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3 years ago

For 4-5, write each conditional in “if-then” format.

Mathematics

1 answer:

4vir4ik [10]3 years ago

6 0

Answer:

4. If the perpendicular lines for four right angles, then they have formed a parallelogram.

5. If the product of two odd integers is odd, then the problem is incorrect. (Not 100% sure on this one, sorry.)

6. The following statement is true

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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

Could u help me ? I really can’t figure this out it’s driving me crazy

Irina18 [472]

Answer:

The answer is 1

One

Uno

Aight nvm

By adding 5 to both side we will just get x2= -4+5

-4+5=1

7 0

3 years ago

If tan (t) = -1.4 what is the tan(-t) ???

Svetradugi [14.3K]

1.4 is the answer pretty sure

5 0

3 years ago

8) Carol earns $5.25 per hour. She worked 15 hours

brilliants [131]

the answer is $78.75 i did the math to this problem

5 0

3 years ago

The perimeter of a college athletic field is 100 meters and the length is 16 m more than the width. Find the length and the widt

Inga [223]

P=100
L=16+w
W=w
so we know that Perimeter is all the sides added so 2l+2w
so 100=(2(16+w))+(2(w))
100=32+2w+2w
100=32+4w
68=4w
w=17
so L=16+w therefore L=16+17 L=33
so L=33 and W=17

4 0

4 years ago