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8090 [49]
3 years ago
15

X² + y² = 34x + y =8​

Mathematics
1 answer:
Nataly [62]3 years ago
4 0

Step-by-step explanation:

{x}^{2}  +  {y}^{2}  = 34 \\ x + y = 8 \\ x = 8 - y \\ substitute \: x \: in \\  {x}^{2}  +  {y}^{2}  = 34 \\  {(8 - 4)}^{2}  +  {y}^{2}  = 34 \\  {(8 - 4) }^{2}  =  {y}^{2}  - 16y + 64 \\   {y}^{2}  - 16y + 64 +  {y}^{2}  = 34 \\  {2y}^{2}  - 16y + 64 = 34 \\ {2y}^{2}  - 16y + 64  - 34 = 0 \\  {2y}^{2}  - 16y + 30 = 0 \\ 2 {y}^{2}  - 6y - 10y + 30 = 0 \\ (2 {y}^{2}  - 6y) - (10y + 30) = 0 \\ 2y(y - 3) - 10(y - 3) = 0 \\ (2y - 10)(y - 3) \\ 2y = 10 \\ y  = \frac{10}{2}  \\ y = 5 \\ or \\ y = 3 \\ if \: y = 5 \:  \: x = 3 \\ if \: y = 3 \:  \:  x = 5

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Sum of two numbers is 84. If one of the numbers exceeds the other by 12, the numbers are
djverab [1.8K]

Answer:

54 and 30

Step-by-step explanation:

84÷2=42-12=30

42+12=54

5 0
3 years ago
You cut a circular hole 1/4 -inch in diameter in a piece of cardboard. With the cardboard 30 inches from your face, the Moon fit
Stolb23 [73]

Answer:

The Moon's diameter is greater than 1,500 miles

Step-by-step explanation:

we know that

1\ mile=63,360\ inches

1,500\ miles=1,500*63,360=95,040,000\ inches

240,000\ miles=240,000*63,360=15,206,400,000\ inches

by proportion

Find the Moon's diameter

Let

x-----> the Moon's diameter in inches

\frac{x}{15,206,400,000}=\frac{0.25}{30}\\ \\x= 15,206,400,000*0.25/30\\ \\x=126,720,000\ inches

Compare

126,720,000\ inches> 95,040,000\ inches

therefore

The Moon's diameter is greater than 1,500 miles

3 0
3 years ago
The sum of three consecutive odd numbers is 69. What are the three numbers?
n200080 [17]

Answer:

21, 23, 25

Step-by-step explanation:

Ok, so this one may seem a little tricky, so I'll try to explain it as best as I can. :)

So because they are consecutive odd numbers, that means they are odd numbers that are one after the other. This means each number is 2 apart from the next. So by using this, we know that there is a difference of 6 between the highest and lowest number. Now let's try and make an equation:

3o + 6 = 69

Now in order to get O by itself we have to subtract 6 from both sides:

3o = 63

Now we just have to divide by three on both sides:

o = 21

So now, we know that the lowest number is 21, but we have to add 2 to get 23, and then another 2 to get 25.

Hope this helps :)

5 0
3 years ago
Read 2 more answers
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
jonny [76]

Answer:

∠13 ≅ ∠16   - Vertical Angles Theorem

∠10 ≅ ∠14  - corresponding angles for parallel line p and q cut by the transversal s

∠5 ≅ ∠13  - corresponding angles for

parallel lines r and s cut by

the transversal q

∠1 ≅ ∠5 - corresponding angles for

parallel lines r and s cut by

the transversal q

Step-by-step explanation:

Linear Pair Theorem won't be used. When you look at the lines on the image you see that 13 and 16 are vertical from each other making there answer the vertical angles theorem. When you look at 10 and 14 you see that they lie on p and q with s going in the center of them. When you look at 5 and 13 they lie on s and r with q going down the middle of them. With 1 and 5  they also lie on p  and q but r goes down the center of them instead of s.

6 0
3 years ago
Read 2 more answers
How many times larger is 3 x 1015 than 6 x 1010
Deffense [45]

it is 3,000 times larger! that is the difference.

8 0
3 years ago
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