11
What is the value of this expression?
3 1/6 + 8 2/9 - 1 1/2

Answer:

55 and 10

I hope this helps

Answer:

Hello the vertex point is (4, -6)

this parabola opens upwards because the coefficient of x is positive.

The answer is B, good luck!

The number of times a student must raise the object to expand the given energy level is 6800 times.

Work is defined as transferring energy into an object so that there is some displacement. Energy is defined as the ability to do work. Work done is always the same. Energy can be of different types such as kinetic and potential energy.

Here, W=8.0×10⁶, m=60 kg, g=9.8 ms⁻² and h=2.0 m

We know that, W=mghn

Now, n=W/mgh

n=8.0×10⁶/(60×9.8×2)

= 6800 times

Therefore, the number of times a student must raise the object to expand the given energy level is 6800 times.

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The solution for this equation is (3¹)⁴=81.

The power of a number defines how many times to use the number in multiplication, Powers are also called Exponents or Indices.

If the power is positive, multiply the number by itself that many times. If the power is negative, multiply the number's reciprocal by itself that many times. If the power is zero, the result will always be 1.

For example, 8^2 could be called “8 to the power 2” “8 to the second power”, or simply “8 squared”.

A number, ​X​, to the power of 2 is also referred to as ​X​ squared.

X​ is called the base number.

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The function f(x) is 4x³ + 20x² + 5x - 31.

What is a function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each part of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given:  function f(x) is divided by 2x + 3, the quotient is 2x² + 7x - 8 and the remainder is -7.

When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:

f(x) = d(x)q(x) + r

Now putting values of d(x) = 2x+3, q(x) = 2x² + 7x - 8 and r = -7, we get

f(x) = (2x+3)(2x² + 7x - 8) - 7

f(x) = 4x³ + 14x² - 16x + 6x² + 21x - 24 - 7

f(x) =  4x³ + 20x² + 5x - 31

Hence, the function f(x) is 4x³ + 20x² + 5x - 31.

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Answer:

f(x) shifts for log(DWX)

Step-by-step explanation:

The three methods which are used to represent a set are word description, roster method and set-builder notation.

What is a set?

The way that sets are represented by a person is always the same which is as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.

The three methods used to represent a set are as follows;

1. Word description

It is the method of representing a set under which we simply use words for describing the elements of the given set.

For example: A is the set of all natural numbers less than 8.

2. Roster method

It is the method of representing a set under which the elements of the set are listed by separating them with commas and in curly brackets.

For example: A = {1,2,3,4,5,6,7}

3. Set-builder notation

It is the method of representing a set under which only the property of the elements of the given set are written.

For example: A = {x ,x ∈ N and x<8}

Hence, the above stated methods are used to represent a set.

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Answer:

12π m²

Step-by-step explanation:

We are interested in calculating the area bounded by the given arcs .

we know that if [tex]\theta[/tex] is the angle subtended at the centre by the arc , then ; the area is given by ,

[tex]\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 \\[/tex]

here we have ,

Therefore on substituting the respective values, we have;

[tex]\longrightarrow Area =\dfrac{120^o}{360^o}\times \pi (6m)^2 \\[/tex]

Simplify,

[tex]\longrightarrow Area =\dfrac{1}{3}\times \pi \times 36m^2 \\[/tex]

[tex]\longrightarrow \underline{\underline{ Area = 12\pi \ m^2}} \\[/tex]

And we are done!

Answer: The result is 12π m²

To solve, we must find the Area of the circle, for this we must do the following:

[tex] \: \sf{Area} = \cfrac{ \sf{θ} }{360 {}^{ \circ} } * \sf{\pi r {}^{2} }[/tex]

Once having the above, we must extract the results that we have to put in the fraction, where:

Once we have the above, we must substitute the respective values...

[tex] \sf Area = \cfrac{120 {}^{ \circ} }{360 {}^{ \circ} } * \pi(6m) {}^{2} [/tex]

Now to finish, let's simplify:

[tex] \sf{Area = \cfrac{1}{3}* \pi * 36m {}^{2} }[/tex]

[tex] \sf Area = 12 \pi \: m {}^{2} [/tex]

Rpt: The result is 12π m²

Answer:24

Step-by-step explanation:

The quotient of the polynomial division is x^2 - 3x + 2.

