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3 years ago

The table below shows an inequality and a number by which to divide both sides.

Mathematics

2 answers:

IRISSAK [1]3 years ago

6 0

Answer:

i dont see a table

Step-by-step explanation:

Murljashka [212]3 years ago

4 0

I need a table to help you solve this

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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 $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

For the first parenthesis:

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

We can rewrite this as:

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

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

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

For the second parenthesis:

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

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)

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

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

3 years ago

Kwame borrowed 300 Ghana cedis from a finance company. He repaid the loan in six equal installment 55 Ghana cedis. How much inte

Bumek [7]

Answer:

The amount of interest, he payed is 30 Ghana Cedis

Step-by-step explanation:

The amount Kwame borrowed from the finance company, P = 300 Ghana Cedis

The amount he repaid in each installment, M = 55 Ghana Cedis

The number of installments with which he repaid the loan, n = 6 installments

The amount of interest, "i", he payed, is given by the following formula;

The amount of interest, he payed, i = M × n - P

Therefore, i = 55 × 6 - 300 = 30

The amount of interest, he payed = i = 30 Ghana Cedis.

3 0

3 years ago

A square has a maximum

Stolb23 [73]

Answer:

Step-by-step explanation:

Square: 4 equal sides

If x is one of the sides:

Perimeter: 4x

12: 4x

x=3

7 0

3 years ago

What is 2/3 + 1/6 ?

algol13

Answer:

5/6

Step-by-step explanation:

First: 2/3=4/6

Then: 4/6+1/6=5/6

6 0

3 years ago

Read 2 more answers

during a winter storm, the price of the road salt had a 230% increase write 230% as a mixed numberin simplest form

amid [387]

Answer:

2.3

Step-by-step explanation:

move the decimal to the right two times

8 0

3 years ago