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3 years ago

24 < 4x - 3 +5x + 6 a.) x > 3 b.) x > 7/3 c.) x < 7/3 d.) x < 3

Mathematics

1 answer:

lawyer [7]3 years ago

4 0

Solution:

Simplify the RHS:

24 < 4x - 3 + 5x + 6
=> 24 < 9x - 3 + 6

Further simplify the RHS:

=> 24 < 9x + 3

Subtract 3 both sides:

=> 24 - 3 < 9x

Simplify the LHS:

=> 21 < 9x

Divide both sides by 9:

=> 21/9 < 9x/9
=> 7/3 < x

Switch signs:

=> x > 7/3

Now, graph the line.

Line attached~

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Answer:

At least 11 two-point baskets

Step-by-step explanation:

In her last basketball game, Casey scored 46 points.

In the current game, she has scored 24 points so far.

Difference $=46-24=22$ points

If Casey wants her total score in her current game to be at least as great as her score in the last game, then she has to make at least

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3 years ago

Mario invests 1,500 in a savings account that earns 2% interest a year. He also plans to set aside $50 cash a month. A:2100(1.02

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Answer:

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Step-by-step explanation:

x is in years

Let's just think about the investment of 1500 in an account earning 2% per year.

Before the years even start, you are at 1500 ( present value).

The next year (year 1), it would be 1500*.02+1500=(1500)(1.02).

The next year (year 2), it would be 1500(1.02)(.02)+1500(1.02)=1500(1.02)(1.02).

We keep multiplying factors of (1.02) each time.

So for year x, you would have saved 1500(1.02)^x.

Now we are saving 50 cash per month. Per year this would be 12(50) since there are 12 months in a year. 12(50)=600.

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The third year you would have 600(3) or 1800.

Let's put this together:

1500(1.02)^x + 600x

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4 years ago

Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.

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 (f - g)(x) = 4x + 1 - 2x² - 3
(f - g)(x) = -2x² + 4x + 1 - 3
(f - g)(x) = -2x² + 4x - 2
Domain: {x|-∞ < x < ∞}, (-∞, ∞)
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(g - f)(x) = 2x² - 4x + 3 + 1
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Domain: {x| -∞ < x < ∞}, (-∞, ∞)

4. (f · g)(x) = (4x + 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
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Domain: {x| -∞ < x < ∞}, (-∞, ∞)

5. $(\frac{f}{g})(x) = \frac{4x - 1}{2x^{2} + 3}$
Domain: 2x² + 3 ≠ 0
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2x² ≠ 0
2 2
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x ≠ 0
(-∞, 0) ∨ (0, ∞)

6. $(\frac{g}{f})(x) = \frac{2x^{2} + 3}{4x - 1}$
Domain: 4x - 1 ≠ 0
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x ≠ 0
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