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ki77a [65]
3 years ago
5

The three angles of a triangle measure 2x – 6, 3x + 5, and 2x + 20. What is the measure of the smallest angle in degrees

Mathematics
1 answer:
Radda [10]3 years ago
8 0

Answer:

Smallest angle = 40

Step-by-step explanation:

Angle sum property:Sum of all three angles of triangle is 180

2x - 6 + 3x + 5 + 2x + 20 = 180   {Combine like terms}

2x + 3x + 2x - 6 + 5 + 20 = 180

                     7x  + 19       = 180            {Subtract 19 from both sides}

                                  7x = 180 - 19

                                  7x = 161               {Divide both sides by 7}

                                    x = 161/7

x = 23

2x - 6 = 2*23 - 6 = 46 - 6 = 40

3x + 5 = 3*23 + 5 = 69 + 5 = 74

2x + 20 = 2*23 + 20 = 46 + 20 = 66

Smallest angle = 40

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Radda [10]

Answer:

1. Your answer would be C) 2√3-5√2.

2. Your answer would be -39.7i.

3. Your answer would be -1.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
HELP HELP HELPH EPLHEPLHEPLHEPLHEPLEP
Soloha48 [4]

<u>Answers:</u>

1a) y=-10/3x+90

1b) 20

1c) -18

2a) 2.8

2b) How much the heights of five basketball players vary from the average height.

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<u>Explanations:</u>

<u>1a)</u> The trend line is linear, so we just need to find the slope and y-intercept to find an equation for it. Our y-intercept is (0,90), or 90, and our slope is -10/3. <em>Our equation is now y=-10/3x+90.</em>

<u>1b) </u>To find when x=21, we plug 21 into our equation where the x is. Now we do the math.

y=-10/3(21)+90 (plug in)

y=-70+90 (simplify by multiplying -10/3 by 21)

y=20 (simplify by adding -70 to 90)

<em>Therefore, we can predict that when x is 21, y is 20.</em>

<u>1c) </u>To find when y=150, we plug 150 into our equation where the y is. Now we do some more math.

150=-10/3x+90 (plug in)

60=-10/3x (subtract 90 from both sides

-18=x (divide both sides by -10/3)

<em>Therefore, we can predict that when y is 150, x is -18.</em>

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<u>2a) </u>The mean absolute deviation (or MAD for short) of a data set is calculated as such:

<u>Step 1) </u>Find the mean (average) by finding the sum of the data values, then dividing the sum of the data values by the number of data values. In this case, we have the numbers 65, 58, 64, 61, and 67, which add up to 315. The data set has 5 numbers, so we divide our sum of 315 by 5 to get 63. <em>Therefore, our mean is 63.</em>

<u>Step 2) </u>Find the absolute value of the distance between each data value and the mean. In this case, we find out how far away each data value is from 63, our mean.  To do this, we subtract 63 from each number.

65-63=2

58-63=-5

64-63=1

61-63=-2

67-63=4

Some of these values are negative, but we're using absolute value so they all become positive. <em>We now have a new set of values: 2, 5, 1, 2, and 4.</em>

<u>Step 3)</u> Finally, we calculate the mean of our new set of values. In this case, we will add up 2, 5, 1, 2, and 4 to get 14 and divide by 5 to get our MAD of 2.8. <em>Therefore, the MAD (and the answer to problem 2a) is 2.8.</em>

<u>2b)</u> Now we just find out what the MAD means in this context. The MAD always is a measure of variance in a data set. In this context, it's describing how much the heights (in inches) of five people on a basketball team vary from the average height.

Hope this helps!

3 0
3 years ago
Which represents a total cost of 2 dance tickets at a price of c for each, less a one-time $5 discount?
Eduardwww [97]

The statement is represented as 2(c- 5). Option D

<h3>What are algebraic expressions?</h3>

Algebraic expressions are expressions consisting of variables, terms, factors, and constants.

They are also made up of mathematical operations such as addition, bracket, subtraction, division, multiplication, etc

From the information given, we have;

  • total cost of 2 dance tickets
  • price of c for each, less a one-time $5 discount

Expressed as;

2(c- 5)

Thus, the statement is represented as 2(c- 5). Option D

Learn more about algebraic expressions here:

brainly.com/question/4344214

#SPJ1

7 0
1 year ago
Suppose that the functions r and a are defined for all real numbers x as follows. r(x)=2x-1 S(x)=5x write the expressions for (r
NeTakaya

\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}

<h2>Explanation:</h2>

In this exercise, we have the following functions:

r(x)=2x-1 \\ \\ s(x)=5x

And they are defined for all real numbers x. So we have to write the following expressions:

First expression:

(r-s)(x)

That is, we subtract s(x) from r(x):

(r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}

Second expression:

(r\cdot s)(x)

That is, we get the product of s(x) and r(x):

(r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}

Third expression:

Here we need to evaluate:

(r+s)(-2)

First of all, we find the sum of functions r(x) and s(x):

(r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1

Finally, substituting x = -2:

(r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}

<h2>Learn more: </h2>

Parabola: brainly.com/question/12178203

#LearnWithBrainly

5 0
3 years ago
Simplify. <br><br> 54+4(34−12)2<br><br><br><br> Enter your answer in the box.
gtnhenbr [62]

Answer:

230

Step-by-step explanation:

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54+88×2

54+176

230

3 0
2 years ago
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