What equation does this represent?

The sum of two numbers is 8, and the sum of their squares is 34. what is the larger number

bija089 [108]

Answer:

The larger number is 5.

Step-by-step explanation:

Let the numbers be represented by x and y. Then:

x + y = 8 is their sum, and

x² + y² = 34 is the sum of their squares.

Let's solve this system of equations using substitution. Since x + y = 8,

x = 8 - y. Subbing this 8 - y for x into the second equation, we get:

(8 - y)² + y² = 34, or

64 - 16 y + y² + y² = 34

Simplifying, we get first: 30 - 16y + 2y² = 0, and then:

2y² - 16y + 30 = 0, and after reducing, y² - 8y + 15 = 0.

This factors into (y - 3)(y - 5) = 0, and so y = 3 and y = 5.

The larger number is 5.

6 0

4 years ago

(2x10^3)x(4x10^2) how do you do it help!

Sergio039 [100]

Answer:

800000x^3

Step-by-step explanation:

6 0

4 years ago

The heights of 40 randomly chosen men are measured and found to follow a normal distribution. An average height of 175 cm is obt

AVprozaik [17]

Answer:

95% two-sided confidence interval for the true mean heights of men is [168.8 cm , 181.2 cm].

Step-by-step explanation:

We are given that the heights of 40 randomly chosen men are measured and found to follow a normal distribution.

An average height of 175 cm is obtained. The standard deviation of men's heights is 20 cm.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average height = 175 cm

$\sigma$ = population standard deviation = 20 cm

n = sample of men = 40

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the true mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ]

= [ $175-1.96 \times }{\frac{20}{\sqrt{40} } }$ , $175+1.96 \times }{\frac{20}{\sqrt{40} } }$ ]

= [168.8 cm , 181.2 cm]

Therefore, 95% confidence interval for the true mean height of men is [168.8 cm , 181.2 cm].

The interpretation of the above interval is that we are 95% confident that the true mean height of men will be between 168.8 cm and 181.2 cm.

3 0

3 years ago

What is the solution of the system X - 3y = -13 and 5x + 7y = 34

hammer [34]

Answer:

The solution for this system is x = 1/2 and y = 9/2

Step-by-step explanation:

1. We have this system of equations:

x - 3y = -13 and 5x + 7y = 34

2. Let's try to find out the value of x on the first equation:

x - 3y = - 13

x = 3y - 13

3. Now, let's replace x on the second equation for finding y:

5x + 7y = 34

5 (3y - 13) + 7y = 34

15y - 65 + 7y = 34

22y = 34 +65

22y = 99

2y = 9 (Dividing by 11 at both sides)

y = 9/2 (Diving by 2 at both sides)

4. Now, let's find out the value of x on the first equation, using the value of y:

x - 3y = - 13

x - 3 (9/2) = - 13

x - 27/2 = -13

x = -13 + 27/2

x = (-26 + 27)/2 (Adding - 13 and 27/2)

x = 1/2

5. Finally, let's prove the values of x and y are correct on the second equation of the system:

5x + 7y = 34

5 (1/2) + 7 (9/2) = 34

5/2 + 63/2 = 34

(5 + 63)/2 = 34

68/2 = 34

34 = 34

It has been proved that x = 1/2 and y = 9/2 are correct

5 0

3 years ago

Consider the quadratic function f(y) = 8y2 – 7y + 6. What is the constant of the function?

Over [174]

The constant is 6. A constant is just the number on its own. Quadratics follow the form f(x) = ax^2+bx+c. The c is the constant.

7 0

3 years ago