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m_a_m_a [10]
3 years ago
11

The variables x and y are related proportionally. When x = 8, y = 14. Find y when x = 32.

Mathematics
1 answer:
KengaRu [80]3 years ago
6 0

Answer:

y = 56

Step-by-step explanation:

given that x and y are proportional then

y = kx ← k is the constant of proportionality

to find k use the given condition y = 14 when x = 8

k = \frac{y}{x} = \frac{14}{8} = \frac{7}{4}, thus

y = \frac{7x}{4}

when x = 32

y = \frac{7(32)}{4} = 56


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Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back
ankoles [38]

Answer:

The trip normally takes 8 minutes

Step-by-step explanation:

The given information states that the away distance the boat traveled = 400 m

The time traveled at the same initial  speed , v₁, by the boat on the way back = 2 minutes

The increase in speed of the boat by Pilar =  10 m/min

The new speed, v₂ = v₁ + 10

The time for the return trip, t₂ = 60 seconds (1 minute) faster than time for the trip, t₁

t₂ = t₁ - 1

Therefore we have;

v₁ × t₁ = v₁×2 + v₂×(t₂-2) = 400

v₁×2 + (v₁ + 10)×(t₂-2) = 400

(v₁ + 10)×t₂ - 20 = 400

But v₁ = 400/t₁ = 400/(t₂ + 1)

Which gives;

(400/(t₂ + 1) + 10)×t₂ - 20 = 400

10×(t₂²+ 36·t₂-2)/(t₂+1) = 400

10·t₂²+ 10·t₂-420 = 0

t₂²+ t₂-42 = 0

(t₂ - 7)(t₂ + 6) = 0

t₂ = 7 minutes or -6 minutes

Given that t₂ is a natural number, we have, t₂ = 7 minutes

Whereby, t₂ = t₁ - 1, we have;

7 =  t₁ - 1

t₁ = 1 + 7 = 8 Minutes

The trip normally takes 8 minutes

3 0
3 years ago
Please help me out!!
solniwko [45]
The slope is 1 because it is parallel and y=x+b, so, 2=-3+b and b=5
y=x+5

8 0
3 years ago
12 is what percent of 96
DaniilM [7]
12 * 100 = 1200/96 = 12.5 
Answer = 12.5%
You mulitply 12 by a hunndred, since a percent means "out of a hundred." Then, you divide that, by 96, since, you want to find the percent out of 96.

8 0
3 years ago
At the toy store, 3 toy cars cost $2.61. How much does it cost to buy 15 toy cars?
Masteriza [31]
Use a ratio \frac{3}{2.61}= \frac{15}{x} . 13.05 dollars.
7 0
3 years ago
Read 2 more answers
Find the equation of a line that passes through the point (-2,3) and has a gradient of 3.
nadya68 [22]

Answer:

y = 3x+9

Step-by-step explanation:

The standard form of equation of a line is in the form y = mx + c

m is the gradient

c is the y intercept

Get the y-intercept

Substitute m = 3 and the point (-2, 3) into the formula y = mx+c

3 = 3(-2) + c

3 = -6+c

c = 3+6

c = 9

Get the required equation;

y = 3x + 9

Hence the required equation is y = 3x+9

5 0
3 years ago
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