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3 years ago

15

Meg purchased a stereo system at a local store. It cost $675. She paid for it in six equal installments of $139 each. How much i

nterest did she pay?
Explanation plz. Would like to know how to solve for future questions.

1 answer:

yawa3891 [41]3 years ago

8 0

Answer:

159

Step-by-step explanation:

She paid 6 payments of 139

6*139 = 834

The cost was 675

834-675 =159

The interest was 159

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The ages of Aman and Arun are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present

Viktor [21]

Answer:

Aman's age = 20, Arun's age = 28

Step-by-step explanation:

Let $x$ = Aman's age

Let $y$ = Arun's age

- - - -

$x+4+y+4=56$ (Sum of their age is 56 after 4 years in the future)

$x+y+8=56$

$x+y=48$

$\frac{x}{y} = \frac{5}{7}$ (Ages are in the ratio 5:7)

$x=\frac{5}{7}y$

Now, we can use substitution to find for Arun's age:

$x+y=48$

$\frac{5}{7}y+y=48$

$\frac{12}{7}y=48$

$y=28$

∴ Arun is $28$

To find for Aman's age, we can use substitution:

$x+y=48$

$x+28=48$

$x=20$

∴ Aman is 20

Hope this helps :)

8 0

3 years ago

Ivan plans to reorganize the music on his MP3 players . He has 9 1/3 music of rock and hip-hop . After the change he is planning

faltersainse [42]

9 1/3 = 28/3 --> 140/15
2 4/5 = 14/5 --> 42/15

9 1/3 > 2 4/5
Therefor Ivan is planning on removing rock and hip-hop music from his MP3 players

4 0

3 years ago

Which graph represents the solution set for the system 2x + 5y ≤ 9 and 3x + 5y ≤ 9?

Brut [27]

Answer:

The answer is graph B. Have a nice day!

Step-by-step explanation:

3 0

2 years ago

Umnica [9.8K]

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(a)/(a^2-16)+(2/(a-4))-(2/(a+4))=0

Simplify ————— a + 4 <span>Equation at the end of step 1 :</span><span> a 2 2 (—————————+—————)-——— = 0 ((a2)-16) (a-4) a+4 </span><span>Step 2 :</span> 2 Simplify ————— a - 4 <span>Equation at the end of step 2 :</span><span> a 2 2 (—————————+———)-——— = 0 ((a2)-16) a-4 a+4 </span><span>Step 3 :</span><span> a Simplify ——————— a2 - 16 </span>Trying to factor as a Difference of Squares :

<span> 3.1 </span>     Factoring: <span> a2 - 16</span>

Theory : A difference of two perfect squares, <span> A2 - B2  </span>can be factored into <span> (A+B) • (A-B)

</span>Proof :<span>  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 <span>- AB + AB </span>- B2 =
        <span> A2 - B2</span>

</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.

Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4
Check : <span> a2  </span>is the square of <span> a1 </span>

Factorization is :       (a + 4)  •  (a - 4)

<span>Equation at the end of step 3 :</span> a 2 2 (————————————————— + —————) - ————— = 0 (a + 4) • (a - 4) a - 4 a + 4 <span>Step 4 :</span>Calculating the Least Common Multiple :

<span> 4.1 </span>   Find the Least Common Multiple

      The left denominator is :      <span> (a+4) •</span> (a-4)

      The right denominator is :      <span> a-4 </span>

<span><span>                  Number of times each Algebraic Factor
            appears in the factorization of:</span><span><span><span>    Algebraic
    Factor    </span><span> Left
Denominator </span><span> Right
Denominator </span><span> L.C.M = Max
{Left,Right} </span></span><span><span> a+4 </span>101</span><span><span> a-4 </span>111</span></span></span>

Least Common Multiple:
(a+4) • (a-4)

Calculating Multipliers :

<span> 4.2 </span>   Calculate multipliers for the two fractions

    Denote the Least Common Multiple by  L.C.M
    Denote the Left Multiplier by  Left_M
    Denote the Right Multiplier by  Right_M
    Denote the Left Deniminator by  L_Deno
    Denote the Right Multiplier by  R_Deno

   Left_M = L.C.M / L_Deno = 1

   Right_M = L.C.M / R_Deno = a+4

Making Equivalent Fractions :

<span> 4.3 </span> Rewrite the two fractions into<span> equivalent fractions</span>

Two fractions are called <span>equivalent </span>if they have the<span> same numeric value.</span>

For example : 1/2 and 2/4 are equivalent, <span> y/(y+1)2 </span> and <span> (y2+y)/(y+1)3 </span>are equivalent as well.

