The equation of line CD is (y-3) = -2(x-4). What is the slope of a line perpendicular to line CD? a. 2 b. -2 c. 1/2 d. -1/2

Answers

Answer 1

Answer: The equation of line CD is given as (y - 3) = -2(x - 4), which is in the slope-intercept form (y = mx + b) with a slope (m) of -2.

To find the slope of a line perpendicular to CD, you can take the negative reciprocal of -2:

Negative reciprocal of -2 is 1/2.

So, the slope of a line perpendicular to line CD is c. 1/2.

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Newton's second law says force (f) is equal to mass (m) times acceration (a). A scientist wants to calculate the force of an object where the acceleration of gravity (g) is 9.8 m/s2. Use the function to calculate the force for an object with a mass (m) of 0.29 kilograms.

Answers

Force = mass x accerelation
= 0.29 x 9.8
= 2.842 N

Answer:

2.842 N

Step-by-step explanation:

Newton's second law is given by the equation $F=ma$

Where,

F is the force in Newtons
m is the mass in kilograms (kg)
a is acceleration given in meters per second squared

Given in the problem,

m = 0.29 kg, and

a = 9.8 meters per second squared

Substituting into the formula gives us F:

$F=ma\nF=(0.29)(9.8)\nF=2.842$ Newtons (N)

The sum of two numbers is 19, and their difference is 55. What are the two numbers?

Answers

Answer:

37 and -18

Step-by-step explanation:

Let one number be x and other y

1 x + 1 y = 19 .............1

1 x -1 y = 55 .............2

Eliminate y

multiply (1)by 1

Multiply (2) by 1

1 x 1 y = 19

1 x + -1 y = 55

Add the two equations

2 x = 74

/ 2

x = 37

plug value of x in (1)

1 x + 1 y = 19

37 + 1 y = 19

1 y = 19 -37

1 y = -18

y = -18

37 and -18

Final answer:

The two numbers, which sum to 19 and have a difference of 55, are 37 and -18.

Explanation:

The sum and difference of two numbers can provide the solution to the problem. In this case, the sum of the two numbers is 19 and the difference is 55. To solve this, we start by setting up two equations based on the problem: x + y = 19 and x - y = 55.

Then we solve these equations simultaneously. We can add the two equations together to eliminate 'y'. This gives us 2x = 74, or x = 37. Substituting x = 37 into the first equation, we get 37 + y = 19, which gives y = -18.

So, the two numbers are 37 and -18.

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The length of a rectangular room is 7.9m and it's width is 8.6m. Find the area of the room.

Answers

Length x Width=Area
Multiply
8.6 x 7.9= 67.94cm^2

$Formula = Length * Width=Area$

$8.6 * 7.9= 67.94cm^2$

Determine whether the two lines are parallel, perpendicular, coinciding, or only intersecting.y = - 3x + 8
6x + 2y =1
Choose the correct answer below.
parallel
only intersecting
perpendicular
coinciding

Answers

Answer:

The lines are parallel

Final answer:

The two lines, y = -3x + 8 and 6x + 2y = 1, are parallel because they both have the same slope of -3.

Explanation:

To determine whether the two lines are parallel, perpendicular, coinciding, or only intersecting, one must look at their slopes. The slope of a line in the form y = mx + b is given by 'm'.

If two lines have the same slope, they are parallel. If the product of their slopes is -1, they are perpendicular. If the lines have the same slope and same y-intercept, they coincide.

{p}The first line given is y = -3x + 8, so its slope is -3.

The second line, 6x + 2y = 1, needs to be rearranged into the form y = mx + b. If you subtract 6x from both sides and divide by 2, you get y = -3x + 0.5. Thus, the slope of the second line is -3 as well.

Since both lines have the same slope of -3, they are parallel.

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If the circumference of a baseball is 24 cm what is the volume of the object

Answers

$2\pi R=24cm\ \ \ /:2\pi\n\nR=(24)/(2\pi)\n\nR=(12)/(\pi)\ (cm)\n\nV=(4)/(3)\pi R^3\n\nV=(4)/(3)\pi\cdot\left((12)/(\pi)\right)^3=(4)/(3)\pi\cdot(1728)/(\pi^3)=(2304)/(\pi)\ (cm^3)\approx=(2304)/(3.14)\approx733.76\ (cm^3)$

A ball is dropped form a height of 100 inches. The ball bounces, each time reaching a lower and lower height. The height of each bounce is 75% of the previous bounce. What height will the ball reach after bouncing four times? How many bounces does it take for the ball to reach a height of less than one inch?

Answers

After the 'n'th bounce, the ball returns to a maximum height of

   (100) times (0.75)^n .

-- After 4 bounces, the maximum height is (100) (0.75)^4 = 31.64 inches.

-- To look for the maximum height of 1 inch,    (100) (0.75)^x = 1

Let's take the log of each side: log(100) + x log(0.75) = 0

Subtract log(100) from each side: x log(0.75) = -log(100)

Divide each side by log(0.75) :     x = -log(100) / log(0.75).

log(100) = 2 . So ... x = -2 / log(0.75) = -2 / -0.124939 = 16.00785

So the ball returns to a slim hair more than 1 inch high on the 16th bounce,
and returns to definitely less than 1 inch high on the 17th bounce.

75% of a number is as much as 3/4 of the same number, so:

1st bounce: 3/4 * 100 = 75
2nd bounce: 3/4 * 75 = 56,25
3rd bounce: 3/4 * 56,25 = 42,1875
4th bounce: 3/4 * 42,1875 = 31,640625
5th bounce: 3/4 * 31,640625 = 23,73046875
6th bounce: 3/4 * 23,73046875 = 17,7978515625
7th bounce: 3/4 * 17,7978515625 = 13,348388671875
8th bounce: 3/4 * 13,348388671875 = 10,01129150390625
9th bounce: 3/4 * 10,01129150390625 = 7,508468627929688
10th bounce: 3/4 * 7,508468627929688 = 5,631351470947266
11th bounce: 3/4 * 5,631351470947266 = 4,223513603210449
12th bounce: 3/4 * 4,223513603210449 = 3,167635202407837
13th bounce: 3/4 * 3,167635202407837 = 2,375726401805878
14th bounce: 3/4 * 2,375726401805878 = 1,781794801354408
15th bounce: 3/4 * 1,781794801354408 = 1,336346101015806
16th bounce: 3/4 * 1,336346101015806 = 1,002259575761855
17th bounce: 3/4 * 1,002259575761855 = 0,7516946818213909

Answers:

After bouncing four times, the ball will reach a height of 31,640625 inches.
The ball will reach a height of less than one inch after 17 bounces.

PS: I know it's kind of a walk-around, by it still gives us the answer :)

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