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2 years ago

Write the sphere in standard form. 4x2 + 4y2 + 4z2 − 24x + 16y = 1

Mathematics

1 answer:

dybincka [34]2 years ago

5 0

Answer:

(x -3)^2 +(y +2)^2 +z^2 = 13.25

Step-by-step explanation:

Divide by 4 and complete the squares.

x^2 -6x +y^2 +4y +z^2 = 1/4

(x^2 -6x +9) +(y^2 +4y +4) +z^2 = 13 1/4

(x -3)^2 +(y +2)^2 +z^2 = 13.25

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2 years ago

Which expression is equivalent to 3(5+4)

guajiro [1.7K]

Answer:

3(15+12)

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3(5+4)

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2 years ago

A middle school held a Career Exploration Day where students could choose to hear an adult talk about his or her career. 15 stud

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Answer:

5/12

Step-by-step explanation:

15 students went to hear the doctor speak and 21 students went to other sessions

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2 years ago

The average value of two positive numbers is 30% less than one of the two numbers. By which percentage is average value bigger t

Viefleur [7K]

Answer:

75% bigger

Step-by-step explanation:

Let the first number be x and the second be y.

So:

$Average = \frac{x + y}{2}$

And:

$Average = (1 - 30\%) * x$ -----30% less than x

Substitute $Average = (1 - 30\%) * x$ in $Average = \frac{x + y}{2}$

$\frac{x + y}{2} = (1 - 30\%) * x$

$\frac{x + y}{2} = (1 - 0.30) * x$

$\frac{x + y}{2} = 0.70 * x$

$\frac{x + y}{2} = 0.70x$

Cross multiply

$x + y = 0.70x * 2$

$x + y = 1.40x$

Collect like terms

$1.40x - x = y$

$0.40x = y$

Make x the subject

$x = \frac{y}{0.40}$

$x = 2.50y$

So, the average is:

$Average = (1 - 30\%) * x$

$Average = (1 - 30\%) * 2.50y$

$Average =0.70 * 2.50y$

$Average =1.75y$

Rewrite as:

$Average =(1 + 0.75)y$

Express as percentage

$Average =(1 + 75\%)y$

This means that the average is 75% bigger than the second number

6 0

2 years ago