On a hot summer day, Judith and her friends decided to have a water fight. They threw water balloons for 1 hour and 13 minutes. When all the water balloons were gone, they sprayed water with hoses for 21 minutes. The water fight ended at 1:08 P.M. when Judith's dad showed up with ice cream. What time did the water fight start?

Step-by-step explanation:

To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of the equilateral triangles over the height of the solid.

The height of the solid is given by the difference between the upper and lower bounds of the base, which are y = 4 and y = x^2, respectively. The cross-sectional area of an equilateral triangle with sides of length 2x is given by (x^2 * √3)/4.

So, the volume of the solid is given by the integral:

V = ∫[x^2, 4] (x^2 * √3)/4 dx

Using the antiderivative of x^2 * √3 / 4, which is (2x^3 * √3)/(12), we can find the definite integral:

V = [2x^3 * √3]/12 from x^2 to 4

Evaluating the definite integral and simplifying, we get:

V = 16 units^3

So, the volume of the solid is 16 units^3.

Answer:

the volume of the solid is 16 units^3

Step-by-step explanation:

The zeroes of the given function are + 1 and - 1 respectively.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

y = x² - 1

For the zeros of the function substitute {y} = 0. We get -

x² - 1 = 0

x² = 1

x = ± 1

Therefore, the zeroes of the given function are + 1 and - 1 respectively.

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Step-by-step explanation:

the slope is always the factor of x and the ratio

y coordinates difference / x coordinates difference

when going from one point on the line to another.

in short : y/x

the perpendicular slope is -x/y.

the ratio is turned upside down, and the sign is flipped.

so, the begin of our equation is

y = (1/3)x + b

b (the y-intercept, which is the y-value when x = 0) we get by using the given point and is coordinates:

-7 = (1/3)×6 + b = 2 + b

b = -9

so, the whole equation is

y = (1/3)x - 9

Check the picture below.

so we know it has a vertex at (2 ,3 ) and it also passes through (-2 , -1), then

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=2\\ k=3\\ \end{cases}\implies y=a(~~x-2~~)^2 + 3\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases}[/tex]

[tex]-1=a(-2-2)^2 + 3\implies -4=a(-4)^2\implies -4=16a \\\\\\ \cfrac{-4}{16}=a\implies -\cfrac{1}{4}=a\hspace{10em}\boxed{y=-\cfrac{1}{4}(x-2)^2 + 3}[/tex]

Possible pair of measurements if they are congruent figures are,

⇒ ∠W = 140°

⇒ ∠X = 94°

⇒ ∠Y = 79°

⇒ ∠Z = 47°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Lincoln is measuring the angles of quadrilateral WXYZ to determine whether  it is congruent to the quadrilateral shown in figure.

Now, We know that;

If two figure are congruent to each other then there corresponding angles and side are equal to each other.

So, The angles of quadrilateral WXYZ are,

⇒ ∠W = 140°

⇒ ∠X = 94°

⇒ ∠Y = 79°

⇒ ∠Z = 47°

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g⁻¹(x) = ∛(x²/2 + 3)  is the inverse of  the function g(x)= √(2x³-6)

In mathematics, the inverse function of a function g (also called the inverse of g) is a function that undoes the operation of g.

g(x)= √(2x³-6)

Let g(x) = y

So we can say y = √(2x³-6)

We will then make x the subject:

y = √(2x³-6)

y² = 2x³-6

y² + 6 = 2x³

2x³ = y² + 6

x³ = y²/2 + 6/2

x³ = y²/2 + 3

x = ∛(y²/2 + 3)

since x = g⁻¹(y)  = ∛(y²/2 + 3)

Thus, g⁻¹(x) = ∛(x²/2 + 3)      (Replace y with x)

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so the correct answer is the square route of it cause a anylis of a+b=c yup

Step-by-step explanation:

Answer: UTV

Step-by-step explanation:

When you join the lines U, T and V, the number 40 is written between it,

It means it is 40 degrees

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Answer:

The common difference is 2.

The two equations can be rearranged to get two equations with one variable on each side. The equations become 4a = -9 - 3b and 2a = -1 - 5b. By dividing both sides of the first equation by 4, the equation becomes a = -2.25 - 0.75b. Substituting this value of a into the second equation gives -4.5 - 3.75b = -1. Solving this equation for b gives b = 1.2.

