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Flura [38]
3 years ago
15

**PLEASE HELP ASAP** Betsy is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?

Mathematics
1 answer:
Nina [5.8K]3 years ago
5 0
We analyze the chart and observe that the linear function is y=x, since this relation holds for all values in the table.  Drawing this line over the quadratic function shows that they intersect twice, at both the positive and negative x-coordinates.

This is by far the easiest way to solve this problem, but if you're interested in learning how to do it algebraically, read on!  To prove this more rigorously, we can find that the equation of the parabola is y=\frac13 x^2 - 2.  Substituting in y=x, we find that the intersection points occur where \frac13 x^2 - 2 = x, or \frac13 x^2 - x - 2 = 0, or x^2 - 3x - 6 = 0.

This equation doesn't factor nicely, so we use the quadratic formula to learn that x = \frac{3 \pm \sqrt{3^2 - 4 \cdot 1 \cdot (-6)}}{2} = \frac{3 \pm \sqrt{33}}{2}.  Hence, the x-coordinates of the intersection points are \frac{3 + \sqrt{33}}{2}, which is positive, and \frac{3 - \sqrt{33}}{2}, which is negative.  This proves that there are intersection points on both ends of the axis.
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Anthony will be competing in a body building competition in 12 months. he initially weighs 160 pounds and by the end of 12 month
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Is (9, 1) a solution to the equation y = x - 8? <br> yes<br> or no
velikii [3]

Answer:

yes

Step-by-step explanation:

y = 9

x = 1

1 = 9 - 8

7 0
3 years ago
The sides of a triangle are (x+3), (x+4), and (x+7). Find the value of x if the perimeter of the triangle is 104
timurjin [86]

Answer:

x = 30

Step-by-step explanation:

The perimeter is the sum of all of the sides of a shape. Therefore, because the sum is equivalent to 104 inches and we are given the lengths of all three sides, we can add the three sides together and set them equal to 104 in order to solve for x.

(x + 3) + (x + 4) + (x + 7) = 104 Drop the parentheses.

x + 3 + x + 4 + x + 7 = 104 Combine like terms (variables first!).

3x + 3 + 4 + 7 = 104 Now, combine constant terms.

3x + 14 = 104 Subtract 14 from both sides.

3x = 90 Divide by 3 on both sides of the equation.

x = 30

6 0
3 years ago
A standard deck of 52 cards contains 4 suits: hearts, clubs, diamonds, and spades. Each suit contains cards numbered 2 through 1
Vesnalui [34]

Answer:

2 / 13

Step-by-step explanation:

Number of cards in a standard deck = 52

Number of 4's = 4 ( 1 for each suit)

Number of 6's = 4 (1 for each suit)

Probability, P = required outcome / Total possible outcomes

P(a 4) = 4 / 52 = 1/ 13

P(a 6) = 4 /52 = 1/13

Probability of either a 4 or a 6

P(a 4) + P(a 6)

1/13 + 1/13

= 2 / 13

3 0
3 years ago
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