If 5 and (5+ square root 5) are two of the
roots of a third degree polynomial with integer coefficients, what is the other root?

Dilation

By maintaining the object's orientation or shape, this type of translation either expands or contracts the object. This is referred to as resizing.

What is Graph Transformation?

A graph can be transformed to produce a different version of the one that came before it. The x-y plane can be used to translate or shift the graphs. In addition to these modifications, they may also be stretched.

Types of Stretching of Graphs

Consider the case where we need to lengthen a graph by a factor of 2. Next, change the y value. Now, each point of the function F's form (x, y) shifts to the point (x, 2y)*

Adjust the x value if a graph needs to be stretched horizontally by a factor of two. The point (2x, y) in function F is now the new location for all points with the form (x, y) in function F.

Types of Translation in Graphs

A graph is horizontally translated by moving the base graph to the left or right in relation to the x-axis. Consider that if we want to move a graph horizontally by 1 unit, we would also need to change the x value.

A graph's base graph is moved up or down in the y-axis direction when it is vertically translated. Each point on a graph is moved b units vertically to translate the graph in that many directions.

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The x-coordinate of the ordered pair for the solution of the system of given equations is 10.4.

To find the solution to a system of equations, we need to find the values of the variables that make both equations true at the same time.

In this case, we are looking for the x-coordinate of the solution. To find this, we can solve the system of equations by eliminating one of the variables.

We can start by eliminating y from the equations by substituting the expression for y in the first equation into the second equation:

x + 6(-x + 10) = 8

x - 6x + 60 = 8

-5x + 60 = 8

-5x = -52

x = 10.4

The x-coordinate of the solution is 10.4.

This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.

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x + 6(-x + 10) = 8

x - 6x + 60 = 8

-5x + 60 = 8

-5x = -52

x = 10.4

The x-coordinate of the solution is 10.4.

This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.

The Additive Inverse of the number 3 is -3 that is "Negative 3".

The Inverse (Additive) of the number is defined as the number which when added to original number the result is zero .

the number is given as "3" ,

We let the additive inverse be = "a" ;

According to above definition of additive inverse ,

we get ;

3 + a = 0 ;

On simplifying further ,

we get ;

a = -3 .

the sum of 3 and -3 is written as  3 +(-3) ⇒ 3 - 3 = 0 .

Therefore , the additive inverse is "-3" .

The given question is incomplete , the complete question is

What is the additive inverse of the number 3 ?

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For given function the correct solution is g'(t) = 20 for some t in the interval.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function and if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.

Given that g(10)= 220

g(0)= 20

So putting values in condition of differentiation for increasing function we get:

[tex]\frac{g(10)-g(0)}{10-0}[/tex]

= [tex]\frac{220-20}{10}[/tex]

=20

Hence as we can see that the correct solution for given function is g'(t) = 20 .

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A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given that g(10)= 220

g(0)= 20

So putting values in condition of differentiation for increasing function we get:

= 220-20/2

=20

Answer:

Below

Step-by-step explanation:

Filter out the - 2

y =   -2 ( x^2 - 5/2 x)     - 1      Now 'complete the square'

y = -2 ( x^2 - 5/2x + 25/16)  +  50/16     -1      Now simplify:

 =   -2(x-5/4)^2 + 34/16         This will have vertex at  5/4, 34/16

The definition of SSS, SAS, and AAS congruency conditions is shown.

SSS condition:

In accordance with the SSS rule, two triangles are considered to be congruent if their corresponding three sides are equal on both triangles.

SAS condition:

The two triangles are congruent if two sides and the included angle of one triangle match those of a second triangle by two sides and the included angle.

AAS condition:

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, the definition of SSS, SAS, and AAS congruency conditions is shown.

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The two numbers we have to find are 24 and 84.

So, we have been given that there are 2 numbers, and the difference between them is 60.

Let the two numbers be x and y. Let the larger number be x and the smaller number be y.

x-y = 60

When x is divided by y, the quotient is 3 and the remainder is 12.

By division lemma, we can clearly say x= 3y + 12

Now, we have two equations -

x-y=60 and x=3y+12

=>60+y=3y+12

=> y=24

If y=24 and we know x-y=60. This implies that x is equal to 84.

Hence the two numbers 24 and 84.

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Answer:

5%

Step-by-step explanation:

To solve this problem, we need to use the formula for simple interest, which is I = PRT, where I is the interest earned, P is the principal amount, R is the interest rate, and T is the length of time the money is invested. We know that I = 1350, P = 3000, and T = 9, so we can rearrange the formula to solve for R: R = I / (P * T) = 1350 / (3000 * 9) = 0.05. Therefore, the interest rate is 5%.

Answer: 5% per year

Step-by-step explanation:

First, take 1350 divided by 3000, then times 100% = 45% for 9 years

Then take 45 divided by 9 = 5% per year

Let m s the slope of the given equation 2y+3x-1. So m=-3/2.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

m =Δy/Δx = change in y/change in x

where "m" represents a line's slope.

