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3 years ago

Write a polynomial function in standard form with the given zeros. x= 2,-3,-5

Mathematics

1 answer:

kifflom [539]3 years ago

4 0

F(x) = (x -2)(x +3)(x +5)
.. = x^3 +6x^2 -x -30 . . . . . your polynomial in standard form.

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An investment of $29,000 was made by a business club. The investment was split into three parts and lasted for one year. The fi

lina2011 [118]

Answer:

The amounts of three parts of the investment are 18000, 6000, 5000 respectively.

Step-by-step explanation:

An investment of $29,000 was made by a business club.

Let the amount of first and second investment be x and y respectively. So, the amount of third investment is (29000-x-y).

The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 2250.

$0.08x+0.06y+0.09(29000-x-y)=2250$

On simplification we get

$-0.01x-0.03y+2610=2250$

$-0.01x-0.03y=2250-2610$

$-0.01x-0.03y=-360$

$0.01x+0.03y=360$ ..... (1)

The interest from the first investment was 4 times the interest from the second.

$0.08x=4(0.06y)$

$0.08x=0.24y$

$x=3y$ .... (2)

From (1) and (2) we get

$0.01(3y)+0.03y=360$

$0.03y+0.03y=360$

$0.06y=360$

Divide both sides by 0.06.

$y=6000$

Put this value in equation (2).

$x=3(6000)=18000$

The amount of third investment is

$29000-x-y=29000-18000-6000=5000$

Therefore the amounts of three parts of the investment are 18000, 6000, 5000 respectively.

7 0

3 years ago

The function g has an inverse. The function g − 1 determines the number of folds needed to give the folded paper a thickness of

Amanda [17]

Answer:

$\mathbf{g^{-1} (t) = log _2 \ 20 \ t}$

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

$g(n )= (05)2^n$

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

<u>SOLUTION:</u>

If we represent g(n) with t;

Then

$\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}$

Taking logarithm of both sides; we have :

$\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}$

4 0

4 years ago

*please help me out if you know how to solve, last person I asked just put a random awnser for point, the problem is bellow and

kicyunya [14]

For both of these, we will divide the wanted outcome by the number of possible outcomes. We will end up with a decimal. A decimal multiplied by 100 becomes a percent.

[a] 50%

$\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{student failed}}{\text{Period 2's class}} =\frac{12}{24} =0.5,\:0.5*100=50\%$

[b] 52%

$\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{student failed from Period 3}}{\text{fails from both classes}} =\frac{13}{25} =0.52,$