4a + 3b = -9

2a + 5b = -1

4a = -9 - 3b

2a = -1 - 5b

a = -2.25 - 0.75b

-4.5 - 3.75b = -1

b = 1.2

a = -2.25 - 0.75(1.2)

a = -1.95

The given set of equations is a simultaneous equation. This means that both equations have the same two variables, a and b. To solve for a and b, we must rearrange the equations so that each equation has only one variable on one side. We can do this by subtracting 3b from the first equation and 5b from the second equation. This gives us the equation 4a = -9 - 3b and 2a = -1 - 5b.

Next, we divide both sides of the first equation by 4 to get a = -2.25 - 0.75b. We can then substitute this into the second equation to get -4.5 - 3.75b = -1. Solving this equation for b gives us b = 1.2. Finally, we can substitute this value of b back into the first equation to get a = -1.95. This means that the solutions for a and b are a = -1.95 and b = 1.2.

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The length of sides BC and XC in the triangle are 8.66 and 10 units respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

From the triangle shown, using trigonometric ratio:

sin(30) = 5/XC

XC = 10

Also:

tan(30) = 5/BC

BC = 8.66

The length of BC and XC are 8.66 and 10 units respectively

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The cost of each apple is $0.56 while the cost of each banana is $0.8

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Let a represent the cost of each apples and b represent the cost of each bananas. Four apples and three bananas cost £4.48:

4a + 3b = 4.48      (1)

Also, three apples and four bananas cost £4.76, hence:

3a + 4b = 4.76    (2)

Solving both equations simultaneously gives:

a = 0.56, b = 0.8

The cost of apple is $0.56 while the cost of banana is $0.8

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Answer:

So the expression is equivalent to 18x + 15.

Step-by-step explanation:

The expression 5(4x+3)-2x simplifies to:

= 20x + 15 - 2x (distributing the 5)

= 18x + 15 (combining like terms)

So the expression is equivalent to 18x + 15.

a. Adding the same number to two numbers produces the same result. Example: 4 + 3 = 7, 7 + 3 = 10, b. Commutative Property: Order does not matter. Example: 4 + 7 = 7 + 4.

The Density Property of Real Numbers states that between any two real numbers, there are an infinite number of other real numbers. This means that for any two real numbers, no matter how close or far apart they are, there is always a third number between them. An example of this property would be if we have two numbers, 4 and 7. If we add 3 to each of these numbers, we will get the same result. 4 + 3 = 7, and 7 + 3 = 10. This shows that no matter what two real numbers we pick, there will always be a third number between them, and when we add the same number to both of them, we will get the same result. Another property of numbers is the Commutative Property, which states that the order of the numbers doesn’t matter when performing certain operations. For example, when adding two numbers, 4 + 7 = 7 + 4. This means that it doesn’t matter which number comes first when adding. This property applies to other operations as well, such as multiplication, division, and subtraction.

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Answer:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Step-by-step explanation:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Answer:

Let's call the travel fee "t" and the hourly fee "h". Then the total cost of a repair, y, can be represented as:

y = t + hx

We can use the two given pieces of information to write two equations and solve for t and h:

2h + t = 100

6h + t = 260

Subtracting the first equation from the second, we get:

4h = 160

Dividing both sides by 4, we get:

h = 40

Substituting this value of h back into the first equation, we get:

2h + t = 100

2(40) + t = 100

80 + t = 100

Subtracting 80 from both sides, we get:

t = 20

So the total cost of a repair, y, as a function of the number of hours spent fixing a leak, x, can be represented as:

y = 20 + 40x

Step-by-step explanation:

Answer:y=40x+20

Step-by-step explanation:

Answer:

C. 4

Step-by-step explanation:

The initial value would be four because that's what the value is at the start of the graph.

The circumference of the circle is 2π x 2, or 12.57 units.

To find the circumference of a circle, we use the formula C = 2πr, where C is the circumference, π is a constant value of 3.14, and r is the radius of the circle. In this case, the radius of the circle is 2 units. So, we plug the values into the formula and get 2π x 2 = 12.57 units. This means that the circumference of the circle is 12.57 units. To put it another way, the circumference is equal to the diameter of the circle (2 units) multiplied by the value of pi (3.14). Therefore, the circumference of a circle with a radius of 2 units is 12.57 units.

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Alex will take 3.75 gallons of fuel to drive five hours to visit his family in city B.

