The height of a cylinder is twice the radius of its base. A cylinder has a height of 2 x and a radius of x. What expression represents the volume of the cylinder, in cubic units? 4πx2 2πx3 πx2 + 2x 2 + πx3

The value of the variable expression 6.(x- 9) - 5 when x = 5 is -29.

To evaluate the variable expression for x = 5, we simply substitute 5 for x in the expression.

6.(x- 9) - 5 = 6.(5- 9) - 5

= 6.(-4) - 5

= -24 - 5

= -29

Therefore, the value of the variable expression 6.(x- 9) - 5 when x = 5 is -29.

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Answer:

10 units.

2√7 units.

- (or 5.29 units to the nearest hundredth)

Step-by-step explanation:

If the 2 sides are legs of the triangle ( that is they are at 90 degrees to each other) the third side, by Pythagoras  theorem:

=  √(6^2 + 8^2)

=  √100

= 10 units.

The other possibility is that 8 is the length of the hypotenuse, in which case

The third side

=  √(8^2 - 6^2)

=  √28

= 2√7 units.

Answer:

36.4 yards

Step-by-step explanation:

The coordinates of origin is (12, 11) while coordinates of final landing is (34, 40)

Considering two points, x1, y1 and x2, y2, the distance between them is given by

[tex]d=\sqrt {(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

Similarly, the distance between these two given points will be

[tex]d=\sqrt {(34-12)^{2}+(40-11)^{2}}\\d=36.4005494464026\approx 36.4 yd[/tex]

Therefore, the distance is 36.4 yards

Answer:

2w + 2

Step-by-step explanation:

Width = w

Twice its width  = 2*w =2w

2 inches more than twice its width = 2w + 2

Length = 2w + 2

Answer:

b

Step-by-step explanation:

Area of the shaded region =[ (3x-2)(x+3) ] - [ x*6 ]

= 3x*x +3x*3 + (-2)*x  + (-2)*3 - 6x

=3x² + 9x - 2x - 6 - 6x      {bring like term together}

=3x² + 9x - 2x - 6x - 6

= 3x² + x - 6           {9x - 2x - 6x = 9x - 8x = x}

Area = 24 square units

3x² + x - 6 = 24

3x² + x - 6 - 24 = 0

3x² + x - 30 = 0

Product = 3* -30 = -90

Sum = 1

Factors = 10 , (-1)

3x² + x - 30 = 0

3x² - 9x + 10x - 10*3 = 0

3x*(x - 3) +10*(x - 3) = 0

(x-3)(3x +10) = 0

3x + 10 is ignored because measurements will not be in negative values.

x - 3 = 0

x = 3

Answer: The value of the investment would be $4,075

Step-by-step explanation: The initial investment, that is, the principal is given as $2500, and it was invested for a period of 10 years at the rate of 6.3%. Using the simple interest calculation formula, the investment would have a present value as follows;

Interest = P x R x T

Where P = amount invested (2500), R = rate of interest (6.3 or 0.063) and T = number of years (10)

Interest = 2500 x 0.063 x 10

Interest = 1575

The value of the investment at 6.3% after 10 years is now;

Initial investment + Interest

2500 + 1575 = 4075

Therefore the value of the investment is $4,075

Answer:

$584.72

Step-by-step explanation:

$262.40+$304.46+$76.04 = $642.90

$642.90 - ($642.90 * 15%) = $546.47

$546.47 + ($546.47 * 7%) = $584.72

Answer:

158

Step-by-step explanation:

Answer:

13.5 ft2

Step-by-step explanation:

At = Ap/2

= 27/2

= 13.5 ft2

Answer: The number of quarters can be 1, 3, 5 or 7

Step-by-step explanation:

Megan has A quarters and B dimes.

The value of a quarter is $0.25 and the value of a dime is $0.10

Then we have that:

A*$0.25 + B*$0.10 = $1.95

We want to know the different possible values of A.

Now, it is usefull to see the different multilpes of 0.25 (this is the odd multyples of 0.25) we only care for the ones that have a 5 in the undredth place, becauses we only can ad multiple of $0.10, so the 5 in the undredth place needs to come from this

Then the possible values of A are the odd numbers such that A*0.25 is smaller than 1.95, let's do the math:

0.25*1 = 0.25 (here 1.95 - 0.25 = 1.70, then B = 1.70/0.10 = 17) the pair is B = 17 and A = 1

0.25*3 = 0.75 (here 1.95 - 75 = 1.20, then B = 1.20/0.10 = 12) the pair is B = 12 and A = 3.

