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yulyashka [42]
3 years ago
15

The tens digit is twice the units digit. Reverse the digits, add 2 and the new number is 34 less than the original number. Find

the original number.

Mathematics
1 answer:
inna [77]3 years ago
3 0

Answer:

Step-by-step explanation: X and Y represent the digits.

The tens digit is twice the units digit.

The digit in the Tens place has 10× its base value, so we can set up equations to model the information given.

10x +y 10y +x are Original & Reversed numbers

X = 2y means the Tens digits is twice the units digit.

10y + x +2 = 10x +y - 34 models the statement: The reversed number plus two is 34 less than the original number.

Substitute 2y for x to solve for y

10y +2y +2= 10(2y) + y -34

Distribute and combine like terms

12y + 2 = 20y +y - 34

34 +2 = 21y -12y

36 = 9y Divide both sides to find the value of y.

4 = y

X = 2(4) Substitute 4 for y to find x

X = 8

Original number: 84 Reversed number: 48

Substitute into equation model

48 +2= 84 -34

50 = 50

True!

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2144.66in³

Step-by-step explanation:

Radius = 8 inches.

To determine the amount of sphere to make the ball, we'll have to find its volume.

Volume of a sphere = 4/3 * Πr³

V = 4/3*Πr³

Π = 22/7

V = 4/3 * 22/7 * 8³

V = 2144.66inches³

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The amount of plastic required is 2144.66in³.

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3 years ago
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Alina [70]

Answer:

(4,-3)

Step-by-step explanation:

If you graph this point, then it will be in the 3rd quadrant.

A 180 degree rotation will put it in the 1st quadrant.

And the extra 90 degrees will put in in the 4th quadrant, so we know that in (x,y), x is positive, and y is negative. then if you theoretically rotate it, since you are rotating it 90 degrees, 3 times, you will have to switch the x and y, since 3 is an odd number. so the final answer is (4,-3).

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Find the slope and Y-intercept for each table, and then write an equation.
Leni [432]

Answer:

a. Slope = 2; y-intercept = 2

b. Slope = 2; y-intercept = 3

c. Slope = 2; y-intercept = -1

d. Slope = -2; y-intercept = 5

e. Slope = -3; y-intercept = -5

d. Slope = -2; y-intercept = 1

Step-by-step explanation:

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8 0
3 years ago
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liraira [26]

Answer:

22.9m

Step-by-step explanation:

Using Pythagorean theorem, we can get two equations using the angles.

From Point A:

∠A = 20°

AB = 20m

From Point B:

∠B = 29°

BD = x

What we are looking for is the opposite side of each right triangle, each person makes because we have one adjacent side. We also know that both opposite sides will be equal.

So we use this formula for both point of views:

Tan\theta=\dfrac{Opposite}{adjacent}

Where:

Opposite = height of the building

Adjacent = distance from the building

We are looking for the opposite side so we can tweak our formula to get an equation for the height

height=(Tan\theta)(distance)

Using our given, we can solve for the distance of point B to D:

(Tan20)(20+x) = (Tan29)(x)\\\\(0.3640)(20+x) = (0.5543)(x)\\\\\dfrac{(7.28+0.3640x)}{0.5543}=x\\\\13.1337 + 0.6567x = x\\\\13.1337 = x - 0.6567x\\\\13.1337 = 0.3433x\\\\\dfrac{13.1337}{0.3433}=x\\\\38.2572 = x

The distance of point B to D is 38.2572 m.

Now that we know the distance of BD we can solve for the height of the building using only the given from point B.

height=(Tan\theta)(distance)

height=(Tan29)(38.2572m)

height=(0.5543)(38.2572m)

height=21.21m

But this is only the height from the line of sight. To get the height of the building from the ground, we just add the height of the viewer, which is 1.7m.

21.21m + 1.7m = 22.91m

The closest answer is: 22.91 m

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3 years ago
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