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Bogdan [553]
3 years ago
9

If f(x) = 3x - 1 and g(x) = x + 2, find (f - g)(x).

Mathematics
1 answer:
Marina86 [1]3 years ago
6 0

Answer:

\boxed{\sf (f - g)(x) = 2x - 3}

Given:

f(x) = 3x - 1

g(x) = x + 2

To Find:

(f - g)(x)

Step-by-step explanation:

\sf (f -g)(x) = f(x) - g(x) \\ \\   \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: =(3x - 1) - (x + 2) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: =3x - 1 - x - 2 \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: =3x - x - 1 - 2 \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: =(3x - x) - (1 + 2) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: =2x - (1 + 2) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: =2x - 3

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Use the quadratic formula s to solve 2y^2-6y-8=0
Korvikt [17]

Answer:

{4, - 1}

Step-by-step explanation:

Given

2y² - 6y - 8 = 0 ← in standard form

with a = 2, b = - 6, c = - 8

Using the quadratic formula to solve for y

y = ( - (- 6) ± \sqrt{(-6)^2-(4(2)(-8)} ) / (2 × 2)

  = ( 6 ± \sqrt{36+64} ) / 4

  = ( 6 ± \sqrt{100} ) / 4

  = ( 6 ± 10 ) / 4

x = \frac{6+10}{4} = \frac{16}{4} = 4

OR

x = \frac{6-10}{4} = \frac{-4}{4} = - 1

Solution is { 4, - 1 }

6 0
3 years ago
2. What's the area of the figure, which has sides of length 6 and 8? A. 42 B. 48 C. 28 D. 14
Natasha2012 [34]

Answer:

B. 48

Step-by-step explanation:

The area of a rectangle is length times width

A = l*w

A = 6*8

A = 48

8 0
3 years ago
Read 2 more answers
Determine whether line AB and line CD are parallel, perpendicular, or neither. A( 4, 2), B(-3, 1), C(6, 0), D(-10, 8)
Lapatulllka [165]

Answer:

<h2>neither</h2>

Step-by-step explanation:

If AB an CD are parallel, then their slopes are the same.

If AB and CD are perpendicular, then the product of their slopes is equal -1.

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Calculate the both slope:

A(4,\ 2),\ B(-3,\ 1)\\\\m_{AB}=\dfrac{1-2}{-3-4}=\dfrac{-1}{-7}=\dfrac{1}{7}\\\\C(6,\ 0),\ D(-10,\ 8)\\\\m_{CD}=\dfrac{8-0}{-10-6}=\dfrac{8}{-16}=-\dfrac{1}{2}\\\\=============================

m_{AB}\neq m_{CD}

The line AB and line CD are not parallel

m_{AB}\cdot m_{CD}=\left(\dfrac{1}{7}\right)\left(-\dfrac{1}{2}\right)=-\dfrac{1}{14}\neq-1

The line AB and line CD are not perpendicular.

6 0
3 years ago
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babymother [125]
The first one is 6÷12×24
4 0
3 years ago
Steph,andra,emily,and becca are planning a road trip from their hometown to san antonio
morpeh [17]

Answer:

a. Emily should begin her turn as the third driver at point (1, -0.5).

b. Emily's turn to drive end at point (-2.5, -3.75).

Step-by-step explanation:

Let assume that the group of girls travels from their hometown to San Antonio in a straight line. We know that each location is, respectively:

Hometown

H(x,y) = (8,6)

San Antonio

T(x,y) = (-6,-7)

Then, we can determine the end of each girl's turn to drive by the following vectorial expression based on the vectorial equation of the line:

Steph

S(x,y) = H(x,y) + \frac{1}{4}\cdot [T(x,y)-H(x,y)] (1)

S(x,y) = (8,6) + \frac{1}{4}\cdot [(-6,-7)-(8,6)]

S(x,y) = (8,6) +\frac{1}{4}\cdot (-14,-13)

S(x,y) = (4.5,2.75)

Andra

A(x,y) = H(x,y) + \frac{2}{4}\cdot [T(x,y)-H(x,y)] (2)

A(x,y) = (8,6) + \frac{2}{4}\cdot [(-6,-7)-(8,6)]

A(x,y) = (8,6)+\frac{2}{4}\cdot (-14,-13)

A(x,y) =(1, -0.5)

Emily

E(x,y) = H(x,y) + \frac{3}{4}\cdot [T(x,y)-H(x,y)] (3)

E(x,y) = (8,6) + \frac{3}{4}\cdot [(-6,-7)-(8,6)]

E(x,y) = (8,6)+\frac{3}{4}\cdot (-14,-13)

E(x,y) = (-2.5, -3.75)

a. <em>If the girls take turns driving and each girl drives the same distance, at what point should they stop from Emily to begin her turn as the third driver? </em>

Emily's beginning point is the Andra's stop point, that is, A(x,y) =(1, -0.5).

Emily should begin her turn as the third driver at point (1, -0.5).

b. <em>At what point does Emily's turn to drive end?</em>

Emily's turn to drive end at point (-2.5, -3.75).

7 0
2 years ago
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