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dimulka [17.4K]
3 years ago
9

Consider the following piece-wise function. Which of the below correctly describes the graph shown?

Mathematics
1 answer:
elena55 [62]3 years ago
6 0

Answer:

C.

f(x)=\left\{\begin{array}{l}\dfrac{1}{2}x-3,\ \ x

Step-by-step explanation:

The graph of the piecewise function consists of two linear functions which graphs meets at point with x-coordinate x = 2.

1. The left linear function is determined for all x < 2 and is passing through the points (0,-3) and (-2,-4). So, its slope is

\dfrac{-4-(-3)}{-2-0}=\dfrac{-1}{-2}=\dfrac{1}{2}

and its equation is

y-(-3)=\dfrac{1}{2}(x-0)\\ \\y=\dfrac{1}{2}x-3

2. The right linear function is determined for all x ≥ 2 and is passing through the points (2,-2) and (3,1). So, its slope is

\dfrac{1-(-2)}{3-2}=\dfrac{3}{1}=3

and its equation is

y-1=3(x-3)\\ \\y=3x-8

3. Hence, the expression for the piece-wise function is

f(x)=\left\{\begin{array}{l}\dfrac{1}{2}x-3,\ \ x

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Answer: 14x + 42

7(2x+4)+14

14x + 28 + 14

<u>14x + 42</u>

Step-by-step explanation:

6 0
3 years ago
The graph shows the solution to a system of inequalities:
tangare [24]

Answer:

Option A. 4x+3y\leq 12 and x\geq 0

Step-by-step explanation:

we know that

The solution of the first inequality is the shaded area below the solid line 4x+3y=12

The solid line passes through the points (0,4) and (3,0) (the y and x intercepts)

therefore

The first inequality is

4x+3y\leq 12

The solution of the second inequality is the shaded area to the right of the solid line x=0

therefore

The second inequality is

x\geq 0

7 0
2 years ago
8a – 10 = 6a in words​
Ipatiy [6.2K]

Answer:

10 subtracted from the product of 8 and 'a' is equal to the product of 6 and 'a'

Step-by-step explanation:

3 0
2 years ago
A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What pe
kicyunya [14]

Answer:

(a) 5.48%

(b) 17.82 years

(c) 21.19%

(d) 15.21 years

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

µ=12 years and σ=2.5 years.

(a) What percent of the radios will function for more than 16 years?

For x = 16

z = 16 - 12/2.5

z = 1.6

Probability value from Z-Table:

P(x<16) = 0.9452

P(x>16) = 1 - P(x<16)

1 - 0.9452

= 0.054799

Converting to percentage = 0.054799 × 100

= 5.4799%

Approximately = 5.48%

(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.

find the z score of the 99th percentile = 2.326

Hence:z = (x-μ)/σ

2.326 = x - 12/2.5

Cross Multiply

2.326 × 2.5 = x - 12

5.815 = x - 12

x = 12 + 5.815

x = 17.815

Approximately = 17.82 years

(c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years?

When x < 10

Hence,

z = 10 - 12/2.5

z = -0.8

Probability value from Z-Table:

P(x<10) = 0.21186

Converting to percentage

0.21186 × 100

= 21.186%

Approximately = 21.19%

(d) If 10% of the radios will function for more than X years, find X.

The z score would be : 100 - 10%

= 90th percentile z score

We find the z score of the 90th percentile = 1.282

Hence:z = (x-μ)/σ

1.282 = x - 12/2.5

Cross Multiply

1.282 × 2.5 = x - 12

3.205 = x - 12

x = 12 + 3.205

x = 15.205

Approximately = 15.21 years

4 0
2 years ago
You have to write 0.33 as a fraction.how do you choose the denominator?
yaroslaw [1]
100 is the easiest because 1/100 =0.01
33/100=0.33
8 0
3 years ago
Read 2 more answers
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