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2 years ago

Given that f(x) = 5x - 10 and g(x) = x + 3, find f(g(-1)).

2 answers:

5 0

$\bf \begin{cases} f(x) = 5x-10\\ g(x) = x + 3 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(-1)=(-1)+3\implies \boxed{g(-1) = 2} \\\\\\ f(~~g(-1)~~)\implies f\left( \boxed{2} \right) = 5(2)-10\implies \stackrel{f(~g(-1)~)}{f(2)}=0$

balu736 [363]2 years ago

3 0

Answer:

Step-by-step explanation:

Evaluate g(- 1) then use this result to evaluate f(x)

g(- 1) = - 1 + 3 = 2, then

f(2) = (5 × 2) - 10 = 10 - 10 = 0

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Craig Browning bakes cookies for the elementary school cookie sale. His chocolate chip cookies sell for $1.00 a dozen, and his o

Volgvan

Answer and Step-by-step explanation:

Let

Number of chocolate chip cookies = x

Number of oatmeal brownie cookies = y

Bake chocolate chip cookies up to 20 dozen = x≤ 20

Bake oatmeal brownies up to 40 dozen= y≤40

Total cookies = x + y ≤ 50

Number of oatmeal brownie will be no more than three times the number of chocolate chip= y≤3x

From the inequality:

X + y=50

y = 3x

By putting the value of y, we get

x + 3x = 50

4x = 50

X = 12.5

By putting the value of x=12.5 in equation y = 3x, we get

Y = 3(12.5)

= 37.5

Craig should make 12.5 dozen chocolate chip and 37.5 dozen oatmeal brownies in order to make more money.

8 0

2 years ago

Find the slope of the line passing through the points D (10, 8) and E (-4,4)

RUDIKE [14]

Answer:

Slope=2/7

Step-by-step explanation:

Slope=rise/run

$rise = 8 - 4 = 4 \\ run = 10 - ( - 4) = 14 \\ slope = \frac{4}{14} = \frac{2}{7}$

8 0

2 years ago

Find the domain of the function. Express the exact answer using interval notation.

Naya [18.7K]

Answer:

(-oo, -8/3) U (-8/3, oo)

Step-by-step explanation:

Hope this helps.

8 0

1 year ago

Rampur Sarpanch requested one of his villager to donate a 6m wide land adjusted to his 132.8m long side of his right triangular

Furkat [3]

Answer:

The answer is 3030.72 m³

Step-by-step explanation:

Please refer to attached file for graphical representation.

Formulas used:

Area = (a*b)/2

Trigonometry: Tan (t) = opposite/adjacent

Assume:

Villager plot has 3 sides: hypotenuse=C, adjacent=A, opposite=B

Plot given has 3 sides: hypotenuse=z, adjacent=y, opposite=x

Angle common between them is t.

Step 1:

For t:

Tan (t) = a/b

Tan (t) = 123/50

Tan (t) = 2.46

Step 2:

For y:

Tan (t) = y/x

2.46 = y/6

y = 2.46*6

y = 14.76

Step 3:

Villagers old plot area: B = (a*b)/2 = (123*50)/2

B = 3075 m³

Step 4:

Plot donated area: C = (x*y)/2 = (6*14.76)/2

C = 44.28 m³

Step 5:

Villager remaining plot:

A = B-C

A= 3075-44.28

A = 3030.72 m³

Download docx

7 0

2 years ago

Rebecca has 12 photos she wants to hang side by side on her wall.A. If she only wants to display 8 of the photos, in how many wa

Mariana [72]

If she will choose 8 from 12 photos, the total number of ways she can choose is given by a combination of 12 choose 8, since the order of the photos doesn't matter.

The formula for a combination of n choose p is:

$C(n,p)=\frac{n!}{p!(n-p)!}$

For n = 12 and p = 8, we have:

$C(12,8)=\frac{12!}{8!(12-8)!_{}}=\frac{12\cdot11\cdot10\cdot9\cdot8!}{8!\cdot4!}=\frac{12\cdot11\cdot10\cdot9}{4\cdot3\cdot2}=495$

So there are 495 ways.

If she wants to arrange the 12 photos, the total number of ways is given by the factorial of 12:

$12!=12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2=479001600$

There are 479,001,600 ways.

Since 10 photos already have specific places, we need to calculate the number of ways to arrange the other two photos in the two remaining places.

In this case, there are only 2 ways of organizing the remaining two photos:

Photo 1 first, photo 2 last, or photo 1 last and photo 2 first.

6 0

9 months ago