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3 years ago

Solve equations 5-5x=14-8x 3(2y-5)=4y-7

Mathematics

1 answer:

GaryK [48]3 years ago

5 0

5-5x=14-8x
-5x=9-8x
3x=9
x=3

3(2y-5)=4y-7
6y-15=4y-7
2y-15=-7
2y=8
y=4

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Alex wrote 103.903 in expanded form as 100+3x1+9x1/100+3x1/1,000 explain his mistake and how to correct it

11111nata11111 [884]

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3 years ago

Determine the value of x to the nearest thousandth in the equation 8(2)^x+3=48

solong [7]

You probably mean either

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$8\cdot2^{x+3} = 48$

Write 8 = 2³, so that in the first interpretation,

$8\cdot2^x = 2^3 \cdot 2^x = 2^{x + 3}$

and in the second,

$8\cdot2^{x+3} = 2^3 \cdot 2^{x+3} = 2^{x + 6}$

Then in the first interpretation, we have

$2^{x + 3} + 3 = 48 \implies 2^{x + 3} = 45 \implies x + 3 = \log_2(45) \implies x = \log_2(45) - 3 \approx \boxed{2.492}$

Otherwise, the second interpretation gives

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3 years ago

If x= 19 feet and y = 12 feet, what is the area and perimeter of the figure above?

Delicious77 [7]

All we need to do to solve this problem is calculate the area of a rectangle and the area of a circle, then add them!

____________________________

First, let's do the rectangle!

Area of a rectangle = length x width

or in this case... Area = "x" times "y"

Area = 19 × 12 = 228 square feet!

________________________________

Now, let's do the circle!

Area of a circle = πr² ... (r = radius)

* In this diagram, the diameter of the circle is also the same length as "y"!

* And remember that radius is half of the diameter.

radius = 6

Now, let's actually calculate the area

Area = π(6)² ⇒ 36π

Area = 113.1 (I rounded up the decimals!)

_______________________________________

*But wait! Look at the figure! It looks like HALF of the circle's area was included when we calculated the area of the rectangle! This means that we should divide the area of the circle (that we just calculated) in half!

Area of the HALF CIRCLE = 113.1 ÷ 2 = 56.5

Now let's add the area of the rectangle to the area of the half-circle to find the area of THE ENTIRE FIGURE!

228 + 56.5 = 284.5

284.5 square feet is our answer!

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3 years ago