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3 years ago

5

What is the equation of a line that passes through the point (-3,-11) and is parallel to the line whose equation is 2x - y = 4 i

n slope-intercept form?

1 answer:

Tema [17]3 years ago

6 0

Answer:

$\displaystyle y = 2x - 5$

Step-by-step explanation:

−11 = 2[−3] + b

$\displaystyle -5 = b \\ \\ y = 2x - 5$

* Parallel Lines have SIMILAR <em>RATE OF</em><em> </em><em>CHANGES</em><em> </em>[<em>SLOPES</em>], so 2 remains the way it is.

I am joyous to assist you anytime.

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Factor Trinomials:

notka56 [123]

Answer:

1. $2(x+2)(x+5)$

2. $8(x+4)^{2}$

Step-by-step explanation:

<u>Problem #1:</u>

1. Find the GCF (Greatest Common Factor)

$GCF = 2$

2. Factor out the GCF and simplify.

$2(x^{2} +7x+10)$

3. Factor $x^{2} +7x+10$

<u>Which two numbers add up to 7 and multiply to 10?</u>

2 and 5

<u>Rewrite the expression using the above.</u>

$(x+2)(x+5)$

4. Done!

$2(x+2)(x+5)$

<u>Problem #2:</u>

1. Find the GCF (Greatest Common Factor)

$GCF=8$

2. Factor out the GCF and simplify.

$8(x^{2} +8x+16)$

3. Use the perfect square formula. $a^{2} +2ab+b^{2} =(a+b)^{2}$

$a = x\\b=4$

$(x+4)^{2}$

4. Done!

$8(x+4)^{2}$

8 0

3 years ago

Which set of data contains two outliers?

Alisiya [41]

Answer:

101, 135, 131, 99, 138, 136, 140

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3 years ago

The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

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3 years ago

Which statement about rational numbers is true?

Ilya [14]

Answer:

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Step-by-step explanation:

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Answe

Step-by-step explanation:

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