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Ivan
2 years ago
12

Otis has $6.72, and he wants to buy some pencils that cost $1.12 each. How many pencils can he buy?

Mathematics
1 answer:
eduard2 years ago
3 0

Answer:

Otis can buy 6 pencils...

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Use the functions to answer the question.
Lelechka [254]

Answer:

3 and 9

if f(x)=x^2+13 and g(x)=12x-14

Step-by-step explanation:

So when we are looking for the intersection of two functions, we are trying to figure out when they are the same.  When you think same, you should think equal (=).

So we want to find when f(x)=g(x) for x.

f(x)=g(x)

x^2+13=12x-14

Let's get everything to one side.

Subtracting 12x and adding 14 to both sides.

x^2+13+14-12x=0

I'm going to reorder the left hand side and also simplify the 13+14 part:

x^2-12x+27=0

Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.

Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.

So the factored form of our equation is

(x-3)(x-9)=0

Since the product is 0, then at least one of the factors must be 0.

So we want to solve both x-3=0 and x-9=0.

x-3=0 can be solved by adding 3 on both sides. This gives us x=3.

x-9=9 can be solved by adding 9 on both sides. This gives us x=9.

The intersection of f and g happens at x=3 or x=9.

5 0
3 years ago
Read 2 more answers
Toney tossed a coin off a bridge. The path of the coin's height can modeled by the equation below. h(t) = − 16 t^2 + 40 t + 20 W
Snowcat [4.5K]

Answer:80

Step-by-step explanation:

6 0
3 years ago
Which expression is equivalent to
lions [1.4K]

Answer:

12x⁶+24x⁵-180x⁴/ 30x³+240x²+450x

Step-by-step explanation:

(x-3)(x+5)=x²+2x-15

12x⁴(x²+2x-15)= 12x⁶+24x⁵-180x⁴

(x+3)(x+5)=x²+8x+15

30x(x²+8x+15)= 30x³+240x²+450x

4 0
3 years ago
Which equation fits?
Anuta_ua [19.1K]
The equation that fits is y=3x+1
7 0
3 years ago
Read 2 more answers
30 POINTS AVAILABLE
kherson [118]

Answer:

\large\boxed{(x-2)^2+(y-1)^2=34}

Step-by-step explanation:

The equation of a circle in standard form:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)

Substitute:

h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute the coordinates of the points (2, 1) and (5, -4):

r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}

Finally we have:

(x-2)^2+(y-1)^2=(\sqrt{34})^2

3 0
3 years ago
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