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2 years ago

Graphing linear equations questions 1-13

Mathematics

1 answer:

Brums [2.3K]2 years ago

7 0

1. the graph of 2x + 1 = y for all real numbers will be a line. the graph with the restricted domain will be a line segment meaning it has endpoints (1, 3) and (4, 9).

2. is open ended, meaning you can make A, B, C anything you want as long as what they specify is met.
(a) A = 0
(0)x + By = C
let's make B = 1 and C = 5
y = 5

(b) B = 0
Ax + (0)y = C
let's make A = 1 and C = 5
x = 5

(c) C = 0
Ax + By = 0
let's make both A and B = 1
x + y = 0

3. plot both intercepts (x on x-axis, y on y-axis) then draw a line through the dots.

4-7. linear equations do not have exponents on any of the variables. 1/y is the same as y^(-1) so both 4 and 7 are non-linear.

8-13. you will have to graph these. put them in slope intercept form: y = mx+b if they're not already , plot the y-intercept first (0, b) then use the slope m draw the line by going rise over run.

example 13.
3x + 4y = 12
4y = -3x + 12
y = (-3/4) + 3
plot (0,3)
go down -3 , right 4 make a point.
reverse from (0,3) go up 3 left -4 and make a point. connect with line.

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

kobusy [5.1K]

Well, I bet you want your answer right away! So here it is.

Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).

To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.

(f + g)(x) = f (x) + g(x)

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(gf)(x)=g(x)f(x)= \small{\dfrac{3x+2}{4-5x}}=4−5x3x+2

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(gf)(x)=4−5x3x+2

Hope I helped! :) If I did not help that's okay.

-Duolingo

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Step-by-step explanation:

A suitable probability calculator can tell you the 5th percentile of this distribution.

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15 feet 10 inches is how many inches in all

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Answer:

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Step-by-step explanation:

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2 years ago

A^2-b^2 a^2b-ab^2 -------------- ÷ ---------------a^2b+ab^2 a^2b- ab^2

Damm [24]

Answer:

$\huge{= \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} }}$

Step-by-step explanation:

$\huge{ \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} } \div \frac{ {a}^{2b} - {ab}^{2} }{ {a}^{2b} - {ab}^{2} }}$

$\huge{\frac{ {x}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} } \div 1}$

$\huge{\boxed{\green{= \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} }}}}$

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3 years ago

The length of the rectangle is 5/6 of inches and the width of the rectangle is 2/15 of inches. What is the area of the rectangle

Inga [223]

Answer:

W = X in.

L = (3x - 6) in.

A = L*W = (3x-6)X = 45,

3x^2 - 6x = 45

3x(x-2) = 45,

x(x-2) = 15,

x^2 - 2x - 15 = 0

(x-5)(x+3) = 0,

x-5 = 0,

x = 5 in.

x+3 = 0,

x = -3.

Solution Set: x = 5, and x = -3.

Select + value of X:

x = 5

W = x = 5 in.

L = 3x-6 = 3*5 - 6 = 9 in.

Step-by-step explanation:

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2 years ago