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2 years ago

Find X, and the two angle measures.

Mathematics

1 answer:

Snowcat [4.5K]2 years ago

5 0

Answer:

x = -4

m<LMP = 77°

m<NMP = 103°

Step-by-step explanation:

Straight angles by definition have a total measure of 180°.

This means that m<LMP and m<NMP are 180° together.

Therefore m<LMP + m<NMP = 180°.

[substitution property]

(-16x + 13)° + (-20x + 23)° = 180°

[associative property of addition]

(-36x + 36)° = 180°

-36x + 36 = 180

–36 –36

-36x = 144

÷-36 ÷-36

x = -4

_________________

Since m<LMP = (-16x + 13)°.

Using substitution with x = -4:

m<LMP = (-16(-4) + 13)° = (64 + 13)° = 77°.

Since m<NMP = (-20x + 23)°.

Using substitution with x = -4:

m<NMP = (-20(-4) + 23)° = (80 + 23)° = 103°.

This is true because 77° + 103° = 180°.

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3 years ago

How many ways are there to select 12 countries in the United Nations to serve on a council if 3 are selected from a block of 45,

sattari [20]

Answer: There are 2346953264 ways to do so.

Step-by-step explanation:

Since we have given that

Total number of selected countries = 12

Number of selected countries from a block of 45 = 3

Number of selected countries from a block of 57 = 4

So, remaining number of selected countries from a block of 69.

So, 12-(3+4)=12-7=5

Now, we need to find the number of ways, so we will use "Combination" to select that number of countries.

So, it becomes.

$^{45}C_3\times ^{57}C_4\times ^{57}C_5\\\\=14190\times 395010\times 4187106\\\\=2346953264$

Hence, there are 2346953264 ways to do so.

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3 years ago

A number cube is tossed 8 times. What is the probability that the cube never lands on 3?.

tino4ka555 [31]

The probability that the cube never lands on 3 is (D) 23.3%.

<h3>What is probability?</h3>

A probability formula can be used to calculate the likelihood of an occurrence by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that the cube never lands on 3:

Given -

Number cube toss = 8

Required

Probability of not landing on 3.

First, we need to get the probability of landing on 3 in a single toss.

For a number cube,

n(3) = 1 and n(total) = 6

So, the probability is P(3) = 1/6

First, we need to get the probability of not landing on 3 in a single toss.

Opposite probability = 1.

So, P(3) = P(3') = 1.

Make P(3') the subject of the formula.

P(3') = 1 - P(3)
P(3') = 1 - 1/6
P(3') = 5/6

In 8 toss, the required probability is (P(3'))⁸

This gives:

P = (5/6)⁸
P = 390625/1679616
P = 0.23256803936

Approximate to 1 decimal place, P = 23.3%.

Therefore, the probability that the cube never lands on 3 is (D) 23.3%.

Know more about probability here:

brainly.com/question/25870256

#SPJ4

The correct question is given below:
A number cube is tossed 8 times. What is the probability that the cube never lands on 3?

A. 6.0%

B. 10.4%

C. 16.7%

D. 23.3%

5 0

9 months ago

Gavin drove 85 miles on 10 gallons of gas.How many miles can gavin drive on 25 gallons of gas?

bixtya [17]

Answer:

212.5 miles on 25 gallons.

Step-by-step explanation:

Set up a proportion

85 miles on 10 gallons

x miles on 25 gallons.

85/10 = x / 25 Multiply both sides by 25

85*25 / 10 = x Simplify the left

2125 / 10 = x

x = 212.5 miles in 25 gallons.

6 0

3 years ago

A set of points in the xy-coordinate plane meets two conditions, as described.

Pepsi [2]

Answer:

Condition 1: y>0

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Step-by-step explanation:

We are told that we have a set of points in the Cartesian system (i.e. x-y coordinate), so we can define our point as:

$(x,y)$

We are given two conditions and we want to create a system of inequalities. Now, generally speaking, inequalities are expressions relating mathematical expressions through 'comparison' (i.e. less than, greater than, or less/greater and equal to) usually recognized by , $>$ , $\leq$ and $\geq$ , respectively.