First, let's convert the rate of 60 kilometers per hour to miles per hour:

60 kilometers per hour * (1 mile / 1.6 kilometers) = 37.5 miles per hour

Next, we'll use the rate to find out how many miles Alex will drive in 5 hours:

37.5 miles per hour * 5 hours = 187.5 miles

Now that we know the total distance Alex will drive, we can use the information about the fuel consumption (2 gallons every 50 miles) to calculate the number of gallons of fuel he will need:

187.5 miles / 50 miles per 2 gallons = 3.75 gallons

So, Alex will need 3.75 gallons of fuel to drive five hours to visit his family in city B.

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Answer:

x = 14

Step-by-step explanation:

[tex]8^{x-4}[/tex] = 8^10

[tex]8^{14 - 4}[/tex] = 8^10

8^10 = 8^10

Answer:

23

Step-by-step explanation:

so the sum of all side's of a triangle is 180

so if one angle is 62 n the other angle is 95 then to find the third angle you need to

[tex]62 + 95 + x = 180[/tex]

[tex]157 + x = 180[/tex]

[tex]x = 180 - 157[/tex]

[tex]x = 23[/tex]

hope it helps mate

have a nice day :?

the total cost of fencing the garden will be Rs5400.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

area of the garden = 4a  ( a = side )

= 4(18)

= 72m

length of wire required to fence three rounds = 3 × perimeter

= 3 × 72

= 216 m

rate = 25 × 216

= 5400

Hence the total cost of fencing the garden will be Rs5400.

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The ratio of votes for candidate B compared to candidate A is 1.3:1

What is Ratio?

A ratio in mathematics illustrates how many times one number contains another.

If there were a total of 64 votes and 28 votes went to candidate A, then the number of votes for candidate B can be found by subtracting the votes for candidate A from the total number of votes:

64 - 28 = 36

So, candidate B received 36 votes.

To find the ratio of votes for candidate B compared to candidate A, we divide the number of votes for candidate B by the number of votes for candidate A:

36 / 28 = 1.3

Therefore, The ratio of votes for candidate B compared to candidate A is 1.3:1

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The true statement is that the radius is 10

From the question, we have the following parameters that can be used in our computation:

A circle has a diameter of 20

This means that

Diameter = 20

Divide both sides by 2 to determine the radius

So, we have

Radius = 10

This means that the true statement is that the radius is 10

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Answer:

Option 4
y = 2x + 3

Step-by-step explanation:

Equation of a line in slope intercept form is
y = mx + b
where m = slope and b = y-intercept

Slope m = rise/run = Δy/Δx with Δy = change in y values between any two points on the line and Δx = corresponding change in x values

b is the y-intercept, value of y when x = 0 and indicates the point at which the line crosses the y-axis

Let's take two distinguishable integer points on the line

(0, 3) and (1, 5) are two points

rise = Δy = 5 - 3 = 2
run = Δx = 1 - 0 = 1

So slope = 2/1 = 2

Since y = 3 at x = 0, y-intercept b = 3

Equation of line is
y = 2x + 3

Option 4)

Answer:

4)y=2x+3

You can see this clearly as the y-intercept is 3 and going two spaces up and one to the side is the slope.

Step-by-step explanation:

The loss percentage on selling an article is, 75%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The loss made on selling an article is 25% of the cost price.

Let the cost price = 100

Hence, Selling price is,

⇒ 25% of cost price

⇒ 25% of 100

⇒ 25

Thus, The loss is,

⇒ Loss = cost price - selling price / cost price × 100

           = (100 - 25) / 100 × 100

          = 75%

Thus, The loss percentage on selling an article is, 75%.

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At least three functions can be called, including checkweather. The other two functions can be any other functions that the program contains.

The maximum number of functions that can be called when calling the checkweather function depends on the program. If the program contains other functions, then up to three functions can be called, including the checkweather function. When calling the checkweather function, the first function that will be called is the checkweather function itself. After the checkweather function is called, the program will then proceed to call any other functions that have been determined by the program. This means that the maximum number of functions that can be called is at least two, with the checkweather function being one of them.In addition, if the program contains additional functions, then the maximum number of functions that can be called increases to three. For example, if the program contains functions to display the weather forecast, to check the temperature and to generate an alert, then these functions can also be called in addition to the checkweather function. In this case, the maximum number of functions that can be called is three, with the checkweather function still being one of them.

