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3 years ago

8x + y = 9 Convert the following equations to standard form

Mathematics

1 answer:

Citrus2011 [14]3 years ago

5 0

Answer:

x=1/8y+9/8

y=<u>y=−8x+9</u>

Step-by-step explanation:

<u>Let's solve for y.</u>

<u>Step 1: Add -8x to both sides.</u>

<u />

<u>Let's solve for x.</u>

<u>Step 1: Add -y to both sides.</u>

<u>Step 2: Divide both sides by 8.</u>

<u />

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Zoey makes $75 for 3 hours of work. How much money did Zoey make each hour?

stiks02 [169]

75/25 = 3
3x25 = 75
$25 per hour

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3 years ago

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On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, ne

Mrrafil [7]

<h3>Answer: Choice C. (1,0)</h3>

============================================================

Explanation:

Point H is at (-2,2) and J is at (4,-2)

Focusing on the x coordinates, the midpoint is (x1+x2)/2 = (-2+4)/2 = 1.

The y coordinates have a midpoint of (y1+y2)/2 = (2+(-2))/2 = 0.

The midpoint is at (1,0). That's why the answer is choice C.

--------------------------

This next section is optional.

Points I and K are located at (4,3) and (-2,-3) respectively

Averaging the x coordinates gets us (x1+x2)/2 = (4+(-2))/2 = 1

Doing the same for the y coordinates gets us (y1+y2)/2 = (3+(-3))/2 = 0

We end up with the same midpoint (1,0)

The midpoint being the same for both diagonals proves that each diagonal is bisected, ie cut in half.

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3 years ago

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

$336.04 < \mu < 443.96$

The margin of error will increase

The margin of error will decreases

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

$n \ \ \alpha \ \ \frac{1}{E^2 }$

So if the sample size increases the margin of error decrease

The sample proportion is mathematically represented as

$\r p = \frac{210}{500}$

$\r p = 0.42$

Given that the confidence level is 0.99 the level of significance is $\alpha = 0.01$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }$

=> $E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }$

=> $E = 0.0093$

The 99% confidence interval is

$\r p - E < p < \r p + E$

$0.42 - 0.0093 < p < 0.42 + 0.0093$

$0.4107 < p < 0.4293$

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4 years ago

The length of a rectangular is 7/10 ft .and the width is 1/5ft what is the perimeter

Blababa [14]

<h3>Answer:</h3>

$\huge\boxed{1 \frac{4}{5}\ \text{ft}}$

<h3>Explanation:</h3>

Change $\frac{1}{5}$ so that is has a common denominator. $\frac{1*2}{5*2}=\frac{2}{10}$

Make an equation. $\frac{7+7+2+2}{10}$

Add. $\frac{14+4}{10}$

Add. $\frac{18}{10}$

Divide both sides by 2. $\frac{9}{5}$

Convert to a mixed number. $1 \frac{4}{5}$

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3 years ago

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The length of segment HJ if H lies at (-1,7) and J lies at (8,-5)

sukhopar [10]

Answer:

Step-by-step explanation:

To get the length of segment HJ if H lies at (-1,7) and J lies at (8,-5), we will use the formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²+(y₂-y₁)²

From the coordinates x₁ = -1, y₁ = 7, x₂ = 8, y₂ = -5

HJ = √(8-(-1))²+(-5-7)²

HJ = √(8+1)²+(-12)²

HJ = √81+144

HJ = √225

HJ = 15

<em>Hence the length of segment HJ is 15 units</em>

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3 years ago