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3 years ago

Consider the line y=2x-8.

2 answers:

andrey2020 [161]3 years ago

8 0

Answer: The slope of a line parallel to this line is 2. The slope of a line perpendicular to this line is - $\frac{1}{2}$ .

Step-by-step explanation:

You know that your slope for this equation is 2, since that is your “m” in the slope-intercept equation, y = mx + b.

Lets split this into two parts.

Part 1: Finding the parallel slope

We know that the slopes of paralell lines are the same.Therefore, the slope of a line parallel to the one we know would also be 2!

Part 2: Finding the perpendicular slope

We also know that the slopes of perpendicular lines are opposite reciprocals, meaning the the sign (negative or positive) is changed, and the number is flipped over itself. As taught in my pre-algebra class, change the sign, flip the line.

Here is an example:

The opposite reciprocal of the number 5 is - $\frac{1}{5}$ . First, I changed the number to negative, then I figured out that 5 is technically $\frac{5}{1}$ , so I flipped that around.

Now, let’s get on to the real problem. If you do the math, the opposite reciprocal of 2 will be - $\frac{1}{2}$ . Therefore, that is your slope of that perpendicular lime.

Hope this helps! :)

professor190 [17]3 years ago

3 0

Answer:

The slope of a parallel line is 2.

The slope of a perpendicular line is: -1/2

Step-by-step explanation:

The slope of the line y=2x-8 is 2.

Parallel lines has the same slope.

Perpendicular lines has the negative reciprocal of the slope.

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Simplify the expression: -2y^7/14y^5 (the "^" means that the number behind it is a exponent)

Debora [2.8K]

Answer:

2 $y^{5} \sqrt{y}$

Step-by-step explanation:

i hope this helps

4 0

3 years ago

Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that empl

hichkok12 [17]

Answer:

see below for the table values
US labor cost: $115275 per year

Step-by-step explanation:

The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...

(6 days/week)($1.10/day) = $6.60/week

The three laborers working 50 weeks/year will have a labor cost of ...

(3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year

In the US, the labor charge per person per week is ...

(14 hr/day)(6 day/week) = 84 hr/week

That's 40 hours of straight pay and 44 hours of overtime pay, or ...

7.25(40 +1.5(44)) = 7.25(106) = 768.50

For 150 person-weeks per year, the total US labor charge is ...

($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year

The materials cost for a year is ...

($50/rug)(12 rugs/year) = $600/year

The revenue is ...

($2000/rug)(12 rugs/year) = $24,000/year

Profit is the difference between revenue and the total of costs:

profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia

So, the table gets filled as follows:

(labor, material, fixed cost, revenue, profit)

Mongolian-made

($990, $600, $10000, $24000, $12410)

US-made

($115275, $600, $10000, $24000, -$101,875)

The US labor cost would be $115,275.

_____

Comment

For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.

7 0

3 years ago

What is the reason for Statement 3 of the two-column proof?

Ivenika [448]

Refer to the attached image.

Given:

The measure of $\angle JMK= 52^\circ$ and $\angle KML= 38^\circ$ .

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: $\angle JML$ is a right angle.

Proof:

Statements Reasons

1. $m \angle JMK=52^\circ$ Given

2. $m \angle KML=38^\circ$ Given

3. $m \angle JMK+m \angle KML=m \angle JML$

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. $52^\circ+38^\circ = m \angle JML$ Substitution property of equality