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4 years ago

For the function f(x)=2x+1 and g(x)=3x-2, find (f-g)(4)

Mathematics

1 answer:

icang [17]4 years ago

4 0

Answer:

-5

Step-by-step explanation:

Here is how you solve this problem:

First, you set it up like this: 2x+1-3x+2

Second:You are finding f(4) and g(4) so you just plug in 4 for both problems:

2(4)+1-3(4)-2= 9-14= -5

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sierra wants to run a total of 5 1/2 miles. Each lap around the track is 1/4 mile. How many laps around the track does sierra ne

icang [17]

Answer:

She has to run 22 laps around the track.

Step-by-step explanation:

It is 22 laps because each mile means 4 laps on the track and 5 miles multiplied by 4 laps it 20 laps to do 5 miles, and then 1/2 mile times two is 2/4 which is 2 laps. 2 plus 20 is 22 laps.

5 0

3 years ago

Raphael is about to sign a sales agreement for his new car he can choose one of 4 warranties one of 3 exterior combos one color

stealth61 [152]

792 ways to make his decisikn. Multiply all 4 numbers 4x3x11x6 = 792

3 0

3 years ago

Read 2 more answers

Quadrilateral BECK is known to be a rhombus. Two of the vertices are B(3,5) and C(7,-3).

Zanzabum

Answer:

a. The slope of EK is $\frac{1}{2}$

b. The equation of line EK is y = $\frac{1}{2}$ x - $\frac{3}{2}$

Step-by-step explanation:

The form of the equation of a line is y = m x + b, where

m is the slope of the line

b is the y-intercept

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

The rule of the mid-point is ( $\frac{x1+x2}{2},\frac{y1+y2}{2}$ )

∵ BECK is a rhombus

∵ The diagonal is the line that joins two opposite vertices

∵ B and C are opposite vertices in the rhombus

∵ E and K are opposite vertices in the rhombus

∴ BC and EK are the diagonals of the rhombus BECK

∵ The diagonals of the rhombus are ⊥ and bisect each other

∴ EK is ⊥ bisector to BC

→ Let us find the slope and the mid-point of BC

∵ B = (3, 5) and C = (7, -3)

∴ x1 = 3 and y1 = 5

∴ x2 = 7 and y2 = -3

→ Substitute them in the rule of the slope above to find it

∵ m = $\frac{-3-5}{7-3}$ = $\frac{-8}{4}$ = -2

∴ m = -2

∴ The slope of BC = -2

→ To find the slope of EK reciprocal the slope of BC and change its sign

∴ m⊥ = $\frac{1}{2}$

∴ The slope of EK = $\frac{1}{2}$

a. The slope of EK is $\frac{1}{2}$

→ Substitute the value of the slope in the form of the equation above

∵ y = $\frac{1}{2}$ x + b

→ To find b substitute x and y in the equation by the coordinates

of a point on the line

∵ The mid-point of BC is the mid-point of EK

∵ The mid-point of BC = ( $\frac{3+7}{2},\frac{5+-3}{2}$ ) = ( $\frac{10}{2},\frac{2}{2}$ ) = (5, 1)

∴ The mid-point of EK = (5, 1)

→ Substitute x by 5 and y by 2 in the equation

∵ 1 = $\frac{1}{2}$ (5) + b

∴ 1 = $\frac{5}{2}$ + b

→ Subtract $\frac{5}{2}$ from both sides

∴ $-\frac{3}{2}$ = b

→ Substitute the value of b in the equation

∵ y = $\frac{1}{2}$ x + $-\frac{3}{2}$

∴ y = $\frac{1}{2}$ x - $\frac{3}{2}$

b. The equation of line EK is y = $\frac{1}{2}$ x - $\frac{3}{2}$

6 0

3 years ago

Identify a horizontal or vertical stretch or compression of the function ƒ(x) = x2 by observing the equation of the function g(x

igomit [66]

To solve this problem you must apply the proccedure shown below:

1. You have the following parent function given in the problem above:

$f(x)=x^{2}$

2. And you have the function $g(x)=5(x^{2} )$

3. By definition, if you have the function $y=ax^{2}$ and $|a|>1$ it is a vertical stretch.

4. Therefore, you have that:

$|a|=5\\ 5>1$

Therefore the answer is: It is a vertical stretch.

4 0

3 years ago

A circle has an area of 40 square inches. Find the radius to 2 decimal places.

Oksanka [162]

The area of a circle is given by

$A=\pi r^2$

We can solve this equation for r: divide both sides by pi:

$r^2=\dfrac{A}{\pi}$

Consider the (positive) square root of both sides:

$r = \sqrt{\dfrac{A}{\pi}}$

So, in your case, we have

$r = \sqrt{\dfrac{40}{\pi}}\approx 3.57$

7 0

3 years ago