Radius of 256/3π cm³

Answer:

  See attached

Step-by-step explanation:

You want various combinations of the functions g(a) = -3a+1 and h(a) = 3a³ +4a.

The functions have no common factors, so their ratio leaves the function expressions unchanged:

  [tex]\dfrac{g(a)}{h(a)}=\boxed{\dfrac{-3a+1}{3a^3+4a}}[/tex]

The like terms are combined when the functions are added.

  [tex]h(a)+g(a)=(3a^3+4a)+(-3a+1)=3a^3+(4-3)a+1\\\\=\boxed{3a^3+a+1}[/tex]

Similarly, the like terms are combined when the functions are subtracted.

  [tex]g(a)-h(a)=(-3a+1)-(3a^3+4a)=-3a^3+(-3-4)a+1\\\\=\boxed{-3a^3-7a+1}[/tex]

The product is found the way products are usually found. Each term of one of the factors is multiplied by each term of the other factor, and these products are summed. You can think of it as repeated application of the distributive property.

  [tex]g(a)\cdot h(a)=(-3a+1)(3a^3+4a)=-3a(3a^3+4a)+1(3a^3+4a)\\\\=-9a^4-12a^2+3a^3+4a\\\\=\boxed{-9a^4+3a^3-12a^2+4a}[/tex]

The perimeter of the netball court is equal to 92 meters.

What does perimeter mean?

The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline.

A netball court is a rectangle,

it is given that length of the net ball court is equal to 31 meters.

The width of the netball court is equal to 15 meters.

Therefore the perimeter of the netball court is equal to the length of all sides of the rectangle.

Perimeter of netball court = 2(31+15)=92 meters.

Therefore perimeter of the netball court is equal to 92 meters.

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let the third side be b then use the pythagoras theorem

the quadratic equation have been solved and the required graph is attached below.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation:

[tex]\frac{x^{2}-7x+12 }{x^{2} -1}[/tex]

Its a quadratic equation in both numerator and denominator, by dividing the x² will be get a graph as given in the attached file.

Hence, the quadratic equation will be solved and the required graph is attached below.

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Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.

The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist.  An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.

given

We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.

Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.

So in this case we can write:

limx → +∞f(x) = 0

limx → - ∞f(x) = 0

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Step-by-step explanation:

please refer to the sketch

The system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, is an equation, x² = 2x+3, we need to find a system of equations that can be graphed to give the solution of the equation given,

So, the equation is x² = 2x+3

We can write this as,

x²-2x-3 = 0

Now, factorize to find the solution of the equation,

x²-3x+x-3 = 0

x(x-3)+1(x-3) = 0

(x+1)(x-3) = 0

x = -1 and x = 3

So, the solution of the equation is -1 and 3

However, if we consider the equation to be two different systems combined, that is the equation of the straight line and the equation of the basic quadratic function,

y = x² and y = 2x+3

Then the solution to is the intersection of the graph of the straight line and the graph of the quadratic curve.

That is the x-coordinates of the points of intersection are the solutions.

Since, the graphs are intersecting at (3, 9) and (-1, 1) [see the graph]

Therefore, the system of equation is y = x² and y = 2x+3

Hence, the system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

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Answer:

no

Step-by-step explanation:

The property that could be used to determine that the triangles are congruent is the SSA congruent theorem

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

Triangles = QRP and XWY​

On the triangles, we can see that:

This means that we make use of the SSA congruent theorem

The SSA congruent theorem implies that  if two sides and an angle not included between them are respectively equal to two sides and an angle of the other than the two triangles are equal.

In this case, we have

Congruent sides: RQ and HG & PR and HF

Congruent angles: Angles Q and G

Hence, the additional information on the congruency of the triangles is the SSA theorem

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The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].

What are double angle formulae?

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

           =2Cos²θ – 1

            = 1 – 2Sin²θ

Given sinθ = [tex]\frac{4}{5}[/tex]

         cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]

Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]

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The solution for the question found using the double angle formula for cosine is -.7/-25

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

          =2Cos²θ – 1

           = 1 – 2Sin²θ

Given sinθ = 4/5

        cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² =  1-32/25 = -7/25

Therefore Cos(2θ) fund using double angle formula is -

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The correct statement regarding the linear function passing through the coordinates (2, 1), (3,3), (5,7), (6,9) is given as follows:

A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

A linear function represents a proportional relationship if it has an intercept of zero.

For the points in this problem, when x increases by one, y increases by two, hence the slope is given as follows:

m = 2/1 = 2.

Hence:

y = 2x + b.

When x = 2, y = 1, hence the intercept b is given as follows:

1 = 2 + b

b = -1.

