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DiKsa [7]
3 years ago
5

Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$. give all points where they intersect. list the p

oints in order of increasing $x$-coordinate, separated by semicolons.
Mathematics
2 answers:
katovenus [111]3 years ago
8 0
(-2,18):(8,38) Set them equal to each other you get, x^2-6x-16=0, you can factor to get, (x-8)(x+2) to get solutions 8,2 for the x values then plug in for y values.
snow_lady [41]3 years ago
6 0

Answer:

(-2, 18) and (8, 38)

Step-by-step explanation:

First, set the two equations equal to each other to get $2x^2-10x-10=x^2-4x+6$. Combine like terms to get $x^2-6x=16$. To complete the square, we need to add $\left(\dfrac{6}{2}\right)^2=9$ to both sides, giving $(x-3)^2=16+9=25$.

So we have $x-3=\pm5$. Solving for $x$ gives us $x=-2$ or $8$. Using these in our original parabolas, we find the points of intersection to be $\boxed{(-2,18)}$ and $\boxed{(8,38)}$.

Credit: AoPs

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48, -96, 192, -384, 768, etc.

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3 years ago
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108

Step-by-step explanation:

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3 years ago
Let the function f be defined as f(x)= 5x^2 - 7(4x+3). What is the value of f(3)
Katen [24]

Answer:

f(x) = -60 is your answer

Step-by-step explanation:

Plug in 3 for x

f(x) = 5x² - 7(4x + 3)

f(x) = 5(3²) - 7(4(3) + 3)

Follow PEMDAS. First, solve the parenthesis

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4 0
3 years ago
Plz help I’ll pay I promise this is timed
Wewaii [24]

Answer:

you can say u are mutiplying them by two each times see

2:16

4:32

6:48

8:64

10:80

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Step-by-step explanation:

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3 years ago
Sue initially has 5 hours of pop music and 4 hours of classical music in her collection. Every month onwards, the hours of pop m
Snezhnost [94]
<h2>Answer</h2>

f(x) = 5(1.25)x + 4

<h2>Explanation</h2>

To solve this, we are going to use the standard exponential equation:

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a is the initial amount

b is the growth rate in decimal form

x is the time (in months for our case)

Since the hours of classic music remain constant, we just need to add them at the end. We know form our problem that Sue initially has 5 hours of pop, so a=5; we also know that every month onward, the hours of pop music in her collection is 25% more than what she had the previous month, so b=\frac{25}{100} =0.25. Now let's replace the values in our function:

f(x)=a(1+b)^x

f(x)=5(1+0.25)^x

f(x)=5(1.25)^x

Now we can add the hours of classical music to complete our function:

f(x)=5(1.25)^x+5

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3 years ago
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