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Anna [14]
2 years ago
14

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answ

er in the box provided or use the upload option to submit your solution. (3,1) and (-2,3).
Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
7 0

The equation would be 2x + 5y = 11.

To find this, we first have to find the slope of the line. The slope formula is below.

m (slope) = (y2 - y1)/(x2 - x1)

In which (x1, y1) is the first point and (x2, y2) is the second. So we plug in to solve.

m = (3 - 1)/(-2 -3)

m = 2/-5

Now that we have the slope, we can use it along with a point to get the slope intercept form.

y = mx + b

3 = -2/5(-2) + b

3 = 4/5 + b

11/5 = b

Now that we have the equation of y = -2/5x + 11/5 we can manipulate it into standard form.

y = -2/5x + 11/5 -----> add 2/5x to both sides

2/5x + y = 11/5 ----> multiply both sides by 5

2x + 5y = 11

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Factor completely 16x8 − 1.
marta [7]

<u>Given</u>:

The given expression is 16 x^{8}-1

We need to determine the factor of the given expression.

<u>Factor</u>:

Let us rewrite the given expression.

Thus, we have;

\left(4 x^{4}\right)^{2}-1^{2}

Since, the above expression is of the form a^2-b^2, let us apply the identity a^2-b^2=(a+b)(a-b)

Thus, we have;

\left(4 x^{4}+1\right)\left(4 x^{4}-1\right) ------ (1)

Now, we shall factor the term 4x^4-1

4x^4-1=(2x^2)^2-1^2

           =(2x^2+1)(2x^2-1)

Substituting the above expression in equation (1), we have;

\left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)

Therefore, the factor of the given expression is \left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)

Hence, Option B is the correct answer.

5 0
2 years ago
Read 2 more answers
Eric has challenged himself to walk 24,000 steps in 4 days. If Eric walks the same number of steps each day, which function repr
Alborosie
If Eric wanted to walk 24,000 steps in 4 days, he would have to walk 6,000 steps each day (24/4=6). The correct answer would be the bottom answer as saying he has already walked 2 days it would be (y=-6,000(2)+24,000) this would simply out to (y=-12,000+24,000) and then (y=12,000). 
4 0
2 years ago
Adam is working two summer jobs, making $9 per hour washing cars and $8 per hour walking dogs. Last week Adam earned a total of
Phantasy [73]

Answer:

Washing cars= 4 hours

Walking dogs= 10 hours

Step-by-step explanation:

You want to start by creating equations. So one thing we know is that he makes $9 an hour washing cars(x) and $8 walking dogs(y).

$9x+$8y=$116

The second Equation is based off of the hours worked. We know that he worked 6 hours more walking the dogs than he did washing cars, so we can take x(being the washing hours) and add 6 to it to equal y (the number of dog hours).

y=x+6

Now You plug what y equals into the first equation to solve for x.

9x+8(x+6)=116     Next distribute the 8 to each term.

9x+8(x)+8(6)=116

9x+8x+48=116     Add the like terms together (9x+8x)

17x+48=116         Subtract the 48 from both sides

     -48  -48

17x=68             Now divide by 17 on both sides.

______

17    17

x=4                 Finally we can take x and plug it back in to one of the equations in order to solve for y. I'm going to choose the second equation.

y=(4)+6

y=10

8 0
2 years ago
The function h(x) = 2.5x + 20 represents your height in inches, h(x), for x years you have been alive. How many inches tall will
sveticcg [70]

Answer:

Step-by-step explanation:

B

3 0
2 years ago
It takes Evan 6 3/4 hours to mow 3 lawns. it takes him 2 1/3 hours to mow Mr. Smiths yard and 1 3/4 hours to mow Ms. Lee's yard.
Ratling [72]

Answer: 2\frac{2}{3}\ hours

Step-by-step explanation:

Given: The total time taken by Evan to mow the 3 lawns = 6\frac{3}{4}=\frac{27}{4}\ \text{hours}

Time taken by Evan to mow the first lawn =2\frac{1}{3}=\frac{7}{3}\ \text{hours}

Time taken by Evan to mow the second lawn =1\frac{3}{4}=\frac{7}{4}\ \text{hours}

Now,Time taken by Evan to mow the third lawn =\frac{27}{4}-\frac{7}{3}-\frac{7}{4}

⇒Time taken by Evan to mow the third lawn =\frac{81-28-21}{12}

⇒Time taken by Evan to mow the third lawn =\frac{32}{12}=\frac{8}{3}=2\frac{2}{3}\ hours

Hence, the time taken by Evan to mow the third lawn = 2\frac{2}{3}\ hours

7 0
2 years ago
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