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inna [77]
2 years ago
10

The sum of the measures of the angles of a triangle is 180°. The middle-sized angle measures 3° more than 2 times the smallest a

ngle. The middle-sized angle measures 109° less than the largest angle. Find the measure of each angle.​
Mathematics
1 answer:
Anit [1.1K]2 years ago
6 0

Answer:

13° , 29° , 138°

Step-by-step explanation:

let x be the smallest angle , then

2x + 3 is the middle angle and

2x + 3 + 109 is the largest angle

summing the 3 angles and equating to 180

x + 2x + 3 + 2x + 3 + 109 = 180 , that is

5x + 115 = 180 ( subtract 115 from 180 )

5x = 65 ( divide both sides by 5

x = 13

2x + 3 = 2(13) + 3 = 26 + 3 = 29

2x + 3 + 109 = 29 + 109 = 138

the 3 angles are 13° , 29° , 138°

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Citrus2011 [14]
4x+18=14-2x \\ 4x=-4-2x \\ 6x=-4 \\ x= \frac{2}{3}
4 0
3 years ago
A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materi
valentina_108 [34]

Answer:

N(x) = 40 - 2x

P(x) = -2x² + 52 x - 240

maximum profit = 13

Step-by-step explanation:

given data

feeder cost = $6

average sell = 20 per week

price = $10 each

solution

we consider here price per feeder = x

and profit per feeder  id here formula   = x - 6

so that here

total profit will be

P (x)  = ( x - 6 ) Nx

here N(x) is number of feeders sold at price =  x

so formula for N (x)  is here

N(x) = 20 - 2 ( x - 10 )    

N(x) = 40 - 2x

so that

P(x) = (x-6) ( 40 - 2x)

P(x) = -2x² + 52 x - 240

since here

a = -2

b = 52

c = -240

a < 0

so quadratic function have maximum value of c - \frac{b^2}{4a}

so it will be

maximum value = -240 - \frac{52^2}{4(-2)}

maximum value = 98

so here maximum profit attained at

x = \frac{-b}{2a}

x = \frac{-52}{2(-2)}

x = 13

maximum profit = 13

3 0
3 years ago
SOMEONE HELP ASAPPPPPPP!!! PLEASE
Rom4ik [11]
(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj

Specifically, tan74= \frac{h}{34}
h=(34)(tan74)<span class="_wysihtml5-temp-placeholder"></span>
h=118.6 feet.

Please be sure your calculator is set to degrees (not radians) when you do this problem.

(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.

sin = opp/hyp. As the sin Q =  9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.

cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.

You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.

4 0
3 years ago
20 POINTS! TTM
g100num [7]

A relation is (also) a function if every input x is mapped to a unique output y.

In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:

  1. The first graph is exactly a vertical line, so it's not a function.
  2. The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
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  4. Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
  5. The fifth graph is a function, because every vertical line crosses the graph once
  6. The last graph is a function, although discontinuous, for the same reason.
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