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3 years ago

Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?

Mathematics

1 answer:

Sonbull [250]3 years ago

6 0

The correct answer is x = 2 and x = -4.

In order to solve for this, you first need to plug in the f(x) value and solve for the absolute value statement.

f(x) = -5|x + 1| + 3

-12 = -5|x + 1| + 3 ---> subtract 3 from both sides.

-15 = -5|x + 1|----> divide both sides by -5.

3 = |x + 1|

Now that we have solved for the absolute value portion, we need to solve this equation twice. Once removing the absolute value and solving and the other by removing it and making the 3 negative. This is because even if the inside of the markers was -3, it would give us a 3 answer.

3 = x + 1

2 = x

Then the negative version.

-3 = x + 1

-4 = x

And there are your two answers.

You might be interested in

Solve: 5.6 = 3.1 – 12.5|1 – 0.8x|

galben [10]

Answer:

<h3>There are no solutions.</h3>

Step-by-step explanation:

Questions:

Solve: 5.6= 3.1 – 12.5|1 – 0.8x|

To find:

The value of x.

Solutions:

5.6= 3.1 – 12.5|1 – 0.8x|

First, do switch sides.

$\Longrightarrow:\sf{3.1-12.5\left|1-0.8x\right|=5.6}$

Multiply by 10 from both sides.

$\Longrightarrow: \sf{3.1*10-12.5|1-0.8x|*10=5.6*10}$

Solve.

31-125|1-0.8x|=56

Subtract by 31 from both sides.

$\Longrightarrow: \sf{31-125\left|1-0.8x\right|-31=56-31}$

Solve.

$\Longrightarrow: \sf{-125\left|1-0.8x\right|=25}$

Divide by -125 from both sides.

Solve.

$\Longrightarrow: \sf{\dfrac{-125\left|1-0.8x\right|}{-125}=\dfrac{25}{-125}=\boxed{\sf{No\ solutions.}}}$

Therefore, the correct answer is "D. There are no solutions."

I hope this helps, let me know if you have any questions.

5 0

1 year ago

When considering a term(s) inside parentheses, and there is an exponent

MaRussiya [10]

Answer:

distribute; multiply

For instance:

$(4^{2} + 6 )^{3} = 4^{6} + 6^{3}$

7 0

3 years ago

What is the answer ?

djyliett [7]

Answer:

Step-by-step explanation:

3 0

3 years ago

Aliyah bought a car for $32,000. It is now worth $5000 less than half of what she purchased it for. To the nearest tenth of a pe

Reil [10]

32,000 x 0.5 = 16000

16000- 5000 = 11000

11000 / 32000= 0.34375

1- 0.344= 0.656

Answer : D

3 0

3 years ago

The accompanying data contains the depth (in kilometers) and magnitude, measured using the Richter Scale, of all earthquakes

Sunny_sXe [5.5K]

Answer:

Depth:

μ =20.2025 km

M = 15.625 km

Range = 47.15 km

σ ≈ 15.92 km

Q₁ = 5.7375 km

Q₃ = 34.6675 km

Magnitude:

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

Step-by-step explanation:

The given data are;

Depth ${}$ Magnitude

0.76 ${}$ 0.84

4.93 ${}$ 0.47

8.16 ${}$ 0.35

33.58 ${}$ 1.32

21.2 ${}$ 1.61

35.03 ${}$ 4.57

10.05 ${}$ 5.52

47.91 ${}$ 1.99

For the Depth, we have;

The mean, μ = (0.76+4.93+8.16+33.58+21.2+35.03+10.05+47.91)/8 =20.2025 km

The median, M = The (n + 1)/2th term after arranging the term in increasing order as follows;

0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 , the median is therefore;

(8 + 1)/2th term or the 4.5th term which is 10.05 + (21.2 - 10.05)/2 = 15.625 km

The Range = The highest - The lowest value = 47.91 - 0.76 = 47.15 km

The Standard deviation of, σ, is given as follows;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{N}}$

Where;

$x_i$ = The individual data point = (0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 )

N = The total number of data point = 8

Substituting, (using Microsoft Excel) we get;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-20.2025 \right )^{2} }{8}} \approx 15.92 \ km$

Q₁ = The first quartile = The (n + 1)/4th = term arranged in increasing order

Q₁ = The (8 + 1)/4th term = The 2.25th term = 4.93 + (8.16 - 4.93)×0.25) = 5.7375 km

Q₃ = The first quartile = The 3×(n + 1)/4th = term arranged in increasing order

Q₃ = The 3×(8 + 1)/4th term = The 6.75th term = 33.58 + 3×(35.03 - 33.58)×0.25) = 34.6675 km

For the magnitude, we have, using the same formulas and procedures as above;

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

4 0

3 years ago