Using mapping notation to describe a translation up 8 units

umka2103 [35]

Answer:

Slope of required line if both lines are parallel: y=4x-20

Slope of required line if both lines are perpendicular: y=-1/4x+14

Step-by-step explanation:

We need to find equation of line while we are given another line having equation y=4x-6 and passes through point (8,12)

<u><em>Note: Since it is not given if the required line is parallel or perpendicular to the given line. I will solve for both cases.</em></u>

If Both lines are parallel the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are parallel there slopes are same

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=4

Now finding y-intercept

Using slope m=4 and point (8,12) we can find y-intercept

$y=mx+b\\12=4(8)+b\\12=32+b\\b=12-32\\b=-20$

y-intercept of new line is: b=-20

Equation of required line having slope m=4 and y-intercept b=-20 is

$y=mx+b\\y=4x-20$

If Both lines are perpendicular the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are perpendicular there slopes are opposite of each other

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=-1/4

Now finding y-intercept

Using slope m=-1/4 and point (8,12) we can find y-intercept

$y=mx+b\\12=-\frac{1}{4} (8)+b\\12=-2+b\\b=12+2\\b=14$

y-intercept of new line is: b=14

Equation of required line having slope m=-1/4 and y-intercept b=14 is

$y=mx+b\\y=-\frac{1}{4} x+14$

8 0

2 years ago

the perimeter of a square is 36 ft. if you increase the length by 3 feet and decrease the width by 5 feet, what is the area of t

I am Lyosha [343]

Answer:

48 ft²

Step-by-step explanation:

P = 36

W = 36 /4 = 9 = L

(9 + 3) x (9 - 5) = 12 x 4 = 48

3 0

2 years ago

A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:

Sedaia [141]

Answer:

Time:

Car > Truck > Boat.

Cost of produce:

Truck > Boat > Car

Profit

Car > Truck > Boat.

We know that a worker works 400 minutes each day, and the profit that each worker needs to generate is $35, let's find how each worker needs to spend their time.

Let's call T to the number of trucks he makes, C for cars and B for boats.

Then, if he works 400 minutes we have:

T*10 + C*12 + B*8 ≤ 400

this means that the time expended crafting the toys can be, at most, 400 minutes (here you use the inequality because the worker actually can be less effective than the max, maybe tacking a break or something like that)

The other equation is:

T*1 + C*1.5 + B*0.6 ≥ 35

Here we use the inequality because the profit needs to be at least 35$, none the less, the profit can be more than tath.

Notice that if we want to solve the system with for the equal signs, it is:

T*1 + C*1.5 + B*0.6 = 35

T*10 + C*12 + B*8 = 400

We have 3 variables and 2 equations, this means that there are more than one solution for this system.

6 0

2 years ago

What is the volume of the cylinder?

zavuch27 [327]

Answer:

V= 904.896cm^3

Step-by-step explanation:

Volume of a cylinder

V = πr^2h

V - volume of a cylinder

π - pie

r - radius of the cylinder

h - height of the cylinder

Given :

h - 18cm

d - 8cm

d = 2 * radius

r = d/2

r = 8/2

r = 4cm

π - 3.142

Insert the values into the formula of volume of a cylinder

V = πr^2h

V = 3.142 * 4^2 * 18

= 3.142 * 16 * 18

= 904.896cm^3

3 0

3 years ago

Andy puts $10.00 worth of gasoline in his motor scooter. If the price per gallon is $2.89, how many gallons did he buy?

Ksju [112]

3.46

10 divided by 2.89 = 3.46

6 0

2 years ago

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