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3 years ago

Please help! 20 points possible!

Mathematics

1 answer:

Vadim26 [7]3 years ago

8 0

Answer:

1) See Attachment.

2) The slope is -2/3.

3) The y-intercept is y=2.

Step-by-step explanation:

We have the two points (6, -2) and (-3, 4) and we know that they are on the same line.

Part 1)

In order to graph a line given two points, we simply need to plot those two points and then draw a line through them.

Please see the attachment.

We would plot (6, -2) and (-3, 4). Then, use a straightedge to connect the two points.

Part 2)

To find the slope, we can use the slope formula.

The slope formula for the slope between any two points is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where (x₁, y₁) and (x₂, y₂) are our two points.

So, let‘s let (6, -2) be (x₁, y₁) And (-3, 4) be (x₂, y₂). Substituting them into the slope formula yields:

$m=\frac{4-(-2)}{-3-6}$

Evaluate:

$m=\frac{6}{-9}=-2/3$

So, the slope is -2/3.

We can confirm this using our graph. Remember that the slope measures rise over run.

We are going down by 2 for every 3 to the right.

Part 3)

The y-intercept is where the graph crosses the y-axis.

From the graph, we can see that the graph crosses the y-axis at (0, 2).

Therefore, the y-intercept is y=2.

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2 years ago

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How man

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Answer:

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Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

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Assume that a prior survey suggests that about 22% of air passengers prefer an aisle seat.

This means that $\pi = 0.22$

How many randomly selected air passengers must you survey?

We need a sample of n, and n is found for which $M = 0.051$ . So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

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$0.051\sqrt{n} = 2.327\sqrt{0.22*0.78}$

$\sqrt{n} = \frac{2.327\sqrt{0.22*0.78}}{0.051}$

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Rounding up

358 randomly selected air passengers must be surveyed.

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3 years ago

Find the value of x using angle properties & the measure of

Jobisdone [24]

Answer:

15.

$x = 20$

16.

$\angle BFH$ = $100\textdegree$

$\angle CBD$ = $100\textdegree$ (if needed)

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

17.

$x = 7$

18.

$\angle BFH$ = $68\textdegree$

Step-by-step explanation:

15. The two following angles, which is $\angle CBD$ and $\angle BFH$ , are Corresponding Angles. Write an expression by using the following measurements from $\angle CBD$ and $\angle BFH$ . Then, solve the expression for the value of $x$ :

$\angle CBD$ = $5x$

$\angle BFH$ = $3x + 40$

$5x = 3x + 40$

Solve for $x$ :

$5x = 3x + 40$

$5x - 3x = 3x - 3x + 40$

$2x = 40$

$\frac{2x}{2} = \frac{40}{2}$

$x = 20$

16. After you have the value $x$ use it to find the actual measurements of both $\angle CBD$ and $\angle BFH$ , by applying $x$ to the following expressions from both $\angle CBD$ and $\angle BFH$ and solve them:

-The value of $x$ :

$x = 20$

-Solve for $\angle CBD$ :

$\angle CBD$ = $5x$

$5(20)$

$100$

-The actual measurement of $\angle CBD$ :

$\angle CBD$ = $100\textdegree$

-Solve for $\angle BFH$ :

$\angle BFH = 3x + 40$

$3(20) + 40$

$60 + 40$

$100$

-The actual measurement of $\angle BFH$ : (if needed)

$\angle BFH$ = $100\textdegree$

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

17. The two following angles, which is $\angle BFE$ and $\angle DBF$ are Alternate Interior Angles .Write an expression by using the following measurements from $\angle BFE$ and $\angle DBF$ . Then, solve the expression for the value of $x$ :

$\angle BFE$ = $16x$

$\angle DBF$ = $4x + 84$

$16x = 4x + 84$

-Solve for $x$ :

$16x = 4x + 84$

$16x - 4x = 4x - 4x + 84$

$12x = 84$

$\frac{12x}{12} = \frac{84}{12}$

$x = 7$

18. After you have the value $x$ use it to find the actual measurement of $\angle DBF$ , by applying $x$ to the expression from $\angle DBF$ and solve it and find the actual measurement of an angle that is not labeled, which is $\angle BFH$ :

-The value of $x$ :

$x = 7$

Solve for $\angle DBF$ :

$\angle DBF$ = $4x + 84$

$4(7) + 84$

$28 + 84$

$112$

-The actual measurement of $\angle DBF$ :

$\angle DBF$ = $112\textdegree$

-Since both $\angle DBF$ and $\angle BFH$ are supplementary (two angles that equals to $180\textdegree$ ), and you want to find the actual measurement of $\angle BFH$ , Use the measurement of $\angle DBF$ and subtract it from $180\textdegree$ :

$\angle DBF - 180\textdegree$

$112\textdegree - 180\textdegree = 68\textdegree$

-The actual measurement of $\angle BFH$ :

$\angle BFH$ = $68\textdegree$

8 0

3 years ago