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3 years ago

5

When a number is decreased by 20% of itself, the result is 16. what is the number?

1 answer:

kati45 [8]3 years ago

4 0

The answer will be 20. 16=80%. 1=0.2%.100%=20

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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:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

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3 years ago

For the cereal box, name each of the following

zaharov [31]

Answer:

AB , AD , EF , EH all intersect AE ⇒ answer (c)

Step-by-step explanation:

∵ AE segment passing through A and E

∴ Each segment passing through A and E intersects AE

∴ AB intersects AE at A

∴ AD intersects AE at A

∴ EF intersects AE at E

∴ EH intersects AE at E

∴ The answer is (c)

Step-by-step explanation:

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A toy cannon ball is launch from a cannon on top of a platform the equation h(t)= -5t + 14t + 2 gives the height h, in meter, of

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Answer:

<h2>how long air in the earth ok good</h2>

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Read 2 more answers

12 is what percent of 96

AysviL [449]

12.5
12=96x/100
x=(100*12)/96
x=1200/96
x=12.5

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Your class hopes to collect at least 325 cans of food for the annual food drive there were 132 cans donated the first week in th

malfutka [58]

132+(132+146)=410 cans

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