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kykrilka [37]
3 years ago
11

The sum of two numbers is 11. The sum of their squares is 65. Find the numbers. (How do you get the answer?)

Mathematics
1 answer:
Stels [109]3 years ago
7 0
X is the number
<span>The sum of two numbers is 11, so other number is : 11 - x

</span><span>The sum of their squares is 65
</span>
x^2 + (11 - x)^2 = 65
x^2 + 121 - 2(x)(11) + x^2 = 65
2x^2 - 22x + 121 = 65
2x^2 - 22x + 121 -  65 = 0
2x^2 - 22x + 56 = 0
2(x^2 - 11x + 28) = 0
2(x - 7)(x -4 ) = 0
x - 7 = 0
x = 7

x - 4 =0
x =4

answer: the numbers are 4 and 7

double check:

<span>sum of two numbers is 11:
4 + 7 = 11

</span><span>The sum of their squares is 65
</span><span>4^2 + 17^2 = 16 + 49 = 65

</span>
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A partial proof was constructed given that MNOP is a parallelogram.
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A diagram of parallelogram MNOP is attached below

We have side MN || side OP and side MP || NO

Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.

Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size. 

∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines

∠N+∠O=180° and ∠O+∠P=180°

∠N and ∠P are of equal size

we deduce further that ∠M and ∠O are of equal size

Hence, the correct statement to complete the proof is

<span>∠M ≅ ∠O; ∠N ≅ ∠P

</span>

4 0
3 years ago
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Point L is on line segment KM . Given KM = 5x + 10 , LM = 4x , and KL = 3x , determine the numerical length of KL
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You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expres
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Solve −3x2 + 30x − 90 = 0. x equals 5 plus or minus 2i square root of 5 x equals 5 plus or minus i square root of 5 x equals 10
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5 0
3 years ago
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F is a polynomial of degree 6. f has a root of multiplicity
frutty [35]

Answer:

f(x) = 0.43 * (x - 3)^{2}  * (x-1)^{3}*(x + 10)

Step-by-step explanation:

We have a 6th degree polynomial  f(x)

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a =  -29,721.6/-69,120

a =  0.43

so

f(x) = 0.43 * (x - 3)^{2}  * (x-1)^{3}*(x + 10)

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