Explain how to find the quotient of: (8a3+31a2-20a-5)/(8a-1)

Answer:

[tex] \displaystyle{\frac{2810}{3}} \pi \: \: \text{cm} ^{3} [/tex]

Step-by-step explanation:

The solid shape is composed of a cone and a hemisphere.

Let's work out the radius of the cone since the hemisphere and the cone share the same radius.

Let the radius be r cm.

Volume of cone= [tex] \displaystyle{\frac{1}{3} \pi {r}^{2} h}[/tex]

Substituting the volume and height of the cone:

[tex]270\pi = \displaystyle{\frac{1}{3} (\pi)( {r}^{2} )(10)}[/tex]

Simplify:

[tex] \frac{10}{3} {r}^{2} = 270[/tex]

[tex]81 = {r}^{2} [/tex]

Square root both sides:

[tex]r = \sqrt{81} [/tex]

r= 9

The volume of a hemisphere is half the volume of a sphere.

Volume of hemisphere

[tex] = \displaystyle{ \frac{1}{2}( \frac{4}{3} )(\pi )( {r}^{3}) }[/tex]

[tex] = \displaystyle{ \frac{2}{3}\pi {r}^{3} }[/tex]

Substituting the value of r:

Volume of hemisphere

[tex] = \displaystyle{ \frac{2}{3} (\pi)(10^{3} )}[/tex]

[tex] = \displaystyle{ \frac{2}{3}(1000)(\pi) }[/tex]

[tex] = \displaystyle{\frac{2000}{3} \pi}[/tex]

Volume of the shape

= volume of cone + volume of hemisphere

[tex] = \displaystyle{(270 + \frac{2000}{3} })\pi[/tex]

[tex] = \displaystyle{ \frac{2810}{3} \pi} \: \: \text{{cm}}^{3} [/tex]

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Only if two figures can be precisely mapped to one another using transformations are two figures said to be congruent.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

Only if two figures can be precisely mapped to one another using transformations are two figures said to be congruent. Due to the stiff transformations' preservation of the distance and angle scales, all related sides and angles are congruent.

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There are 50 odd integers from 1 to 100.

Odd integers  are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd integer by 2, then it will leave a remainder. In other words, numbers in the form of [tex]2k + 1[/tex], where [tex]k[/tex] ∈ [tex]Z[/tex] (i.e. integers) are called odd numbers.

First odd number is 1 from 1 to 100.

Last odd number is 99 from 1 to 100.

Total odd numbers = 99+1 ÷ 2 = 50

There are 50 odd integers from 1 to 100.

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As per the concept of inverse function, the domain of f is the range of f⁻¹, and the domain of f⁻¹ is the range of f.

The term inverse function in math is referred as the function y=f(x) can be obtained by switching x and y and solving for y and then the value y will be replaced with f⁻¹ as this denotes the inverse of the function f.

Here we need to find the domain of f is the _____of f⁻¹, and the _____ of f⁻¹ is the range of f.

As we all know that the domain refers the set of all inputs of the function and range refers the set of all outputs of the function.

Based on these definition we have identified that the domain of function is always be the range of inverse function f.

Similarly, the range of inverse function f is always the domain of the function f.

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Answer:

800 m^2

Step-by-step explanation:

= 1250 - 450

= 800 m^2 est la superficie de la terre de M. Vergne

j'espère que ma réponse t'aidera.

Answer: 6.5%

Step-by-step explanation: 312/4 = 78

78/1200 = 0.065

0.065 x 100 = 6.5%

On solving the provided question, we can say that, A 4 cm Cube has a 96 cm2 total surface area.

Total surface area is the total area, which includes the curved portion and any bases. It refers to the entire surface area of the thing. The total area will be the sum of the two areas if the shape has a curved base and surface.

The cube's surface area is calculated as six times the square of its side lengths. 6a2, where an is the cube's side length, serves as its representation. Basically, it refers to the overall surface area.

total surface area of a cube of 4 cm is 96 cm2

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Answer: (n-2) * 180

Step-by-step explanation:

The formula for the sum of the interior angle measures of a polygon with n sides is (n - 2)180 degrees.

Answer:

integers have signs like -&+ while whole numbers are ALWAYS positive

Answer:

136

Step-by-step explanation:

because 32 times 4 is 128 and 32 divided by 4 is 8 that together is 136 its dived by four because 15 is 1/4 of 60 which is an hour

Answer: 136 copies in 4 minutes and 15 seconds

Step-by-step explanation:

First, we need to find how many copies the machine makes per second

a minute has 60 seconds. Divide the number of copies made per minute by 60

32/60

simplify

8/15

It can make 8/15 copies per second.

It takes a minute to print 32 copies, so multiply the number of copies per minute by 4 minutes

32*4=128

128 copies in 4 minutes

now 8/15 * 15 =120/15 = 8

128+8=136

Choices B and C are both correct statements.

