Answer:
First angle = 30°
Second angle = 60°
Third angle = 90°
Step-by-step explanation:
x + y + z = 180
y + z = 5x
z = y + 30
then:
y + (y+30) = 5x
2y + 30 = 5x
x = (2y+30)/5
then:
x + y + z = 180
{(2y+30)/5} + y + y+30 = 180
{(2y+30)/5} + 2y + 30 = 180
{(2y+30)/5} = 180 - 30 - 2y
{(2y+30)/5} = 150 - 2y
2y+30 = 5(150-2y)
2y+30 = 5*150 + 5*-2y
2y+30 = 750 - 10y
2y + 10y = 750 - 30
12y = 720
y = 720/12
y = 60°
x = (2y+30)/5
x = (2*60 + 30)/5
x = (120+30)/5
x = 150/5
x = 30°
z = y + 30
z = 60 + 30
z = 90°
Check:
x + y + z = 180°
30° + 60° + 90° = 180°
Answer:
A Juan le quedan 45 empanadas.
Step-by-step explanation:
Dado que Juan vende 180 empanadas al día, y por la mañana vende las dos terceras partes y por la tarde la cuarta parte de lo que queda, para determinar cuántas empanadas le queda por vender en la noche se debe realizar el siguiente cálculo:
180 x 2 / 3 = 120
180 - 120 = 60
60 x 1/4 = 15
60 - 15 = 45
Por lo tanto, a Juan le quedan 45 empanadas.
Answer:
The required result is proved with the help of angle bisector theorem.
Step-by-step explanation:
Given △ABD and △CBD, AE and CE are the angle bisectors. we have to prove that
Angle bisector theorem states that an angle bisector of an angle of a Δ divides the opposite side in two segments that are proportional to the other two sides of triangle.
In ΔADB, AE is the angle bisector
∴ the ratio of the length of side DE to length BE is equal to the ratio of the line segment AD to the line segment AB.
→ (1)
In ΔDCB, CE is the angle bisector
∴ the ratio of the length of side DE to length BE is equal to the ratio of the line segment CD to the line segment CB.
→ (2)
From equation (1) and (2), we get
Hence Proved.
a) The amount earned by Kurt by selling the break-even units of painting at $38 each is <u>$1,064</u>.
b) The number of paintings that Kurt will be selling at the break-even point is <u>28</u>.
<h3>What is the break-even point?</h3>
The Break-even point is the sales units at which the seller's total revenue equals the total costs.
At the break-even point, there is no profit or loss.
<h3>Data and Calculations:</h3>
Fixed costs = $112
Variable cost = $34
Selling price = $38
Contribution margin = $4 ($38 - $34)
Contribution margin ratio = 10.53% ($4/$38 x 100)
Break-even point (units) = Fixed costs/Contribution margin per unit
= 28 units ($112/$4)
Break-even point (dollars) = $1,064 ($38 x 28)
Learn more about the break-even point at brainly.com/question/21137380
#SPJ1