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

f(x) = x^3 - 6x^2 + 11x - 6

Factor = (x-3)

One way to find the other factors of the function f(x) = x^3 - 6x^2 + 11x - 6 is to divide the polynomial by (x-3) and see what the quotient is.

To do this, we have

Quotient = f(x)/Factor

Substitute the known values in the above equation, so, we have the following representation

Quotient = (x^3 - 6x^2 + 11x - 6)/(x - 3)

Using a graphing calculator, we have

Quotient = x^2 - 3x + 2

Hence, the quotient is x^2 - 3x + 2

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Complete question

One factor of the function f(x) = x^3 - 6x^2 + 11x - 6 is (x-3)

Determine the quotient of the polynomial and the factor

All solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).

To find all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9, we need to solve for the intersection of the linear equation and the quadratic equation. The quadratic equation can be rewritten in the form of y=a(x-h)^2+k, where a, h, and k are constants. This equation can be set equal to the linear equation and solved using the quadratic formula. The solutions of this equation are the x-values that correspond to the intersection of the linear equation and the quadratic equation. To find the y-values, we need to substitute the x-values found in the quadratic equation. Therefore, all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).

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The inequality that models this scenario is given as 10x + 9y ≥ 450

An equation is an expression showing the relationship between numbers and variables.

Let x represent the number of minutes that Armando will kickbox and y represent the number of minutes he will swim.

Kickboxing, he burns 10 calories per minute and he burns 9 calories a minute while swimming. He wants to burn at least 450 calories each day, hence:

10x + 9y ≥ 450

The inequality is given as 10x + 9y ≥ 450

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Answer:

x = 38°

Step-by-step explanation:

sum of interior angle

=(n - 2 )180

=(8 - 2)180

=(6)180

=1080°.

the value of x

=(x + 55)° + (3x + 20)° + 4x° + (4x - 10)° + (6x - 55)° + (3x + 52)° + 3x° + (2x + 30)° = 1080°

= x + 3x + 4x + 4x + 6x + 3x + 3x + 2x + 55 + 20 - 10 - =55 + 52 + 30 = 1080.

=26x + 92 = 1080

=26x = 1080 - 92

=26x = 988

=26x/26 = 988/26

x = 38°

A linear programming problem consists of a linear function to be to be maximized or minimized. It is subject to a set of constraints given in the form of linear equations or inequalities.

Linear programming is the programming in which selecting the best possible choice from those available alternatives whose constraint function and the objective function can be referred to as the linear mathematical function.

Linear programming is used for the optimization of linear objective.

It is used as constrained optimization, from where the objective functions and constraints all are linear.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables

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On solving the provided question, we can say that the inequality we have ( -3, 2 ) => 2x - y>-8

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here the inequality

we have ( -3, 2 )

y - 2 > 2(x+3)

y-2 > 2x +6

2x - y>-8

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Answer:

150

Step-by-step explanation:

x - .14x = 129

.86x = 129   Divide both sides by .86

x = 150

After rounding off the median of the given data would be 38.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.

So, calculate as follows:

22, 25, 25, 36, 39, 48, 53, 70

TErms are even: Average of two middle terms to get median.

Median = 36 + 39/2

Median = 37.5

Rounding off: 38

Therefore, after rounding off the median of the given data would be 38.

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The derivative of the problem is dy/dx = (2cosx)/(1-sinx)²

The given function is Y=1+sinx/1-sinx

d/dx (u/v) = [u (dy/dx) - v (dv/dx) ] / v²or less formerly

(u/v) =[ [(v (du) = u(dv)] / v²

(Remember the rule in word; " vdu minus udv all over v squared)

So with Y=1+sinx/1-sinx then,

Let u = 1+sin x ⇒du/dx= cos x and

v = 1-sin x⇒dv/dx = -cos x

Then, [d/dx(u/v) = u(dy/dx) - u(dv/dx)] / v²

dy/dx = [(1-sinx)(cosx) - (1+sinx)(-cosx)] / (1-xin x)²

This implies that dy/dx =[ cosx - sin x +cosx +sin xcosx] / (1-sinx)²

Therefore, dy/dx = (2cos x)/(1-sinx)²

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The statement is true, the scale factor maintains the proportions between the sides.

