Surface area
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Answer:

The lake's shape is a cylinder. The volume of a cylinder is given as: V=πhr^2 where r equals the radius, and h the depth. Therefre, the volume of the lake is:

V=πhr^2

V=π(20ft)(32,5ft)^2

V=66.364,1875‬ ft^3.

Given that 66.364,1875‬ ft^3 equals 496.44 gallons, we can say that 496.44 gallons of water is required to fill the lake.

Answer:

Step-by-step explanation:

Alright.  I can't really explain much but i can get your answer.

AS A DECIMAL: 1.047197551196597746154214461093167628065723133125035273658

As a property:

π/3

Sorry if its wrong... I tried lol

Answer:

The answer would be 2

Step-by-step explanation:

Answer:

The answer is 4x-3 because all your doing is subtracting 3x from 4x

Simplifying

3x2 + 5x + -7x + 3 + -5x2 + 2 = 0

Reorder the terms:

3 + 2 + 5x + -7x + 3x2 + -5x2 = 0

Combine like terms: 3 + 2 = 5

5 + 5x + -7x + 3x2 + -5x2 = 0

Combine like terms: 5x + -7x = -2x

5 + -2x + 3x2 + -5x2 = 0

Combine like terms: 3x2 + -5x2 = -2x2

5 + -2x + -2x2 = 0

Solving

5 + -2x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square. Divide all terms by

-2 the coefficient of the squared term:

Divide each side by '-2'.

-2.5 + x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.

-2.5 + x + 2.5 + x2 = 0 + 2.5

Reorder the terms:

-2.5 + 2.5 + x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0

0.0 + x + x2 = 0 + 2.5

x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5

x + x2 = 2.5

The x term is x. Take half its coefficient (0.5).

Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.

+ 0.25 + x2 = 2.5 + 0.25

Combine like terms: + 0.25 = 1.25

1.25 + x2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75

1.25 + x2 = 2.75

Factor a perfect square on the left side:

(x + 0.5)(x + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting

(x + 0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + 0.5 = 1.658312395

Simplifying

x + 0.5 = 1.658312395

Reorder the terms:

0.5 + x = 1.658312395

Solving

0.5 + x = 1.658312395

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.

0.5 + -0.5 + x = 1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0

0.0 + x = 1.658312395 + -0.5

x = 1.658312395 + -0.5

Combine like terms: 1.658312395 + -0.5 = 1.158312395

x = 1.158312395

Simplifying

x = 1.158312395

Subproblem 2

x + 0.5 = -1.658312395

Simplifying

x + 0.5 = -1.658312395

Reorder the terms:

0.5 + x = -1.658312395

Solving

0.5 + x = -1.658312395

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.

0.5 + -0.5 + x = -1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0

0.0 + x = -1.658312395 + -0.5

x = -1.658312395 + -0.5

Combine like terms: -1.658312395 + -0.5 = -2.158312395

x = -2.158312395

Simplifying

x = -2.158312395

Solution

The solution to the problem is based on the solutions

from the subproblems.

x = {1.158312395, -2.158312395}

We are given that the cost of each shirt = $12.25

It is given that she bought total 'x' shirts, each of cost $12,25.

So, the cost of 'x' shirts is  dollars

Also, there is a shipping charge of $3.99

So, the total cost of 'x' shirts is

Since, the shirts cost her total $77.49.

We have the equation,

12.25x + 3.99 = 77.49

Answer:

Cone diameter = 18 m therefore radius = 9 m

Lateral Area = PI * radius * slant height

Lateral Area = 3.14 * 9 * 15 = 423.90 square meters

Step-by-step explanation:

Final answer:

The lateral surface area of a cone with a diameter of 18 meters and a slant height of 15 meters is approximately 423.9 square meters, calculated using the formula LSA = πrl with π approximated as 3.14.

Explanation:

The student is asking about finding the lateral surface area of a cone with a given diameter and slant height, where the diameter is 18 meters and the slant height is 15 meters. To find the lateral surface area (LSA) of a cone, the formula LSA = πrl can be used, where 'r' is the radius of the base and 'l' is the slant height of the cone. Since the diameter is 18 meters, the radius is half of that, which is 9 meters. Using 3.14 as the approximation for π (pi), we can calculate the lateral surface area.

The calculation would be as follows:

Find the radius (r): Diameter / 2 = 18m / 2 = 9m.

Use the formula LSA = πrl: LSA = 3.14 * 9m * 15m.

Calculate the LSA: LSA = 3.14 * 135m².

LSA = 423.9m², which is the lateral surface area of the cone.

Therefore, 423.9 square meters is the closest approximation to the lateral surface area of the given cone.

the slope is -3 and the y intercept is -2

Answer: (y-3)(4y-5)

Step-by-step explanation:

4*15= 60. 60= -12 x -5

4(y-12)(y-5)

(y-3)(4y-5)

8+8=16 so 16/5 16÷5=3.2 32%

32% is the answer I think. Hope this helps

Answer:

32%

Step-by-step explanation:

8 + 8 = 16.

