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Elis [28]
3 years ago
13

The angle measures are represented by algebraic expressions.

Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
8 0

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

- <u><em>From the attached figure</em></u>

# 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

- <u><em>From the attached figure</em></u>

# 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

- <u><em>From the attached figure</em></u>

# 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

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If the sum of three consecutive numbers is 36. Find the numbers.
aleksandrvk [35]

Answer:

11, 12, 13

Step-by-step explanation:

x is the first number

(x + 1) is the second number

(x + 2) is the third number

x + x+1 + x+2 = 36

3x + 3 = 36

3x = 36 - 3

3x = 33

x = 11  ← the first number

the second number  = x + 1 = 11 + 1 = 12

the third number = x + 2 = 11 + 2 = 13

8 0
3 years ago
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Pls help me, i need to get my grade up as soon as I can
Aleksandr [31]

Answer:

106 and 93

Step-by-step explanation:

The whole thing has to add up to 360

4 0
2 years ago
Is the ordered pair (-8,-7) a soulution to the equation 3x+10=2y
Gemiola [76]

Answer:

yes

Step-by-step explanation:

To determine if (- 8, - 7 ) is a solution to the equation

Substitute the values of x and y into the equation and if both sides are equal then it is a solution.

left side : 3(- 8) + 10 = - 24 + 10 = - 14

right side : 2y = 2(- 7) = - 14

Since both sides are - 14 then (- 8, - 7 ) is a solution to the equation.

8 0
2 years ago
X2 + 8x = 15 help me ​
svlad2 [7]

Answer:

x₁ = - 4 + √31

x₂ = - 4 - √31

Step-by-step explanation:

x² + 8x = 15

x² + 8x - 15 = 0

x = [- 8 ± √8² - 4×1×(-15)]/(2×1)

x = (-8 ± 2√31)/2

x₁ = (-8 ± 2√31)/2

x₁ = - 4 + √31

x₂ = - 4 - √31

3 0
3 years ago
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When expressing sets, you may write "inf" for infinity and "U" for union.
GarryVolchara [31]

Answer:

The complement of the given set in interval notation is(-\infty,-5]\cup(6,\infty). It can we written as (-inf,5]U(6,inf).

Step-by-step explanation:

The given set in interval notation is

(−5,6]

It means the set is defined as

A=\{x|x\in R,-5

If B is a set and U is a universal set, then complement of set B contains the elements of universal set but not the elements of set B.

Here, universal set is R, the set set of all real numbers.

U=\{x|x\in R\}

The complement of the given set is

A^c=U-A

A^c=\{x|x\in R,-\infty

Complement of the given set in interval notation is

A^c=(-\infty,-5]\cup(6,\infty)

Therefore the complement of the given set in interval notation is(-\infty,-5]\cup(6,\infty). It can we written as (-inf,5]U(6,inf).

3 0
3 years ago
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