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3 years ago

Graphing linear equations questions 1-13

Mathematics

1 answer:

Brums [2.3K]3 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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Show work and Factor 4x^2+xy-18y^2

grigory [225]

Answer:

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Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

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3 years ago

I need only 16 and 17 please help

Nesterboy [21]

9514 1404 393

Answer:

16. a: (-90°, (4, 3)); b: (90°, (0, 3)); c: (-90°, (0, 0))

17. a: (down, (4, -1)); b: (right, (4, 3)); c: (up, (5, 2))

Step-by-step explanation:

We don't know what notation you're used to seeing for rotations. Here. we'll use the form [degrees CCW, (center)]. (CW angles are negative.) In any rotation, the center is the point that is invariant (remains in the same place)

16.

a) The tail is invariant, so the rotation is (-90°, (4, 3)).

b) The tip is invariant, so the rotation is (90°, (0, 3)).

c) The origin is invariant, so the rotation is (-90°, (0, 0))

17.

a) The tail is invariant, so the arrow is pointing down with the tip at (4, -1).

b) The center is invariant, so the arrow is reversed. It is pointing right with the tip at (4, 3).

c) Point (2, 3) is invariant, so the arrow is pointing up with the center at (5, 0). The tip is at (5, 2).

_____

<em>Additional comment</em>

If you have trouble visualizing these rotations, you might find it useful to trace the arrow on a piece of (semi-)transparent medium (plastic or tracing paper) so that you can move it as required to match the descriptions in the problem statement. A pin, or a dot on your tracing, can serve to fix the center of rotation. A little hands-on never hurts in math and geometry.

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