0.25*5 = 1.25 (here 1.95 - 1.25 = 0.70, then B = 0.70/0.10 = 7) the pair is B = 7 and A = 5

0.25*7 = 1.75 (here 1.95 - 1.75 = 0.20, then b = 0.20/0.10 = 2) The pair is B = 2 and A = 7

Answer:

see explanation

Step-by-step explanation:

In any circle the ratio of the arc length to the circumference of the circle is equal to the degree measure of the arc to 360°

Answer:

Beth area=16 in²

Adam width=4 in

Step-by-step explanation:

Considering the attached image, Beth's area will be 4*4=16in²

Since Adams area is 12 more then his area will be 12+16=28 in²

Since area is given as A=lw where l is length and w is width then

28=7w

w=28/7=4 in

The attached figure is used for question parts

Final answer:

The area of a larger square with side lengths twice that of a smaller square is four times greater. This is because the scale factor for areas is the square of the scale factor for lengths, leading to an area of 64 square inches for the larger square, compared to 16 square inches for the smaller one.

Explanation:

When Marta has a square with a side length of 4 inches and then creates a similar square with dimensions that are twice the first square, we are working with a scale factor in geometry. As the new square has side lengths that are twice that of the original square (4 inches x 2 = 8 inches), the area of the larger square will be greater than that of the smaller square. To find the area of the larger square, we square the side length (8 inches x 8 inches), which gives us 64 square inches. This is exactly four times the area of the first square (4 inches x 4 inches = 16 square inches), since the scale factor for the areas of similar figures is the square of the scale factor for their corresponding lengths.

In the context of the examples given, this principle applies to understanding how the area of shapes scales when their dimensions are proportionally increased or decreased. The scale factor can be used to calculate dimensions or area of similar figures in various geometric problems.

Answer:

317

Step-by-step explanation:

Since the ratio is 1:232, multiply 232 by 16.4:

[tex]232*16.4=d[/tex]

[tex]d=3804.8 in[/tex]

Divide by 12 to find the feet

[tex]3804.8[/tex]÷[tex]12=d[/tex]

[tex]d=317.066[/tex]

Round to the nearest foot

[tex]d=317[/tex]

Final answer:

To find the actual stadium distance from home plate to left field, convert 16.4 inches to feet and then multiply by the scale factor of 232, resulting in approximately 317 feet.

Explanation:

The student is asking how to convert a scale model measurement to the actual size measurement. Given the scale of 1:232 and the model's distance from home plate to left field as 16.4 inches, we can find the actual stadium distance by multiplying the model measurement by the scale factor.

First, convert inches to feet: 16.4 inches × (1 foot / 12 inches) = 1.3666667 feet (rounded to seven decimal places).

Then multiply by the scale factor to get the distance in the actual stadium: 1.3666667 feet × 232 = 317.0666674 feet, which we round to 317 feet to the nearest foot.

Therefore, the distance from home plate to left field in the actual stadium is approximately 317 feet.

Answer:

6a+27x

it's simple math there is no work needed

Answer: A. 6a +27x

combine like terms

18a - 12a

12x + 15x

Answer:

C

Step-by-step explanation:

The area of the composite figure to the nearest whole number is 13 ft².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Given:

Radius= 2 feet

As, Area of a single Quadrant = πr²/4

and, For 3 semi circle

= πr²/4 + πr²/4 + πr²/4 or 3 (πr²/4)

= 3 x 3.14 x 2 x 2 /4

= 9.42 ft²

and, Area of Square

= s x s

= 2 x 2

= 4 ft²

So, the Area of Figure = 4 + 9.42 = 13.42 ft²

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Answer:

189 cm³

Step-by-step explanation:

V = lwh

V = 9*7*3

V = 189 cm³

Hope this helped! :)

Answer:

V =189 cm^3

Step-by-step explanation:

V = l*w*h

V = 3 cm* 9 cm * 7 cm

V =189 cm^3

Answer:x-2+10=12

We move all terms to the left:

x-2+10-(12)=0

We add all the numbers together, and all the variables

x-4=0

We move all terms containing x to the left, all other terms to the right

x=4

Step-by-step explanation:

Answer:

36 miles

Step-by-step explanation:

His entire journey, represented with a diagram, is in the shape of a right angle triangle.

We need to first find the hypotenuse of the triangle, then, add all the sides together:

hyp² = opp² + adj²

hyp² = 9² + 12²

hyp² = 81 + 144 = 225

Find the square root of both sides:

hyp = 15 miles

Therefore, adding the three sides together:

Total distance traveled = 9 + 12 + 15

Total distance traveled = 36 miles

He would ride 36 miles altogether.

