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4 years ago

Find the simple interest earned to the nearest cent for a principal, interest rate and time.

Mathematics

1 answer:

Alexus [3.1K]4 years ago

7 0

<h3>Answer: 70.19 dollars</h3>

==================================

Work Shown

P = principal = 658

r = interest rate in decimal form = 0.16

t = time in years = 8/12

----

i = simple interest

i = P*r*t

i = 658*0.16*(8/12)

i = 70.18667

i = 70.19

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Calculate the rectangular prism with a length of 5.6cm, a with of 2.1 cm, and a height of 6.6cm.

Inessa05 [86]

5.6 x 2.1 x 6.6 = 77.616 2 significant figures would be 78 cm³ 2 decimal places would be 77.62 cm³

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%2By%3D1%7D%20%5Catop%20%7Bx-2y%3D4%7D%7D%20%5Cright.%20%5C%5C%5Clef

brilliants [131]

Answer:

<em>(c)</em> $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

Step-by-step explanation:

<u>Cramer's Rule</u>

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

4 0

4 years ago

3a² + 11a – 42<br><br>this is factoring in algebra 2 (high school) <br>

N76 [4]

To factor,

1) First multiply coefficient of a² and constant no,

That is,

3×(-42)=-126

Since the<u> resultant no is negative</u>, you should find two such factors of 126 <u>which</u> <u>will give us the coefficient of a (=11)</u> on subracting those factors.

2) Find the factor

126=2×3×3×7

=18×7

18 and 17 are factors of 126

Also,18-7 =11.

So they are required factors for factoring,

Once you have understood above steps you can solve on your own. All you need to do is split 11 into factors ,take common terms and you will get answer.

<u>Answer:</u>

3a²+11a-42

=3a²+(18-7)a -42

=3a²+18a-7a-42

=3a(a+6) -7(a+6)

=(a+6)(3a-7)

3 0

3 years ago

A shopper buys cat food in bags of 3 lbs. Her cat eats 34 lb each week. How many weeks does one bag last?

Vika [28.1K]

11 weeks hope this helps

3 0

3 years ago

A four-sided polygon has sides that measure 1 cm, 5cm, and 7 cm. (Forth side not given). What is the perimeter?

yaroslaw [1]

Answer:

(13+x)cm

Step-by-step explanation:

Given data

Length of sides

1cm, 5cm, 7cm

Since the shape is four-sided and the fourth side is not given, let the fourth side be x

The perimeter of the polygon is

P= 1+5+7+x

P= 13+x

Hence the perimeter of the polygon is

P= (13+x)cm

3 0

3 years ago