Choices A and D are both false.

The y-intercept of the line tells us about the situation when Justine started the race she was 10 kilometers from the finish line.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given, a line whose y-intercept is at y = 10 which is represented by the distance remaining in kilometers. Since x shows the time spent running that means at x = 0 she started running.

Therefore, The y-intercept of the line reveals that Justine was 10 kilometers from the finish line when she started the race.

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According to the given figure, we can conclude that ∠LMN is 90° in the given triangle LMN.

A right triangle is a triangle having one right angle or two perpendicular sides.

It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or originally rectangle triangle.

The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question, and its "adjacent" side is the one that faces it.

We use special terminology to define the sides of right triangles.

The hypotenuse of a right triangle is always the side across from the right angle.

Therefore, according to the given figure, we can conclude that ∠LMN is 90° in the given triangle LMN.

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Answer:

(-3, -2)

Step-by-step explanation:

To find the value of y so that the line passing through the two given points has a slope of 1, we can use the formula for the slope of a line, which is given by:

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

In this case, we know that the slope of the line is 1, so we can set up the equation:

1 = (y - (-2)) / (-9 - (-3))

Solving for y, we get:

1 = (y + 2) / 6

Therefore, y = 1 * 6 - 2 = 4, so the value of y that we are looking for is 4.

Alternatively, we can use the two given points to write the equation of the line in slope-intercept form, which is given by:

y = mx + b

In this case, we know that the slope of the line is 1, so we can write the equation as:

y = x + b

We also know the coordinates of one of the points on the line, (-3, y), so we can substitute these values into the equation to solve for b:

y = (-3) + b

Substituting the value of y that we found earlier, 4, we get:

4 = (-3) + b

Solving for b, we get:

b = 4 + 3 = 7

Therefore, the equation of the line that passes through the two given points and has a slope of 1 is y = x + 7. This equation is in slope-intercept form, so it shows us the value of y when x is 0, which is 7. Since the y-coordinate of one of the given points is -2, we know that this point must be (-3, -2), and we can verify that this point satisfies the equation y = x + 7.

The value of the discriminant for 2x² + 5x + 7 = 0 is -31.

The discriminant of a quadratic equation is the part of the equation used to determine the number and type of solutions. It is calculated by subtracting 4 times the coefficient of the squared term, a, from the coefficient of the linear term, b, squared. This is then divided by four times the coefficient of the squared term, a.

In this case, the equation is 2x² + 5x + 7 = 0.

The discriminant for this equation is calculated as follows:

Discriminant = b² - 4ac

Discriminant = (5)² - 4(2)(7)

Discriminant = 25 - 56

Discriminant = -31

Therefore, the value of the discriminant for 2x² + 5x + 7 = 0 is -31.

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    The correct option is A)289

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division. For example 3x+2x-5

Given here, x²+74x+2021=y²

                   x²+2×37x + 37² = y²-652

                                 (x+37)²= y²-652

                                 (x+37)²- y² = -652

                       (x+y+37) (x-y+37) = 289 × -2

 thus, x+y+37 = 289 . . . .(1)

         x-y+37  = -2  . , . . . . .(2)

Solving the two equations we get x = 125 & y=164

Thus x+y = 125+164

                = 289

Hence option A) is the correct answer

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Answer:

2/1

Step-by-step explanation:

Answer:

the answer is 2!

Step-by-step explanation:

you count the rise over run

count from where it meets a whole number to where it meets another whole number and then you have your answer!

for this you count from (3,3) to (2,1) which is 2/1 making it 2

Answer:

Hi,

The first one is the second one, the one on the top right. This is because you add two branches every step.

I'm not so sure about the second question. sorry ! hope it helps tho

Answer:

Zero is a real number in math

Step-by-step explanation:

Zero is considered to be both a real and an imaginary number.

The pair of linear equations 3x+2y= 5 and 2x-3y= 7 have one unique solution.

The number of solutions for a pair of equations can be determined by looking at the coefficients of the variables in the equations. In particular, the number of solutions will depend on whether the coefficients of the variables are the same or different.

In this case, the pair of equations 3x+2y= 5 and 2x-3y= 7 have different coefficients for the variables x and y. Specifically, the coefficient of x is 3 in the first equation and 2 in the second equation, and the coefficient of y is 2 in the first equation and -3 in the second equation.

When the coefficients of the variables are different, there is exactly ONE solution to the system of equations. This is because the two equations will intersect at a single point in the x-y plane, which is the solution to the system of equations.

Therefore, based on the coefficients of the variables in the equations 3x+2y= 5 and 2x-3y= 7, we can conclude that there is only ONE solution to this system of equations.

--The question is incomplete, answering to the question below--

"How many solutions does the pair of equations 3x+2y= 5 and 2x-3y= 7 have?"

