Marie has 50 pages in her notebook. She made a graph of the kinds of writing on all of the pages she has

Plot the following points to create a rectangle.

Tanya [424]

Answer:

(5, -1)

Step-by-step explanation:

The three coordinates of a triangle are given as:

(5,3), (-5,3), (-5,-1).

To find:

The missing vertex = ?

Solution:

Let us label the vertices:

A (5,3),

B(-5,3),

C(-5,-1).

Let the missing vertex be ( $x, y$ ).

Let us recall the properties of a rectangle.

The <em>opposite sides</em> of the rectangle are equal and parallel to each other.

Let us consider the side AB, we can see that only x coordinate is changed from A to B.

Let us consider the side BC, we can see that only y coordinate is changed from B to C.

A and B are adjacent vertices.

Similarly the opposite vertices will be C and D.

Same pattern will be followed in CD as that of AB.

x coordinate will be changed by same difference as that of AB.

Change in x coordinate from D to C = $-5-x$

Change in x coordinate from A to B = $-5-5 =-10$

Equating them:

$-5-x=-10\\\Rightarrow x = 5$

Same pattern is followed in BC and AD.

Their change in y coordinate will be same.

$-1-3=y-3\\\Rightarrow y =-1$

Missing vertex is <em>(5, -1)</em>.

Please refer to the attached image for the rectangle.

3 0

4 years ago

Which equation represents the line that passes through the points (2, 4) and (1, -3)?

zhannawk [14.2K]

Answer:

y = 7x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (1, - 3)

m = $\frac{-3-4}{1-2}$ = $\frac{-7}{-1}$ = 7, thus

y = 7x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 4), then

4 = 14 + c ⇒ c = 4 - 14 = - 10

y = 7x - 10 ← equation of line

6 0

4 years ago

Please help this for my pre calculus finals

dsp73

Answer:

a) It will take 17.71 years

b) It will take 17.58 years

c) I will earn $6.60 more in compound continuously

Step-by-step explanation:

a) Lets talk about the compound interest

- The formula for compound interest is A = P (1 + r/n)^(nt)

, Where:

- A = the future value of the investment, including interest

- P = the principal investment amount (the initial deposit)

- r = the annual interest rate (decimal)

- n = the number of times that interest is compounded per unit t

- t = the time the money is invested

* Lets solve the problem

∵ The money deposit is $2000

∵ The rate is 6.25%

∵ The interest is compound quarterly

∵ The future value is $6000

∴ P = 2000

∴ A = 6000

∴ r = 6.25/100 = 0.0625

∴ n = 4

∴ t = ?

∵ A = P (1 + r/n)^(nt)

∴ 6000 = 2000 (1 + 0.0625/4)^4t ⇒ divide both sides by 2000

∴ 3 = (1.015625)^4t ⇒ insert ㏑ for both sides

∴ ㏑(3) = ㏑(1.015625)^4t

∵ ㏑(a)^b = b ㏑(a)

∴ ㏑(3) = 4t ㏑(1.015625) ⇒ divide both sides by ㏑(1.015625)

∴ 4t = ㏑(3)/㏑(1.015625) ⇒ divide both sides by 4

∴ t = [㏑(3)/㏑(1.015625)] ÷ 4 = 17.71

* It will take 17.71 years

b) Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:

A = P e^rt

- A = the future value of the investment, including interest

- P = the principal investment amount (the initial amount)

- r = the interest rate

- t = the time the money is invested

* Lets solve the problem

∵ The money deposit is $2000

∵ The rate is 6.25%

∵ The interest is compound continuously

∵ The future value is $6000

∴ P = 2000

∴ A = 6000

∴ r = 6.25/100 = 0.0625

∴ t = ?

∵ A = P e^rt

∴ 6000 = 2000 e^(0.0625 t) ⇒ divide both sides by 2000

∴ 3 = e^(0.0625 t) ⇒ insert ㏑ to both sides

∴ ㏑(3) = ㏑[e^0.0625 t]

∵ ㏑(e^a) = a ㏑(e) ⇒ ㏑(e) = 1 , then ㏑(e^a) = a

∴ ㏑(3) = 0.0625 t ⇒ divide both sides by 0.0625

∴ t = ㏑(3)/0.0625 = 17.5778

* It will take 17.58 years

c) If t = 5 years

# The compound quarterly:

∵ A = P (1 + r/n)^(nt)

∴ A = 2000 (1 + 0.0625/4)^(4×5)

∴ A = 2000 (1.015625)^20 = $2727.08

# Compound continuously

∵ A = P e^(rt)

∴ A = 2000 e^(0.0625×5) = $2733.68

∴ I will earn = 2733.68 - 2727.08 = $6.60

* I will earn $6.60 more in compound continuously

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