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Digiron [165]
3 years ago
12

How does the graph of y = 3x compare to the graph of y = 3–x?

Mathematics
2 answers:
bekas [8.4K]3 years ago
7 0
<h2>Answer and explanation:</h2>

In this problem, we have two functions. Let's call the first functions as:

y=f(x)=3x

and the second function:

y=g(x)=3-x

So we can compare this functions as follows:

  • f(x) has a positive slope while g(x) has a negative slope.

  • f(x) passes through the origin of the system of coordinates while g(x) cuts the y-intercept at y=3

  • g(x) has an x-intercept at x=3 while f(x) cuts the origin.
olga nikolaevna [1]3 years ago
6 0

Answer:

Both graphs represent the equation of a line

Step-by-step explanation:

Both graphs represent the equation of a straight line with the equation:

y = mx + c

Where m = the slope of the line and

c = intercept

Comparing both equations to the equation of a line given above:

In the first equation y = 3x

The slope, m = 3 (Positive slope)and

Intercept, c = 0

In the equation y = 3 -x

the slope, m = -1 (negative slope)

Intercept, c = 3

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Rhombus ABCD with vertices A(2, 6), B(6, 7),<br> C(5, 3), and D(1, 2): 180°
Korvikt [17]

Answer:

Step-by-step explanation:

Rule for the rotation of a point 180° about the origin is,

(x, y) → (-x, -y)

Therefore, images of the points after the rotation of 180° will be,

A(2, 6) → A'(-2, -6)

B(6, 7) → B'(-6, -7)

C(5, 3) → C'(-5, -3)

D(1, 2) → D'(-1, -2)

Now we can plot these points on the graph as attached.

6 0
3 years ago
Find the unit rate. 21 3/4 meters in 2 1/2 hours
anyanavicka [17]
(21 3/4) / (2 1/2) =
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6 0
3 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

5 0
3 years ago
We have 12 pumpkin pies that need to be shared evenly between 16 people
Artyom0805 [142]
You can divide 16 and 12, which will get you 1 and 1/4 a person left, but rounded will get 2
7 0
3 years ago
99g in the ratio 5:2:4
uranmaximum [27]

Answer:

45:18:36

Step-by-step explanation:

99 = 5x +2x+4x\\99=11x\\x=9\\

substitute x back into 5x:2x:4x

Therefore, 99 in the ratio of 5:2:4...

45:18:36

4 0
3 years ago
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