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4 years ago

Select the ordered pairs that represents a solution to the functions below. F(x)= - x^2 +5.F(x)=x^2+5.

Mathematics

1 answer:

svp [43]4 years ago

6 0

Answer:

(0,5)

Step-by-step explanation:

(1) y = -x² + 5

(2) y = x² + 5

2y =10 Added (1) and (2)

(3) y = 5 Divided each side by 2

5 = x² + 5 Substituted (3)into (2)

0 = x² Subtracted 5 from each side

x = 0 Took the square root of each side

The only ordered pair that represents a solution to both functions is (0, 5).

The graph of the second function is an upward-opening parabola (y = x²) translated up five units.

The graph of the first function is a downward-opening parabola (y = -x²) translated up five units.

The two graphs meet at their common vertex, (0, 5).

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3 years ago

#3 (1 pt) A certain baseball card is very rare and is currently worth $2000. If the price of this card increases by 3% a year,

Galina-37 [17]

Answer:

$2000x(1.03)ˣ

Step-by-step explanation:

This is known as compound interest.

100% + 3% = 103%, so we put this into a decimal: 1.03

We now put this into the equation:

$2000x(1.03)ˣ

If you want to work out the price after, say 3 years, then you would change x to 3, so the equation becomes

$2000x(1.03)³

You can then use a calculator to work out the answer.

6 0

3 years ago

Help help I don’t really get this???

insens350 [35]

Answer:

Question 4: $y=\displaystyle -\frac{4}{5}x$

Question 5: $y=-5x-3$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope of the line and b is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).

Question 4

1) Determine the slope (m)

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$ where two points that pass through the line are $(x_1,y_1)$ and $(x_2,y_2)$

In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:

$\displaystyle m=\frac{-4-4}{5-(-5)}\\\\\displaystyle m=\frac{-4-4}{5+5}\\\\\displaystyle m=\frac{-8}{10}\\\\\displaystyle m=-\frac{4}{5}$

Therefore, the slope of the line is $\displaystyle -\frac{4}{5}$ . Plug this into $y=mx+b$ as the slope (m):

$y=\displaystyle -\frac{4}{5}x+b$

2) Determine the y-intercept (b)

On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (b) is 0. Plug this into $y=\displaystyle -\frac{4}{5}x+b$ :

$y=\displaystyle -\frac{4}{5}x+0\\\\y=\displaystyle -\frac{4}{5}x$

Question 5

1) Determine the slope (m)

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:

$\displaystyle m=\frac{-3-2}{0-(-1)}\\\\\displaystyle m=\frac{-3-2}{0+1}\\\\\displaystyle m=\frac{-5}{1}\\\\m=-5$

Therefore, the slope is -5. Plug this into $y=mx+b$ :

$y=-5x+b$

2) Determine the y-intercept (b)

On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (b) is -3. Plug this into $y=-5x+b$ :

$y=-5x+(-3)\\y=-5x-3$