What is the solution of each equation?


a
no solution
b
infinitely many solutions
c
8
d
-8

Answer:

[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]

And, the distance from P to (0, -2) will be:

[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]

So sum of the two distances must be 6. Therefore:

[tex]d_1+d_2=6[/tex]

Now, by substitution:

[tex](\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6[/tex]

Simplify. We can subtract the second term from the left:

[tex]\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}[/tex]

Square both sides:

[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]

We can cancel the x² terms and continue squaring:

[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]

We can divide both sides by -4:

[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]

Adding 9 to both sides yields:

[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]

And, we will square both sides one final time.

[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]

Distribute:

[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]

The 36y will cancel. So:

[tex]4y^2+81=9x^2+9y^2+36[/tex]

Subtracting 4y² and 36 from both sides yields:

[tex]9x^2+5y^2=45[/tex]

And dividing both sides by 45 produces:

[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

Answer:

Surface area of cuboid = 352 cm

Step-by-step explanation:

Given that:

Height of cuboid = 8 cm

Length of cuboid = 12 cm

Width of cuboid = 4 cm

Surface area = 2lw + 2lh + 2hw

Putting all the values;

Surface area = 2*12*4 + 2*12*8 + 2*8*4

Surface area = 96 + 192 + 64

Surface area = 352 cm

Hence,

Surface area of cuboid = 352 cm

Answer:

12

Step-by-step explanation:

4 pounds is 22 people

8 is 44

12 is 66

Answer:

20°,40°,75°

Step-by-step explanation:

Subtract the number from 90 and turn the difference to a degree

Answer:

180

Step-by-step explanation:

Step-by-step explanation:

For a quadratic equation to have no real roots, the discriminant b² - 4ac must be negative.

For px² + 8x + 2 = 0,

We have a = p, b = 8 and c = 2.

=> (8)² - 4(p)(2) < 0

=> 64 - 8p < 0

=> 8p > 64

=> p > 8

Hence the range for p is p > 8.

Answer:

maybe 68?

Step-by-step explanation:

Answer:

∠ AFE = 35°

Step-by-step explanation:

∠ EFD = ∠ BFC = 55° ( vertically opposite angles )

Since BD is a straight line , then

∠ EFD + ∠ AFE + AFB = 180°, that is

55° + ∠ AFE + 90° = 180

∠ AFE + 145° = 180° ( subtract 145° from both sides )

∠ AFE = 35°

Answer:

73 degrees

Step-by-step explanation:

Answer:

there aint no picture

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

(7 + 2x) / 3 = 5

Cross product

7 + 2x = 5 * 3

7 + 2x = 15

Subtract 7 from both sides

2x = 15 - 7

2x = 8

Divide both sides by 2

x = 8/2

x = 4

Answer:40

Step-by-step explanation:

100+10+10=3x

3x=120

Divide both sides by 3

X=40

Answer:

40

Step-by-step explanation:

add 100+10+10 and divide it by 3

Answer:

its false

Step-by-step explanation:

5+4-6=24

9-6=24

3=24 3 does not equal to 24 so its false

Answer:

The answer is 25

Step-by-step explanation:

6•5=30

30+20=50

50/-2=25

Answer:

no solutions

Step-by-step explanation:

i guess   im

Answer:

4

Step-by-step explanation:

It's a opposite of -4 so the opposite would be 4

Answer:

4

Step-by-step explanation:

The opposite of -4 is 4

In addition

The absolute value of -4 is also 4

Therefore, the answer is 4.

Answer:

1/64

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

25 plus 7 is 32

32 minus 3 is 29

29 plus 16 is 45

hmmm well that's a  lil too hard for my smol brain to process but hmmm well when I think about it, it really gets my brain thinking and ummm well you see it's uh hmm you add the yeah to that and hmmmm well ahhh that looks to be about right uuuuuuuuuh

45....

.....or is it?

hmmmmmmmmmmmmmmm

Answer:

32 F

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

x+5x<12

x+5x=12

12-5x

=7

7 divide by 1

=7

Answer:

B

Step-by-step explanation:

First you add 3x+x because they are like terms.

3x+x-7=10  

Your New Simplified Equation:

4x-7=10  

Now, you have to take out the -7 by adding a positive 7. Also you                          have to add +7 on the other side so add 7 to 10.

Your New Simplified Equation:

4x=17      Now, you divide both sides by 4.

Your New Simplified Equation:

x= 17/4 So, that's your answer :)

Answer:

(3x+1)(2x+1)

Step-by-step explanation:

Answer:

[tex]x2[/tex]=[tex]\frac{5-\sqrt{113} }{8} , x2 = \frac{5+\sqrt{113} }{8}[/tex]

Step-by-step explanation:

hope this help and if you can give me brainliest

Answer:5m+22-15n

Step-by-step explanation:

Answer: 16pi

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + y = 25

2x - y = 6           Solve for y in this the second equation. Add y to both sides

2x  = 6 + y         The ys on the left cancel. Subtract 6 from both sides.

2x - 6 = y

Put this value of y into the first equation

x + y = 25

x + 2x - 6 = 25      Combine on the left

3x - 6 = 25           Add 6 to both sides.

3x = 25 + 6           Combine the right

3x = 31                   Divide by 3

x = 31 / 3            

x = 10.333333

x + y = 25

10.33333 + y = 25  Subtract 10.33333

y = 25 - 10.333333

y = 14.666666

x + y = 25

10.33333 + 14.66666

25 approximately.

2x - y = 6

2*10.33333 - 14.66666

20.66666 - 14.66666

6

You should note that those numbers are repeating decimals

2x - 6 = y