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laila [671]
4 years ago
8

I NEED HELP jimthompson5910

Mathematics
2 answers:
Musya8 [376]4 years ago
6 0

I'll do the first four problems to get you started

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

Problem 15

<h3>Answer:  40%</h3>

-----------------

Explanation:

The price dropped by $60, since 150-90 = 60. This is the discount, which is the amount you save. Divide this over the original price ($150) and we get 60/150 = 0.40 = 40%

Therefore, the price has been reduced by 40%. If we take 40% of 150, then 0.40*150 = 60 showing that 40% of $150 is 60 dollars. This matches up with the discount value mentioned earlier. So it helps verify the answer.

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

Problem 16

<h3>Answer: 20%</h3>

-----------------

Explanation:

The pay raised by 12-10 = 2 dollars. So the percent increase is 2/10 = 0.20 = 20%

Note how 20% of 10 = 0.20*10 = 2 is the pay raise amount; meaning that 2 is 20% of 10.

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

Problem 17

<h3>Answer: 50%</h3>

-----------------

Explanation:

I'll use a formula this time, but we could follow the same idea as the previous problems. This is to give another approach.

A = old value = 8

B = new value = 12

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (12-8)/8 ] * 100%

C = (4/8)*100%

C = 0.50*100%

C = 50%

50% is the same as half of the value. Note how half of 8 is 4, ie 50% of 8 = 0.50*8 = 4. So this is the amount of increase when going from 8 to 12.

Side note: The "B-A" portion in the numerator represents the change in value. We divide this change over the original amount "A" and then multiply by 100% to get the percent change we're after.

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

Problem 18

<h3>Answer:  24%</h3>

-----------------

Explanation:

I'll use the formula again

A = old value = 3.00

B = new value = 2.28

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (2.28-3.00)/3.00 ] * 100%

C = (-0.72/3.00)*100%

C = -0.24*100

C = -24%

The negative percent change means we have a percent decrease. So we have a 24% decrease. Since your teacher is asking about how much the percent reduction is, we'll write the positive version of this percentage.

Problems 19 through 22 will follow the same ideas as shown in the previous problems.

ZanzabumX [31]4 years ago
3 0
15. 40%
16. 20%
17. 50%
18.24%
19. 20%
20. 75%
21. 37.5%
22. 60%
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Express the recurring decimal 0.56 as a fraction in its simplest form.
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Solve the equation for y <br> y-4=1/2(x-8)
earnstyle [38]

Here's how:

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The equation now takes the shape :

  2y+x-16  = 0

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4.2     Solve   2y+x-16  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

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The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2y+x-16  = 0 and calculate its properties

Graph of a Straight Line :

 

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Calculate the X-Intercept :

When y = 0 the value of x is 16/1 Our line therefore "cuts" the x axis at x=16.00000

 x-intercept = 16/1  = 16.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 8.000 and for x=2.000, the value of y is 7.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 7.000 - 8.000 = -1.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -1.000/2.000 = -0.500

Geometric figure: Straight Line

 Slope = -1.000/2.000 = -0.500

 x-intercept = 16/1 = 16.00000

 y-intercept = 16/2 = 8

Geometric figure: Straight Line

 Slope = -1.000/2.000 = -0.500

 x-intercept = 16/1 = 16.00000

 y-intercept = 16/2 = 8

Rearrange:

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

                    y-4-(-1/2*(x-8))=0

Step by step solution :

Step  1  :

           1

Simplify   —

           2

Equation at the end of step  1  :

                   1

 (y - 4) -  (0 -  (— • (x - 8)))  = 0

                   2

Step  2  :

Equation at the end of step  2  :

                  (x - 8)

 (y - 4) -  (0 -  ———————)  = 0

                     2  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

             y - 4     (y - 4) • 2

    y - 4 =  —————  =  ———————————

               1            2    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       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:

(y-4) • 2 - ((8-x))     2y + x - 16

———————————————————  =  ———————————

 2y + x - 16

 ———————————  = 0

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Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

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

Here's how:

2y+x-16

 ——————— • 2 = 0 • 2

    2  

Now, on the left hand side, the  2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  2y+x-16  = 0

Equation of a Straight Line

4.2     Solve   2y+x-16  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2y+x-16  = 0 and calculate its properties

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 8/1 so this line "cuts" the y axis at y= 8.00000

 y-intercept = 16/2  =  8

Calculate the X-Intercept :

When y = 0 the value of x is 16/1 Our line therefore "cuts" the x axis at x=16.00000

 x-intercept = 16/1  = 16.00000

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