As the intercept is different of zero, this is not a proportional relationship, and option A is correct.

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It will it take 56 years for the account value to reach $20,900.

This amount is calculated based on the principal amount of a loan or the first deposit in a savings account. Simple interest does not compound, thus, a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.

formula for calculating Simple Interest, S.I:

S.I = P * R * T

            100

Where,

S.I =  Simple Interest

P =Pricipal

R = rate ( in percentage)

T= Time

To how long will it take for the account value to reach $20,900

S.I = $20,900

R = 6.5%

P =$ 5,700

T =?

S.I = P * R * T

            100

$20,900 = $ 5,700 * 6.5 * T

                            100

Cross multiplying and Making Time, T  subject of the formula we have:

$20,900 * 100 = $ 5,700 * 6.5 * T

T=   $20,900 * 100

         $ 5,700 * 6.5

T=  56.41

T ≈  56 years

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Answer:

sq root of 21=7

Step-by-step explanation:

we need to use Pythagoras theorem

so distance(isa-jul)^2 +distance(ele-jul)^2= distance(isa-ele)^2

now just do the square root and there you go.

Answer:

8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones

(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the

following conditions are all true:

• The two-digit integer 8R is divisible by 3.

• The three-digit integer 8RS is divisible by 4.

The four-digit integer 8RST is divisible by 5.

The digits of N are not necessarily all different.

The number of possible values for the integer N is

(A) 8

(B) 16

(C) 12

(D) 10

87

(E) 14

Since 8R is divisible by 3, R must be a multiple of 3. The possible values for R are 3, 6, and 9.

Since 8RS is divisible by 4, S must be a multiple of 2. The possible values for S are 0, 2, 4, 6, and 8.

Since 8RST is divisible by 5, T must be 0 or 5.

The possible values for N are therefore:

8000 + 300 + 00 + 0 = 8300

8000 + 600 + 00 + 0 = 8600

8000 + 900 + 00 + 0 = 8900

8000 + 300 + 20 + 0 = 8320

8000 + 600 + 20 + 0 = 8620

8000 + 900 + 20 + 0 = 8920

8000 + 300 + 40 + 0 = 8340

8000 + 600 + 40 + 0 = 8640

8000 + 900 + 40 + 0 = 8940

8000 + 300 + 60 + 0 = 8360

8000 + 600 + 60 + 0 = 8660

8000 + 900 + 60 + 0 = 8960

8000 + 300 + 80 + 0 = 8380

8000 + 600 + 80 + 0 = 8680

8000 + 900 + 80 + 0 = 8980

8000 + 300 + 00 + 5 = 8305

8000 + 600 + 00 + 5 = 8605

8000 + 900 + 00 + 5 = 8905

8000 + 300 + 20 + 5 = 8325

8000 + 600 + 20 + 5 = 8625

8000 + 900 + 20 + 5 = 8925

8000 + 300 + 40 + 5 = 8345

8000 + 600 + 40 + 5 = 8645

8000 + 900 + 40 + 5 = 8945

8000 + 300 + 60 + 5 = 8365

8000 + 600 + 60 + 5 = 8665

8000 + 900 + 60 + 5 = 8965

8000 + 300 + 80 + 5 = 8385

8000 + 600 + 80 + 5 = 8685

8000 + 900 + 80 + 5 = 8985

There are a total of 30 possible values for N. The answer is therefore (E) 14.

Step-by-step explanation:

Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.

(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.

(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness

(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.

Step-by-step explanation:

The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.

Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.

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Answer:

+ 8

Step-by-step explanation:

This is an arithmetic progression (AP) as there is a common difference between successive terms.

For example, looking at the first two terms,

Difference = 2nd term - 1st term

                  = -11 -(-19)

                  = -11 + 19

                  = +8

To check,

Looking at the second and third terms,

Difference = 3rd term - 2nd term

                  = -3 -(-11)

                  = -3 + 11

                  = +8

Hence, there is a common difference of +8 between consecutive terms, making it an AP.

The key features of the graph of the given equation -8x + 20y = 240 include the following:

D. As x → -∞, y → ∞.

E. The y-intercept is (0, 12).

H. The x-intercept is (-30, 0).

Making y the subject of formula in order to determine the slope, we have:

20y = 8x + 240

Dividing both sides of the equation, we have:

y = 8x/20 + 240/20

y = 8x/20 + 12

Therefore, the slope is equal to 8/20.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

When x = 0, the y-intercept is given by;

20y = 8(0) + 240

y = 240/20

y = 12.

Therefore, the y-intercept is equal to (0, 12).

When y = 0, the x-intercept is given by;

-8x + 20(0) = 240

x = -240/8

x = -30

Answer:

2[tex]\pi[/tex] [tex]units^{2}[/tex]

Step-by-step explanation:

BC is equal to 4 because 5*4=20.

