How can I solve these problems

Mathematics

2 answers:

telo118 [61]3 years ago

8 0

For the first 6 problems you need to know that all the angles in a triangle are equal to 180°.

for example: #1

60 + 75 + x = 180
x = 180 - (60 + 75)
x = 180 - 135
x = 45°

for numbers 7 and 8, you just need to know that vertical angles are equal to each other.

for example: #7

3x = 45°
x = 45 ÷ 3
x = 15°

for number 9, you need to know that those to angles add up to give you 180° because lines are 180°.

for example: #9

5x + 12 + 68 = 180°
5x + 80 = 180
5x = 180 - 80
5x = 100
x = 100 ÷ 5
x = 20°

I really hope that this made sense to you and that this actually helped you.

KATRIN_1 [288]3 years ago

4 0

Answer:

Step-by-step explanation:

Easy the three angles of a triangle equal 180 degrees

so 60+75 = 135 --> 180-135=

1) 145

2) 35

3) no since the tops a 100 and its a Isosceles triangle two corners left it be 40 for each corner

4) 34 for both x's cause 34+34+112. = 180

5) 180- 120= 60- 10 = 50/4 is (12.5)= x

6) x = 15 cause it be 120- 60 to get 60

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Every set of three points must be collinear.

maria [59]

Answer:

I suppose you're trying to make a triangle of some sort on a plane! So, in this case, yes the three points would reside all on the same plane. Making all three of them collinear.

3 0

3 years ago

In how many different ways can 2/15 be represented as 1/a+1/b, if a and b are positive integers with a greater than or equal to

Dmitrij [34]

Answer:

There are three possible combinations of positive integers such that a > b:

(1) a = 15 and b = 15

(2) a = 20 and b = 12

(3) a = 45 and b = 9

Step-by-step explanation:

Notice that the possible factors (different from "1") of the denominator "15" are: 3, 5, and 15.

The answer for the case a = 15 and b = 15 is obvious since :

$\frac{1}{15} + \frac{1}{15} = \frac{2}{15}$

Then the possibility of a multiple of 5 for one of the denominators (let's say 5*n) and a multiple of 3 (let's say 3*m)for the other one gives the general equation:

$\frac{1}{5n} +\frac{1}{3m} =\frac{2}{15}$

which should verify the following as we try to solve for one of the unknowns multiplicative factors which by the way have to be positive for the requirement given in the problem:

$\frac{5n+3m}{15mn} =\frac{2}{15}\\\frac{5n+3m}{mn} =\frac{2}{1}\\5n+3m=2mn\\\frac{5n+3m}{mn} =2\\\frac{5}{m} +\frac{3}{n} =2\\\frac{5}{m}=2-\frac{3}{n}$

This last equation is very simple to analyze using integer values for "n" which would render a positive value on the right hand side, and then check from that set the ones that give an integer for the value "m".

Those found were:

For n=3, and m=5, a=15, and b=15 (the obvious solution discussed above)

$\frac{1}{15} +\frac{1}{15}=\frac{2}{15}$