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Pepsi [2]
3 years ago
15

The ratio of the the number of Sally's stickers to the number of Eric's stickers was 3:5. Sally then brought another six sticker

s and the ratio became 9:10. How many stickers did Eric have?
Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Answer: Eric has 20 stickers

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

Explanation:

x = number of stickers Sally starts with

y = number of stickers Eric has

x/y is the ratio of the two values. This ratio is 3/5. So x/y = 3/5 which cross multiplies to 5x = 3y. We can divide both sides by 5 to end up with x = 3y/5

"Sally the bought another six stickers" meaning she starts with x and bumps up to x+6. Eric's sticker count stays the same. The ratio is now (x+6)/y. We can replace the x with 3y/5 and simplify

(x+6)/y = (3y/5+6)/y

(x+6)/y = (3y/5+30/5)/y

(x+6)/y = [ (3y+30)/5 ]/y

(x+6)/y = (3y+30)/(5y)

Now set this equal to the new ratio 9/10 and solve for y

(3y+30)/(5y) = 9/10

10(3y+30) = 9(5y) ... cross multiply

30y+300 = 45y

300 = 45y-30y

300 = 15y

15y = 300

y = 300/15

y = 20

Eric has 20 stickers. At this point you can stop as your teacher doesn't seem to want to know Sally's count. However, I'll keep going to show how to get that value.

x = 3y/5

x = 3*20/5 ... replace y with 20

x = 60/5

x = 12

Sally starts off with 12 stickers. Note how x/y = 12/20 = 3/5 meaning that the ratio x:y = 12:20 reduces to 3:5 (divide both parts by 4)

If we add 6 stickers to Sally's count, then she now has x+6 = 12+6 = 18 stickers. It leads to the ratio 18:20 = 9:10 (divide both parts by 2). So the answer is confirmed.

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Answer:

Base = 32 cm

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Step-by-step explanation:

Area of a triangle can be calculated as:

Area = \frac{1}{2}\times Base \times Height

We are given that the base of triangle exceeds the height by 7 cm. This can be expressed in an equation form as:

Base = Height + 7

Lets use B to represent base and H to represent height

B = H + 7

The equation of area can be stated as:

Area=\frac{1}{2}bh\\\\ Area=\frac{1}{2}(h+7)(h)\\\\ 400=\frac{1}{2}h(h+7)\\\\ 800=h^{2}+7h\\\\ h^{2}+7h-800=0

This is a quadratic equation which can be solved using a quadratic equation as shown below:

h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25

Since the height cannot be negative, we'll consider the positive value only i.e height is equal to 25 cm.

Therefore, the length of base will be 25 + 7 = 32 cm.

8 0
3 years ago
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Inga [223]

Answer:

g(x) = \frac{x+3}{x-3}

Step-by-step explanation:

From the picture attached,

Given function is,

f(x) = x + 1

We have to find the value of g(x) if the composite function has been given as,

f[g(x)] = g(x) + 1 = \frac{2x}{(x-3)}

g(x) = \frac{2x}{(x-3)}-1

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Therefore, g(x) = \frac{x+3}{x-3} will be the answer.

5 0
2 years ago
Eli walked 12 feet down the hall of his house to get to the door. He continued in a straight line out of the door and across the
tekilochka [14]
Part A:

The drawing representing Eli's walking pattern is attached.


Part B:
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Part C:
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5 0
3 years ago
I dont understand this at all. I really need help! ​
Westkost [7]

Hello!

\large\boxed{x^{4}}

Recall that:

\sqrt[z]{x^{y} } is equal to x^{\frac{y}{z} }.  Therefore:

\sqrt[3]{x^{2} } = x^{\frac{2}{3} }

There is also an exponent of '6' outside. According to exponential properties, when an exponent is within an exponent, you multiply them together. Therefore:

(x^{\frac{2}{3} })^{6}  = x^{\frac{2}{3}* 6 }  = x^{\frac{12}{3} } = x^{4}

3 0
2 years ago
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Answer:

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Step-by-step explanation:

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