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ipn [44]
3 years ago
8

Solve the inequality − x 2 <4 -x2<4

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
3 0
1 and 2 I hope this help you :)
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Let $f(x)$ be a quadratic polynomial such that $f(-4) = -22,$ $f(-1)=2$, and $f(2)=-1.$ Let $g(x) = f(x)^{16}.$ Find the sum of
Murrr4er [49]

Answer:

The sum of the coefficients of the terms in (-1.5·x² + 0.5·x + 4)¹⁶ that have even degree is  -4273411167.501

Step-by-step explanation:

The parameters given are;

f(-4) = -22

f(-1) = 2

f(2) = -1

g(x) = f(x)¹⁶

The function f(x) is presented as follows;

f(x) = a·x² + b·x +c

We have;

-22 = a·(-4)² + b·(-4) +c

-22 = a·16 - 4·b +c ..............(1)

2 = a·(-1)² + b·(-1) +c

2 = a - b +c...........................(2)

-1 = a·(2)² + b·(2) +c

-1 = 4·a + 2·b +c...................(3)

Solving the equations (1), (2), and (3) by using an online linear systems solver, we get;

a = -1.5, b = 0.5, c = 4

Therefore, f(x) = -1.5·x² + 0.5·x + 4

f(x)¹⁶ = (-1.5·x² + 0.5·x + 4)¹⁶ which gives the coefficients of the even terms as follows;

656.841 - 19267.331 + 248302.054 - 1772904.419 + 6735603.932 - 2868054.635 - 119602865.901 + 750783340.827 + -2542435585.611 + 5338903756.992 - 6048065910.25 -1031335136 + 17223697920 - 32238338048 + 32107397120 - 17716740096 = -4273411167.501.

3 0
3 years ago
Sandra saves 11% of her salary for retirement. This year her salary was $1,000 more than in the previous year, and she saved $4,
Katyanochek1 [597]

First find her salary this year by dividing the amount she saved by the percentage saved:

$4,620 / 0.11 = $42,000

Her salary now is $1000 more than the previous year, so now subtract $1000 from her present salary:

42,000 - 1,000 = $41,000

5 0
3 years ago
If sales tax is 6 percent, how much sales tax must you pay on an oven that costs $362?
nekit [7.7K]

Answer:

Sales tax is 6%

The cost of the oven is $362

Sales tax for the oven will be 6% of $362

=6/100 x $362

=0.06 x $362

=$21.72

Step-by-step explanation:

6 0
2 years ago
Explain why f(x) is continuous at x=3
Elina [12.6K]

Answer:

f is not  defined at x = 3 ⇒ answer (b)

Step-by-step explanation:

∵ f(x) = x² - x - 6/x² - 9 is a rational function

∴ It will be undefined at the values of x of the denominator

∵ The denominator is x² - 9

∵ x² - 9 = 0 ⇒ x² = 9 ⇒ x = ±√9

∴ x = ± 3

∴ f(x) can not be defined at x = 3

∴ The f(x) can not be continuous at x = 3

∴ The answer is (b)

6 0
3 years ago
Read 2 more answers
What is the slope of the line that passes through the points (4, -9)(4,−9) and (8, -3) ?(8,−3)? Write your answer in simplest fo
faltersainse [42]

Answer:

\frac{3}{2}

Step-by-step explanation:

I am assuming that you mean (4,−9) and (8, -3).

m=\frac{rise}{run}=\frac{-3+9}{8-4}=\frac{6}{4}=\boxed{\frac{3}{2}}

Hope this helps.

6 0
3 years ago
Read 2 more answers
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