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bija089 [108]
3 years ago
10

Help find the missing lengths round to nearest tenth

Mathematics
1 answer:
Mama L [17]3 years ago
6 0

Answer:

<h2>x = 20.8</h2><h2>y = 22.3</h2>

Step-by-step explanation:

  • Theta is 21 degrees
  • x is the adjacent side
  • 8 is the opposite side
  • y is the hypothenuse

SOH - CAH - TOA

Since the opposite side is given and we need to find the length of the adjacent side, we can use tangent to solve for x.

tan 21=\frac{opposite}{adjacent} \\tan 21 =\frac{8}{x} \\0.384 =\frac{8}{x} \\0.384x =8 \\x=\frac{8}{0.384} \\x=20.84

Since the opposite side is given and we need to find the length of the hypotenuse, we can use sine to solve for y.

sin 21=\frac{opposite}{hypotenuse} \\sin21 =\frac{8}{y} \\0.358 =\frac{8}{y} \\0.358y=8 \\y=\frac{8}{0.358} \\y=22.32

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Part B:  (0,2500); It represents the profit that can be made by reducing $0 in the shirts' price.

Part C: Yes, it has a zero. Its zero is (25,0) and that represents the amount of profit made by reducing $25 from the price of each shirt being sold, which means if it sells for $0 by reducing $25 from the price of each shirt, then the x-coordinate must also represent the original price of each shirt, $25.

Step-by-step explanation:

Part A: Look at the graph! The highest y-value should be the maximum of each graph, which can be located at the vertex of a quadratic function. In this graph, the vertex is (2.5, 2531.25), where which its y-value contains the highest point of a graph, since the graph is concave down.  

<u>Part B</u>

y=a(x-2.5)^{2} +2531.25\\

0=a(25-2.5)^{2} +2531.25\\

a(22.5)^{2} =-2531.25

506.25a =2531.25

a=-5

y=-5(x-2.5) ^{2}+2531.25

y=-5(0-2.5)^{2} +2531.25

y=-31.25+2531.25

y=2500

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