All categories

3 years ago

consider the line y= 2/3x-0. Find the equation of the line that is parallel to this line and passes through the point (8, 4).

1 answer:

3 0

Point-slope form of a line: we need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)

slope intercept form :
y=m+b

m=slope

If the line is parallel to y=2/3 x-0, the line will have the same slope, therefore the slope will be: 2/3.

Data:
(8,4)
m=2/3

y-y₀=m(x-x₀)
y-4=2/3(x-8)
y-4=2/3 x-16/3
y=2/3 x-16/3+4
y=2/3 x-4/3 (slope intercept form)

Answer: The equation of the line would be: y=2/3 x-4/3.

if we have the next slope "m",then the perendicular slope will be:
m´=-1/m

We have this equation: y=2/3 x+0; the slope is: m=2/3.

The perpendicular slope will be: m`=-1/(2/3)=-3/2

And the equation of the perpendicular line to : y=2/3 x+0, given the point (8,4) will be:

y-y₀=m(x-x₀)
y-4=-3/2 (x-8)
y-4=-3/2 x+12
y=-3/2x + 12+4
y=-3/2x+16

answer: the perpendicular line to y=2/3 x+0 , given the point (8,4) will be:
y=-3/2 x+16

You might be interested in

I'm a famous young artist but I've never been able to draw a dog

Sladkaya [172]

Then try your best and reach your limit

7 0

3 years ago

You are offered the following gamble based on coin flips. If the first heads occurs on the first flip, you get $2. If the first

Andrews [41]

Answer:

infinity

Step-by-step explanation:

a) the expected value of this gamble in dollars is Infinity

i.e

expected value = $\frac{1}{2}*2 + \frac{1}{4}*4 + \frac{1}{8}*8 + \frac{1}{16}*16 + ... + \to \infty (infinty) \\$

= $1+1+1+1+1 + ... = \infty$

When offered, most people say they would pay only less than $10 to play this game.

What are two reasons why people are willing to pay so much less than the expected value?

These people are ready to pay less than $10 to play this game due to the fact that people usually overlook the unlikely event when making decisions. In a bid to that logic, they gamble in order to double their amount of money and the probability that heads may never come is ignored by these people and they may hope for a likely event i.e a head every time they play the game.

Also, the expected value is so humongous that if and only if that the first head appears after a long series of tails which is very less certain to occur, because mostly people would think that on an average the length of a series of tails ( or heads) is somewhat near 10 or so, but definitely infinity.

3 0

3 years ago

In 2010, the population of a city was 161,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 6.7%.

solniwko [45]

Answer:

99%

Step-by-step explanation:

2010 population = 161,000

From 2010 to 2015, the population grew by 8%.

2010 to 2015 = 161,000 + (8% of 161,000)

= 161,000 + (0.08 * 161,000)

= 161,000 + 12,880

= 173,880

2010 to 2015 = 173,880

From 2015 to 2020, it fell by 6.7%

2015 to 2020 = 173,880 - (6.7% of 173,880)

= 173,880 - (0.067 * 173,880)

= 173,880 - 11,649.96

= 162,230.04

2015 to 2020 = 162,230.04

what percent did the city grow from 2010 to 2020.

= 161,000 / 162,230.04 × 100

= 0.9924179270374 × 100

= 99.241792703743

Approximately, 99% to the nearest whole number

4 0

2 years ago

To go to the school footsall game, a student would pay $2.00 for each drink purchases,

kotykmax [81]

Answer: 2d

Step-by-step explanation:

You multiply the cost by the amount d, to find the total cost. Since it wants an expression, there is no equal sign.

4 0

3 years ago

Sean used the $1,200 he got from his graduation party to open a savings account. If the account earns 1% interest each month and

Greeley [361]

Answer:

$\$1,920$

Step-by-step explanation:

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=5*12=60\ months\\ P=\$1,200\\r=0.01$

substitute in the formula above

$A=\$1,200(1+0.01*60)$

$A=\$1,200(1.6)=\$1,920$

6 0

2 years ago