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3 years ago

12

3. POPULATION The population of Ghostown, USA is decreasing at a rate of

1 answer:

Strike441 [17]3 years ago

8 0

277 years because 831 people/3 people per year = 277 years

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On Thursday the basketball coach ordered 12 pizzas for 36 players who came in for practice. How many pizzas does the coach need

Paraphin [41]

Answer:16

Step-by-step explanation:Next day there will be (36+12) or 48 players.

For 36 players 12 pizzas are needed

For 1 player 12/36 pizzas are needed

For 48 players 12/36*48 or 16 pizzas are needed

3 0

3 years ago

Consider the function f(x) = 20/√x and its second-degree polynomial P2 (x) = 20 - 10(x-1) + 7.5(x-1)^2 at x=0.8. Compute the val

krok68 [10]

Answer:

$f (0.8) = 22.3607$ and $P_{2} (0.8) = 22.300$ .

Step-by-step explanation:

According to the statement, $f (x) = \frac{20}{\sqrt{x}}$ and $P_{2}(x) = 20 - 10 (x-1) + 7.5 (x-1) ^ 2$ . Based on these definitions, at $x=0.8$ produce:

$f (0.8) = \frac{20}{\sqrt {0.8}} = 22.3607$ . On the other hand, you have to:

$P_{2} (0.8) = 20 - 10 (0.8 -1) +7.5 (0.8 -1)^2$

$P_{2} (0.8) = 20 - 10 (-0.2) +7.5 (-0.2)^2 = 22.300$

Then, it can be affirmed that $f (0.8) = 22.3607$ and $P_{2} (0.8) = 22.300$ .

3 0

4 years ago

A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

<u>For the first parenthesis:</u>

$x^{2}+6x+b^{2}$

We can rewrite this as:

$x^{2}+2(3)x+b^{2}$

Hence in this case $b=3$ and $b^{2}=9$ :

$x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}$

<u>For the second parenthesis:</u>

$y^{2}-8y+b^{2}$

We can rewrite this as:

$y^{2}-2(4)y+b^{2}$

Hence in this case $b=-3$ and $b^{2}=9$ :

$y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}$

Then, equation (5) is rewritten as follows:

$(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16$ (6)

<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>

Rearranging:

$(x-3)^{2}+(y-4)^{2}=100$ (7)

At this point we have the circle equation in the center radius form $(x-h)^{2} +(y-k)^{2}=r^{2}$

Hence:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

8 0

4 years ago

CAN SOMEONE PLEASE HELP

morpeh [17]

Answer:

Step-by-step explanation:

5 0

2 years ago

skelet666 [1.2K]

Answer:

See explanation

Step-by-step explanation:

You forgot to give the coordinates of C.

Note that, the mapping for 90° clockwise rotation around the origin is given by:

$(x,y)\to (-y,x)$

Assuming the coordinates of C were (-6,6), then the coordinates of C after a 90° clockwise rotation

around the origin is (-6,-6)

8 0

3 years ago