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3 years ago

An Electrician charges $30 for a service call plus $75 per hour of service. If he charged 210 how many hours did he work?

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

3 0

30 + 75x= 210
Subtract 30 from both sides
75x=180
Divide both sides by 75
X =2.4

Worked 2.4 hours

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In Circle P, m EA=58, m BC=42, m CD=90, find:

elena55 [62]

Circle theorem states that the angle that an arc subtends at the center of a

circle is twice the angle subtended at the circumference.

The values are as follows;

m∠EDA = 90°
m∠BDC = 21°
m∠BEC = 21°
$m\widehat{AB}$ = 80°
m∠AEB = 40°
m∠ECA = 29°
m∠BAC = 21°
$m\widehat{ED}$ = 90°
m∠ECD = 45°
m∠ACB = 40°
m∠EBD = 45°
m∠ADB = 40°
m∠CAD = 45°
m∠EAB = 90°
m∠EBC = 90°

Reasons:

$\displaystyle 1. \ \mathbf{m\angle EDA} = \frac{1}{2} \cdot m\angle EPC$ Angle subtended at center is twice angle at circumference.

m∠EPC = 180°

∴ m∠EDA = 0.5 × 180° = 90°

2. $m\widehat{BC}$ = 42°, therefore, m∠BPC = 42°

$\displaystyle \ m\angle BDC= \frac{1}{2} \cdot m\angle BPC$

m∠BDC = 0.5 × 42° = 21°

3. m∠BEC = m∠BDC = 21°

4. $m\widehat{AB}$ = 180° - (58° + 42°) = 80°

5. $\mathbf{m\widehat{AB}}$ = m∠APB by definition

m∠AEB = 0.5 × m∠APB

m∠AEB = 0.5 × 80° = 40°

6. m∠ECA = 0.5 × m∠AE

Therefore;

m∠ECA = 0.5 × $m\widehat{EA}$

m∠ECA = 0.5 × 58° = 29°

m∠ECA = 29°

7. m∠BAC = 0.5 × $\mathbf{m\widehat{BC}}$

m∠BAC = 0.5 × 42° = 21°

m∠BAC = 21°

8. $m\widehat{ED}$ = 180° - $\mathbf{m\widehat{CD}}$

$m\widehat{ED}$ = 180° - 90° = 90°

$\mathbf{m\widehat{ED}}$ = 90°

9. m∠ECD = 0.5 × $\mathbf{m\widehat{ED}}$

m∠ECD = 0.5 × 90° = 45°

10. m∠ACB = 0.5 × $m\widehat{AB}$

m∠ACB = 0.5 × 80° = 40°

11. m∠EBD = 0.5 × $\mathbf{m\widehat{ED}}$

m∠EBD = 0.5 × 90° = 45°

12. m∠ADB = 0.5 × $\mathbf{m\widehat{AB}}$

m∠ADB = 0.5 × 80° = 40°

13. m∠CAD = 0.5 × $\mathbf{m\widehat{CD}}$

m∠CAD = 0.5 × 90° = 45°

14. m∠EAB = 0.5 × $\mathbf{m\widehat{EABC}}$

m∠EAB = 0.5 × 180° = 90°

15. m∠EBC = 0.5 × $\mathbf{m\widehat{EABC}}$

m∠EBC = 0.5 × 180° = 90°

Learn more about circle theorems here:

brainly.com/question/25101481

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3 years ago

Find the slope of the line that passes through the points (2,-20) and (1,-20).

amm1812

Answer:

$\displaystyle m=0$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Slope Formula: $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (2, -20)

Point (1, -20)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]: $\displaystyle m=\frac{-20+20}{1-2}$
[Fraction] Subtract/Add: $\displaystyle m=\frac{0}{-1}$
[Fraction] Divide: $\displaystyle m=0$

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Answer:

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