MATHEMATICS HIGH SCHOOL

Determine if the following lines are parallel, perpendicular, or neither. y=x-8 x+y=-5

Answers

Answer 1

Answer:

Answer:

To determine if two lines are parallel or perpendicular, we need to examine their slopes.

First, let's rearrange the second equation, x+y=-5, to slope-intercept form (y = mx + b):

y = -x - 5

In this form, we can see that the slope of the second line is -1.

The first equation, y=x-8, is already in slope-intercept form, y = mx + b, where the slope is 1.

Comparing the slopes, we can see that the slopes of the two lines are different. The slope of the first line is 1, and the slope of the second line is -1.

Since the slopes are not equal, the lines are not parallel.

Now, let's determine if the lines are perpendicular:

Two lines are perpendicular if the product of their slopes is -1.

The slope of the first line is 1, and the slope of the second line is -1.

Since 1 * -1 = -1, the product of the slopes is -1.

Therefore, the lines y = x - 8 and x + y = -5 are perpendicular.

Step-by-step explanation:

Answer 2

Answer:

Answer: Perpendicular

Step-by-step explanation:

Our task is to identify if these lines are parallel or not. The lines are :

$\rm{y=x-8}$
$\rm{x+y=-5}$

A good move would be to write these two equations in the same format. The easiest one is slope-intercept. Equation 1 is already in this form, but the second one isn't.

To write the second equation in slope-intercept, all we need to do is subtract x from both sides, and we get:

$\rm{y=-5-x}$

Now, switch the terms:

$\rm{y=-x-5}$

The slope of the first line is 1, and the slope of the second line is -1.

They can't be parallel, since their slopes are not the same. For them to be perpendicular, their slopes should be negative reciprocals of each other.

Is -1 the negative inverse of 1? Yes.

∴ The lines are perpendicular.

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Determine the inverse for the function f(x)= 4x+20

Answers

Answer:

6.40

Step-by-step explanation:

The image of the point (1, -2) after a rotation of 180° about the origin is:

Answers

Answer:

$(-1,2)$

Step-by-step explanation:

We have been coordinates of a point $(1,-2)$ . We are asked to find the coordinates of the point after a rotation of 180° about the origin.

We know that after rotating a point 180° about the origin, the coordinates of point changes their signs to opposite. The rule of rotating a point 180° about the origin is $(x,y)\rightarrow (-x,-y)$ .

After rotating the point $(1,-2)$ 180° about the origin its coordinates would be:

$(1,-2)\rightarrow (-1,--2)$

$(1,-2)\rightarrow (-1,2)$

Therefore, the coordinates of the given point after a rotation of 180° about the origin would be $(-1,2)$ .

The answer is (-1,2)

Write the point-slope form of the equation of the line through the given point with the given slope.Through (-2,0) slope=2

Answers

$the\ point-slope\ formula:y-y_1=m(x-x_1)\n===============================\n\n(-2;\ 0)\to x_1=-2;\ y_1=0\ and\ m=2\n\ntherefore\n\ny-0=2(x-(-2))\n\ny=2(x+2)\n\n\boxed{y=2x+4}$

Steps:
1. Your point slope formula is
Y-Y1=m(x-x1)
2. Y1=0 m=2 (slope) x1=-2
3. Do substitution
4. Your answer is
Y-0=2(x +2)
Ps: in case you are wondering why I put plus 2 instead of negative 2 is because you are supposed to do the opposite when subtracting a negative

Mrs. Myles gave the same test to both her first and third period class. In first period, the mean was 75 and the range was 30. In third period, the mean was 85 and the range was 50. Which is a true statement?A) Most of third period scored in the 80's.
B) More people had a score in the 70's in first period.
C) On average, third period did better than first period.
D) On average, first period did better than third period.

Answers

The right answer for the question that is being asked and shown above is that: "C) On average, third period did better than first period. " In third period, the mean was 85 and the range was 50. The statement that is true is that C) On average, third period did better than first period.

Answer:

C) On average, third period did better than first period

Step-by-step explanation:

Usa test prep

Express each number in standard form
-9.5x10-3
This is 10 to the -3 power

Answers

$-9.5*10^(-3)=-9.5*0.001=-0.0095$

Help nott sure if im right

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