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Vlada [557]
4 years ago
10

Write an equation in slope-intercept form for a line that passes through the point (4,-7) and has a slope

Mathematics
1 answer:
iren [92.7K]4 years ago
8 0

Answer: y = 3x - 19

Step-by-step explanation:

The equation of line in the slope intercept form is give as :

y = mx + c , where m is the slope and c is the y - intercept.

The points given : ( 4 , -7 )

slope = 3

Using the formula

y - y_{1} = m (x - x_{1} )

substituting the given values , we have

y - (-7) = 3 ( x - 4 )

y +7 = 3x - 12

y = 3x -12 - 7

y = 3x - 19

This gives the equation of the line in slope - intercept form.

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Write the equation of the line parallel to 5x + y = -2 that goes through the point (2, -3).​
gladu [14]

Answer:

y = -5x + 7

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Define

5x + y = -2

Random point (2, -3)

Step 2: Rewrite

y = -5x - 2

m = -5

Step 3: Write parallel line

y = -5x + b

-3 = -5(2) + b

-3 = -10 + b

7 = b

y = -5x + 7

8 0
3 years ago
Find the 10th term of the geometric sequence 1, 3, 9, ...
ladessa [460]

Answer:

a(10) = 3^9 = 19683

Step-by-step explanation:

In this sequence each new term is equal to 3 times the previous term.  Thus, 3 is the common ratio.  The first term is 1.

The general formula for the nth term of a geometric sequence i

a(n) = a(1)*r^(n -1), where r is the common ratio.

Here, a(n) = 1*3^(n - 1), and so

the 10th term is

           a(10) = 1*3^(10 - 1), or

            a(10) = 3^9 = 19683

3 0
3 years ago
Quotient + remainder <br> I need help I would have 20 points
nexus9112 [7]

We want to compute

\dfrac{-5x^4+4x^3-20x^2+15x-16}{-x^2-3}

The goal is to write it in the following form:

-5x^4+4x^3-20x^2+15x-16=Q(x)(-x^2-3)+R(x)

First step: How many "copies" of -x^2 does -5x^4 contain? We can write -5x^4=(-x^2)(5x^2), so the answer is 5x^2 copies.

If we distribute 5x^2 to -x^2-3, we get

5x^2(-x^2-3)=-5x^4-15x^2

If we were done, then this product would have matched the numerator at the start. But it doesn't; there are still some terms that need to vanish. In particular, we still have to account for

(-5x^4+4x^3-20x^2+15x-16)-(-5x^4-15x^2)=4x^3-5x^2+15x-16

Second step: How many copies of -x^2 can we find in 4x^3? Well, 4x^3=(-4x)(-x^2), so the answer is -4x. Then

(5x^2-4x)(-x^2-3)=-5x^4+4x^3-15x^2+12x

but this still doesn't match the original numerator. We still have to deal with

(-5x^4+4x^3-20x^2+15x-16)-(5x^2-4x)(-x^2-3)=-5x^2+3x-16

Third step: How many copies of -x^2 can we get out of -5x^2? -5x^2=5(-x^2). Then

(5x^2-4x+5)(-x^2-3)=-5x^4+4x^3-20x^2+12x-15

This also doesn't match the original numerator. We have a difference between what we have and what we want of

(-5x^4+4x^3-20x^2+15x-16)-(5x^2-4x+5)(-x^2-3)=3x-1

But we also can't divide 3x into chunks of -x^2, and we can't continue the division algorithm.

Our final answer would be

\dfrac{-5x^4+4x^3-20x^2+15x-16}{-x^2-3}=5x^2-4x+5+\dfrac{3x-1}{-x^2-3}

For the second problem, you should find

\dfrac{-15x^3-13x+4}{5x^2+2}=-3x+\dfrac{-7x+4}{5x^2+2}

4 0
3 years ago
When is the product of 2 integers less than or equal to both of the two factors
Anvisha [2.4K]
When Your Integers Are Negative Or Positive. Some Of Them Are Rational Numbers witch Those Are Factors and Decimals. Positives Are Number That Are Larger For A Example 2,3,4,5 and So On. In the Other Hand Negatives smaller For Example There -2,-3,-4,-5 and So On.
4 0
3 years ago
When oceanic and continental plates converge, the oceanic plate tends to go under the continental plate where the plates eventua
liraira [26]

Answer: Lava.

Step-by-step explanation: This process is called subduction, lava would form under the plates since all the rock would melt therefore liquid rock or lava.

5 0
3 years ago
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