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Assoli18 [71]
2 years ago
9

Rodney is starting a tutoring business.

Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
7 0

Answer:

(a) 20 + 14(s)

(b)$146

Step-by-step explanation:

Use s as your variable per session.

$20 is a flat fee as a sign up for tutoring.

Therefore, 20 + 14s is the expression.

(b) 14x9=126 + 20 = 146

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3. A postal carrier can
Delicious77 [7]

Answer:

6 hours. ( I DID IT USING PROPORTIONS!)

Step-by-step explanation:

houses/hours

130/2.5= 312/x

(cross multiply)

130x = 780

130x/130 = 780/ 130 (divide each by 130)

6 = h

7 0
3 years ago
Read 2 more answers
At 3 p.m. an oil tanker traveling west in the ocean at 14 kilometers per hour passes the same spot as a luxury liner that arrive
schepotkina [342]
<span>N(t) = 16t ; Distance north of spot at time t for the liner. W(t) = 14(t-1); Distance west of spot at time t for the tanker. d(t) = sqrt(N(t)^2 + W(t)^2) ; Distance between both ships at time t. Let's create a function to express the distance north of the spot that the luxury liner is at time t. We will use the value t as representing "the number of hours since 2 p.m." Since the liner was there at exactly 2 p.m. and is traveling 16 kph, the function is N(t) = 16t Now let's create the same function for how far west the tanker is from the spot. Since the tanker was there at 3 p.m. (t = 1 by the definition above), the function is slightly more complicated, and is W(t) = 14(t-1) The distance between the 2 ships is easy. Just use the pythagorean theorem. So d(t) = sqrt(N(t)^2 + W(t)^2) If you want the function for d() to be expanded, just substitute the other functions, so d(t) = sqrt((16t)^2 + (14(t-1))^2) d(t) = sqrt(256t^2 + (14t-14)^2) d(t) = sqrt(256t^2 + (196t^2 - 392t + 196) ) d(t) = sqrt(452t^2 - 392t + 196)</span>
3 0
3 years ago
2y+18=42 what is y, and how would you find it?
Nesterboy [21]

Answer:

y=12

Step-by-step explanation:

Use order of operations. Subtract 18 from both sides and the divide by 2.

2y+18 -18=42-18

2y=24

y=12

3 0
3 years ago
What's a real world problem for 1/3x+10=3/5x?
lions [1.4K]
The answer is x= 2/75
4 0
3 years ago
A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6
katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is 49\ ft

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

h(t)=-16t^{2} +63t+4

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

h(3)=-16(3)^{2} +63(3)+4=49\ ft

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

h(t)=-16t^{2} +63t+4

Group terms that contain the same variable, and move the constant to the opposite side of the equation

h(t)-4=-16t^{2} +63t

Factor the leading coefficient

h(t)-4=-16(t^{2} -(63/16)t)

Complete the square. Remember to balance the equation by adding the same constants to each side

h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})

h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})

Rewrite as perfect squares

h(t)-(67,600/1,024)=-16(t-(63/32))^{2}

h(t)=-16(t-(63/32))^{2}+(67,600/1,024)

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

h(t)=-16t^{2} +63t+4

For h(t)=0

0=-16t^{2} +63t+4

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0
3 years ago
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