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zavuch27 [327]
3 years ago
6

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of w(r(x))

Mathematics
2 answers:
shepuryov [24]3 years ago
8 0

(-infinity,0] is the answer.

Paladinen [302]3 years ago
5 0
Range is the outputs possible
w(r(x))=(2-x^2)-2
w(r(x))=2-x^2-2
w(r(x))=-x^2

therefor the range is from 0 to -∞
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\boxed{(x - a)(x - b) = 0}

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

x =  -  \frac{1}{3}  \\ x = 5

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

(x +  \frac{1}{3} )(x -  5) = 0

Here we can convert the expression x+1/3 to this.

x +  \frac{1}{3}  = 0 \\  3x + 1 = 0

Rewrite the equation.

(3x + 1)(x - 5) = 0

Simplify by multiplying both expressions.

3 {x}^{2}  - 15x + x - 5 = 0 \\ 3 {x}^{2}  - 14x  - 5 = 0

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

3 {(5)}^{2}  - 14(5)  - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0

3( -  \frac{1}{3} )^{2}  - 14( -  \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) +  \frac{14}{3}  - 5 = 0 \\  \frac{1}{3}  +  \frac{14}{3}  -  \frac{15}{3}  = 0 \\  \frac{15}{3}  -  \frac{15}{3}  = 0 \\ 0 = 0

The equation is true for both roots.

<u>Answer</u>

\large \boxed {3 {x}^{2}  - 14x - 5 = 0}

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The Jones family has saved a maximum of $750 for their family vacation to the beach.  While planning the trip, they determine th
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Answer:

Value of h greater than 5.4 will make inequality false.

Step-by-step explanation:

This question is incomplete; here is the complete question.

The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine that the hotel will average $125 a night and tickets for scuba diving are $75. The inequality can be used to determine the number of nights the Jones family could spend at the hotel 750 ≥ 75 + 125h. What value of h does NOT make the inequality true?

From the given question,

Per night expense (expected) = $125

If Jones family stays in the hotel for 'h' days then total expenditure on stay = $125h

Charges for scuba diving = $75

Total charges for stay and scuba diving = $(125h + 75)

Since Jones family has saved $750 for the vacation trip so inequality representing the expenses will be,

125h + 75 ≤ 750

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That means number of days for stay should be less than equal to 5.4

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