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2 years ago

Find all the unknown angle measures in the diagram. Justify your answer for each angle measure.

Mathematics

1 answer:

Jet001 [13]2 years ago

4 0

Answer:

∠1 is 90° because it is a right angle

To find angle 2, we must add the given angles and x then make the equation equal to 180°, which we next solve for x;

x + 90 + 30 = 180

x + 120 = 180

-120 -120

x = 60, ∠2 = 60°

Angle 5 is vertical to angle 1 which equals 90 degrees, and vertical angles are congruent meaning that they measure the same degrees so therefore ∠5 = 90°

Angles 4 and 40° are vertical to angle 2 which measures 60 degrees;

40 + x(where x equals angle 4) = 60

-40 -40

x = 20, ∠4 = 20°

Specified earlier, angles 40° and 4 are equal to 60°, this means that angle three added to angles 40° and 4 will be equal to 90 degrees since angle 1 is 90 degrees and the other three angles will have to equal 90 degrees because they are supplementary.

So we set up the equation;

40 + 20(angle four) + x = 90

60 + x = 90

-60 -60

x = 30, ∠3 = 30°

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1,574/18 Long Division Please And Thank You

Sveta_85 [38]

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this is gonna just keep repeating....so ur answer is 87.444.....or 87 4/9

3 0

3 years ago

Read 2 more answers

Deshaun works as a tutor for 15 an hour and as a waiter for an hour. This month, he worked a combined total of hours at his two

Valentin [98]

Answer:

Total Earning = 15b + M(N - b)

where:

b is the total hours worked as a tutor

M is the amount earned by Deshaun per hour as a waiter

N is the total number of possible hours Deshaun can work in a month

Step-by-step explanation:

Let the number of hours Deshaun works daily as a waiter be w

and the time worked daily as a tutor be t

Deshaun earns $15 per hour as tutor hence daily earnings on tutoring = 15t

Let Deshaun earn $M per hour as waiter, hence daily earning as a waiter is Mw

The total possible hours Deshaun can work in a month is dependent on conditions not specified.

However, assuming 24 working days (6 days weekly for 4 weeks) in a month with maximum approved work hours of 12 hours daily

total hours Deshaun can work will equal 24 x 12 = 288hrs

Note: This 288hrs is an estimate and can change based on applicable hours of work daily and number of working days in a month; it can also be represented as N

If b is the total hours Deshaun worked as a tutor this month,

the hours Deshaun can work as a waiter in a month is equal to 288 - b

Hence in a month, Deshaun will earn 15b as a tutor and M(288-b) as a waiter or optionally M(N - b)

Therefore combined dollar amount earned in a month is

Total Earning = 15b + M(N - b)

7 0

2 years ago

A forest fire is found at midnight. It covers 1200 acres then. It is spreading at a rate of f(t)= 5âˆšt acres per hour. By how m

Eddi Din [679]

Answer:

49 acres

Step-by-step explanation:

Given that:

Initial coverage = 1200 at midnight

Spread rate = 5√t acres per hour

By how many acres will the fire grow between 6am and 10 am

Hours between (6 - 10) am = 6 hours

Take the integral of the rate function with upper limit = 6 and lower limit = 0

∫5√t dt at t = 6, t = 0

5∫√tdt = 5∫t^1/2 dt at t = 6, t = 0

5 (t^1/2 + 1 / 1/2 + 1) at t = 6, t = 0

5 ( t^3/2 / 3/2) at t = 6, t = 0

5 * 2/3 (t^3/2)

[10/3 *t^3/2] at t = 6, t = 0

(10/3 * 6^3/2) - (10/3 * 0^3/2)

(10/3 * 14.696938) - 0

48.989794

= 49 acres ( approximately)

3 0

3 years ago

Lonnie works weekends at his uncle’s apple orchid. He has 47 baskets of apples to pack. Each basket holds 35 apples. How many ap

alex41 [277]

Answer:

Step-by-step explanation:

baskets times apples

47 times 35

=1645

pls mark me brainliest

8 0

2 years ago

12 out of 84 balloons Maggie prepared for her brother’s party were green. What part of all balloons was green?

netineya [11]

Answer:

The part of all balloons green was, $\frac{1}{7}$

Step-by-step explanation:

As per the statement: 12 out of 84 balloons Maggie prepared for her brother’s party were green.

⇒ Total number of balloons = 84 and

Number of balloons were green = 12

we have to find what part of all balloons were green.

In a fraction,

the top number (i.e numerator) says how many part we have and
the bottom number (i.e denominator) says that how many equal parts, the whole is divided into.

The part of all balloons were green = $\frac{\text{Number of balloons were green}}{\text{Total number of balloons}}$

Substitute the given values we have;

The part of all balloons were green = $\frac{12}{84} =\frac{1}{7}$

Therefore, the part of all balloons green was, $\frac{1}{7}$

6 0

2 years ago