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Rom4ik [11]
2 years ago
14

Tanner needs repairs for his truck. He can take it to Gary’s Garage for a service charge of $40 plus $30 per hour. He can also t

ake it to Casey’s Car House for a service charge of $60 plus $20 an hour. At how many hours would it cost Tanner the same amount to take his truck to either garage? How much would he pay at this number of hours?
Mathematics
1 answer:
oksano4ka [1.4K]2 years ago
5 0

Answer:

Step-by-step explanation:

G=30t+40, C=20t+60, C=G

30t+40=20t+60, subtract 40 from each side

30t=20t+20, subtract 20t from each side

10t=20, divide each side by 10

t=2

So both garages charge the same fot two hours of work.

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Consider the function f(x) defined by the finite set f(x)={(−2,5),(0,4),(1,−3)}. Graph the function f(x) and the transformation
Lelu [443]

let's calculate it step by step.

I'll assume that the function we look for is quadratic, because we only got 3 points

I plotted the 3 points for checking the equation later, and some intuited insight. see screenshot 1

let's write the general form of quadratic equations:

f(x) = a*x² + b*x + c

our goal is to correctly determine a, b and c

since we know from the 2nd point that

f(0) = a*0² + b*0 + c = 4

we can say

<em><u>c = 4</u></em>

this one comes almost for free

now to the next point, the 3rd one

f(1) = a*1² + b*1 + 4 = -3

we can write it as

a + b + 4 = -3

we can rearrange that to

<em><u>a = -b -7</u></em>

lastly, to the first point

f(-2) = a*(-2)² + b*(-2) + 4 = 5

simplified to

4a -2b + 4 = 5

since sort of defined a, let's plug it into our newest equation

4*(-b-7) -2b +4 = 5

we just swapped a for what its equal to.

now we just got numbers and b's

simplify it to

-4b -28 -2b +4 = 5

-6b -24 = 5

-6b = 29

<em><u>b = -29/6</u></em>

now we use the exact value of b to plug it into the rather simple equation from earlier. into this one

a = -b -7

a = -(-29/6) -7

a = 29/6 -42/6

<em><u>a= -13/6</u></em>

now that we got a, b and c we can write the whole equation

<em><u>f(x) = -13/6*x² -29/6*x +4</u></em>

see the graphic check in screenshot 2

second part of the problem:

if we want to move the whole graph 4 units down, we effectivly just cancel the +4 part

g(x) = f(x) -4 = f(x) = -13/6*x² -29/6*x +4 -4

<em><u>g(x) = -13/6*x² -29/6*x</u></em>

see screenshot 3 for the graph

5 0
2 years ago
What is distributive property? <br>​
Svet_ta [14]

Answer:

To distribute means to divide something or give a share or part of something. For example, for the problem <em>4</em><em>(</em><em>6</em><em>+</em><em>2</em><em>)</em>, you would use the distributive property and distribute the 4. Making the end result, <em>2</em><em>4</em><em>+</em><em>8</em>.

5 0
2 years ago
Find r if 0=pi/6 rad sector 64m^2
kap26 [50]

Given:

Area of a sector = 64 m²

The central angle is \theta=\dfrac{\pi}{6}.

To find:

The radius or the value of r.

Solution:

Area of a sector is:

A=\dfrac{1}{2}r^2\theta

Where, r is the radius of the circle and \theta is the central angle of the sector in radian.

Putting A=64,\theta=\dfrac{\pi}{6}, we get

64=\dfrac{1}{2}r^2\times \dfrac{\pi}{6}

64=\dfrac{\pi}{12}r^2

64\times \dfrac{12}{\pi}=r^2

\dfrac{768}{\pi}=r^2

Taking square root on both sides, we get

\sqrt{\dfrac{768}{\pi}}=r

16\sqrt{\dfrac{3}{\pi}}=r

Therefore, the value of r is 16\sqrt{\dfrac{3}{\pi}} m.

6 0
2 years ago
A colony of 85 bacteria doubles in size every 126 minutes. What will the population be 378
SVETLANKA909090 [29]

Answer:

680 Bacteria

Step-by-step explanation:

378 is evenly divisible by 126, which is equal to 3.

The first 126 minutes, the 85 bacteria will double to 170 bacteria.

The second 126 minutes (252 minutes total), the 170 bacteria will double to 340 bacteria.

The final 126 minutes (378 minutes total), the 340 bacteria will double to 680 bacteria total.

If this helped, a brainliest would be greatly appreciated!

6 0
2 years ago
Read 2 more answers
I will mark you brainliest if your answer is right
rusak2 [61]
12.72 is the answer
8 0
3 years ago
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