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CaHeK987 [17]
3 years ago
12

An angle measures 12 degrees less than three times it's supplement. Find the measure of the angle.

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
4 0

supplementary angles = 180 degrees

 so x = angle 1

y = angle 2

y = 3x-12

x + 3x-12 =180

4x-12 = 180

4x = 192

x = 192/4 = 48

y = 3(48) -12 = 144-12 = 132

132 +48 = 180

 the angle is 132

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A rectangle has a length of 45 inches less than 4 times its width. if the area of the rectangle is 3325 square inches, find the
Maru [420]

The length of the rectangle is based on its width, so let's call width w and put the length in terms of the width. We are told that the width is 45 less than 4 times the width, so the length is 4w - 45. Area is found by multiplying length times width and we are given the area as 3325. So we will set up length times width and solve for w, which we will then use to solve for l. 3325 = (4w - 45)(w). Multiplying out we have 3325=4w^2-45w. Move the constant over by subtraction and then we will have a quadratic that can be factored to solve for w. 4w^2-45w-3325=0. We would put that through the quadratic formula to solve for w. When we do that we get that w = 35 and w = -23.75. The 2 things in math that will never EVER be negative is time and distance/length, so -23.75 is out. That means that the width is 35. The length is 4(35) - 45 which is 95. The dimensions of your rectangle are length is 95 and width is 35. There you go!

8 0
2 years ago
Please help me with my homework :)
n200080 [17]

Step-by-step explanation:

x = 36

y = 48

z = 72

hope it helps

3 0
2 years ago
Read 2 more answers
Solve. <br> | 3x + 1 | = 2
qwelly [4]
Since this is an absolute value equation, it will have two answers. For the first answer, take away the absolute value bars and solve 3x + 1 = 2. Subtract 1 from both sides to get 3x = 1 and divide each side by 3 to get x = 1/3. Now onto the second solution. This time, take away the absolute value bars and make the other side of the equation, the 2, negative, to get 3x + 1 = -2. Now solve this by subtracting 1 from each side to get 3x = -3 and divide each side to get the other answer which is x = -1. The answer is x = -1 or 1/3, hope this helps!
8 0
2 years ago
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A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. mater
BartSMP [9]
Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x²        (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
C = 20(1.651)² + 180/1.651 = $163.54

Answer: $163.54

7 0
2 years ago
Match the inequality to the graph of its solution.
Tema [17]
The first graph is c. c - 7 < 3.
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3 0
3 years ago
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