In a group of 30 high school students, 15 play football, 19 play basketball and 6

The angle measures are represented by algebraic expressions.

Anuta_ua [19.1K]

Answer:

The value of x is 0.5

The value of y is 0.8

The value of z is 0.9

Step-by-step explanation:

* Lets explain how to find the values of x , y and z

- From the attached figure

# $l_{1}$ and $l_{2}$ intersect each other at a point

- When two lines intersect each other at a point they formed

congruent vertical opposite angles

∴ The angle of measure (50z + 13)° = the angle of measure (80z - 14)°

because thy are vertical opposite angles

∴ 50z + 13 = 80z - 14

- Add 14 to both sides

∴ 50z + 27 = 80z

- Subtract 50z from both sides

∴ 27 = 30z

- Divide both sides by 30

∴ $z=\frac{27}{30}=\frac{9}{10}=0.9$

* The value of z is 0.9

- From the attached figure

# The angles of measures (50z + 13)° and (45x + 19/2)° have sum

of 90°

∴ 50z + 13 + 45x + 19/2 = 90

∵ z = 0.9

∴ 50(0.9) + 13 + 45x + 19/2 = 90

∴ 45 + 13 + 45x + 9.5 = 90

- Add like term in the left hand side

∴ 67.5 + 45x = 90

- Subtract 67.5 from both sides

∴ 45x = 22.5

- Divide both sides by 45

∴ x = 0.5

* The value of x is 0.5

- From the attached figure

# There is a ray perpendicular to line $l_{1}$

∴ The measure of the angle whose measure (225y/2)° is 90°

∴ $\frac{225y}{2}=90$

- Multiply both sides by 2

∴ 225y = 180

- Divide both sides by 225

∴ $y=\frac{180}{225}=\frac{4}{5}=0.8$

* The value of y is 0.8

8 0

4 years ago

What equation do I need to use?

goldenfox [79]

To ease your problem, consider "L" as you x-axis
Then the coordinate become:
A(- 4 , 3) and B(1 , 2) [you notice that just the y's changed]

This is a reflection problem.
Reflect point B across the river line "L" to get B', symmetric of B about L.
The coordinates of B'(1 , -1) [remember L is our new x-axis]
JOIN A to B' . AB' intersect L, say in H
We have to find the shortest way such that AH + HB = shortest.
But HB = HB' (symmetry about L) , then I can write instead of
AH + HB →→ AH + HB'. This is the shortest since the shortest distance between 2 points is the straight line and H is the point requiered

6 0

4 years ago

Taylor purchased 9 pints of ice cream for a party. If each guest will be served exactly 1 2 2 1 pint of ice cream, how many gu

Neporo4naja [7]

Complete question :

Carly purchased 9 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pint of ice cream, what is the greatest number of gusts that Carly can serve

Answer:

15 guests

Step-by-step explanation:

Given that:

Total pints of icecream = 9 1/2

Fraction of ice cream pints per guest = 3/5 pints

Number of guest that can be served :

Total pints / fraction per guest

9 1/2 ÷ 3/5

19/2 * 5/3

95 / 6

= 15.8 guest

Hence, greatest Number of guest that can be served = 15

8 0

3 years ago

System of equations y=1/2x +5 y=3x -5

Art [367]

Answer: 4

Step-by-step explanation:

Set them equal to each other since they're both equal to y

3x-5=.5x +5

add 5 to both sides

3x=.5x+10

subtract .5x from both sides

2.5x=10

divide both sides by 2.5

x= 4

5 0

3 years ago

Brian rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 6 given that the first roll is

Alona [7]

If the first roll is a three, then the only chance of the sum of the two numbers being less than six is if you roll a 1 or a 2.
That is 2/6 chance, or simplified, a 1/3 chance.

I hope this Helps!

8 0

4 years ago

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