Mathematics, 28.01.2020 17:48 aliciaa101

The number of seats in the first five rows of an amphitheater is shown in the table below.

Answers: 3

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F(n)=an+b
We need to find "a" and "b"

when n=1→f(n)=f(1)=18 (see the table), replacing n=1 and f(n)=18 in the equation above, we have:
n=1→f(1)=a(1)+b→a+b=18 (1)

when n=2→f(n)=f(2)=24 (see the table), replacing n=2 and f(n)=24 in the equation above, we have:
n=2→f(2)=a(2)+b→2a+b=24 (2)

We have a system of 2 equations and 2 unknwons:
(1) a+b=18
(2) 2a+b=24

Subtractict equation (1) from equation (2):
Equation (2) - Equation (1):
2a+b-(a+b)=24-18→2a+b-a-b=6→a=6

Replacing "a" by 6 in equation (1):
(1) a+b=18→a=6→6+b=18→6+b-6=18-6→b=12

Then the equation is:
f(n)=an+b; a=6, b=12
f(n)=6n+12

f(n)=6n+12

Answer from: Quest

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

$y=-\dfrac{1}{2}x+8$

is for x = 0. substitute:

$y=-\dfrac{1}{2}(0)+8=0+8=8$

y-intercept is 8 → point (0, 8).

10 points and brainliest its for my semester test

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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The number of seats in the first five rows of an amphitheater is shown in the table below.

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