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4 years ago

Which equation is perpendicular to y = 4x - 6 and passes through point (8, 12).

Mathematics

1 answer:

sergeinik [125]4 years ago

7 0

Answer:

The line is ;

4y = -x + 56

y = -x/4 + 14

Step-by-step explanation:

Generally, the equation of a straight line is;

y = mx + c

where m represents the slope

so for y = 4x - 6

The slope is 4

If two lines are perpendicular, the product of their slopes is -1

So for the second line, the slope will be -1/4

The equation in the point slope format will be ;

y-12 = -1/4(x-8)

y-12 = -x/4 + 2

Multiply through by 4

4y-48 = -x + 8

4y = -x + 8 + 48

4y = - x + 56

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Select the graph that correctly represents ƒ(x) = –2(x + 4)2 – 1.Find the equation of the parabola with its focus at (3,4) and i

IgorC [24]

Answer:

Equation of parabola: 8*(y - 2) = (x - 3)^2

y = (1/8)*(x - 3)^2 + 2

Step-by-step explanation:

focus at (3,4) and its directrix y = 0.

Focus equation: (h, k + c) = (3, 4)

Directrix equation y = k - c = 0

so h = 3, k + c = 4, k - c = 0

Solve the system : k + c = 4 and k - c = 0

add the equations together: k + c + k - c = 4 + 0

2k = 4

k = 2

so k + c = 4, 2 + c = 4, c = 2

4c (y - k) = (x - h)^2

4*2 *(y - 2) = (x - 3)^2

8*(y - 2) = (x - 3)^2

3 0

3 years ago

How long will it take for $2500 to double if it is invested at 6% annual interest compounded 6 times a year? Enter exact calcula

12345 [234]

Answer:

Part 1) $t=11.610\ years$

Part 2) $t=11.552\ years$

Step-by-step explanation:

Part 1) we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06\\n=6$

substitute in the formula above

$5,000=2,500(1+\frac{0.06}{6})^{6t}$

$2=(1.01)^{6t}$

Apply log both sides

$log(2)=log[(1.01)^{6t}]$

$log(2)=(6t)log(1.01)$

solve for t

$t=log(2)/[6log(1.01)]$

$t=11.610\ years$

Part 2) we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06$

substitute in the formula above

$5,000=2,500(e)^{0.06t}$

$2=(e)^{0.06t}$

Apply ln both sides

$ln(2)=ln[(e)^{0.06t}]$

$ln(2)=(0.06t)ln(e)$

$ln(2)=(0.06t)$

$t=ln(2)/(0.06)$

$t=11.552\ years$

3 0

3 years ago

Help me plz with this

andre [41]

You have to multiply each pair of sides and then add all the numbers together which would give you your answer

5 0

4 years ago

Read 2 more answers

Due 10/2

SpyIntel [72]

Answer: The water level drops each hour by 0.1472 inches/hour.

Step-by-step explanation:

We are given that Between 9 AM and 6:10 AM the water level in a swimming pool decreased by 5/12 inches assuming that the water level decreased at a constant rate.

Firstly, we will find the number of hours between 6:10 AM and 9 AM, that is;

Number of hours = From 6:10 AM and 9 AM, there are 2 hours and 50 minutes

So, Number of hours = = 2.833 hours

Also, the water level in a swimming pool decreased by = = 0.417 inches

Now, to find how much did the water level drop each hour, we will divide the amount of water level in a swimming pool decreased by the time interval given, that is;

= 0.1472 inches/hour.

This means that the water level drops each hour by 0.1472 inches/hour.

0.1472 as a fraction is 92/625

5 0

3 years ago

Loretta is a single mom with two kids. In 2009 her gross income was $61,840. She filed

zvonat [6]

Answer:

$30,920

Step-by-step explanation:

Divide $61,840 by 2

5 0

3 years ago