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3 years ago

Find f(g(-4)) if f(x) =7/x+2 and g(x) = (x + 5)^2. Options: -5/2 , -7/2 , 37/4 , 7/3

Mathematics

1 answer:

aev [14]3 years ago

5 0

Answer:

7/3

Step-by-step explanation:

f(x) =7/(x+2)

g(x) = (x + 5)^2

f(g(-4))=

First find g(-4)

g(-4) = (-4+5)^2

=(1)^2 =1

Then find f(1)

f(1)= 7/(1+2)

= 7/3

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A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standa

nignag [31]

For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.

The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n

Where:

α= 5%

α/2 = 2.5%

t 0.025, 19 = 2.093 (check t table)

n = 20

df = n – 1 = 20 – 1 = 19

So plugging in our values:

8.41 ± 2.093 * 0.77 √ 1 + 1/20

= 8.41 ± 2.093 * 0.77 (1.0247)

= 8.41 ± 2.093 * 0.789019

= 8.41 ± 1.65141676

= 6.7586 < x < 10.0614

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3 years ago

Given △XPS≅△DNF, find the values of x and y.

White raven [17]

Answer:

x = 3

y = 15

Step-by-step explanation:

If △XPS ≅△DNF, their corresponding sides would be congruent. This implies that:

XP ≅ DN

PS ≅ NF

XS ≅ DF

Given that:

XP = 4y - 3

DN = 57

NF = 51

XS = 17x + 3

DF = 54

Therefore:

XP = DN

4y - 3 = 57 (Substitution)

Add 3 to both sides

4y = 57 + 3

4y = 60

Divide both sides by 4

y = 60/4

y = 15

Also,

XS = DF

17x + 3 = 54 (substitution)

Subtract 3 from each side

17x = 54 - 3

17x = 51

Divide both sides by 17

x = 51/17

x = 3

4 0

3 years ago

Find the sum of the first 8 terms of the sequence. Show all work for full credit.

aliina [53]

$1, -3, -7, -11, ...\ \ \ \ \rightarrow\ \ \ the\ arithmetic\ sequence\\\\the\ difference\ of\ the\ sequence\ is\ \ \ \ d=-3-1=-4\\\\the\ sum:\ \ \ \ S_n= \frac{\big{2\cdot a_1+(n-1)\cdot d}}{\big{2}} \cdot n\\\\\\S_8= \frac{\big{2\cdot1+(8-1)\cdot(-4)}}{\big{2}} \cdot8=(2-28)\cdot4=-26\cdot4=-104\\\\Ans.\ The\ sum\ is\ -104.$

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3 years ago

Read 2 more answers

A camp counselor starts from home and drives to a campground. The expression 130−60t represents the distance, in miles, the coun

telo118 [61]

Answer:

The value 60 represents the speed of the vehicle the counselor is driving.

Step-by-step explanation:

Linear Function

The linear relationship between two variables d and t can be written in the form

$d=mt+b$

Where m is the slope (or rate of change of d with respect to t) and b is the y-intercept or the point where the graph of the line crosses the y-axis

The function provided in our problem is

$d=130-60t$

Where d is the distance in miles the counselor still needs to drive after t hours. Rearranging the expression:

$d=-60t+130$

Comparing with the general form of the line we can say m=-60, b=130. The value of -60 is the slope or the rate of change of d with respect to t. Since we are dealing with d as a function of time, that value represents the speed of the vehicle the counselor is driving. It's negative because the distance left to drive decreases as the time increases

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3 years ago

What is the answer to 2(x+1)<x+3

Temka [501]

2x+2 < x+3
2x-x < 3-2
x <1

5 0

3 years ago