Answer:

36

Step-by-step explanation:

1% of 100 is 1.  

5% of 100 is 5.

12% of 100 is 12.

If you're going to ask an easy question, then please give me a thanks at least

Answer:

The second bubble

Step-by-step explanation:

In a 30 60 90 triangle as shown here a is always 1/2 the hypotenuse (Which the hypotenuse is 6) and then just add [tex]\sqrt{3}[/tex] to the end of it to get b

So, lets demonstrate

a = 1/2 * 6 = 3

b = a*[tex]\sqrt{3}[/tex] = a[tex]\sqrt{3}[/tex] = 3[tex]\sqrt{3}[/tex]

So,

a = 3

b = 3[tex]\sqrt{3}[/tex]

Answer:

1/15

Step-by-step explanation:

The first thing to do is to change both denominators so that they're the same. In this case, that would be 15.

Then, whatever you do to the denominator, you must also do to the numerator.

[tex]\frac{9}{15}[/tex] + x = [tex]\frac{10}{15}[/tex]

X = 1/15

Answer:

Median

Step-by-step explanation:

Remember ...

Mean = Average

Median = Middle

Mode = Most (the number that appears most)

Final answer:

The midpoint value of a data set arranged in order is the median, which is the central value dividing the dataset into two halves.

Explanation:

The midpoint value of a data set, where the values are arranged in ascending or descending order, is known as the median. The median is the value that divides the dataset in half so that there are an equal number of values above and below it. In a dataset with an odd number of data points, the median is the middle value. For an even number of data points, the median is the average of the two central values. The mode is the most frequently occurring value in a set, while an outlier is an observation that is significantly different from the rest of the data. The mean represents the average of all values in the data set.

Choosing the appropriate measure of the center of data — whether mean, median, or mode — depends on the specific characteristics of the dataset, such as the presence of outliers and the distribution shape. The median is especially useful when the dataset contains outliers that may skew the mean.

[tex]\frac{0.25}{-0.25}[/tex] simplified will give us -1.

It's not a whole number, because it's negative. It isn't irrational because there is a determined answer. While it is rational, it more fits into integer - which is a less broad scope than rational.

Answer: 2/3x-13/12=-5/12x

Step-by-step explanation:

The equivalent equation is (8x + 5x)/12 = (3 + 10)/12 and x = 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

(2/3)x - 5/6 = -(5/12)x + 1/4

Add like terms.

(2/3)x + (5/12)x = 1/4 + 5/6

(8x + 5x)/12 = (3 + 10)/12

13x / 12 = 13/12

x = 1

Thus,

x = 1

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Answer:

the answer is 28

Step-by-step explanation:

i guessed ngl

Answer:

Bb 2ent option 28

Step-by-step explanation:

Answer:

[tex]\dfrac{\pi}{2} cm[/tex]

Step-by-step explanation:

Given two concentric circles where:

Length of the intercepted arc for a central angle of [tex]\dfrac{\pi}{2} =\dfrac{\frac{\pi}{2} }{2\pi} X2\pi r=\dfrac{\pi r}{2}[/tex]

For the larger circle of radius 5cm, Length of the intercepted arc[tex]=\dfrac{5\pi}{2}[/tex]

For the smaller circle of radius 4cm, Length of the intercepted arc[tex]=\dfrac{4\pi}{2}[/tex]

Difference in Arc length

[tex]=\dfrac{5\pi}{2}-\dfrac{4\pi}{2}\\=\dfrac{\pi}{2} cm[/tex]

The difference in arc lengths between the two concentric circles for a central angle of π/2 radians is approximately 1.57 cm.

To compare the lengths of arcs intercepted by the same central angle in two concentric circles, we use the formula for arc length, which in a circle is a portion of its circumference that corresponds to the central angle. For a central angle π/2 radians, the arc length is given by (rθ), where r is the radius of the circle and θ is the central angle in radians.

For the smaller circle, the arc length is 4 cm × π/2 = 2π cm, and for the larger circle, it is 5 cm × π/2 = 2.5π cm. The difference in arc lengths is 2.5π cm - 2π cm = 0.5π cm. Using the approximate value of π as 3.14159, the difference in arc lengths is approximately 1.57 cm.

Answer:

1/8

Step-by-step explanation:

Answer:

4 out of the 8

Step-by-step explanation:

Because there are 8 marbles total in the bag and only 4 of them are white.