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KATRIN_1 [288]
2 years ago
14

The sum of two numbers is 39. the second number is 6 more than half of the first number. let a represent the firstnumber and let

b represent the second number. what are the two numbers? use the table to answer the question.
Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
6 0

Answer:

  • a = 22
  • b = 17

Step-by-step explanation:

Givens

Let a = the first number

Let b = the second number

Equations

a + b = 39

b = 1/2 * a + 6

Put the second equation into the first one

a + 1/2 * a +   6 = 39                  Simplify the left.

(3/2)a + 6 = 39                           Subtract 6 from both sides

(3/2)a + 6 - 6 = 39 - 6                Combine

(3/2)a = 33                                  Multiply both sides by 2

3a = 33*2

3a = 66                                       Divide both sides by 3

3a/3 = 66/3

a = 22

b = 1/2 a + 6

a = 22

b = 1/2 * 22 + 6

b = 11 + 6

b = 17

Check

22 + 17 = 39

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After 4 new students joined a class, the class had 32 students. Which equation can be used to find n, the number in the class be
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Answer:

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Therefore, the initial number was 28 and the equation is n+4=32

Since no choices were provided, the equation that can be modified is n+4=32

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What is %90, percent of 20?
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The dot plot below shows the number of passengers in some cars:
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<h2>Answer:</h2>

The statement which best describe the shape of the data is:

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1.If a line with a slope of -3 crosses the y-axis at (0,7), what is the equation of the line?
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y = mx + b    "m" is the slope, "b" is the y-intercept (the y value when x = 0)


1. slope: -3

y-intercept: 7

y = -3x + 7

Your answer is B

y + 3x = 7   Subtract 3x on both sides

y = -3x + 7


2. y + 9(x + 3) = 0     Multiply/distribute 9 into (x + 3)

y + 9x + 27 = 0      Subtract 9x and 27 on both sides to get "y" by itself

y = -9x - 27

slope: -9

y-intercept: -27 or (0,-27)

Your answer is D


3. Point-slope form:   y - y₁ = m(x - x₁)

slope: -11

(x₁ , y₁) = (-5, 7)


y - 7 = -11(x - (-5))  The two negative signs becomes a positive

y - 7 = -11(x + 5)

Your answer is C


4. For this question, I think you get it from point-slope form to slope-intercept form (I'm not sure, but you still get the same answer if you just do slope-intercept form)

slope: -4

(x₁ , y₁) = (2, -8)


y - y₁ = m(x - x₁)

y - (-8) = -4(x - 2)

y + 8 = -4(x - 2)     Multiply/distribute -4 into (x - 2)

y + 8 = -4x + 8       Subtract 8 on both sides to get "y" by itself

y = -4x

Your answer is A

3 0
3 years ago
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