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3 years ago

Write the slope-intercept form of the line that passes through (1, -2) and is parallel to the line y = 4x + 2.

Mathematics

2 answers:

Naily [24]3 years ago

8 0

Use

y-y1=m(x-x1)

y-(-2)=4(x-1) Now why 4??Because parallel lines have the exact same slope

y+2=4x-4

y=4x-4-2

y=4x-6

Hope it helps!

$GraceRosalia$

~Just a teen who listens to music

seraphim [82]3 years ago

4 0

Parallel lines have the same slope.

Given the linear equation, y = 4x + 2:

Since the slope = 4, then we can assume that the slope of the line parallel to y = 4x + 2 will have the same slope.

We’ll use this slope and the given point, (1,-2), and plug these values into the slope-intercept form (y = mx + b) to solve for the y-intercept (b):

y = mx + b
-2 = 4(1) + b
-2 = 4 + b

Subtract 4 from both sides to isolate and solve for b:

-2 - 4 = 4 - 4 + b
-6 = b

Therefore, the y-coordinate of the y-intercept is -6 . Now, we can finally establish the linear equation of the line parallel to y = 4x + 2, which is:

y = 4x - 6.

Attached is a screenshot of the graph of both equations to show that we came up with a line parallel to the original equation.

Please mark my answers as the Brainliest if you find my explanations helpful :)

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If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600? If the co

Sphinxa [80]

Answer:

Using continuous interest 6.83 years before she has $1600.

Using continuous compounding, 6.71 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

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

$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

$(1.035)^{2t} = \frac{1600}{1000}$

$(1.035)^{2t} = 1.6$

$\log{1.035)^{2t}} = \log{1.6}$

$2t\log{1.035} = \log{1.6}$

$t = \frac{\log{1.6}}{2\log{1.035}}$

$t = 6.83$

Using continuous interest 6.83 years before she has $1600

If the compounding is continuous, how long will it be?

We have that $P(0) = 1000, r = 0.07$

Then

$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

$e^{0.07t} = 1.6$

$\ln{e^{0.07t}} = \ln{1.6}$

$0.07t = \ln{1.6}$

$t = \frac{\ln{1.6}}{0.07}$

$t = 6.71$

Using continuous compounding, 6.71 years.

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3 years ago

Jill grew 40 flowers with 4 seed packets. With 5 seed packets, how many total flowers can Jill have in her garden? Solve using u

ad-work [718]

The answer is 50
The answer is 50 because it told you that he had 40 seeds with 4 packets and if you add another packet it makes 50 because each packet had 10 in it

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3 years ago

How long was each sprinkler used? The water output rate for the Rodriguez family's sprinkler was 15L per hour. The water output

Lelechka [254]

Answer:

Rodriguez family's sprinkler used for 40 hours

Perry family's sprinkler used for 15 hours.

Step-by-step explanation:

Let "x" be the number of hours Rodriguez family's sprinkler used and "y" be the number of hours Perry family's sprinkler used.

Now let's form two equations using the given information.

x + y = 55 ------------(1)

Using the output, we can form another equation.

15x + 20y = 900 -----(2)

Now we have to solve these two equations to find the number of hours each sprinkler used.

We can use substitution method to solve these two equations.

From the equation (1), we can write

x = 55 - y

Now plug in x = 55 - y in the equation (2), we get

15(55 - y) + 20y = 900

Using the distributive property a(b -c) = ab - ac, we get

15(55) - 15y + 20 y = 900

825 - 15y + 20y = 900

Simplifying the above equation, we get

5y = 900 - 825

5y = 75

Dividing both sides by 5, we get

y = 15

Now plug y = 15 in x = 55 - y to find the value of x.

x = 55 - 15

x = 40

So, Rodriguez family's sprinkler used for 40 hours

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3 years ago

6 1/4 - 2 3/4 = ? please help lol

sergeinik [125]

Answer:

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Step-by-step explanation:

Rewriting our equation with parts separated

=6+1/4−2−3/4=6+1/4−2−3/4

Solving the whole number parts

6−2=4/6−2=4

Solving the fraction parts

1/4−3/4=−2/4 1/4−3/4=−2/4

Reducing the fraction part, 2/4,

−2/4=−1/2−2/4=−1/2

Combining the whole and fraction parts

4−1/2=3 1/2

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3 years ago

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lapo4ka [179]

7(3)=(7*5) -( x*2)

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35-21= 14

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3 years ago

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