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Triss [41]
2 years ago
11

8. Find the measures of the three angles of a triangle if the sum of the measure of the first angle and three times

Mathematics
1 answer:
scoray [572]2 years ago
6 0

Answer:

C is the answer

Step-by-step explanation:

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Find five consecutive integers such that: "the sum of the first and 4 times the third is equal to 60 less than 3 times the sum o
Monica [59]

Consecutive integers are integers that come one after another in order. For example, 2, 3, and 4 are all consecutive integers, as well as 100, 101, and 102. In general, if we have some integer n, the consecutive integers following it will be n + 1, n + 2, n + 3, etc. Here, we have five. If we

  • Call the first integer n,
  • Then the second integer will be n + 1,
  • The third will be n + 2,
  • The fourth will be n + 3,
  • And the fifth will be n + 4.

Now, let's break down the equation in English. We'll use #1, #2, #3, #4, and #5 as stand-ins for the five integers just so we can get things set up, then we'll replace them with the expressions we came up with in the first part. Starting from the beginning of the statement, let's translate words to symbols:

  • "The sum of the first and 4 times the third" → #1 + 4 × #3
  • "is equal to" → = (maybe obvious, but still!)
  • "60 less than 3 times the sum of the second, fourth, and fifth" → 3 × (#2 + #4 + #5) - 60

Putting that all together, we get the equation

#1 + 4 × #3 = 3 × (#2 + #4 + #5) - 60.

Replacing our stand-ins for the expressions we came up with, it becomes

n + 4(n + 2) = 3[(n + 1) + (n + 3) + (n + 4)] - 60

We can now start to simplify our equation to find n (the first integer) and the rest will follow easily from that. I'll start by focusing on the left side. We can distribute and combine like terms like so:

n + 4(n+2) = n + 4n + 8 = 5n + 8

Dealing with the right, we can get rid of some redundant parentheses and carry out the same process:

3[(n + 1) + (n + 3) + (n + 4)] - 60 = 3(n + 1 + n + 3 + n + 4) - 60

= 3(3n + 8) - 60 = 9n + 24 - 60 = 9n - 36

Our simplified equation now becomes

5n + 8 = 9n - 36.

Subtracting 5n from either side:

8 = 4n - 36

Adding 36 to either side:

44 = 4n

And dividing either side by 4:

11 = n.

We now know that our first integer is 11, which means that our 5 consecutive integers are 11, 12, 13, 14, and 15.

7 0
3 years ago
Satoranaing
Natali [406]

The statements that are true about the given points on the line are; Options B, C and D

<h3>How to identify points on a Plane?</h3>

A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.

Let us check each of the given options;

A) There are exactly two planes that contain points A, B, and F;

If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.

Since we can't make two planes with them, then the statement is false.

B) There is exactly one plane that contains points E, F, and B;

Due to the same reasoning in part A, the statement is true assuming the points are not collinear.

C) The line that can be drawn through points C and G would lie in plane X;

The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.

D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.

E) The only points that can lie on plane Y are points E and F.

This statement is false because infinite points can lie on a plane.

Read more about plane points at; brainly.com/question/11958640

#SPJ1

4 0
2 years ago
Question 1
8090 [49]

Question 1- A

Question 2- C

Question 3- B

Question 4- C

Question 5- A

4 0
3 years ago
What set of fractions is ordered from least to greatest? A) 2/5,1/4,3/8 B) 3/8,2/5,1/4 C) 1/4,3/8,2/5 D) 3/8,1/4,2/5
LenaWriter [7]

Answer:

C) 1/4,3/8,2/5

Step-by-step explanation:

First of all, let's rewrite all the fractions listed as decimal numbers:

\frac{2}{5}=0.400

\frac{1}{4}=0.250

\frac{3}{8}=0.375

So the correct order from least to greatest should be

0.250, 0.375, 0.400

Which corresponds in fractional form to

1/4, 3/8, 2/5

So the correct option is

C) 1/4,3/8,2/5

6 0
3 years ago
Find the values of x and y.
rusak2 [61]

Triangle = 180

180 - 40 ( Because acute angle)


130 ÷ (3+5) = 16.25


3 x 16.25 = 48.75

5 x 16.25 = 81.75




X = 81.25

Y = 48.75

3 0
3 years ago
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