16/5

16 ÷ 5

= 3.2

= 32%

In any inequality or equation, a number that does not change is called​ a constant.

A number that does not change in any inequality or equation is called a constant.

Equations are not always balanced on both sides using an "equal to" sign in mathematics. Sometimes it might be about a "not equal to" connection, meaning that something is superior to or inferior to another. In mathematics, an inequality is a connection between two numbers or other mathematical expressions that results in an unequal comparison.

A constant in algebra is a single integer or, occasionally, a letter (such as a, b, or c) that stands in for a fixed number. something constant or unalterable a number that is supposed not to change the value in a particular mathematical discussion, for example, a number that has a fixed value in a certain scenario, globally, or that is distinctive of some substance or instrument

a concept in logic with a predetermined name

Therefore, A constant is a quantity that does not alter in any inequality or equation.

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Answer:

a) Similar

b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)

c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)

Step-by-step explanation:

Given:

Rectangle 1 has length = x

Rectangle 1 has width = y

Rectangle 2 has length = kx

Rectangle 2 has width = ky

(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?

Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.

(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

Perimeter of Rectangle = 2*(Length + Width)

Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y

Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky

                                          = k(2x+2y)

                                          = k(Perimeter of Rectangle 1)

Hence proved that Perimeter of rectangle 2 is k times the perimeter of rectangle 1.

(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.

Area of Rectangle = Length * width

Area of Rectangle 1 = x * y

Area of Rectangle 2 = kx*ky

                                  = k^2 (xy)

                                  = k^2 (Area of rectangle 1)

Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.

Final answer:

Rectangles 1 and 2 are similar due to proportional dimensions. The perimeter of Rectangle 2 is proven to be k times the perimeter of Rectangle 1 by factoring out the scale factor. Similarly, the area of Rectangle 2 is k² times the area of Rectangle 1, as shown by multiplying the scaled dimensions.

Explanation:

(a) Yes, Rectangle 1 and Rectangle 2 are similar because the sides of Rectangle 2 are proportional to the sides of Rectangle 1. This means that the two rectangles have the same shape but different sizes, which is the definition of similarity in geometry.

(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, consider the perimeter of Rectangle 1, which is 2x + 2y. When each dimension is multiplied by k, the new length is kx and the new width is ky, so the perimeter of Rectangle 2 is 2(kx) + 2(ky) = 2kx + 2ky. Factoring out the common factor of k gives k(2x + 2y), which is k times the perimeter of Rectangle 1.

(c) For the area of Rectangle 2, the area of Rectangle 1 is xy. After scaling by k, the new dimensions of Rectangle 2 are kx and ky, so its area is (kx)(ky) = k²(xy), which shows that the area of Rectangle 2 is k² times the area of Rectangle 1.

To find the answer, you have to set each one equal to each other.

(160 + 40x = 55x)

Now, you just solve for X.

55x - 40x = 15x

160 / 15 = 15 / 15x

This means 160/15 = x, or is equal to

10 2/3

Answer:

C is the answer

Step-by-step explanation:

Answer:

The time at which the ball will reach its maximum height is t= 3 seconds.

Step-by-step explanation:

To find the the time at which the ball will reach its maximum height,  we need to solve the model given - 3x2 + 18x +7

since h(t) is the height given we can re-write the equation as:

h(t)= -3(t)² + 18t +7

Differentiating the above equation

[tex]\frac{dt}{dh} = -6t + 18[/tex]

When the ball is at maximum height [tex]\frac{dt}{dh}=0[/tex]

0=-6t+18

-18 = -6t

=> t= -18/-6

=> t= 3

the time at which the ball will reach its maximum height is t= 3 seconds.

We can find the maximum height by putting value of t in equation:

h(3) = -3(3)²+ 18(3) +7

h(3)= -27 + 54 + 7

h(3)= 34 ft

Answer:

three seconds

Step-by-step explanation:

Answer:

16=8x2

I hope this helps you!!

The possible values of the lengths and widths of the rectangle are (16, 1) and (8, 2).

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, The area of the rectangle is 16 square units.

Therefore, (length×width) = 16.

So, the possible dimensions are multiples of 16 which is,

(length, width) = (16, 1) (8, 2).

(4, 4) is not admissible as it would make it a square.

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Answer:

[tex]15.23[/tex]

Step-by-step explanation:

First, we can make an equation by adding all the ages together and dividing it by the sum of the frequencies.

[tex](13*7)+(14*12)+(15*18)+(16*9)+(17*5)+(18*4)+(19*2)[/tex]

Now simplify.

[tex](13*7)+(14*12)+(15*18)+(16*9)+(17*5)+(18*4)+(19*2) = 868[/tex]

We can divide this number by the sum of the frequencies.

[tex]\frac{868}{7+12+18+9+5+4+2} \\ \\ \frac{868}{57} \\ \\ 15.23[/tex]

Answer:

Step-by-step explanation:

First you need to find the total number of years of all the people tracked.