Slope can also be written as

tanθ  = Δy/Δx

The given equation is:

2y+3x-1=0

Separate y

2y= -3x+1

y= -3/2x +1/2

Comparing it with equation of line y=mx+c where m is the slope we conclude that slope of the given equation is m=-3/2.

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Answer:

theans its a= exist 4.0million

The total surface area of the rectangular prism in the figure is 348 cm²

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.

It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.

The formula for total surface area of a rectangular prism is

TSA = 2 (lh +wh + lw ) Square units

= 2( 8 *9 + 6 * 9 + 8 * 6 )

= 2 (174)

= 348 cm²

The rectangular prism have a Total surface area of  348 cm²

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You get £354.28 a month extra for limited capability for work.

If you have a "restricted capability for work-related activity," £354.28 per month (the higher rate) is included in your award. An evaluation of one's "work capability" is what determines this. In some cases, the work capability amount cannot be included in your award right away; instead, there is typically a three-month "waiting period." When you submit supporting medical documentation to the Department of Work and Pensions, this will ordinarily start. You should take the work capacity evaluation while you're waiting.

A lesser rate of the work capability amount of £132.89 might have been included in your award prior to April 3, 2017, if you were only determined to have a "limited capability for work" during this assessment (and not a limited capability for job-related activity).

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The slope of 4x - Y = -1 is 4.

We know that the general form of the equation of a straight line is:

y = mx + c,

where y represents the y intercept of the straight line, m represents the slope and c is the constant in it.

Let us re-arrange the given equation 4x - Y = -1 into Y = 4x + 1.

Now we compare this equation Y = 4x + 1 with the general equation of a straight line y = mx + c.

We conclude that here, m = 4 and c = 1.

Hence, we get that the slope of the given equation  Y = 4x + 1 is 4.

The question is incomplete, the complete question is:

What is the slope of 4x - Y = -1?

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To find an expression for V(t), we can integrate V'(t) with respect to t. Doing so, we have:

V(t) = ∫V'(t) dt = ∫5700(t − 10) dt = 5700 ∫(t − 10) dt = 5700 [t^2/2 - 10t] + C

Since V(t) is the resale value of the computers, the constant of integration C should be the initial value of V(t), which is the cost of the computers. Therefore, we have:

V(t) = 5700 [t^2/2 - 10t] + 300000

Now, to find the value of the computers after 5 years, we can substitute t = 5 into the expression for V(t):

V(5) = 5700 [5^2/2 - 10*5] + 300000 = 5700 [25/2 - 50] + 300000 = 5700 [-12.5] + 300000 = -67500 + 300000 = 232500

Thus, the computers would sell for approximately $232,500 after 5 years.

Explanation: The function V'(t) gives the rate at which the resale value of the computers changes with time. In other words, it gives the slope of the function V(t) at any point in time. To find the function V(t) itself, we need to integrate V'(t) with respect to t. The constant of integration C is added to the result of the integration to ensure that the initial value of V(t) is equal to the cost of the computers. Once we have the expression for V(t), we can find the value of the computers at any point in time by substituting the appropriate value for t into the expression. In this case, we found that the value of the computers after 5 years is approximately $232,500.

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To find the value of x and y, the length of the side opposite an angle, you need to know the measure of the angle and the lengths of the sides of the angle.

The measure of the angle is usually represented by the letter 'x', and the lengths of the sides are usually represented by the letters 'a' and 'b'. If you know the values of these three quantities, you can use the following formula to find the value of y, which is the length of the side opposite the angle:

y = tan(x) × a

If you know the values of x and y, you can use the following formula to find the value of a, which is the length of the side adjacent to the angle:

a = y / tan(x)

If you know the values of x and a, you can use the following formula to find the value of y:

y = a × tan(x)

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Rotation would be the first answer...Your second answer would be dilation. If this is wrong, I'm so sorry

Answer:

soln:

x+16=4x-5

16+5=4x-x

21/3=x

Therefore x=7

When numbers are arranged in ascending order, they are done so from least to largest.

When numbers are arranged in ascending order, they are done so from least to largest.

We must first compare the numbers before we may arrange them in any order.

Compare first, then order.

Numbers arranged in ascending order: Determine how many digits each number has.

Numbers can be arranged in ascending order, from the least value to the highest value.

The arrangement is left to right.

Increasing order is another name for ascending order.

An ascending sort will organize numbers from smallest to largest and text from A to Z because ascending signifies moving upward.

For numbers, descending is going from largest to smallest, and for text, it's from Z to A.

Therefore, when numbers are arranged in ascending order, they are done so from least to largest.

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The mean of the following data is 8.

To find: Mean of given numbers.

Given data is 5, 7, 9, 11

Mean: It is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here, sum of observations is 5+7+9+11=32

Sum of observations is 32

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data

Total number of observation is 4

The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.

