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NARA [144]
3 years ago
12

Mrs.Silverstein sold 91 cupcakes at a food fair. The cupcakes were sold in boxes of "a baker's dozen. which is 13. She sold all

the cupcakes at $15 per box. How much money did she receive?
Mathematics
1 answer:
Serggg [28]3 years ago
3 0
Mrs.Silverstein made $105
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At a sale on winter clothing, Cody bought four pairs of gloves and four hats for $36.00. Tori bought three pairs of gloves and f
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Answer:

gloves cost $5

hats cost $4

Step-by-step explanation:

four pairs of gloves and four hats for $36.00

4g + 4h = 36

three pairs of gloves and four hats for $31.00

3g + 4h = 31

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

Subtract the second equation from the first

  4g + 4h = 36

-( 3g + 4h = 31 )

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   g           = 5

gloves cost $5

substitute for g = 5 into either equation

4(5) + 4h = 36

20 + 4h = 36

Subtract 20 from both sides

4h = 16

Divide both sides by 4

h = 4

hats cost $4

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If the quadratic formula is used to find the solution set of 3x2 + 4x - 2 = 0, what are the solutions?
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Answer:

x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}

Step-by-step explanation:

Compare ax^2+bx+c to 3x^2+4x-2.

We have a=3,b=4,c=-2.

The quadratic formula is for solving equations of the form ax^2+bx+c=0 and is x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}.

So we are going to plug in our values in that formula to find our solutions,x.

If you want to notice it in parts you can.

Example I might break it into these parts and then put it in:

Part 1: Evaluate b^2-4ac

Part 2: Evaluate -b

Part 3: Evaluate 2a

------Let's do these parts.

Part 1: b^2-4ac=(4)^2-4(3)(-2)=16-12(-2)=16+24=40.

This part 1 is important in determining the kinds of solutions you have. It is called the discriminant.  If it is positive, you have two real solutions.  If it is negative, you have no real solutions (both of the solutions are complex).  If it is 0, you have one real solution.

Part 2: -b=-4 since b=4.

Part 3: 2a=2(3)=6.

Let's plug this in:

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

or in terms of our  parts:

x=\frac{\text{Part 2} \pm \sqrt{\text{Part 1}}}{\text{Part 3}}

x=\frac{-4 \pm \sqrt{40}}{6}

40 itself is not a perfect square but it does contain a factor that is.  That factor is 4.

So we are going to rewrite 40 as 4 \cdot 10.

x=\frac{-4 \pm \sqrt{4 \cdot 10}}{6}

x=\frac{-4 \pm \sqrt{4} \cdot \sqrt{10}}{6}

x=\frac{-4 \pm 2\cdot \sqrt{10}}{6}

I'm going to go ahead and separate the fraction like so:

x=\frac{-4}{6} \pm \frac{2 \cdot \sqrt{10}}{6}

Now I'm going to reduce both fractions:

x=\frac{-2}{3} \pm \frac{1 \cdot \sqrt{10}}{3}

x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}

6 0
3 years ago
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