We want to see if the statement "Scale factors figures must be the same proportions on all sides from the original figure." is true or false.

Suppose we have a polygon with N sides, such that the lengths of each side are:

{L₁, L₂, L₃,...}

If we apply a scale factor k, we just need to multiply each one of these lengths by k, then we will get:

{k*L₁, k*L₂, k*L₃,...}

Now, let's take the proportion between the new lengths for sides 1 and 2, we will get:

(k*L₁)/(k*L₂) = L₁/L₂

The scale factor disappears, then the proportions are maintained,

The statement is true.

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The factorization of the provided question is basically -11a(a-1).

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring. You will mostly learn this idea in your lower secondary classes from grades 6 to 8.

A polynomial is an expression made up of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative exponents. Polynomials are commonly used in algebra and in various mathematical disciplines.

Given,

11a-11a²

Taking common terms

-11a(a-1).

by factorizing 11a-11a²

we get -11a(a-1).

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Answer:

10d

Step-by-step explanation:

p = d

10p = ?

Cross multiply

(10pd)/p = 10d

Answer:  The equation that represents the situation is d = k/p, where k is a constant.

This equation states that the number of days taken to complete the work (d) is inversely proportional to the number of people working on the job (p).

Given that 10 people work on the job and it takes them d days to complete it, we can substitute these values into the equation:

d = k/10

We don't know the value of k, so we can't find out the number of days it takes with 10 people working.

Step-by-step explanation:

Liam has 5 quarters, 10 dimes and  and 7 nickels.

1 dollar is 100 cents - a full dollar, so 100 cents.

One dollar is written on one side of the coin, sometimes as "$1".

1 quarter dollar equals 25 cents - 1/4 of a dollar equals 25%, so 25 cents

On one side of the coin, a quarter dollar is written.

1 dime is 10 cents - 1/10th of a dollar, so 10%, so 10 cents, dime begins with d, decimal begins with, and decimal is base-10. One dime is written on one side of the coin.

1 nickel is 5 cents - made of nickel alloy, 1 cent/penny is possibly not made of nickel because it costs more than 1 cent, so it begins with 5 cents.

On one side of the coin, five cents are written.

Let d be the no. of dimes, n be the no. of nickels and q be the no. of quarters.

Given that

2q = d

n + 3 = d

money in dimes = money in quarters

10d = 25q

d can be written as

d = q/2

So

10(2q)  = 25q

2q/q = 25/10

q = 2.5

as 2.5 cant be a number for quarter, lets double it

q = 5

d = 2q

d = 2(5)

d = 10

n = d - 3

n = 10 - 3

n = 7

Thus, Liam has 5 quarters, 10 dimes and  and 7 nickels.

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The vertex for the given function is (1, -25) and the zeros are (6, 0)(-4, 0).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given y = (x - 1)² - 25

converting the equation in form of y = ax² + bx + c

y = x² + 1 - 2x - 25

y = x² - 2x - 24

vertex of a quadratic equation is given by (-b/2a, -D/4a)

b = -2, a = 1, c = -24

D = b² - 4ac

D = (-2)² - 4(-24)

D = 4 + 96

D = 100

vertex is, -b/2a = -(-2)/2 = 1

and -D/4a = -100/4 = -25

vertex are (1, -25)

and for zeros put y = 0

y = x² - 2x - 24

x² - 2x - 24 = 0

x² - 6x + 4x - 24 = 0

x(x - 6) + 4(x - 6) = 0

(x - 6)(x + 4) = 0

x = 6 and x = -4

zeros are (6, 0)(-4, 0)

Hence option C is correct.

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The equation has 2 valid solutions; no extraneous solutions.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Factorisation : The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Radicals :In the same way that addition is the opposite of subtraction in mathematics, a radical, also known as a root, is the opposite of an exponent. The square root, denoted by the symbol  is the smallest radical.

