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Tresset [83]
3 years ago
12

I need help solving this

Mathematics
1 answer:
pentagon [3]3 years ago
5 0
Y=mx+b where m=slope=(dy/dx) and b=y-intercept (value of y when x=0)

You have two points...(1,-2),(3,2) so

m=(y2-y1)/(x2-x1)=(2--2)/(3-1)

m=4/2=2 now that you have the slope...

y=2x+b, you can use either point to solve for the y-intercept, I'll use (3,2)

2=2(3)+b

2=6+b

b=-4 so the line is:

y=2x-4
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Step-by-step explanation:

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Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.
laila [671]

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
  • if |a|< b then a<b or a>-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

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3 years ago
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Step-by-step explanation:

rate \:of \: driving \\  =  \frac{278}{4}  \\  = 69.5 \: mph

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