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4 years ago

Which function corresponds to the table?

Mathematics

2 answers:

Anni [7]4 years ago

7 0

It is c) y=-2x+3
Beacuse you just put x as in table etc. 0,1,2 and then change the y with y as in table 3,1,-1.

BaLLatris [955]4 years ago

3 0

Answer: Choice C) y = -2x+3

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Work Shown:

Using the slope formula, find the slope of the line through (0,3) and (1,1)
m = (y2 - y1)/(x2 - x1)
m = (1 - 3)/(1 - 0)
m = (-2)/(1)
m = -2
The slope is -2

The y intercept is 3 since x = 0 leads to y = 3 in the first row of the table
So b = 3

Plug m = -2 and b = 3 into y = mx+b
y = mx+b
y = -2x+3

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Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

How do you find 15% of 160?

Tomtit [17]

Divide 160 by .15 because when you want to divide a number by a percent, you move the decimal in front of the percent number.

7 0

3 years ago

Read 2 more answers

Calculate the exact value of <br><br><br><br>2.76 over 0.8 + 8. 7 2square

ludmilkaskok [199]

Do you have any options?

5 0

3 years ago

The table below shows the fifth powers of different numbers:

g100num [7]

Part A

Yes y is a function of x. Specifically the equation is y = x^5
For any given input, there is exactly one output

Notice how if x = 1 then y = x^5 = (1)^5 = 1
Notice how if x = -1 then y = x^5 = (-1)^5 = -1
Notice how if x = -2 then y = x^5 = (-2)^5 = -32
Notice how if x = 2 then y = x^5 = (2)^5 = 32

In general,
x^5 = x*x*x*x*x
there are five copies of x multiplied

A more specific example
3^5 = 3*3*3*3*3
there are five copies of '3' multiplied

=====================================================

Part B

All we do is replace x with 4 and use PEMDAS to simplify
f(x) = 2x+12
f(4) = 2(4)+12
f(4) = 8+12
f(4) = 20

The value of f(4) is 20
What does it mean? It is the total cost of renting the bowling lane for 4 hours. If you rent it for four hours, then you'll pay a total of $20.

The portion 2x = 2*4 = 8 is the variable cost which depends on how long you play. The more hours, the more the variable cost goes up
The fixed cost is 12. This is always fixed as this is the price to get in the door. If you play for 0 hours, but somehow got in the door, then you still pay $12
In total, variableCost+fixedCost = 8+12 = 20 = totalCost

4 0

3 years ago

Simplify the expression-9(-8p+12)-6p

lana [24]

Answer:

219.345115

Step-by-step explanation:

-9(-8p+12)-6p

= 219.345115

6 0

3 years ago