Polynomial uing Remainder Theorem and Factor Theorem checking uing ynthetic diviion. X^4 - x^3 - 3x^2 4x 2 ÷ (x 2)

Answer:

xy = 16

Step-by-step explanation:

\(\frac{1}{x}\) + \(\frac{1}{y}\) = \(\frac{1}{2}\) ( multiply through by 2xy to clear the fractions )

2y + 2x = xy ← factor out 2 from each term on the left side

2(y + x) = xy

substitute x + y = 8 into the left side

2(8) = xy , that is

xy = 16

Answer:

c) T(−1, 3) ° Rotation,180°

Step-by-step explanation:

Explanation:-

First we will apply transformation is

Rotation of 180°  then we will apply transformation is changes  

(x,y) to (-x ,-y)

a)

Given vertex T(  2 ,2 )

T( 2 ,2 )→ T( -2 ,-2)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

T( -2 ,-2) → T¹ ( -2 -1 ,-2 +3)

The new vertex is  T¹ ( -3 ,1)

b)

Given vertex U(  4 ,2 )

U( 4 ,2 )→ U( -4 ,-2)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

U -4 ,-2) → U¹ ( -4 -1 ,-2 +3)

The new vertex is  U¹ ( -5 ,1)

c)

Given vertex R(  3 ,5 )

R( 3 ,5 )→ R( -3,-5)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

R( -3 ,-5) → R¹ ( -3 -1 ,-5 +3)

The new vertex is  R¹ ( -4 ,-2)

d)

Given vertex S(  1 ,3 )

S( 1 ,3 )→ S( -1 ,-3)

Next we will apply rule

Horizontal translation left '1' units and Vertical translation up 'd' units

S( -1,-3) → S¹ ( -1 -1 ,-3 +3)

The new vertex is  S¹ ( -2,0)

Answer:

15%

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

\(\frac{99}{660} =\\\\\frac{3}{20} =\\\\\frac{15}{100}\)

99 is 15% of 660

Answer:

C. Number of blocks needed is 27.

Step-by-step explanation:

The dimension of the container = 9 inches by 9 inches by 9 inches

The blocks has a dimension = 3 inches by 3 inches by 3 inches

A. To determine the number of blocks needed to fill the container, divide the volume of the container by the volume of each block.

B. volume of container = length x width x height

volume of each block = length x width x height

Number of blocks needed = \(\frac{volume of container}{volume of each block}\)

C. volume of container = length x width x height

                              = 9 x 9 x 9

                              = 729

volume of container = 729 cubic inches

volume of each block = length x width x height

                                = 3 x 3 x 3

                                = 27 cubic inches

Thus,

Number of blocks needed = \(\frac{volume of container}{volume of each block}\)

                                       = \(\frac{729}{27}\)

                                       = 27

The number of blocks needed is 27.

=======================================================

Explanation:

The -2 outside the first matrix multiplies to every item inside that first matrix.

So the x updates to -2x in the upper left corner.

That -2x adds to the 3 in the upper left corner of the second matrix. The sum -2x+3 must be equal to the value in the upper left corner of the third matrix.

Everything is focused on the upper left corner.

So we must solve -2x+3 = x

Doing so leads to...

-2x+3 = x

3 = x+2x

3 = 3x

3x = 3

x = 3/3

x = 1

Answer:

Isometry: An isometry is a transformation that maintains congruency.  This means that the transformation does not change the figure's size or shape.

Make sure your child is familiar with the Cartesian coordinate system including the horizontal x-axis, the vertical y-axis, and the (x,y) convention used for locating points.

If you have not already done so, you may wish to review this congruency lesson with your child.

Translations

This section will help your child to translate congruent figures on a Cartesian plane. It will also introduce translation vectors which show the distance and direction of the translation.

Translations

Figure J is the pre-image. Figure S is translated.

A figure is a translation if it is moved without rotation.

Translation Vector

A Translation Vector is a vector that gives the length and direction of a particular translation. Vectors in the Cartesian plane can be written (x,y) which means a translation of x units horizontally and y units vertically.

figure being translated

Vectors translations can be written as shown in either of these two ways:

format example for writing vectors

This vector can be said to be ray AB or vector D.

You translate a figure according to the numbers indicated by the vector.  So if one point on a figure has coordinates of (-3,3)  and the translation vector is (-1,3), the new coordinate is (-4,6). You add or subtract according to the signs in the numbers in the vector.

