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3 years ago

Which is an equation in point slope form of the line that passes through the points (7, 5) and (-4, -1)

Mathematics

1 answer:

emmasim [6.3K]3 years ago

5 0

Answer:

y = (6/11)x + 13/11

Step-by-step explanation:

y = mx + c

m = (-1-5)/(-4-7) = -6/-11 = 6/11

y = (6/11)x + c

When x = 7, y = 5

5 = (6/11)(7) + c

5 = 42/11 + c

c = 5 - 42/11

c = 13/11

y = (6/11)x + 13/11

11y = 6x + 13

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Find the limit (enter 'DNE' if the limit does not exist)

vaieri [72.5K]

Answer:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)=2$

Step-by-step explanation:

We need to first simplify the expression using rationalization(i.e. if a square root term exists in the denominator, then multiply and divide the whole expression by the denominator(but the change the sign of its middle term))

here, we need to find:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\right)$

first we'll rationalize our expression:

$\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\left(\dfrac{\sqrt{-2x^2-6y^2+1}+1}{\sqrt{-2x^2-6y^2+1}+1}\right)$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{(\sqrt{-2x^2-6y^2+1}+1)^2-(1)^2}$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-2x^2-6y^2+1-1}$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-(2x^2+6y^2)}$

$\sqrt{-2x^2-6y^2+1}+1$

this is our simplified expression, now we can apply our limits:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)$

$\sqrt{-2(0)^2-6(0)^2+1}+1$

$1+1$

$2$

the limit does exists and it is 2.

5 0

3 years ago

Jack and Jill both begin working new jobs for the summer. Jack is offered $18 per hour and will also be given $699 up front for

egoroff_w [7]

Answer:

349.5

Step-by-step explanation:

3 0

3 years ago

There are four cups of milk how many ounces of milk are in 4 cups (8 oz in a cup)

nadya68 [22]

Answer:

convert 4 cups to ounces:

4 cups = 32oz

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Can anyone please help me with number 17?

sweet-ann [11.9K]

The answer is G. I know because, 1.75 * 3 (slices of pizza) = 5.25.

13.75 - 5.25 = 8.5

8.5 / 4 (hot dogs) = 2.1 (price per hot dog)

We can apply this to Sarah by saying

2 * 1.75 = 3.5

3 * 2.1 = 6.3

Added equals 9.8 or 9.75 (Sarah's total)

Correct me if I am wrong hope this helps:)

7 0

3 years ago

Which of the following is equivalent to (n-3)(n-5) a. n2-8n+15, b. n2+8n-15, c. n2-15n+8

solong [7]

Foil the binomials

First: n*n=n^2
Outer: n*-5=-5n
Inner: -3*n=-3n
Last: -3*-5=15

Put it together and simplify
n^2-5n-3n+15
n^2-8n+15

Final answer: A

5 0

3 years ago