The radius is 2. The equation for the area of a circle is [tex]\pi r^2[/tex].

Therefore, if we plug in 2 we will get [tex]4\pi[/tex].

But then we divide by 2 to get 2[tex]\pi[/tex] [tex]units^{2}[/tex] as our answer.

Hope this helped! :)

On solving the provided question, we cans ay that - here in triangles, triangle ABC is congruent to triangle A`B`C`

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

Here,

two triangles are there

triangle ABC and triangle A`B`C`

AB =A`B`

BC = B`C`

AC =A`C`

So, by sss property

both are congruent

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Answer: -3√3

Step-by-step explanation: Factor out the square roots from each term

2√54 -> 6√6

√27 -> 3√3

3√24 -> 6√6

The equation becomes 6√6 - 3√3 - 6√6

By combining like terms we can eliminate 6√6

This leaves us with -3√3 as the simplified solution

Answer:

-3√3

Step-by-step explanation:

do the hcf method to get all the values outside

hcf of 54= 2, 3, 3, 3

hcf of 27 = 3, 3, 3

hcf of 24 = 2,2,3,3

2✓2×3×3×3 - √3,3,3 - 3√2,2,3,3

take out the common factor and multiply it with the value we have outside leave it if it doesnt have a number

2×3√2×3 - 3✓3 -3×2×3

6√6 - 3√3 - 3×2×3

6×3 - 3√3 - 3×2×3

18-18 - 3✓3

-3√3

Answer:

1809/27=67 is your answer........

Answer:

true

Step-by-step explanation:

20 away from nothing is 20

Answer:

Step-by-step explanation:

20-0=20

Example 1: Suppose you have 20 friends and they are given the choice of choosing a sport from cricket or basketball. All of them decide to play cricket and 0 chooses basketball. So, the total number of students who decided cricket is 20 students(20-0=20).

Example 2: Suppose you have 20 chocolates and you give 0 chocolates to your sister then you have a total of 20 chocolates(20-0=20).

Example 3: Suppose there are 20 students in a class and 0 were absent out of them. So, the total number of students that were present are 20 students(20-0=20).

Example 4: Suppose you have 20 clothes in your wardrobe and you gave 0 clothes for washing. So, the total number of clothes in the wardrobe is 20 clothes(20-0=20).

The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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Answer:

they are intersecting.. so, there's one solution. the ordered pair is (-1,4).

The value of the function f(x) at x = - 2, - 1, 0, 1 are - 4, - 1, 2, 5.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 3x + 2.

Now,

At x = - 2, f(x) = 3(-2) + 2 ⇒ f(x) = - 4.

At x = - 1, f(x) = 3(-1) + 2 ⇒ f(x) = - 1.

At x = 0, f(x) = 3(0) + 2 ⇒ f(x) = 2.

At x = 1, f(x) = 3(1) + 2 ⇒ f(x) = 5.

This can also be written in the form of ordered pairs

(- 2, - 4), (- 1, - 1), (0, 2), (1, 5).

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The distance that the minute hand moves in 50 minutes, given that it started at 7 minutes, is 258 degrees.

A rotatation around the clock by the minute hand, is a full 360 degrees as it begins at 12 and ends at 12 .

If a minute hand is at 7 minutes, then it means that the degrees moved is:

= 7 / 60  x 360

= 42 degrees

At 50 minutes, the degrees moved is :

= 50 / 60 x 360

= 300 degrees

Seeing as the minute hand started at 7 minutes, the distance moved is :

= 300 - 42

= 258 degrees

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The solution of given algebra question is-The number of candies in each box is 12.

In algebra, the fundamental concepts are numbers, parameters, constants, expressions, coefficients, linear equations, and quadratic equations. Additionally, it requires adding, subtracting, multiplying, and dividing basic arithmetic operations within the algebraic formulas.

Multiplication and division tasks should be completed first from left to right, followed by addition and subtraction tasks from left to right.

Let the number of candies in the box be x

Total candies with Josh=5x+15

Total candies with Diego=6x+3

Since, they have same number of candies,

Hence,

5x+15=6x+3

6x-5x=15-3

x=12

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Answer:

Below

Step-by-step explanation:

"Lynn is making a snack. The recipes call for 3/8 cup of water for oats and 1/4 cup"

(I changed the numbers to fractions ....)

she needs   3/8 + 1/4 cup ....add them together by finding a common denominator

1/4 = 2/8    

then   3/8 + 2/8 = (3+2)/8 = 5/8 cup

  if she has one cup of water she has enough....she only needs 5/8 cup