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MrMuchimi
3 years ago
10

A linear function has the same y-intercept as x + 4y = 20 and its graph contains the point (3, 6). Find the slope of the linear

function.
Mathematics
1 answer:
vitfil [10]3 years ago
5 0

Answer:

1/3 is the slope.

Step-by-step explanation:

First, we need to find the y-intercept of x + 4y = 20.

x + 4y = 20

Subtract x from both sides.

4y = -x + 20

Divide both sides by 4.

y = -1/4x + 5

Input 0 as x to find the y-intercept.

y = -1/4(0) + 5

Simplify.

y = 5


Now we know the y-intercept is (0,5). Now we need to include to find a slope that contains (0,5) and (3,6). We can use the slope formula:

\frac{y_{2}-y_{1}}{x_{2}-x_1}}

(5 - 6)/(0 - 3) = m

-1/-3 = m

Simplify.

1/3 = m

1/3 is the slope.

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A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the ce
nika2105 [10]
It the wiper blade (and arm) made a full rotation, 2 circles would be formed.

One small circle with radius b, and a larger circle with radius a+b.


The areas of these 2 circles are respectively:

\pi b^2=\pi\cdot 5^2=25 \pi (in^2)    and

\pi (a+b)^2=\pi (14+5)^2=361\pi (in^2)


120° is 1/3 of a complete angle 360° which form a circle, so the areas formed by the arm of length b, and the arm + the wiper blade (a+b) are:

\frac{25 \pi}{3} and \frac{361\pi}{3} in squared respectively.

the actual wiped area is \frac{361\pi}{3}-\frac{25 \pi}{3}= \frac{336\pi}{3}=112\pi \approx351.7 (in squared)


Area of the window is 54*24= 1296 (in squared)

thus, the ratio of the wiped area to the whole area of the window is 351.7/1296=0.271

Converted to percentages, this is 27.1%


Answer: 27.1%

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3 years ago
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3 years ago
Estimate the solution of the equation x - 8.1=5.3 to the nearest whole number
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3 0
3 years ago
Read 2 more answers
Ms. Wall will roll two number cubes. What is
bonufazy [111]
Probability of rolling a sum of 9 or a sum that is even from two number cubes is
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Explanation:
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For getting an even number as sum, we can have (1,1) or (1.3) or (1,5) or (2,2) or (2,4) or (2,6) or (3,1) or (3,3) or (3,5) or (4,2) or (4,4) or (4,6) or (5,1) or (5,3) or (5,5) or (6,2) or (6,4) or (6,6) 18 options, probability is 18/36 or 1/2.

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