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3 years ago

Write the equation of the line that passes through the given point and is parallel to the given line.

Mathematics

1 answer:

romanna [79]3 years ago

3 0

<u>(Note: this answer is assuming that the equation has to be put in slope-intercept format.)</u>

Answer:

$y = \frac{1}{2} x - \frac{5}{2}$

Step-by-step explanation:

1) Let's use the point-slope formula to determine what the answer would be. To do that though, we would need two things: the slope and a point that the equation would cross through. We already have the point it would cross through, (-3,-4), based on the given information. So, in the next step, let's find the slope.

2) We know that the slope has to be parallel to the given line, $y = \frac{1}{2}x - 8$ . Remember that slopes that are parallel have the same slope - so, let's simply take the slope from the given equation. Since it's already in slope-intercept form, we know that the slope then must be $\frac{1}{2}$ .

3) Finally, let's put the slope we found and the x and y values from (-3, -4) into the point-slope formula and solve:

$(y- (-4)) = \frac{1}{2} (x - (-3))\\y + 4 = \frac{1}{2} (x + 3))\\y + 4 = \frac{1}{2}x+ \frac{3}{2} \\y = \frac{1}{2}x + \frac{3}{2} - 4\\y = \frac{1}{2}x + \frac{3}{2} - \frac{8}{2} \\y = \frac{1}{2}x - \frac{5}{2}$

Therefore, $y = \frac{1}{2}x - \frac{5}{2}$ is our answer. If you have any questions, please do not hesitate to ask!

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Tori is cutting fabric squares to make a quilt. Her squares on average are 5 in. on each side with a standard deviation of 0.1 i

lapo4ka [179]

Answer:

$\approx 68\%$

Step-by-step explanation:

For normal distributions only, all data falls within approximately 68% of one standard deviation, 95% of two standard deviations, and close to 100% of three standard deviations. The standard deviation is far too small to represent two or three standard deviations, hence $\implies \boxed{68\%}$ .

*Important: This problem would be unsolvable if the question did not say her cuts were normally distributed, because the information above is only applicable to normal distributions.

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3 years ago

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There are 62 lobsters in one line, 60 lobsters in another line, 56 lobsters in the third line, and 59 lobsters in the last line.

faust18 [17]

Answer:

helo

Step-by-step explanation:

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3 years ago

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Given the recursive formula for an arithmetic sequence find the common difference and the 52nd term

Mice21 [21]

Answer:

Common difference(d) $a_{52}$

(21) -10 -548

(22) -7 -323

(23) 10 547

(24) -100 -5118

Step-by-step explanation:

Let the common difference be denoted by 'd'.

Also the nth difference of an arithmetic sequence is given by: $a_{n}=a_{1}+(n-1)\times d$

(21)

We are given a recursive formula as:

$a_{n}=a_{n-1}-10$

The first term is given by:

$a_{1}=-38$

The common difference for an arithmetic sequence is given by:

$a_{n}-a_{n-1}$

Hence, here we have the common difference as:

$d=-10$

The nth term of an arithmetic sequence is given by:

$a_{n}=a_{1}+(n-1)\times d$

Here $a_{1}=-38$ and $d=-10$ .

Hence, $a_{52}=-38+(52-1)\times (-10)$

Hence, $a_{52}=-548$

(22)

$a_{n}=a_{n-1}-7$

$a_{1}=34$

The common difference for an arithmetic sequence is given by:

$a_{n}-a_{n-1}$

Hence, here we have the common difference as:

$d=-7$

Here $a_{1}=34$ and $d=-7$ .

Hence, $a_{52}=34+(52-1)\times (-7)$

Hence, $a_{52}=-323$

(23)

$a_{n}=a_{n-1}+10$

$a_{1}=37$

The common difference for an arithmetic sequence is given by:

$a_{n}-a_{n-1}$

Hence, here we have the common difference as:

$d=10$

Here $a_{1}=37$ and $d=10$ .

Hence, $a_{52}=37+(52-1)\times (10)$

Hence, $a_{52}=547$

(24)

$a_{n}=a_{n-1}-100$

$a_{1}=-18$

The common difference for an arithmetic sequence is given by:

$a_{n}-a_{n-1}$

Hence, here we have the common difference as:

$d=-100$

Here $a_{1}=-18$ and $d=-100$ .

Hence, $a_{52}=-18+(52-1)\times (-100)$

Hence, $a_{52}=-5118$

5 0

4 years ago

Help with math question <br> thanks so much

liubo4ka [24]

I'm not for sure but I think that it would be the first option <span />

8 0

3 years ago

IZ) Samantha wants to determine the height of a flagpole at school. Her eye level is 4.6 feet from the ground and

makvit [3.9K]

Answer:

69 feet.

Step-by-step explanation:

See the attached diagram.

AB is the height of the flagpole and DE is the height of Samantha.

Now, ∠ CEB = 68°

Now, AC = DE = 4.6 feet, and CE = AD = 26 feet {Given}

Then, $\tan 68 = \frac{CB}{CE} = \frac{CB}{26}$

⇒ CB = 26 tan 68 = 64.35 feet.

Now, height of the flagpole is AB = AC + CB = 4.6 + 64.35 = 68.95 feet ≈ 69 feet. (Answer) (Approximate}

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4 years ago