Substituting values in above formula,

=[tex]\frac{32}{4}[/tex]

=8

Therefore, the mean is 8.

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Answer:

15 weeks

Step-by-step explanation:

read the graph at the number of words correct

those past 15.words count the weeks in the y.axis

The point (3,-1) is situated in the fourth quadrant.

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes. The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.

Given

Quadrant of (3, -1)

Due to the fact that x is positive and y is negative, the point is situated in the fourth quadrant.

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The equation x² + 4x = 0 has no real roots for any value of k.

The equation x² + 4x = 0 can be solved by using the Quadratic Formula. We can rearrange the equation to be in the form of ax² + bx + c = 0. In this case, a = 1, b = 4 and c = 0. We can then plug these values into the Quadratic Formula to find the roots of the equation.

The Quadratic Formula is x = [-b ± √(b² - 4ac)] / 2a

Plugging in our values of a, b, and c we get: x = [-4 ± √(-4² - 4(1)(0))] / 2(1)

Simplifying this equation we get: x = [-4 ± 0] / 2

The equation simplifies to: x = [-4 / 2] and x = [0 / 2].

Since both of these roots are imaginary, the equation x² + 4x = 0 has no real roots for any value of k.

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The roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.

To find the roots of a quadratic equation, we must first convert the equation into the standard form ax² + bx + c = 0. In this case, the given equation is already in this form, so we can proceed with solving. To solve, we use the quadratic formula, which is x = (-b ± √(b² - 4ac))/2a.So, we have x = (-5 ± √(25 - 4(2)(3))/2(2). Simplifying, we get x = (-5 ± √(13))/4. The quadratic formula yields the values x = -3 and x = -1/2. Therefore, the roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.

x = (-5 ± √(25 - 4(2)(3))/2(2)

= (-5 ± √(13))/4

= -3, -1/2

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The length of the sides a and b with one decimal place value are 9.4 cm and 12 cm.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Applying the Pythagorean theorem.

a² = 8² + 5²

a² = 64 + 25

a = √89

a = 9.4 cm

17² = b² + 12²

289 = b² + 144

b² = 289 - 144

b² = 145

b = √145

b = 12 cm

Thus,

The length of side a is 9.4 cm.

The length of side b is 12 cm.

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The relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights:

the volume of cone = 1/3 ×  volume of cylinder

In this question we need to find the relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights.

Consider a cylinder with radius r and vertical height h.

We know that the formula for the volume of cylinder.

V1 = π × r² × h                  ..........(1)

Now consider a cone with radius r and vertical height h.

Using the formula for the volume of cone,

V2 = 1/3 × π × r² × h

From equation (1),

V2 = 1/3 × V1

the volume of cone = 1/3 ×  the volume of cylinder

Therefore, volume of cone = 1/3 ×  volume of cylinder

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For a given probability distribution, The random variable also contains discrete values, The variance and standard deviation are computed in terms of Expected values E(X).

The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

for discrete probability distribution , E(x) = x*P(x)

for continuous probability distribution ,  E(x) = x *f(x)

Variance = [tex]E(X^2)-(E(X))^2[/tex]

standard deviation = [tex]\sqrt {Variance}[/tex]

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The vertical asymptotes can be simply found by equating the denominator of a function to zero and solving for x, but the vertical asymptotes requires consideration of the highest degrees of x in numerator and denominator.

A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.

A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph moves closer to the line as the inputs go closer to 0 or -1.

Find the x values where the function is undef for the purpose of determining a function's vertical asymptotes. Consider the degree of the numerator and the degree of the denominator while looking for a function's horizontal asymptotes. The horizontal asymptote is y = 0 if the degree of the numerator is smaller than the degree of the denominator. There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote is y = the coefficient of the highest-degree term in the numerator divided by the coefficient of the highest-degree term in the denominator if the degree of the numerator and denominator are equal.

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Answer:

about 43% or 43.3%

Step-by-step explanation:

First, add up the total amount of computers in the computer lab:

14 + 16 = 30

We are told that 16 of the 30 computers are laptops so we can think of this percentage problem as its own equation

13    is    what percent   of  30

13    =            %              x     30

now to solve by dividing 13 by 30 using a calculator:

13/30 = 0.433...

This approximates to 43% or 43.3%

Answer:

10

Step-by-step explanation:

2272-875=1397

Factors of 1397: 1, 11, 127, 1397

Where's the three-digit number? ==> 127 is the three-digit number

875/127 = 6.889

1397/127=11

2272/127=

(875+1397)/127=

875/127 + 1397/127=  ==> substitute 11 for 1397/127 and 6.889 for 875/127

6.889 + 11 = 17.889

Hence, 2272/127=17.889

Hence, 2272 and 875 have the same remainder when divided by 127.

Now add the digits:

1+2+7=10