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Zigmanuir [339]

3 years ago

12

Marc has 45 Cds in his collection, and Corinna has 61. If Marc buys 4 new CDs each month and Corinna buys 2 new CDs each month,

after how many months will Marc and Corinna have the same number of CDs Write an equation to solve

1 answer:

Mkey [24]3 years ago

4 0

After 8 months they both will have 77 CD's

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Find all the critical points of h(x) = x^3 − 3x^4 and categorize them as local

neonofarm [45]

Answer:

0 is an inflection point

1/4 is a local maximum.

Step-by-step explanation:

To begin with you find the first derivative of the function and get that

$h'(x) = 3x^2 - 12x^3$

to find the critical points you equal the first derivative to 0 and get that

$3x^2 - 12x^3 = 0, x = 0,1/4$

To find if they are maximums or local minimums you use the second derivative.

$h''(x) = 6x-36x^2$

since $h''(0) = 0$ is neither an inflection point, and since $h''(1/4) = -3/4$ then 1/4 is a maximum.

6 0

3 years ago

How to solve an expression with variables in the exponents?

gtnhenbr [62]

Answer:

use logarithms

Step-by-step explanation:

Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.

__

You will note that this approach works well enough for ...

a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents

(x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs

but doesn't do anything to help you solve ...

x +3 = b^(x -6)

There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.

__

Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.

In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.

8 0

2 years ago

Nadia is investigating rotations about the center of regular polygons that carry the regular polygon onto itself. She claims tha

GalinKa [24]

Answer:

$\theta_1 \ n\ \theta_2 = 120, 240$

Step-by-step explanation:

The question is incomplete, as the angles of rotation are not stated.

However, I will list the angles less than 360 degrees that will carry the hexagon and the nonagon onto itself

We have:

$Nonagon = 9\ sides$

$Hexagon = 6\ sides$

Divide 360 degrees by the number of sides in each angle, then find the multiples.

<u>Nonagon</u>

$\theta = \frac{360}{9} =40$

List the multiples of 40

$\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320$

<u>Hexagon</u>

$\theta = \frac{360}{6} =60$

List the multiples of 60

$\theta_2 = 60, 120, 180, 240, 300$

List out the common angles

$\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320$

$\theta_2 = 60, 120, 180, 240, 300$

$\theta_1 \ n\ \theta_2 = 120, 240$

This means that, only a rotation of $120, 240$ will lift both shapes onto themselves, when applied to both shapes.

The other angles will only work on one of the shapes, but not both at the same time.

7 0

3 years ago

What are the x-intercepts of x^2– 3x = 4?

Sindrei [870]

Answer:

x^2-3x=4

x^2-3x-4=0

x^2-4x+x-4=0

x(x-4)+1(x-4)=0

(x+1)(x-4)=0

x=-1,4

x- intercepts in the point (-1,0) and (4,0)

Step-by-step explanation:

3 0

3 years ago

PLEASE HELP ASAP THERE ARE 20 POINTS ON THE LINE! Sierra has to pay 7% taxes on her purchase at IKEA. If the tax is $38.36, what

Dominik [7]

Answer:

$31.36

Step-by-step explanation:

If she has $38.36 and you subtract 7 you would get the answer $31.36. I hope I helpped (◡ ω ◡)

6 0

2 years ago