Mathematics, 04.01.2020 02:31 russelllang606

You begin with $90 in your savings account and your friend begins with $35 in her savings account. you deposite $10 in savings each week, and your friend deposites $15 in savings each week

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Answer from: rudolph34

Part a) The graph in the attached figure (see the explanation)

Part b) The friend is not correct

Step-by-step explanation:

The questions are

a. Write and graph a system of linear equations that represent the amounts in each of your savings accounts

b. Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer.

Part a)

Let

x ----> the number of weeks

y ---> the amount in the saving account

we know that

The linear equation in slope intercept form is equal to

y=mx+b

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

In this problem we have

Your saving accounts

The slope is equal to $m=\$10\ each\ week$

The y-intercept is equal to $b=\$90$

substitute

y=10x+90 ----> equation A

Your friend saving accounts

The slope is equal to $m=\$15\ each\ week$

The y-intercept is equal to $b=\$35$

substitute

y=15x+35 ----> equation B

using a graphing tool

the graph in the attached figure

Part b) Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer

we know that

When solving a system of equations by graphing, the solution of the system is the intersection point both graphs

In this problem, the intersection point is (11,200)

That means ----> In 11 weeks, both you and your friend have the same amount of money saved up, $200

Therefore

The friend is not correct

You begin with $90 in your savings account and your friend begins with $35 in her savings account. y

Answer from: Quest

ik how do do this just give me a few minutes and i will give it to

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

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