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lana66690 [7]
3 years ago
8

Order the following numbers from least to greatest: 105, 10−99, 10−17, 1014, 10−5, 1030

Mathematics
2 answers:
neonofarm [45]3 years ago
8 0
If I understood your question correctly, it should be...
-89, -7, 5, 105, 1014, 1030
JulijaS [17]3 years ago
6 0
Nice mdbdhidjdbdjdhdjsiwj
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Nataly_w [17]

Answer:

Step-by-step explanation:

2x² divide all the three terms so G.C.F.=2x²

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F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,
svetlana [45]

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

so

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

g(x)=2x^2+8x+6

Find the vertex

Factor the leading coefficient

g(x)=2(x^2+4x)+6

Complete the square

g(x)=2(x^2+4x+4)+6-8

g(x)=2(x^2+4x+4)-2

Rewrite as perfect squares

g(x)=2(x+2)^2-2

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

0=2(x+2)^2-2

2(x+2)^2=2

(x+2)^2=1\\x+2=\pm1\\x=-2\pm1

so

The roots or x-intercepts are

x=-1 and x=-3

<u><em>Verify each statement</em></u>

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true  (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

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