The general formula is

Total years = age*frequency for all ages.

Age                 Frequency              Total

13                        7                             91

14                       12                           168

15                       18                           270

16                        9                            144

17                         5                             85

18                         4                             72

19                         2                             38

Totals                 57                            868

The mean is the total number of years / total frequency

mean = 868/57

mean = 15.23

I think the answer is 4:24

Answer:

4 : 24

Step-by-step explanation:

1:6

We need to make the 1 a 4, so we will multiply by 4

What we do to one side, we do to the other

1 *4 = 4

6*4 = 24

1: 6  becomes 4: 24

To estimate the difference between 10 1/9 and 5 14/15, we round them to the nearest whole numbers, 10 and 6, respectively, and then subtract to get an estimated difference of 4.

To estimate the difference between the two numbers 10 1/9 and 5 14/15, we can round them to easier numbers to subtract. 10 1/9 is approximately 10, and 5 14/15 is close to 6 because 14/15 is almost a whole number. Now, we can simply subtract 6 from 10.

10 - 6 = 4

So, the estimated difference between 10 1/9 and 5 14/15 is about 4.

[tex]32a ^{ \frac{9}{2} }b^{ \frac{7}{2} } [/tex]

Answer:

False

Step-by-step explanation:

6 + (-7)n = 34

Plug in -7 for n and see if it's true:

6 + (-7)(-7) = 34

6 + 49 = 34

55 = 34

No, it's not true, so the mystery number is not -7.

ANSWER

C. 9

EXPLANATION

We use the Altitude Theorem,to find the value of a.

According to the altitude theorem, the height of the triangle of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.

[tex]6 = \sqrt{4a} [/tex]

Square both sides to get,

[tex]36 = 4a[/tex]

[tex]9 = a[/tex]

The correct choice is option C.

Answer:

C

Step-by-step explanation:

the answer is 9

Answer:

I think the answer is B

Answer:

the answer is D:  1800 square in

Step-by-step explanation:

find the area of the triangle

area = 1/2 bh

=1/2 (15 inch) (20 inch)

=150 square inch

***then multiply by 2 which gives you 300 square inch***

find the area of the 3 rectangular faces

A=lw

= (25 in) (15 in)

= 375 square inch

A = lw

= (25 in) (20 in)

= 500 square inch

A = lw

= (25 in) (25 in)

= 625 square inch

then add all 3 rectangular faces which equals to 1500 square inch

then add the triangular and rectangular

300 square inch + 1500 square inch = 1800 square inch

Answer:

The answer for study island would be D. 1,800 in2

hope i helped :)

Answer: 1. A Please give me a thanks and a brainly

Step-by-step explanation:

Answer:

The most reasonable Answer is *D.) the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.*

Step-by-step explanation:

Answer:

The answer is D) The bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.

Step-by-step explanation:

The bed bug population has increased because the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.

Answer:

The slope can 1/2 or 0.5

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The slope of a line is defined as ...

slope = (change in y)/(change in x)

Given two points, (x1, y1) and (x2, y2), the slope can be computed using ...

slope = (y2 -y1)/(x2 -x1)

It does not matter which points you call point 1 and point 2. You just need to be consistent.

Using the point values in the order given in the problem statement, we have ...

slope = (4 -6)/(1 -5) = -2/-4

slope = 1/2

Answer: The answer to your question is infinitely many solutions

Step-by-step explanation: There is two solutions to the system of equations, which means there is complex solutions, or in other words many solutions. And when you have more than one solution, you have infinitely many solutions. Hope this helps:)

And please mark my answer the brainliest

hence the numbers are 8 and 13

hope it helps you!!!!!!!!

Final answer:

The two numbers that satisfy the conditions of summing up to 21 and one being 18 less than twice the other are 8 and 13.

Explanation:

To solve the problem, let’s denote the two numbers as x and y. According to the question, the sum of the two numbers is 21, which can be expressed as an equation: x + y = 21. Additionally, we are told that one number is 18 less than two times the other, which gives us another equation: x = 2y - 18.

We can use the method of substitution to solve these equations. First, we will solve the second equation for x, which we already have as x = 2y - 18. Then we will substitute this expression for x in the first equation: (2y - 18) + y = 21. Simplifying we get: 3y - 18 = 21. Adding 18 to both sides gives us 3y = 39. So, dividing both sides by 3 yields y = 13. Now that we have the value of y, we can substitute it back into the equation x = 2y - 18 to get x = 2(13) - 18 which simplifies to x = 8.

Thus, the two numbers in question are 8 and 13.

Answer:

her total grade for class

Hope This Helps!   Have A Nice Day!!

Answer:

-216

(-6)^3

Step-by-step explanation:

-6 * (-6*-6)

-6 * 36

-216

or

-6 * -6 *-6

This is -6 multiplied together 3 times

(-6) ^3

Answer:

a triangle will always have 0 parallel sides

Step-by-step explanation: