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3 years ago

Consider the line y=9x-8

Mathematics

1 answer:

jasenka [17]3 years ago

7 0

Answer:

y=9x+75

Step-by-step explanation:

since we know that the slope must be the same for two lines to be proportional, we are gonna start there.

so our equation is: y= 9x + b

we need to find b to complete our equation, so substitute in the points we were given.

3 = 9(-8) + b

so now,

3 = -72 + b

now we have to isolate b to find out what it is,

3 = -72 + b

+72 +72

so now: 75= b

Put that back into the starting equation: y = 9x + 75

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Suppose you want to build a small walkway around your garden so that there is someplace to walk around and work on your vegetabl

wolverine [178]

Answer:

Approximately 3.5 feet - Option B

Step-by-step explanation:

Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.

( 30 + 2x ) $*$ ( 20 + 2x ) = 1000 - Expand "( 30 + 2x ) $*$ ( 20 + 2x )"

600 + 100x + 4 $x^2$ = 1000 - Subtract 1000 on either side, making on side = 0

4 $x^2$ + 100x - 400 = 0 - Take the "quadratic equation formula"

( Quadratic Equation is as follows ) - $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ,

$x=\frac{-100+\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad \frac{5\left(\sqrt{41}-5\right)}{2}$ ,

$x=\frac{-100-\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad -\frac{5\left(5+\sqrt{41}\right)}{2}$

There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) $\frac{5\left(\sqrt{41}-5\right)}{2}$ . The approximated value however is 3.5081...or approximately 3.5 feet.

4 0

3 years ago

What is two thirds times one fifth

kodGreya [7K]

2/3 x 1/5 = 2/15 that is the answer

6 0

3 years ago

Read 2 more answers

Josie is creating 5 music playlists for her dance classes. She will use a total of 60 songs. Each playlist will have 7 older son

melisa1 [442]

Answer: pls answer

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Anty was riding his bike to school at a speed of 12 mph. When he was of the way there, he got a flat tire. His mother drove him

NemiM [27]

Complete question:

Anty was riding his bike to school at a speed of 12 mph. When he was <u>half </u>of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?

Answer:

His average speed is 19.2 mph

Step-by-step explanation:

Given;

speed of Anty to school half of the way, v₁ = 12 mph

speed of Anty when his mother drove him half of the way, v₂ = 48 mph

The average speed of Anty is calculated as;

$V_{average} = \frac{Total \ distance }{Total \ time }$

The value of the average speed is closer to 12 mph than 48 mph because Anty spent more time moving at 12 mph than at 48 mph.

Let the equal distance travel at each speed = 96 miles

Time taken at 12 mph = $\frac{96 \ mile}{12 \ m/h} = 8 \ hours$

Time taken at 12 mph = $\frac{96 \ mile}{48 \ m/h} = 2 \ hours$

Average speed = $\frac{Total \ distance}{Total \ time } = \frac{96 \ mile \ + \ 96 \ mile}{2\ hr \ + \ 8\ hr} = \frac{192 \ miles}{10 \ hrs} = 19.2 \ mph$

Also, you can assume any other equal distance traveled at each speed, the average speed will still be 19.2 mph.

<u>Check:</u> let the equal distance traveled at each speed = 480 miles

Time taken at 12 mph = 480/12 = 40 hours

Time taken at 48 mph = 480/ 48 = 10 hours

Average speed = (480 + 480) / (40 + 10)

= 19.2 mph

8 0

2 years ago

An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68\%68%68, percent confidence

Komok [63]

Answer:

B. 10000 years old, with a margin of error of 400 years

Step-by-step explanation:

Assuming this complete problem: "12. An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level?"

The possible options are:

A. 9500 years old, with a margin of error of 500 years

B. 10000 years old, with a margin of error of 400 years

C. 9500 years olds, with a margin of error of 50 years

D. 10000 years old, with a margin of error of 40 year

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error for this case is given by this formula:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

For the first case the confidence was 68% so then $\alpha =1-0.68 =0.32$ and $\alpha/2 =0.16$ we can find a critical value on the normal standard distribution that accumulates 0.16 of the area on each tail and this value is $z=\pm 0.994$ , because P(z<-0.944) = 0.16 and P(Z>.944) = 0.16

The margin of error can be expressed like this:

$ME = z_{\alpha/2} SE$

We can solve for the standard error on this case and we got:

$SE = \frac{ME}{z_{\alpha/2}} =\frac{200}{0.994}=201.207$

And then for the new confidence interval we need to calculate the new $z_{\alpha}$ . For the first case the confidence was 95% so then $\alpha =1-0.95 =0.05$ and $\alpha/2 =0.025$ we can find a critical value on the normal standard distribution that accumulates 0.025 of the area on each tail and this value is $z=\pm 1.96$ , because P(z<-1.96) = 0.025 and P(Z>1.96) = 0.025. So then the new margin of error would be:

$ME = z_{\alpha/2} SE = 1.96*201.207=394.366$

The estimation for the mean not changes and from the before and new case is 1000 years. So then the best option for this case would be:

B. 10000 years old, with a margin of error of 400 years

And makes sense since a larger confidence interval means a wider interval.

8 0

3 years ago