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In a given year, a member may get illness benefits for a maximum of 120 days. The total number of permitted compensable days for the next year cannot be increased by any unused fraction being carried forward. For the same condition, the sickness benefit cannot be awarded for more than 240 days.

A daily cash payment is made for each day a member is unable to work as a result of illness or accident.

Qualification Requirements

If a member meets the following criteria, they may be eligible to receive this benefit: Is unable to work due to illness or injury and is confined to a hospital or their home for a minimum of four (4) days;

Has duly notified the SSS directly of the fact of sickness or injury;

Has paid at least three (3) months' worth of payments within the 12-month period immediately preceding the semester of illness or injury.

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The value of y are when x = -2, -1, 0, 1, 2 are -4, 1, 0, -1, 4. The graph of the function attached.

What is coordinate plane?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

Given function is y = x³ - 2x

Putting x = -2 in the equation y = x³ - 2x:

y = (-2)³ - 2×(-2)

y = -4

Putting x = -1 in the equation y = x³ - 2x:

y = (-1)³ - 2×(-1)

y = 1

Putting x = 0 in the equation y = x³ - 2x:

y = (0)³ - 2×(0)

y = 0

Putting x = 1 in the equation y = x³ - 2x:

y = (1)³ - 2×(1)

y = -1

Putting x = 2 in the equation y = x³ - 2x:

y = (2)³ - 2×(2)

y = 4

The points on the equations are (-2,-4), (-1, 1), (0,0), (1,-1), (-2,4).

Plot the points and joint them by curve.

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It becomes

[tex]$$\begin{aligned}5: 8: & 6.5: x \\5 \times x & =8 \times 6.5 \\x & =\frac{8 \times 6.5}{5} \\x & =\frac{52}{5} \\x & =10.4\end{aligned}$$[/tex]

Therefore,

5 machines will take $10.4$ hour to produce the same number of parts.

Equivalent interest rates are interest rates that produce the same future value after one year. For example, 10% compounded quarterly and 10.125% compounded semiannually are equivalent nominal interest rates. If you calculate the future value of $100 invested at either rate for one year, you will obtain $110.38.

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The amount of salt in the tank at the end of one hour is 103 lbs .

Given

Initially there are 100 gal in the tank. There are 6 lbs of salt. The concentration of salt in the tank is 6/100 or 0.06 lbs per gal.

Water flowing in has concentration of 1 lb/gal.

Water flowing out has unknown concentration because mixture is constantly changing.

Tank is losing 1 gal per minute. ( 2 - 2 = 0 )

V ( t ) = 100 - t

s ( t ) = 6 + 2t − 3t ∗ C( t )

C ( t ) = s ( t ) / V ( t )

= 100 - t / 2t − 2t ∗ C( t )

= 6 + 2t / 100 + 2t

After 60 minutes

C ( t ) = 6 + 2 * 60 / 100 + 2 * 60

= 6 + 120 / 100 + 120

= 126 / 220

= 63 / 110

Salt content s( t ) = 6 + 2 * 60 - 3 * 60 * 63 / 110

= 126 - 180 * 63 / 110

= 126 - 103

= 103 lbs

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Both were multiplied by 100 and the quotient of both expressions is 2.5.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

3.75 ÷ 1.50 is equivalent to 375 ÷ 150.

Moving the decimal point 2 places to the right is equivalent to multiplication by 100.

so, both were multiplied by 100.

The quotient is:

3.75 ÷ 1.50 = 2.5

375 ÷ 150 = 2.5

Hence, both were multiplied by 100 and the quotient of both expressions is 2.5.

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When X=3 a polynomial has a value of 61 and when X=3 a value of 143.

Given that,

Let p(x)=3x²−4x²+7x−5 is our polynomial.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Substitute x=3 in above expression,

∴p(3)=3(3) 3−4(3) 2 +7(3)−5

=3(27)−4(9)+21−5

=81−36+21−5

=61

Now,

p(−3)=3(−3)

3 −4(−3) 2 +7(−3)−5

=3(−27)−4(9)−21−5

=−81−36−21−5

=−143

So, value of polynomial when X=3 is 61 and when x=−3 is −143

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Answer:

Hello! Natalie earns a fixed amount of $43 per day. She earns $3 more every toy she sells. Basically, you can set up this equation as 43 + 3n >= 70. This is because she wants to make a least $70 and earns $3 each for "n" toys that she sells. When you solve the inequality, the answer is 9. Subtract 43 from both sides to get 3n >= 37 and divide by 3 to get n >= 9. The answer is A.

Step-by-step explanation:

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Answer:

The linear function which is passing through the points (-20, -268) and (-1, -40) is y + 268 = 12(x + 20). Then the correct option is C.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The table represents some points on the graph of a linear function.

Let the linear relationship is given below.

Answer:

no

Step-by-step explanation:

x=3, y=1

3≠1

therefore x≠y