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3 years ago

Determine whether the lines are parallel or perpendicular or neither. 2x=y−10 and y=−2x

Mathematics

1 answer:

MrRa [10]3 years ago

7 0

Put the first equation in slope-intercept form, or y = mx + b. Start by subtracting y from both sides.

2x - y = -10, subtract 2x from both sides.

-y = -10 - 2x

Divide both sides by negative one.

y = 10 + 2x

To find the slope when the equations are in slope-intercept form you look at the coefficient of x. The first equation has the slope of 2 (which we just found), and the second equation has the slope of -2.

Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Since 2 and -2 are neither of these, your answer is neither.

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A 50. kg remote control car is accelerating on a flat road, and the free body diagram for the car is shown below. If the force o

goldfiish [28.3K]

Answer:

12 m/s²

Step-by-step explanation:

mass of the car = 50 kg

The net force applied to the car is 800 - 200 = 600 N

Form the Newton's second law:

F = m*a

where F is the net force applied to the object, m is the mass of the object, and a is the acceleration of the object.

Then, the acceleration of the car (in m/s²) is:

a = F/m

a = 600/50

a = 12 m/s²

4 0

3 years ago

Lars is planning to purchase a home. He has been approved for a $420,000, 20-year mortgage with an APR of 5.125%.

Alenkasestr [34]

Answer:

Wow - you are asking a LOT of questions. The Monthly Payment Formula is really tricky so I'll solve that for you.

The time of the loan = 20 years * 12 = 240 months

We have to convert the annual rate to a monthly rate and that is done by:

monthly rate = 5.125 / 1,200 = 0.00427083333333333

Monthly pmt = 0.00427083333333333 + [0.00427083333333333 / (1.00427083333333333^240) -1 ] * 420,000

Monthly pmt = 0.00427083333333333 + [0.00427083333333333 / 2.7810190076 -1] * 420,000

Monthly pmt = (0.00427083333333333 +0.0023979718) * 420,000

Monthly pmt = 2,800.90

A calculator to double check is here: https://www.1728.org/calcloan.htm

Step-by-step explanation:

6 0

2 years ago

A ballplayer catches a ball 3.4s after throwing it vertically upward. with what speed did he throw it, and what height did it re

Daniel [21]

From the equation of motion, we know,

$s=ut+\frac{1}{2}at^{2}$

Where s= displacement

u= initial velocity

a= gravitational force

t= time

Displacement is 0 since the ball comes back to the same point from where it was thrown.

A = $-9.8m/s^{2}$ since the ball is thrown upwards.

Plug the known values into the equation.

=> $0=u\left ( 3.4 \right )+\frac{1}{2}\left ( -9.81 \right )(3.4^{2})$

Solving for u gives :

u= 16.67 m/ sec ....... equation (1)

At maximum height, final velocity i.e v is 0

Time take to reach the top = $\frac{3.4}{2} = 1.7 sec$

$v^{2}=u^{2}+2as$

=> $0=(16.67)^{2}+2(-9.81)(s)$

Solving for s we get

s= 14.16 m

4 0

3 years ago

Emily would like to buy some new

bonufazy [111]

Answer:

$14,277.80

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P(1+r/n)^(nt) .....1

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

P = $7,400

t = 8 years

n = 4 (quarterly)

r = 9.5% = 0.095

Using equation 1.

A = $7,400(1+0.095/4)^(4×7)

A = $7,400(1.02375)^(28)

A = $7,400(1.929432606035)

A = $14,277.80

final amount/value after 8 years A =$14,277.80

6 0

2 years ago

Which value of a in the exponential function below would cause the function to stretch?

maxonik [38]

Answer:

“1.5”

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers