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Katen [24]
2 years ago
13

I need help with 4 5 and 6

Mathematics
1 answer:
Akimi4 [234]2 years ago
7 0
<h2>4. Create a table, write an equation,  AND show all your work.</h2>

Currently the stock is $62 and has been decreasing 3% each month. So, if we call x=0 the first month then:

at \ x=0 \ y=62 \\ \\ at \ x=1 \ y=62-62\times 3\%=60.14 \\ \\ at \ x=2 \ y=60.14-60.14\times 3\%=58.3358 \\ \\ at \ x=3 \ y=58.3358-58.3358\times 3\%=56.5857 \\ \\ at \ x=4 \ y=56.5857-56.5857\times 3\%=54.8881 \\ \\ at \ x=5 \ y=54.8881-54.8881\times 3\%=53.2414

So the Table is:

\left[\begin{array}{cc}x & y\\0 & 62\\1 & 60.14\\2 & 58.3358\\3 & 56.5857\\4 & 54.8881\\5 & 53.2414\end{array}\right]

This is an exponential function because it has a constant ratio.

From our values, we can conclude that the equation is:

y=62(100%-3%)^{x} \\ \\ \boxed{y=62(0.97)^{x}}

In five months, the stock will be $53.2414

<h2>5. Write the exponential function</h2>

We are given two points:

P_{1}(0,5) \\ \\ P_{2}(3,135)

We know that the exponential function is given by the form:

y=ab^{x}

So:

\bullet \ If \ x=0 \ then \ y=5 \\ \\ 5=ab^{0} \therefore a=5 \\ \\ \\ \bullet \ If \ x=3 \ y=135 \\ \\ 135=ab^{3} \therefore ab^{3}=135 \\ \\ \\ Finding \ b: \\ \\ \frac{ab^{3}}{a}=\frac{135}{5} \\ \\ b^3=27 \therefore b=\sqrt[3]{27} \therefore \boxed{b=3}

Then:

\boxed{y=5(3)^{x}}

<h2>6. Slope, length and midpoint</h2>

Here we are given two points:

A(4,9) \ and \ B(-2,3)

So, the slope can be found as:

m=\frac{Change \ in \ y}{Change \ in \ x} \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m=\frac{3-9}{-2-4} \\ \\ \boxed{m=1}

Using the distance formula we can find the length:

d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\ \\ d=\sqrt{(-2-4)^2+(3-9)^2} \\ \\ d=\sqrt{36+36} \\ \\ d=\sqrt{72} \\ \\ \boxed{d=6\sqrt{2}}

To find the midpoint, we have to use the midpoint formula:

Midpoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) \\ \\ Midpoint=(\frac{4-2}{2},\frac{9+3}{2}) \\ \\ \boxed{Midpoint=(1,6)}

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Please answer this...​
Romashka [77]
2 in the first column and 5 in the second column
7 0
3 years ago
Click
Mama L [17]

Answer:

(-3 , 0) (0, 2) (6, -6)

Step-by-step explanation:

Solving for x - intercept:

2x - 3(0) = -6

2x = -6

2x/2 = -6/2

x = -3

One point would be (-3 , 0) .

Solving for y-intercept:

2(0) - 3y = -6

-3y = -6

-3y/-3 = -6/-3

y = 2

Another point would be (0, 2).

When 'x' equals 6:

2(6) - 3y = -6

12 - 3y = -6

12 - 12 - 3y = -6 - 12

-3y = -18

-3y/3 = -18/3

y = -6

The third point would be (6, -6).

6 0
3 years ago
How wide is a 3 ft doorway in a 1/4 inch scale drawing?
Crank

Answer:

9 inches

Step-by-step explanation:

Convert from feet to inches by multiplying by 12:

3*12 = 36

Multiply by the scale factor of 1/4:

36*1/4 = 9

9 inches

4 0
1 year ago
Angles of Triangles Practice Riddle
kherson [118]
Would love to help but unsure what you are referring too
7 0
2 years ago
Read 2 more answers
if a knockout tennis competition starts with 64 players how many runs will it take to reach the grand final show your steps usin
snow_tiger [21]

Answer:

  • 5 runs

Step-by-step explanation:

Initial number is 64 players

<u>Number of players reduce twice every run and will be equal to 2 to reach the grand final</u>

  • 64*(1/2)^x = 2
  • (1/2)^x = 1/32
  • 2^-x = 2^-5
  • -x = -5
  • x = 5

Number of runs is 5

64 > 32 > 16 > 8 > 4 > 2

8 0
2 years ago
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