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rewona [7]
3 years ago
9

Use the line graph to solve.

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0
The answer is c. 0.10. Week 4 is plotted at 0.35 and Week 2 is plotted at 0.25. Difference means subtract. 0.35 - 0.25 = 0.10. Hope this helps!
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Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply.
statuscvo [17]

Answer:

A, D, E are true

Step-by-step explanation:

You have to complete the square to prove A.  Do this by first setting the function equal to 0, then moving the 5 to the other side.

x^2-8x=-5

Now we can complete the square.  Take half the linear term, square it, and add it to both sides.  Our linear term is 8 (from the -8x).  Half of 8 is 4, and 4 squared is 16.  So we add 16 to both sides.

(x^2-8x+16)=-5+16

We will do the addition on the right, no big deal.  On the left, however, what we have done in the process of completing the square is to create a perfect square binomial, which gives us the h coordinate of the vertex.  We will rewrite with that perfect square on the left and the addition done on the right,

(x-4)^2=11

Now we will move the 11 back over, which gives us the k coordinate of the vertex.

(x-4)^2-11=y

From this you can see that A is correct.

Also we can see that the vertex of this parabola is (4, -11), which is why B is NOT correct.

The axis of symmetry is also found in the h value.  This is, by definition, a positive x-squared parabola (opens upwards), so its axis of symmetry will be an "x = " equation.  In the case of this type of parabola, that "x = " will always be equal to the h value.  So the axis of symmetry is

x = 4, which is why C is NOT correct, either.

We can find the y-intercept of the function by going back to the standard form of the parabola (NOT the vertex form we found by completing the square) and sub in a 0 for x.  When we do that, and then solve for y, we find that when x = 0, y = 5.  So the y-intercept is (0, 5).

From this you can see that D is also correct.

To determine if the parabola has real solutions (meaning it will go through the x-axis twice), you can plug it into the quadratic formula to find these values of x.  I just plugged the formula into my graphing calculator and graphed it to see that it did, indeed, go through the x-axis twice.  Just so you know, the values of x where the function go through are (.6833752, 0) and (7.3166248, 0).  That's why you need the quadratic formula to find these values.

7 0
3 years ago
Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 times the smaller. If 3 times the larg
marshall27 [118]

Answer:

8 and -2

Step-by-step explanation:

Let the numbers be l and s.

We have equations:

l = 5s + 18

3l + 4s = 16

Solve for s by substituting l into the second equation:

3(5s + 18) + 4s = 16

15s + 54 + 4s = 16

19s = 16 - 54

19s = -38

s = -38/19

s = -2

Find the value of l:

l = 5(-2) + 18

l = -10 + 18

l = 8

3 0
2 years ago
Help?<br><br> a) 2/10 + 8/100<br> b) 13/100 + 4/10<br> c) 6/10 + 39/100<br> D) 70/100 + 3/10
Leni [432]

\green{––––––––––––––––––––––––––––––}

\huge\red{\boxed{\tt{{«ANSWER»}}}}

  • A) 2/10 + 8/100 = <u>0</u><u>.</u><u>2</u><u>8</u>
  • B) 13/100 + 4/10 = <u>0</u><u>.</u><u>5</u><u>3</u>
  • C) 6/10 + 39/100 = <u>0</u><u>.</u><u>9</u><u>9</u>
  • D) 70/100 + 3/10 = <u>1</u>

<u>\green{––––––––––––––––––––––––––––––}</u>

<em><u>#</u></em><em><u>carry </u></em><em><u>on </u></em><em><u>learning </u></em><u><</u><u>3</u>

5 0
2 years ago
Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistent
Eddi Din [679]

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

x = 13.96

x = 14

mathew needs to get 14 gallons of gasoline.

5 0
3 years ago
Which is the value of x in the equation?<br> 4(x-3) = 40
mario62 [17]

Answer:14

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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