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3 years ago

Indicate the equation of the given line in standard form.

Mathematics

1 answer:

s2008m [1.1K]3 years ago

6 0

The line through (a,b) with slope m is

y-b = m(x-a)

Here that's

y + 1 = (3/4) (x - 2)

Let's multiply by 4 to clear the fractions and distribute the constants,

4y + 4 = 3x - 6

Rearranging into standard form,

3x - 4y = 10

Check. The slope is 3/4, good. 3(2) - 4(-1) = 6+4 = 10 good

Answer: 3x - 4y = 10

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How to find compound rate from given values, 10 years after, and initial

dybincka [34]

The formula that calculates the compound rate from the given values is $r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})$

<h3>How to determine the compound interest rate?</h3>

The compound interest formula is:

$I = P(1 + \frac rn)^{nt} - P$

Where:

P represents the principal amount
r represents the compound interest rate
n represents the number of times the interest is compounded
t represents the time in years
I represents the interest

We start by adding P to both sides

$P + I = P(1 + \frac rn)^{nt}$

Divide through by P

$\frac{P + I}{P} = (1 + \frac rn)^{nt}$

Take the nt-th root of both sides

$\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn$

Subtract 1 from both sides

$-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn$

Multiply through by n

$r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})$

In this case, t = 10

So, we have:

$r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})$

Hence, the formula that calculates the compound rate is $r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})$

Read more about compound interest at:

brainly.com/question/13155407

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3 0

2 years ago

$10 000 is borrowed at 10.5% per annum interest. How much interest is owed at the end of the first 10 months?

Leviafan [203]

Answer:

$875 is the interest owed at the end of the first 10 months

Step-by-step explanation:

In this question, we are to calculate how much interest is owed in the first ten months.

There are several routes to this but the one i will like to use is as follows.

we shall calculate the amount owed for a year, afterwards we did use this amount by 12 since there are 12 months in a year. Now we multiply whatever answer we have by 10 to get the amount owed in 10 months.

To calculate the interest, we use the simple interest formula.

Mathematically;

I = PRT/100

where P is the amount borrowed which is $10,000

R is the interest rate which is 10.5% per annum

T is the time which we agreed we would be using 1 year first.

I = (10,000 * 10.5 * 1)/100 = $1050

This is the amount in 12 months. In a single month, this will be 1050/12 = $87.5

This amount in 10 months will be 87.5 * 10 = $875

8 0

3 years ago

Can someone help me ASAP!!!

Nostrana [21]

9514 1404 393

Answer:

f(x) = {-x for x < 2; 2x-3 for x ≥ 2}

Step-by-step explanation:

The blue line extending to the left has a slope of -1 and a y-intercept of 0. Its equation is y = -x. That part of the definition of f(x) is applicable for values of x less than 2. (The open dot at (2, -2) tells you that point is not included.)

The red line extending to the right has a slope = rise/run = 2/1 = 2. The y-intercept can be found by extending the line to the y-axis, or from the computation ...

b = y -mx

b = 1 -2(2) = -3 . . . . . for the point (x, y) = (2, 1)

Then the slope-intercept equation for the red line is ...

y = 2x -3

That part of the definition of f(x) is applicable for values of x ≥ 2. The solid dot tells you the point (2, 1) is included.

Putting these parts together, we get ...

$f(x)=\left\{\begin{array}{cc}-x&\text{if $x$