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3 years ago

Simplify the expression below. Show your Work.

Mathematics

1 answer:

lord [1]3 years ago

8 0

Answer:

7y + 24

Step-by-step explanation:

Think of the negative sign to the left of the parentheses as being -1. Then apply the distributive property. The effect of a negative sign to the left of parentheses or a 1 to the left of parentheses is that each term inside the parentheses changes sign.

-(-7y - 24) = -1(-7y - 24) = (-1)(-7y) - (-1)(24) = 7y - (-24) = 7y + 24

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lora16 [44]

0 bcz modulas function every negative no. in positive
therefore it becomes 6 - 6 I.e equal to 0

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3 years ago

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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:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

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3 years ago

Edmond and Karen were on a walk. It took them 35 minutes to reach their destination. They arrived at their destination at 1:40 P

Leviafan [203]

Answer:

1:05 p.m

Step-by-step explanation:

they took 35 minutes...... and they arrived at 1:40 p.m so 40-35= 5 = 1:05 p.m :)

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3 years ago

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Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equ

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The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 6, Z has the value 9.5. What

RideAnS [48]

Directly proportional to x

z=kx

And inversely proportional to y

z=kx/y we are given the point (x,y,z) of (3, 6, 9.5) so

9.5=3k/6 now multiply both sides by 6

57=3k divide both sides by 3

19=k so now that we know the constant of proportionality:

z=19x/y, and we want to solve for z when x=8 and y=12 so:

z=19(8)/12

z=12 2/3 exact

z≈12.667 (rounded to the nearest thousandth)

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2 years ago