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Answer:

Question 3

First option:
[tex]\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}[/tex]

Question 4
Third option:
[tex]\dfrac{1}{4} \div \dfrac{2}{5}[/tex]

Question 5

Second Option:
[tex]\dfrac{7}{10}[/tex]

Step-by-step explanation:

Question 3

If  [tex]\dfrac{4}{5}[/tex] inches of rain falls every  [tex]\dfrac{2}{3}[/tex] hours then the unit rate in inches per hour is inches [tex]\div[/tex] hours

This would be:
[tex]\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}[/tex]

This is the first option in Question 3 answer choices

Question 4

[tex]\dfrac{\dfrac{1}{4}\;km}{\dfrac{2}{5}\;min}[/tex]

is nothing but the numerator ÷ denominator which would be:

[tex]\dfrac{1}{4} \div \dfrac{2}{5}[/tex]

This is the third option in Question 4 answer choices

Question 5

[tex]\dfrac{1}{2} \div \dfrac{5}{7}\\[/tex]

Flip the divisor [tex]\dfrac{5}{7}[/tex]; it comes [tex]\dfrac{7}{5}[/tex]

Multiply:
[tex]\dfrac{1}{2} \times \dfrac{7}{5}[/tex]

The result is
[tex]\dfrac{7}{10}[/tex]

This is the second option in Question 4 answer choices

Answers:

Question 3: [tex]\frac{\frac{4}{5}in.}{\frac{2}{3}hr.}[/tex]

Question 4: [tex]\frac{1}{4}[/tex] ÷ [tex]\frac{2}{5}[/tex]

Question 5: [tex]\frac{7}{10}[/tex]

Explanations:

Question 3: We're told that rain is falling at a rate of  [tex]\frac{4}{5} in.[/tex] every  [tex]\frac{2}{3} hr.[/tex], and the unit rate we're looking for is inches per hour (or more precisely, inches per 1 hour). Based on these parameters, we know that you have to divide the unit inches by the unit hours. So using the numbers above, the correct complex fraction to represent this situation would be [tex]\frac{\frac{4}{5} in.}{\frac{2}{3} hr.}[/tex] .

Question 4: In this question, we are given a complex fraction and asked to rewrite it as a simple division problem. The complex fraction is [tex]\frac{\frac{1}{4} km.}{\frac{2}{5} min.}[/tex], so in order to write this as a division expression, you simply take the numerator fraction and divide it by the denominator fraction, which will end up being [tex]\frac{1}{4}[/tex] ÷ [tex]\frac{2}{5}[/tex]. Therefore, that will be your answer.

Question 5: Now, we have a division expression and are asked to use the Keep, Change, Flip method to solve the problem. First and foremost, the Keep, Change, Flip method is essentially telling you that when you are dividing by a fraction, you keep the dividend the same, you change the divisor - specifically switching the numerator with the denominator, which is creating the reciprocal of that fraction - and multiply by the reciprocal of the original divisor instead.

                   A good example of the Keep, Change, Flip method from above would be [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]. You keep the dividend, change the divisor, specifically flip the function around to create its reciprocal, and instead multiply by the divisor's reciprocal. Following those steps, [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]  will become [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] or [tex]\frac{1}{2}[/tex] × [tex]3[/tex].

                  Now that we understand how to use the Keep, Change, Flip method, we can use it to solve the expression [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{7}[/tex]. We keep [tex]\frac{1}{2}[/tex] the same, flip [tex]\frac{5}{7}[/tex] to make its reciprocal, and multiply [tex]\frac{1}{2}[/tex] by that instead. So the final answer will be [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{7}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{7}{5}[/tex] = [tex]\frac{7}{10}[/tex].

Have a great day! Feel free to let me know if you have any more questions :)

The figure's area and perimeter are 562.08 m² and 123.68 m, respectively.

The figure in question is composed of a parallelogram and a crescent. The area of the parallelogram may be calculated using the equation base x level, yielding a value of 336 m².

The area of the crescent is calculated using the formula (π x r²)/2, yielding a value of 226.08 m². As a result, the total area of the figure is 562.08 m².

The parallelogram's perimeter is 86 m, while the boundary of the half circle is 37.68 m, for a total perimeter of 123.68 m.

The figure has a surface area of 562.08 m² and a perimeter of 123.68 m.

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