Which system of inequalities has no solution?

Consider a student loan of 22,500 at a fixed APR of 12% for 20 years what is the monthly payment?

PSYCHO15rus [73]

It would be $96.66 per month

4 0

3 years ago

What are the roots of the polynomial equation x3 - 6x = 3x2 - 8? Use a graphing calculator and a system of equations.

makkiz [27]

Answer:

d : 4, 1, -2.

Step-by-step explanation:

There's no need for a calculator in my opinion because we can use the rational root theorem which states that the equations of this form:

$\sum_{i=0}^{n} a_{i}x^i = 0 = a_{0} + a_{1}x + a_2x^2 + ... + a_nx^n = 0\\ a_i \in \mathbb{Z}$

Have rational roots, than the roots are of the form: $\frac{k \cdot a_o}{p \cdot a_n}, \ where \ k, p \in \mathbb{Z}.$

Rewriting the equation we have:

$x^3 - 3x^2 -6x + 8 = 0\\By \ our\ previous \ claim \ x \in D_8 \ where \ D_n \ the \ set \ of \ divisors \ of \ n.\\D_8 = \{\pm 1, \pm 2, \pm 4, \pm 8\} \\We \ plug \ in \ some \ number from \ D_8.\\Letting \ x = -2;\\(-2)^3 -3(-2)^2 -6(-2) + 8 = 0 \ \ \ Thus \ x+2 \ is \ a \ factor.\\We \ can \ now \ simplify \ the \ eq. \ using \ Polynomial \ Long \ Division.$

$x^3 -3x^2 -6x + 8 = (x+2)(Q(x))\\To \ find \ Q \ we \ divide \ the \ original \ equation \ by \ x + 2; which \ yields:\\Q(x) = x^2 - 5x + 4.\\So \ we \ can \ use \ the \ quadratic \ formula \ to \ find \ the \ roots:\\x = 4,x = 1. \\Thus \ x \in \{-2, 1, 4\}. \ \ These \ are \ all \ the \ roots.$

5 0

4 years ago

15 points. Please explain your answer thanks so much.:)

Anni [7]

Answer:

CDJ= 34

Step-by-step explanation:

We know that ADJ = 90 degrees

ADK = 180 degrees and JDK equals 90 degrees so ADJ must equal 90 degrees

ADJ = ADC+CDJ

ADJ =4x+ 3x-8

Since ADJ = 90 degrees

90 = 4x+3x-8

Combine like terms

90 = 7x-8

Add 8 to each side

90+8 = 7x-8+8

98 = 7x

Divide each side by 7

98/7 = 7x/7

14 =x

We want to know CDJ

CDJ = 3x-8

CDJ = 3(14) -8

CDJ = 42-8

CDJ= 34

7 0

4 years ago

I forgot how to do these over winter break. can someone help, please?

Natalija [7]

Answer:

I can help you just post another thing because there is no picture.

Step-by-step explanation:

4 0

3 years ago

The cost of purple dye has been increasing over the last few months, and Robyn uses this dye as part of her tie dye scarf busine

joja [24]

The lowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%

<h3>How to calculate the percentage?</h3>

(Price- Unit Cost)/Price= 20% or 0.2

Price- Unit Cost= 0.2 Price

0.8 Price = Unit Cost

Let Unit Cost be x

Price = x/0.8= 1.25x

Dye is 60% of unit costs= 0.6x

Cost of remaining material= 1 - 0.6x = 0.4x

Unit Cost= Cost of Dye+ Cost of remaining material

So, in order to become unprofitable, Unit Cost must be 1.25x

Therefore

1.25x= Maximum cost of dye+ 0.4x

Maximum Cost of Dye = (1.25-0.4)x = 0.85x

Percentage change in cost of dye= {(0.85x-0.6x)/0.6x}*100= 41.66 or 42%

Therefore, theowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

6 0

2 years ago