The given equation is:

First, we determine the solutions

Add 5 to both sides

Square both sides

Expand

Collect like terms

Expand again

Factorize

Factor out x - 2

Split

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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The equation of a line passing through the points (-3, 3) and (1, 2) is x + 4y = 9

When two points in a plane are given, a line passing through them can be determined. It is the set of all points in the plane that are equidistant from the two given points.

These points form a straight line, which can be represented by an equation with two variables.

The equation of the line can be found using the slope-intercept form or by solving a system of two equations.

The slope of the line is the ratio of the change in the y-coordinate of the two points over the change in the x-coordinate of the two points.

The y-intercept is the point where the line crosses the y-axis. The line can also be expressed in terms of its intercepts on the x and y-axes.

The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

We know that the equation of a line passing through the points (x1, y1) and (x2 , y2) is given by y - y1 = m (x - x1).

m is the slope given by the formula m = (y2 - y1) / (x2 - x1)

Hence on substituting the given points in the equation of a line, we get

y - 3 = m ( x - (-3) ) -------(1)

m =  (y2 - y1) / (x2 - x1)

m = (2 - 3) / (1+3)

m = -1/4

Substituting value of m in equation (1), we get

y - 3 = -1/4 ( x + 3)

4(y - 3) = -x - 3

4y - 12 = -x - 3

x + 4y = -3 +12

x + 4y = 9

Therefore, the equation of a line passing through the points (-3, 3) and (1, 2) is x + 4y = 9

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I recently dropped a large cube, leaving a dent in my floor. The floor's surface contains a triangular hole with sides that are $68, $75, and $77 long. The hole is about this deep:  [tex]$d=12 \sqrt{6}[/tex]

Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure. Triangle examples. Sandwiches, traffic signals, clothing hangers, and a billiards rack are a few instances of triangles in everyday life.

To start, you can determine the sides of the tetrahedron whose apex corresponds to the dent's deepest point. Three of its sides are previously known to be $68,75,77, and since we have perpendicular planes, if these side lengths are x, y, and z, then

[tex]$x^2+y^2=68^2, x^2+z^2=75^2, y^2+z^2=77^2$[/tex] and these three equations solve to

[tex]$x=12 \sqrt{15}, y=4 \sqrt{154}, z=3 \sqrt{385}[/tex]

When the origin of a coordinate frame is located at the point where three perpendicular planes cross and the axes are placed along the edges, the equation for the plane of the triangle hole is

[tex]$\frac{x}{12 \sqrt{15}}+\frac{y}{4 \sqrt{154}}+\frac{z}{3 \sqrt{385}}=1[/tex]

As a result, the distance from the origin, which is the hole's deepest point, to its plane is

[tex]$d=\frac{1}{\sqrt{\frac{1}{144(15)}+\frac{1}{16(154)}+\frac{1}{9(385)}}}[/tex]

Then we get,

[tex]$d=12 \sqrt{6}[/tex]

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Using the inverse function method, the value of x should be x = 7/2 or x = -5

From the case, we know that:

f(x) = (6x + 7) / 2

g(x) = 3x - 5

f⁻¹.g⁻¹(x) ?

First, we need to find the inverse function of each given functions. We assume that:

f⁻¹(x) = p

g⁻¹(x) = q

f⁻¹(x) = (6x + 7) / 2

p = (6x + 7) / 2

2p = 6x + 7

2p - 7 = 6x

x = (2p - 7) / 6

f⁻¹(x) = (2x - 7) / 6

g⁻¹(x) = 3x - 5

q = 3x - 5

q + 5 = 3x

x = (q + 5) / 3

g⁻¹(x) = (x + 5) / 3

Next, we will try to find the value of x

f⁻¹.g⁻¹(x) = 0

(2x - 7) . (x + 5) = 0

     6           3

(2x² - 7x + 10x - 35) = 0

             15

2x² +3x - 35 = 0

(2x -7) (x+5) = 0

x = 7/2 ∨ x = -5

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Answer:

Step-by-step explanation:

480 miles/5 hours=x miles/8 hours

x=480*8/5

x=768 miles(distance)

480/5=96 mph(speed)

Answer: 1560

Step-by-step explanation:1500*1.04=1560