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>
Answer: 0.8238
Step-by-step explanation:
Given : Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with 
and 
.
Let x denotes the scores on a certain intelligence test for children between ages 13 and 15 years.
Then, the proportion of children aged 13 to 15 years old have scores on this test above 92 will be :-
![P(x>92)=1-P(x\leq92)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{92-106}{15})\\\\=1-P(z\leq })\\\\=1-P(z\leq-0.93)=1-(1-P(z\leq0.93))\ \ [\because\ P(Z\leq -z)=1-P(Z\leq z)]\\\\=P(z\leq0.93)=0.8238\ \ [\text{By using z-value table.}]](https://tex.z-dn.net/?f=P%28x%3E92%29%3D1-P%28x%5Cleq92%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5Cleq%5Cdfrac%7B92-106%7D%7B15%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq%20%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq-0.93%29%3D1-%281-P%28z%5Cleq0.93%29%29%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%5Cleq%20-z%29%3D1-P%28Z%5Cleq%20z%29%5D%5C%5C%5C%5C%3DP%28z%5Cleq0.93%29%3D0.8238%5C%20%5C%20%5B%5Ctext%7BBy%20using%20z-value%20table.%7D%5D)
Hence, the proportion of children aged 13 to 15 years old have scores on this test above 92 = 0.8238
Hello!
Simplifying
5x2 + -7x + -3 = 8
Reorder the terms:
-3 + -7x + 5x2 = 8
Solving
-3 + -7x + 5x2 = 8
Solving for variable 'x'.
Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8
Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8
Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0
Begin completing the square. Divide all terms by
5 the coefficient of the squared term:
Divide each side by '5'.
-2.2 + -1.4x + x2 = 0
Move the constant term to the right:
Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2
Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2
Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2
Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2
The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.
Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49
Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49
Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69
Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69
Calculate the square root of the right side: 1.640121947
Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.
Subproblem 1
x + -0.7 = 1.640121947
Simplifying
x + -0.7 = 1.640121947
Reorder the terms:
-0.7 + x = 1.640121947
Solving
-0.7 + x = 1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7
Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947
Simplifying
x = 2.340121947
Subproblem 2
x + -0.7 = -1.640121947
Simplifying
x + -0.7 = -1.640121947
Reorder the terms:
-0.7 + x = -1.640121947
Solving
-0.7 + x = -1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7
Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947
Simplifying
x = -0.940121947
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}
Answer:
Step-by-step explanation:
The ratio of the angle is how the angle relates to each other. Let's say that we try to relate Angle A, B, C and get 1 : 3 : 5. That means Angle B is three times Angle A and Angle C is 5 times Angle A
Thus we get the equation:
A
B = 3A
C = 5A
A + B + C = 180, since all the angles of the triangle is equal to 180 degrees
A + 3A + 5A = 180
9A = 180
A = 20 --> B = 3A = 60 --> C = 5A = 100
So Angle A is 20 degrees, Angle B is 60 degrees, and Angle C is 100 degrees.
Hope that helps!
Answer:
Step-by-step explanation:
To factor the equation, break it into two binomials which multiply to make the equation. To write these binomials (x+a)(x+b), find factors which multiply to -20 and add to -1 for a and b.
20: 1, 2, 4, 5, 10, 20
-5+4 = -1
