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3 years ago

Help please! 10 points available!!

Mathematics

1 answer:

harkovskaia [24]3 years ago

7 0

12- $\frac{4}{5}(x+15)=4$

- $-\frac{4}{5} (x+15)=4-12$

- $-\frac{4}{5} (x+15)=-8x+15 = -8×[tex]- \frac{5}{4}$

x+15=10

x= 10-15

x=-5

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How do you substract two digits for example 60-4 only by the operator plus(+)? only digets >=0 are allowed

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3 years ago

Find (f^-1)'(7) without finding the inverse function where f(x) = 5 – 2x^3.

faltersainse [42]

Step-by-step explanation:

the derivative of an inverse function is

1/f'(f^-1(x))

f'(x) = -6x²

f^-1(7) is solving the original function equation for x under the knowledge that y = 7

7 = 5 - 2x³

2 = -2x³

-1 = x³

x = -1

f'(-1) = -6×(-1)² = -6×1 = -6

so,

(f^-1)'(7) = -1/6

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3 years ago

Please help if you can!

marin [14]

9514 1404 393

Answer:

y = 1/2x^2 +x -15/2

Step-by-step explanation:

The vertex is the point where the graph reaches is extreme: (-1, -8). The y-intercept is (0, -7.5). The x-intercepts are (-5, 0) and (3, 0).

When the quadratic is written in the form ...

y = x^2 +bx +c

the value of b is the opposite of the sum of the x-intercepts. The value of c is their product. These facts would give ...

y = x^2 -(-5 +3)x +(-5)(3) = x^2 +2x -15

The constant in this equation is -15, which is the value y has when x=0. Our actual y-intercept is half that, so the graph we see is this equation scaled by a factor of 1/2:

y = 1/2x^2 +x -15/2

_____

<em>Alternate solution</em>

You can start with the vertex form.

y = a(x -h)^2 +k . . . . . . . vertical scale factor 'a' and vertex (h, k)

On the graph, the vertical scale factor is the vertical difference between the low point (vertex) and the point that is 1 unit right or left. Here, that is ...

-7.5 - (-8) = 0.5 = a

We've already said the vertex is (h, k) = (-1, -8), so the vertex form equation is ...

y = 0.5(x +1)^2 -8

We know the square of a binomial is (a+b)^2 = a^2 +2ab +b^2, so we have ...

y = 0.5(x^2 +2x +1) -8

y = 0.5x^2 +x +0.5 -8 . . . . . eliminate parentheses

y = 0.5x^2 +x -7.5

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3 years ago