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3 years ago

Given that f(x)=6x+2 and g(x)=2x+4/5 solve for g(f(1)) A.1 B.3 C.4 D.8

Mathematics

1 answer:

GrogVix [38]3 years ago

6 0

Answer:

The value of g(f(1)) is 84/5

Step-by-step explanation:

To find the answer to a composite function, start with the function on the inside, which is f(1). So, we input 1 into the f(x) equation and evaluate.

f(x) = 6x + 2

f(1) = 6(1) + 2

f(1) = 6 + 2

f(1) = 8

Now that we have the answer of 8, we can input that in for x in the outside function, which is g(x).

g(x) = 2x + 4/5

g(8) = 2(8) + 4/5

g(8) = 16 + 4/5

g(8) = 84/5

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3 years ago

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

What does the quantity 28-8 represent?

nikklg [1K]

You question implies simple subtraction is needed:

28-8=20

5 0

2 years ago

A gallon of gas costs $4.34.Greg puts 12 gallons of gas in his car,He has a 50-dollar bill.Tell how much Greg will have left,or

Lerok [7]

Greg will need $2.08 more money to buy 12 gallons of gas.

<h3>Further explanation</h3>

A gallon of gas costs $4.34

Greg puts 12 gallon of gas

Greg has $50

First, we are going to calculate how much money does Greg needs for 12 gallon of gas:

= 12 gallon of gas x cost/gallon

= 12 x 4.34

= 52.08

To multiply the decimal it's just the same way as the whole number multiplication, except for the placement of the decimal point in the answer. For the example

4.34 ⇒ 2 decimal place

<u> 12 x</u> ⇒ 0 decimal place

868

52.08 ⇒ 2 decimal place

By doing the same process as the whole number multiplication we got the answer is 52.08, but don't forget to add the decimal point/decimal place. The first factor has 2 decimal place, the second factor has 0 decimal place, so the answer will have two decimal place (2+0 = 2), by adding the decimal place.

The next step , 12 gallon of gas cost $52.08, if he has $50 so it cost more than the money he has, We are going to do a subtraction:

$52.08

<u>$50.00 </u>- ⇒ <em>we put zero so we can the borrowing (regrouping)</em>

$ 2.08

To subtract a decimal number, we need to line up the decimal point, add trailing zero as a placeholder and then do the subtraction

<h3>Learn more</h3>

Total spend brainly.com/question/12203917

Decimal multiplication brainly.com/question/2124592

Decimal multiplication brainly.com/question/1254534

Keywords: multiplication, decimal multiplication, two digits number additional, additional, subtraction decimal, regrouping

3 0

3 years ago