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egoroff_w [7]
3 years ago
11

PLEASE HELP ME WITH THIS PROBLEM!!

Mathematics
1 answer:
madam [21]3 years ago
4 0
To solve this question, we should know the Triangle Inequality Theorem.

The triangle inequality theorem says something like: The sum of any two sides of a triangle must be greater than than the length of the third side

Making that into a formula, considering the side lengths are a, b, and c.
a + b > c
a + c > b
b+ c > a

So:
Lets test answer choice A.

The sides will then be: 34, 12, and 21

34 + 12 > 21 -> 46 > 12 True
12 + 21 > 34 -> 33 > 34 False

A is not the correct answer choice.

Lets try answer choice B.

The sides for this would be: 34, 12, and 30

34 + 12 > 30 -> 46 > 30 True
12 + 30 > 34 -> 42 > 34 True
30 + 12 > 34 -> 42 > 34 True

So B is correct.

Lets try C to make sure.

The side lengths would be: 34, 12, and 46

34 + 12 > 46 -> 46 > 46 False

So C is wrong.

Lets just make sure D is also wrong, and then we will know for sure if B is the answer :)

Side lengths of answer choice D: 34, 12, and 50

34 + 12 > 50 -> 46 > 50 False

So B is indeed our answer. :)

Another way to solve it is to:

We are given side lengths of 34 and 12.

That means the other side has to be greater than the different of 34 and 12 and less than the sum of 34 and 12.

Lets say that c is the third side, then:

34 -12 < c < 34 + 12
22 < c < 46

And by looking at this range, and the answer choices we know that B) 30 is the answer because the others are at the border and since it isn't greater than or equal to/less than or equal to, we can not include it.Or either the answer choices are out of the range.

So the final answer is \boxed{\bf{B)~30~cm}}
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NISA [10]
10x^2-6x^2 = 4x^2
-64-36 = 100
4x^2 -100 = 0
(2x -10)(2x+10)
X = 2/10 and x = - 2/10
5 0
3 years ago
Omar works as a tutor for $15 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 83 hours at his
Alborosie

Answer: 8t+581

Step-by-step explanation:

<h3> The complete exercise is: "Omar works as a tutor for $15 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 83 hours at his two jobs. Let "t" be the number of hours Omar worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month."</h3><h3 />

Let be "t" the number of hours Omar worked as a tutor this month and "w" the number of hours Omar worked as a waiter this month.

Based on the data given in the exercise, you know that Omar worked a combined total of 83 hours this month.

Then, you can represent the number of hours he worked as a waiter this month with this equation:

w=83-t

Since he earns  $15 per hour working has a tutor and $7 per hour working as a waiter, you can write the following expresion to represent the total money earned:

15t+7w

Since w=83-t, you can substitute it into the expression and then simplify it in order to find the final expression that represents the total amount of money Omar earned this month.

This is:

15t+7(83-t)=15t+581-7t=8t+581

4 0
3 years ago
18
Cloud [144]

Answer: 100

5

Step-by-step explanation:

a) The mean of a normal distribution is also the median. Half the population will have values above the mean. Half of 200 is 100, so ...

... 100 students will have grades above 70%.

b) 84% is 14% above the mean. Each 7% is 1 standard deviation, so 14% is 2 standard deviations above the mean. The empirical rule tells you 95% of the population is within 2 standard deviations of the mean, so about 5% of students (10 students) got grades higher than 84% or lower than 56%. The normal distribution is symmetrical, so we expect about 5 students in each range.

... about 5 students will have grades above 84%.

3 0
3 years ago
The owner of a hot dog stand receives a loan of $3,750 at 8.25% for 9 months. find the amount of simple interest.(round to the n
Mkey [24]
Hello! The formula for simple interest is prt. That means you multiply the principal (initial amount) by the rate (simple interest percentage), by the amount of time (could be in months or years). So, the loan is $3,750 and the rate is 8.25% for 9 months. 9 months is 3/4 of the year, because there are 12 months in 1 year and 9/12 is 0.75. Let's multiply. 3,750 * 8.25% (0.0825) is 309.375 Now, multiply that number by 0.75 to get 232.03125 or 232.03 when rounded to the nearest hundredth (cent). The amount of simple interest is $232.03.
7 0
3 years ago
What is 2 X (6+ 2 + 8) -4
VladimirAG [237]

Answer:

The correct answer is 32x - 4

Step-by-step explanation:

1) Simplify 6 + 2 to 8.

2x(8 + 8) - 4

2) Simplify 8 + 8 to 16.

2x \times 16 - 4

3) Simplify 2x × 16 to 32x.

32x - 4

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>32x</u><u> </u><u>-</u><u> </u><u>4</u>.

4 0
3 years ago
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