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MArishka [77]
3 years ago
15

Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, what is g(x) − f(x)?

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
3 0

Answer:

2x - 12

Step-by-step explanation:

g(x) - f(x) = 5x - 10 - 3x - 2 = 2x - 12

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A combination lock has 6 different numbers. You can use any number 0 - 9 in the combination, but each number can only be used ON
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There are 151,200 possible combinations. If you'd like an explanation of my answer, please let me know.
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There are 3 rivers and after each river lies a grave. So there are 3 rivers and 3 graves. A man wants to leave the SAME amount o
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I've had a problem similar to this before. He should start out with 0 flowers. He would have 2 flowers at the first one, so he would put one on the first grave then have one for the second. When he gets to the second, he puts down one flower and the last flower on the 3rd grave.
5 0
3 years ago
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A study sampled 350 upperclassmen (Group 1) and 250 underclassmen (Group 2) at high schools around the city of Portland. The stu
iVinArrow [24]

Answer:

-0.061 < P_1 -P_2< 0.025

Step-by-step explanation:

Give data:

n_1 = 350

n_2 =250

x_1 = 23

x_2 = 21

\hat{P} 1 = \frac{x_1}{n_1} = \frac{23}{350} = 0.066

\hat{P} 2 = \frac{x_2}{n_2} = \frac{21}{250} = 0.084

for 95% confidence interval

\alpha = 1 - 0.95 = 0.05 and \alpha/2 = 0.025

z_{\alpha/2} = 1.96  from standard z- table

confidence interval for P_1  and P_2 is

\hat{P} 1 - \hat{P} 2 \pm z_{\alpja/2} \sqrt{\frac{\hat{P} 1(1-\hat{P} 1)}{n_1} +\frac{\hat{P} 2(1-\hat{P} 2)}{n_2}}

(0.066 - 0.084) \pm 1.96 \sqrt{\frac{0.066(1-0.066)}{350} +\frac{0.084(1-0.084)}{250}}

-0.018 \pm 0.043

confidence interval is

-0.018 - 0.043 < P_1 -P_2

-0.061 < P_1 -P_2< 0.025

7 0
3 years ago
Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find
densk [106]

Answer:

x=4

Step-by-step explanation:

<u>Step 1</u>:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

AC^2 = AB^2 + BC^2

<u>step 2:-</u>

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

(a + b)^2 = a^2 +2ab+b^2

289 = 4x^2 +9(x^2+2x+1)

13x^2 +18x-280 = 0

finding factors  70 X 52 = 3640

13x^2 +70x-52x-280 = 0

13x^2 -52x+ 70x-280 = 0

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and 13x =-70

x=4 and x=\frac{-70}{13}

we can not choose negative value so x value is 4

Final answer:- x = 4

<u>verification:-</u>

<u></u>AC^2 = AB^2 + BC^2<u></u>

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

6 0
3 years ago
Read 2 more answers
are any two regular polygons similar. The area of the smaller figure is about 390 cm^2. choose the best estimate of the area of
galben [10]

Answer:

The best estimate of the area of the larger figure is 693\ cm^{2}

Step-by-step explanation:

step 1

<em>Find the scale factor</em>

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z----> the scale factor

x-----> the corresponding side of the larger figure

y-----> the corresponding side of the smaller figure

so

z=\frac{x}{y}

we have

x=12\ cm

y=9\ cm

substitute

z=\frac{12}{9}=\frac{4}{3} -----> the scale factor

step 2

<em>Find the area of the larger figure</em>

we know that

If two figures are similar, then the ratio of its  areas is equal to the scale factor squared

Let

z----> the scale factor

x-----> the area of the larger figure

y-----> the area of the smaller figure

so

z^{2}=\frac{x}{y}

we have

z=\frac{4}{3}

y=390\ cm^{2}

substitute and solve for x

(\frac{4}{3})^{2}=\frac{x}{390}

(\frac{16}{9})=\frac{x}{390}

x=390*16/9=693.33\ cm^{2}

4 0
3 years ago
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