To calculate equivalent fraction , multiply the <span>Numerator </span>of each fraction, by its respective Multiplier.

<span> L. Mult. • L. Num. a —————————————————— = ————————————— L.C.M (a+4) • (a-4) R. Mult. • R. Num. 2 • (a+4) —————————————————— = ————————————— L.C.M (a+4) • (a-4) </span>Adding fractions that have a common denominator :

<span> 4.4 </span> Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a + 2 • (a+4) 3a + 8 ————————————— = ————————————————— (a+4) • (a-4) (a + 4) • (a - 4) <span>Equation at the end of step 4 :</span> (3a + 8) 2 ————————————————— - ————— = 0 (a + 4) • (a - 4) a + 4 <span>Step 5 :</span>Calculating the Least Common Multiple :

<span> 5.1 </span>   Find the Least Common Multiple

      The left denominator is :      <span> (a+4) •</span> (a-4)

      The right denominator is :      <span> a+4 </span>

<span><span>                  Number of times each Algebraic Factor
            appears in the factorization of:</span><span><span><span>    Algebraic
    Factor    </span><span> Left
Denominator </span><span> Right
Denominator </span><span> L.C.M = Max
{Left,Right} </span></span><span><span> a+4 </span>111</span><span><span> a-4 </span>101</span></span></span>

Least Common Multiple:
(a+4) • (a-4)

Calculating Multipliers :

<span> 5.2 </span>   Calculate multipliers for the two fractions

    Denote the Least Common Multiple by  L.C.M
    Denote the Left Multiplier by  Left_M
    Denote the Right Multiplier by  Right_M
    Denote the Left Deniminator by  L_Deno
    Denote the Right Multiplier by  R_Deno

   Left_M = L.C.M / L_Deno = 1

   Right_M = L.C.M / R_Deno = a-4

Making Equivalent Fractions :

<span> 5.3 </span> Rewrite the two fractions into<span> equivalent fractions</span>

<span> L. Mult. • L. Num. (3a+8) —————————————————— = ————————————— L.C.M (a+4) • (a-4) R. Mult. • R. Num. 2 • (a-4) —————————————————— = ————————————— L.C.M (a+4) • (a-4) </span>Adding fractions that have a common denominator :

<span> 5.4 </span> Adding up the two equivalent fractions

(3a+8) - (2 • (a-4)) a + 16 ———————————————————— = ————————————————— (a+4) • (a-4) (a + 4) • (a - 4) <span>Equation at the end of step 5 :</span> a + 16 ————————————————— = 0 (a + 4) • (a - 4) <span>Step 6 :</span>When a fraction equals zero :<span><span> 6.1 </span> When a fraction equals zero ...</span>

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the <span>denominator, </span>Tiger multiplys both sides of the equation by the denominator.

Here's how:

a+16 ——————————— • (a+4)•(a-4) = 0 • (a+4)•(a-4) (a+4)•(a-4)

Now, on the left hand side, the <span> (a+4) •</span> (a-4) cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
a+16 = 0

Solving a Single Variable Equation :

<span> 6.2 </span>     Solve  :    a+16 = 0<span>

</span>Subtract  16 from both sides of the equation :<span>
</span>                     a = -16

One solution was found :

<span> a = -16</span>

4 0

3 years ago

In the diagram mz3= x+ 30 and mz4 =2x-80. What is the measure of angle 3?

Andreas93 [3]

Given:

Consider the below figure attached with this question.

$m\angle 3=(x+30)^\circ$ and $m\angle 4=(2x-80)^\circ$ .

To find:

The measure of angle 3.

Solution:

From the below figure it is clear that, angle 3 and angle 4 are vertically opposite angles.

We know that, vertically opposite angles are always equal. So,

$m\angle 3=m\angle 4$

$(x+30)^\circ=(2x-80)^\circ$

$x+30=2x-80$

$x-2x=-30-80$

$-x=-110$

$x=110$

Now,

$m\angle 3=(110+30)^\circ$

$m\angle 3=140^\circ$

Therefore, the measure of angle 3 is 140 degrees.

6 0

3 years ago