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Strike441 [17]
3 years ago
6

The low temperature on a certain day is 51°F. The low temperature is 17°F lower than the high temperature, h.

Mathematics
1 answer:
ohaa [14]3 years ago
5 0

Using the change of subject of formula, the high temperature value for the day can be modeled using the expression <em>High temperature = Low temperature - 17°F</em>

<u>Giveb</u><u> </u><u>the</u><u> </u><u>Parameters</u><u> </u><u>:</u>

  • <em>Low</em><em> </em><em>temperature</em><em> </em><em>=</em><em> </em><em>51</em><em>°</em><em>F</em>

<u>The</u><u> </u><u>low</u><u> </u><u>temperature</u><u> </u><u>is</u><u> </u><u>17</u><u>°</u><u>F</u><u> </u><u>lower</u><u> </u><u>than</u><u> </u><u>the</u><u> </u><u>high</u><u> </u><u>temperature</u><u>,</u><u> </u><u>this can be</u><u> </u><u>modeled</u><u> </u><u>as</u><u> </u><u>an</u><u> </u><u>equation</u><u> </u><u>thus</u><u> </u><u>:</u>

<em>Low temperature = High temperature + 17°F</em>

<u>Male</u><u> </u><u>the</u><u> </u><u>high</u><u> </u><u>temperature</u><u> </u><u>the</u><u> </u><u>subject</u><u> </u><u>:</u>

High temperature = Low temperature - 17°F

Therefore, the equation which models the high temperature is : <em>High temperature = Low temperature - 17°F</em>

Learn more :brainly.com/question/25449918

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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,
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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

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we know that

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

we have

x=-1 and x=-3

so

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

therefore

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The vertex is a minimum

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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

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Rewrite as perfect squares

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

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For g(x)=0

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

2(x+2)^2=2

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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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