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VMariaS [17]
3 years ago
5

Austin is saving money to buy a new bike. He needs $120 but has only saved 60% so far. How much more money does Austin need to b

uy the bike?
Mathematics
1 answer:
IgorLugansk [536]3 years ago
6 0
You have to find 60% of 120, which is 72. Then subtract 72 from 120 to find the difference, which is 48. So Austin would need $48 to buy the bike. Hope this helped! :)
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The rate at which sand is poured into a bag is modeled by the function r given by r(t)=15t−2t2, where r(t) is measured in millil
balu736 [363]

Answer:

35 mililiters

Step-by-step explanation:

Given

r(t) = 15t - 2t^2

Required

Accumulated amount from t = 0 to 2

This implies that, we substitute the values of t from 0 to 2 in the function

r(0) = 15*0 - 2*0^2= 0

r(1) = 15*1 - 2*1^2= 13

r(2) = 15*2 - 2*2^2= 22

The accumulated sand (r) is:

t = r(0) + r(1) + r(2)

r = 0 + 13 + 22

r = 35

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2 years ago
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PtichkaEL [24]
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Rewrite the equation by completing the square.<br> 4x^2 + 28x + 49=0
Evgen [1.6K]

Answer:

4(x+3.5)^{2}=0

Step-by-step explanation:

we have

4x^{2}+28x+49=0

step 1

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

(4x^{2}+28x)=-49

step 2

Factor the leading coefficient

4(x^{2}+7x)=-49

step 3

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

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4(x^{2}+7x+12.25)=0

step 4

Rewrite as perfect squares

4(x+3.5)^{2}=0

5 0
2 years ago
A particle in the first quadrant is moving along a path described by the equation LaTeX: x^2+xy+2y^2=16x 2 + x y + 2 y 2 = 16 su
ElenaW [278]

Answer:

\frac{50}{3} cm/sec.

Step-by-step explanation:

We have been given that a particle in the first quadrant is moving along a path described by the equation x^2+xy+2y^2=16 such that at the moment its x-coordinate is 2, its y-coordinate is decreasing at a rate of 10 cm/sec. We are asked to find the rate at which x-coordinate is changing at that time.

First of all, we will find the y value, when x =2 by substituting x =2 in our given equation.

2^2+2y+2y^2=16

4-16+2y+2y^2=16-16

2y^2+2y-12=0

y^2+y-6=0

y^2+3y-2y-6=0  

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(y+3)=0,(y-2)=0

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Since the particle is moving in the 1st quadrant, so the value of y will be positive that is y=2.

Now, we will find the derivative of our given equation.

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We have been given that y=2, x =2 and y'=-10.

2(2)\cdot x'+(2)x'+2(-10)+4(2)\cdot (-10)=0

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Therefore, the x-coordinate is increasing at a rate of \frac{50}{3} cm/sec.

7 0
3 years ago
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Mrrafil [7]

Answer:

pi is 3.14

Step-by-step explanation:

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8 0
1 year ago
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