Work through the two examples below with your child to see how to apply translation vectors.

square translated on cartesian grid

The red square's coordinates are:

(-4,3); (-4,8); (-9,3); (-9,8).

What are the coordinate pairs under a translation vector of (1,-1) as shown by the blue square?

The new coordinates are:

(-3,2); (-3,7); (-8,2); (-8,7).

You can see that the translation did not move the figure far because the vector translation is small.

square translated on cartesian grid

We will try a different vector translation of (3,-9) on the same red square

The new coordinates are:

(-1,-6); (-1,-1); (-6,-6); (-6,-1).

Get you child to try the next example. Do not look at the answer until he or she has tried to work it through the task.

single triangle on cartesian grid

Task: Translate ΔABC with a vector translation of (6,-2)

Steps:

Find the coordinates of Δ ABC.

Add 6 to the X coordinates and subtract 2 (or add -2) from the Y coordinates.

Plot the new coordinates on the grid.

Answer and Explanation

Coordinates of ΔABC are:

(-5,1); (-2.5,7); (0,1)

Add 6 and subtract 2

A1 = (-5 + 6, 1 - 2) = (1,-1)

B1 = (-2.5 + 6, 7 - 2) = (3.5,5)

C1 = (0 + 6, 1 - 2) = (6,-1)

Plot ΔA1B1C1

Rotations

This section will show your child how to rotate a figure about the origin on a Cartesian plane. Work through the two examples below:

Note: Make sure your child knows that the origin is the intersection of the X and Y axes; (0,0) on the Cartesian plane.

Rotation Transformation: Example 1

Look at the four triangles on the Cartesian plane below. Each one is rotated about the origin as shown in the table.

Triangle B Triangle C Triangle D

90° rotation of Triangle A about the origin 90° rotation of Triangle B about the origin 90° rotation of Triangle C about the origin

 180° rotation of Triangle A about the origin 180° rotation of Triangle B about the origin

   270° rotation of Triangle A about the origin

The coordinates are:

Triangle A (-2,2) (-10,2) (-6,8)

Triangle B (2,2) (2,10) (8,6)

Triangle C (2,-2) (10,-2) (6,-8)

Triangle D (-2,-2) (-2,-10) (-8,-6)

Note the pattern in the coordinates for corresponding vertices on the triangles.

Rotation Transformation: Example 2

The coordinates of Pentagon ABCDE are:

(0,4); (7,4); (9,2); (7,0); (0,0)

Pentagon ABCDE is rotated 180° about

the origin making the coordinates of

Pentagon A1B1C1D1E1:

(0,-4); (-7,-4); (-9,-2); (-7,0); (0,0)

Note how the coordinates of

corresponding vertices are opposite

integers (just the +/- sign is different).

This is always the case with 180°

rotations about the origin.

Reflections

This section will help your child to reflect a figure over an axis on a Cartesian plane

Work through the two reflection examples below.

Reflection Transformation: Example 1

The coordinates of LMNO are:

(-7,5); (0,5); (-2,1); (-5,1)

LMNO is reflected over the X-axis

making the coordinates of

L1M1N1O1:

(-7,-5); (0,-5); (-2,-1); (-5,-1)

Note how the x-coordinates remain the

same but the y-coordinates change to

their opposite integer (i.e. the sign changes).

This is always the case with reflections over the X-axis.

Step-by-step explanation:

The solution is, the coordinates of Z'  will be z' = (6,7),

i.e. option B is correct.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Given that,

X' are (5,11).

now, See attachment

Required that,

The image of Z i.e. z'

From the attachment:

X =(7,11)

This implies that:

X' = ( x- 2, y)

Using the same rule for z;

z=(8,7)

z' = (8-2, 7)

z' = (6,7)

Hence, The solution is, the coordinates of Z'  will be z' = (6,7),

i.e. option B is correct.

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i think its b Step-by-step explanation:

\( \frac{5x}{ \frac{5x}{3} } = \frac{15x}{5x} = 3\)

124

4×23 =92(for cats)

4×8=32(for dogs)

then 92+32=124

The volume of the hexagonal prism which is given above would be = 93.53 cm³

To calculate the volume of the given hexagonal prism, the formula that should be used is given below suCh as follows;

Volume of hexagonal prism= 3√3/2*a²h

Where;

a= length of base edge = 3cm

b = height = 4cm.

