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stellarik [79]
3 years ago
11

Which equation, in point-slope form, passes through (-2, 4) and has a slope of 3?

Mathematics
1 answer:
spin [16.1K]3 years ago
8 0

Answer:

y=-2-3x

Step-by-step explanation:

Point-slope form: y-y1=m(x1-x)

In this problem, -2 is x1 and 4 is y1.

As always, m is the slope: 3.

Hence, plug these values into the equation.

y-4=3(-2-x)

Distribute the 3: 3(-2-x)= -6-3x

Now we have y-4=-6-3x

Because we want the y by itself, add 4 to each side of the equation.

y-4=-6-3x

  +4 +4

    y=-2-3x

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The mean of this data set is 9. What number is missing?<br><br> 11,20,_,3,1
kherson [118]
Let the missing number be x

Mean is the total sum of data over the number of data therefore,

(11+20+x+3+1) / 5 = 9
Then simplify
(35 + x) / 5 = 9
Then multiply 5 to both sides
35 + x = 45
Then subtract 35 to both sides to find x
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Hope this helps!

7 0
2 years ago
1. ) Consider the function f(x)=5−7x2,−5≤x≤1
Marat540 [252]
1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.

Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170


Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2

2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:

f'(c)= \frac{f(b)-f(a)}{b-a}

The differentiated form would be f'(x) = -2x. Then,

-2c =  \frac{(4- 0^{2} )-(4- (-1)^{2}) }{0--1}=1

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Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.
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3 years ago
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-3/4

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the rate of change is the slope of the line

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