The diagonal of a tv is 28 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the tv?
Answers
shortest leg is always x ; longest leg is always x√3 ; hypotenuse is always 2x
hypotenuse = 28 inches = 2x = 2(14)
shortest leg = x = 14
longest leg = x√3 = 14√3
The exact length and width of the tv would be 14 inches and 14√3 inches.
Answer:
14 inches by 14 square root of 3 inches
Step-by-step explanation:
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The sum of two times a number and 5 more than the number is the same as the difference between -15 and twice the number. What is the number?
A rectangular painting measures 15 inches by 18 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 90 inches. Determine the width of the frame.
Answers
Answer:
Colin gets of the total money
Step-by-step explanation:
If we let the total amount be "90" (or any multiple of 9), then the solution gets much easy.
Let total money be 90.
Caroline gets 1/9, so that is:
1/9 * 90 = 10
Remaining is 90 - 10 = 80
This 80 is divided in the ratio 1:3, that means Colin gets 1 part and Sarah gets 3 part. That is 1 + 3 = 4 parts altogether.
80 divided in 4 parts is 80/4 = 20 each part.
Colin gets 1 part, that is 1 * 20 = 20
Colin gets 20 OUT OF 90 (total initial).
What proportion is that? We simply divide and reduce!!
20/90 = 2/9
Colin gets of the total money
The proportion that Colin's get from the share is 2 / 9 x
What is proportion?
Proportion says that two ratios (or fractions) are equal.
Therefore,
let the total money they share = x
Hence,
Caroline money = 1 / 9 x
Colin and Sarah share the rest in the ratio 1:3.
Therefore,
Collin share = 1 / 4 × (x - 1 / 9 x) = 1 / 4 × 9x - x/ 9 = 1 / 4 × 8 / 9 x
Collin's share = 1 / 4 × 8 / 9 x = 8 / 36 x = 2 / 9 x
learn more on proportion here: brainly.com/question/14213714
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B) 4 hours
C) 5 hours
D) 7 hours
Answers
The maximum number of hours that Michael can rent a bike is 7 hours. Then the correct option is D.
What is a linear equation?
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A bike rental company charges $50 for the first hour and $25 for each additional hour. Michael must spend no more than $200 on his bike rental for the day.
Let x be the number of hours. Then the linear equation will be
25x + 50 = 200
Simplify the equation, then we have
25x = 175
x = 7
The maximum number of hours that Michael can rent a bike is 7 hours. Then the correct option is D.
More about the linear equation link is given below.
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Hope I helped :)
3x + 2y = 21
Answers
Solve y=2x for y
Substitute (2x) for y in 3x+2y=21
3x+2y=21
3x+22x=21
7x=21 (Simplify)
7x / 7 = 21 / 7(Divide both sides by 7)
x=3
Substitute (3) for x in y=2x:
y=2x
y=(2)(3)
y=6 (Simplified)
y=6 and x=3
Answers
5 < h
Answers
Answer:
-8
Step-by-step explanation:
Turn the equation into slope intercept form [ y = mx + b ]
y + 11 = 2(x + 1.5)
~Distribute right side
y + 11 = 2x + 3
~Subtract 11 to both sides
y = 2x - 8
"b" represents the y-intercept, so, the y-intercept is -8.
Best of Luck!
Answers
Answer:
192 sponsors
Step-by-step explanation:
If Scott started by asking 3 friends to sponsor him, and each of those friends asked three friends to sponsor him on the second week, and this pattern continued for four weeks, you can calculate the total number of sponsors he would have on the 4th week as follows:
Week 1: Scott has 3 sponsors.
Week 2: Each of the 3 sponsors from Week 1 asks 3 friends, so there are 3 x 3 = 9 new sponsors. In total, there are 3 (from Week 1) + 9 (from Week 2) = 12 sponsors.
Week 3: Each of the 12 sponsors from Week 2 asks 3 friends, so there are 12 x 3 = 36 new sponsors. In total, there are 12 (from Week 2) + 36 (from Week 3) = 48 sponsors.
Week 4: Each of the 48 sponsors from Week 3 asks 3 friends, so there are 48 x 3 = 144 new sponsors. In total, there are 48 (from Week 3) + 144 (from Week 4) = 192 sponsors.
So, on the 4th week, Scott would have a total of 192 sponsors.
In the first week, Scott would have 3 sponsors.
In the second week, each of the 3 sponsors would ask 3 friends, resulting in 3 * 3 = 9 sponsors.
In the third week, each of the 9 sponsors would ask 3 friends, resulting in 9 * 3 = 27 sponsors.
Therefore, on the fourth week, each of the 27 sponsors would ask 3 friends, resulting in 27 * 3 = 81 sponsors.
Scott would have 81 sponsors on the fourth week.