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Karo-lina-s [1.5K]

3 years ago

13

Three of the vertices of a rectangle have coordinates (-1, -1), (6, -1), and (-1, 2). What are the coordinates of thefourth vert

ex?

1 answer:

Ivenika [448]3 years ago

6 0

Answer:

(6,2)

Step-by-step explanation:

Diagonals have the same midpoint

(6-1)/2, (-1+2)/2 = (-1+x)/2, (-1+y)/2

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Tom wishes to purchase a property that has been valued at $300,000. He has $30,000 available as a deposit, and will require a mo

Mekhanik [1.2K]

Answer: The total interest paid on the mortgage is $179550

Step-by-step explanation:

The initial cost of the property is $300000. If he deposits $30000, the remaining amount would be

300000 - 30000 = $270000

Since the remaining amount was compounded, we would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 270000

r = 2% = 2/100 = 0.02

n = 12 because it was compounded 12 times in a year.

t = 25 years

Therefore,

A = 270000(1+0.02/12)^12 × 25

A = 270000(1+0.0017)^300

A = 270000(1.0017)^300

A = $449550

The total interest paid on the mortgage is

449550 - 270000 = $179550

3 0

3 years ago

Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.

insens350 [35]

Answer:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

Step-by-step explanation:

Given

$p(x) = \frac{x^2-2x-3}{x+2}$ -- Missing from the question

Required

The behavior of the function around its vertical asymptote at $x = -2$

$p(x) = \frac{x^2-2x-3}{x+2}$

Expand the numerator

$p(x) = \frac{x^2 + x -3x - 3}{x+2}$

Factorize

$p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}$

Factor out x + 1

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

$x -> -2^{-}$ Say x = -3

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

$p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12$

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

$x->-2^{-}, p(x)->-\infty$

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: $x>-2$

Say x = -2.1

$p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1$

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

$x->-2^{+}, p(x)->-\infty$

So, the behavior is:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

6 0

3 years ago

-4 times a number plus 29

kipiarov [429]

-4x+29? I think that's what you're asking.

8 0

3 years ago

The answer and the work that was needed to solve it .

cupoosta [38]

First, you add up all the prices. 1.79 + 2.99 + 4.37 + 0.33 = 9.48. Then, you do 10.00 - 9.48 = 0.52 and that's your answer.

7 0

3 years ago

Read 2 more answers

A and b are positive integers and a–b = 3. Evaluate the following: 27^ (1/3 b)/9^ (1/2 a)

maxonik [38]

Answer:

1/27

Step-by-step explanation:

27^(b/3)/9^(a/2) = (27^(1/3))^b/(9^(1/2))^a = (3^b)/(3^a) = 3^(b-a)

= 3^(-(a-b)) = 3^-3 = 1/3^3 = 1/27

5 0

3 years ago