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Alenkinab [10]
3 years ago
11

Graph the functions on the same coordinate plane.

Mathematics
1 answer:
beks73 [17]3 years ago
7 0

Answer:

select -3 and 2

Step-by-step explanation:

f(x)=g(x) means set them equal and solve for x

x^2+2x-8=-x^2+4

Add x^2 on both sides and subtract 4 on both sides.

2x^2+2x-12=0

Divide both sides by 2

x^2+x-6=0

Think of two numbers that multiply to be -6 and add up to be 1

that is 3 and -2

so The factored form is (x+3)(x-2)=0

So x=-3 or x=2

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Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at
Amiraneli [1.4K]

Answer:

The cubic function is f(x) = (27/32)·x  - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

4 0
3 years ago
Pleaseeeeeeeeeeee
Karo-lina-s [1.5K]

\text{The scientific notation:}\\\\a\times10^n\\\\1\leq a


a.\\(5\times10^3)\times(3.5\times10^{-1})=(5\times3.5)\times(10^3\times10^{-1})\\\\=15.75\times10^{3+(-1)}=15.75\times10^2=1.575\times10\times10^2\\\\=1.575\times10^{1+2}=\boxed{1.575\times10^3}

b.\\(8\times10^2)\div(4\times10^3)=(8\div4)\times(10^2\div10^3)=2\times10^{2-3}\\\\=\boxed{2\times10^{-1}}

c.\\(6\times10^{-3})^2=6^2\times(10^{-3})^2=36\times10^{-3\cdot2}=36\times10^{-6}=3.6\times10\times10^{-6}\\\\=3.6\times10^{1+(-6)}=\boxed{3.6\times10^{-5}}

Used:\\\\a^n\times a^m=a^{n+m}\\\\a^n\div a^m=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}

5 0
3 years ago
Given that the following statement is true
Makovka662 [10]

Answer:

C IS THE ANS COS ALL POLYGONS ARE CLOSED AND IF IT NOT CLOSED IT NOT A POLYGON

5 0
2 years ago
Solve for x.<br> 6x - 3x = 12
expeople1 [14]

Answer:

x=4

Step-by-step explanation:

3x = 12

divide by 3

x =12/3

8 0
3 years ago
Find the slope of the line that contains (-1,9) and (9,9).
Artyom0805 [142]

Answer:

0

Step-by-step explanation:

When we have 2 points, we can find the slope from

m = (y2-y1)/(x2-x1)

   = (9-9)/(9--1)

   = 0/(9+1)

    = 0/10

   0

5 0
3 years ago
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