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nekit [7.7K]
3 years ago
5

Write the equation of a line that passes through the point (-8,6) and has a slope of 1/4

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
4 0

Answer:

y = ax +b

slope = 1/4 => a =1/4

This line passes (-8,6) => (1/4)*(-8) +b =6 => -2 +b =6 => b = 8

=> y =(1/4)x+8

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Find the values of m and b that make the following function differentiable.
KengaRu [80]

f(x)=\begin{cases}x^2&\text{for }x\le2\\mx+b&\text{for }x>2\end{cases}

In order to be differentiable everywhere, f must first be continuous everywhere, which means the limits from either side as x\to2 must be the same and equal to f(2). By definition, f(2)=2^2=4, and

\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}x^2=4

\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}(mx+b)=2m+b

so we need to have 4m+b=4.

For f to be differentiable at x=2, the derivative needs to be continuous at x=2, i.e.

\displaystyle\lim_{x\to2^-}f'(x)=\lim_{x\to2^+}f'(x)

We then need to have

\displaystyle\lim_{x\to2}2x=\lim_{x\to2}m\implies\boxed{m=4}

Then

2m+b=4\implies\boxed{b=-4}

7 0
3 years ago
9x + 1 i need help plz ( again my brain is not working.)
madam [21]

Answer:

9x + 1 = 9x + 1. . LISTEN BECAUSE WHWN 9X IS WITH BASE AND IN 1 THERE IS NO X IN 1. SO,WHEN THERE BASE ARE EQUAL THEN ONLY WE CAN CALCULATE IT.OR TO DO ANY EQUATION OF IT.

4 0
3 years ago
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I need help solving this
Stolb23 [73]

Step-by-step explanation:

So in the equation given, y = 2x - 3

you substitute x for whats given in the table in the x column.

Example

In the graph the first number under the x colum is -1.

y = 2x - 3 in the equation you take out x and put -1.

So now the equation becomes y = 2 × -1 - 3.

Using bedmas to solve the question you should get -5

Which now means y = -5

To plot the point now x would be -1 and y would be -5 (-1, -5)

Same thing for the second number in the x Column.

y = 2 × 1 - 3 which equals -1

To plot it

x = 1 y = -1. (1, -1)

And for the last number 3.

Agai. You substitute x for 3 which makes the equation y = 2 × 3 - 3

this gives you 3 and to plot it

x would be 3 and y would be 3

4 0
2 years ago
Which decimal is equivalent to 2/9?<br> A. 2.2<br> B. 2.9<br> C. 22222<br> D. 0.2
goldenfox [79]

Answer:

The answer is 0.2. It is an irrational number with a repeating 2. It should have a line over the two to represent it repeating.

Step-by-step explanation:

First divide 2 by 9.

Use a calculator or do it by hand.

You get your answer.

3 0
3 years ago
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Given the quadratic function f(x) = 2x + 5x-12, what is the value of f(-2)?
tino4ka555 [31]

Answer:

-26

Step-by-step explanation:

first substitute -2 for x : 2(-2)+5(-2)-12

-4+-10-12

-14-12

-26

-26 is your answer

pls mark me brainliest if this helps !

6 0
3 years ago
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