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tekilochka [14]
3 years ago
8

Which of the following is an equation of a line that is parallel to y = 4 x + 9 ? (Choose all correct equations.)

Mathematics
1 answer:
babymother [125]3 years ago
6 0

Answer:

The second, third and fourth are parallel to the given equation

Step-by-step explanation:

In order to determine if the slopes are the same, put all of the equations in slope-intercept form:  y = mx + b.  In order for lines in this form to be parallel, the m values of each have to be the exact same number, in our case, 4.  Equation 2 has a 4 in the m position, just like the given, so that one is easy.  Equation 2 is parallel.

Let's solve the third equation for y:

12x - 3y = 6 so

-3y = -12x + 6 and

y = 4x - 2.  Equation 3 is parallel since there is a 4 in the m position.

Let's solve the fourth equation for y:

-20x + 5y = 45 so

5y = 20x + 45 and

y = 4x + 9.  Equation 4 is also parallel since there is a 4 in the m position.

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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.

7 0
3 years ago
7 + -6 = what is the answer​
oee [108]

Answer:

answer is 1

I hope it's helps you

7 0
3 years ago
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The standard deviation for a set of data is 8.5. The mean is 215.
mixas84 [53]
The answer to your question is 2.5 hope this helps
6 0
3 years ago
Y=2x-1 and y=x-8 using substitution​
Vitek1552 [10]

Answer:

Step-by-step explanation:

y = 2x - 1

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substitute y = 2x - 1 in equation (i)

2x - 1 = x - 8

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7 0
3 years ago
Someone please help
Lelechka [254]

Answer:

Im sorry im not sure how to do this either lol :/

Step-by-step explanation:

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