^2 = 9 root 2
You can use Triganometry to find th missing length or the sine rule. The sine rule is: a / SinA = b / SinB. Substitute the length 9 root 2 as a and substitute both Sin45 into SinA and SinB the calculator should simply give you the answer... hope this helps

5 0

3 years ago

Solve logx64=3/2 for the unknown parameter.

katrin [286]

Answer:

$x {}^{ \frac{3}{4} } = 64 \\ x = 4 {}^{4} = 256 \: \: \: ans.$

6 0

3 years ago