Volume = 3√3/2 × 3×3 × 4

= 3√3/2× 36

= 93.53cm³

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Answer:

128 Kilometers in 2 hours

Step-by-step explanation:

1 mile is = to 1.6 kilometers

40x1.6 = 64 kilometers which is only 1 hour

64 x 2 = 128 kilometers

Answer:

\(y\ =\ \ \tan\theta\ +2\)

Step-by-step explanation:

The sampling soldiers until her margin of error for a 82% confidence interval is less than 0.004, soldiers should Haley sample is 12,724 soldiers.

The degree of inaccuracy in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced chance of relying on a survey's or poll's findings, meaning that there will be less trust in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

A confidence interval is a measure of how unpredictable a given statistic is. It is typically used in conjunction with the margin of error to indicate how confidently a statistician feels that the findings of an online survey or online poll are worthy of being considered representative of the total population.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi (1-\pi)}{n} }\)

In which, z is the z-score that has a p-value of 1+∝/2.

The margin of error is of:

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\)

Estimate of the proportion of 64%, hence π = 0.64.

94% confidence level

So , ∝ = 0.94 z is the value of Z that has a p-value of , so z = 1.88

Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\\0.008 =1.88\sqrt{\frac{0.64(0.36)}{n} } \\0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)} \\n = 12723.84\\\)

Therefore, Haley should sample 12,724 soldiers.

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Answer:

$4

Step-by-step explanation:

Because 16*.25 is 4

Answer: 12 inches

Step-by-step explanation:

This is a square shaped mirror which means that it takes the shape of a square.

All sides on a square are equal and because the way the find the area of a square is to multiple the Length by the Width, you would be squaring the same number to find the area.

Length of each side = √area

= √144

= 12 inches

To determine h for a two-dimensional eigenspace for λ=3, use the characteristic polynomial and eigenvalues of A. The eigenspace for λ=3 is of dimension 2 if there exist linearly independent vectors, such as x1 and x2. The algebraic multiplicity of eigenvalue λ=3 must be 2, requiring a repeated root of the characteristic equation. The answer is h = 87/24.

The given matrix is A = [3000−21008h30407−3]In order to determine h such that the eigenspace for λ=3 is two-dimensional,

the first step is to obtain the characteristic polynomial and the eigenvalues of the matrix A.The characteristic polynomial can be written as det(A- λI) where I is the identity matrix of order 3.The calculation of det(A- λI) is shown below:

det(A - λI)

= ⎣⎡​3000−λ−21008h30407−3−λ⎦⎤​  

= (3000 − λ)(-3 − λ)(8h30 - λ) + 4h7(-2100)(407 - λ)

On solving the above equation, the following eigenvalues are obtained:λ1 = -3, λ2 = 3, λ3 = 8h30

For the eigenvalue λ=3, we need to find the value of h such that the eigenspace is two-dimensional. For λ=3, let x = [x1 x2 x3] be the eigenvector such that Ax = λx.

Then, we have(A - λI)x =

0⎣⎡​3000−330−21008h30407−3−3⎦⎤​ ⎣⎡​x1​x2​x3​⎦⎤​

= ⎣⎡​0​0​0​⎦⎤​ 3000x1 - 2100x2 + 8hx3

= 0 4hx1 + 7x3

= 0

Solving the above system of equations, we obtain the following expressions:x1 = (-7/4) x3 and x2 = (-3/5) x3

Therefore, the eigenspace for λ=3 is of dimension 2 if and only if there exist linearly independent vectors in the space, say x1 and x2. Thus, we can choose x1 = [-7 0 4h] and x2 = [0 -3 5]. These are linearly independent since x1 does not belong to the span of x2 and vice versa.Since the eigenspace for λ=3 is two-dimensional, the algebraic multiplicity of the eigenvalue λ=3 must be 2. This implies that the eigenvalue λ=3 has to be a repeated root of the characteristic equation. Thus, from the equation for the characteristic polynomial, we have(-3 - 3)(8h30 - 3) = 0This simplifies to 24h - 87 = 0

Therefore, h = 87/24. Hence, the value of h for which the eigenspace for λ=3 is two-dimensional is h = 87/24.Answer: h = 87/24.

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Answer: y=6

Step-by-step explanation:

Data: y=3 and x=12

y=? and x=18

12/3=4 and 18/3=6

y=6

I hope this helps

The algebraic expression for half of a number is x/2.

When we are working in algebra and we want to represent "a number", we use a variable for it.

We do this because "a number" can be any real number.

For example, we can say that a number is represented by the variable x.

Now, to write half of a number, we just need to divide our variable by 2, then we will get:

x/2

That is the algebraic expression.

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Answer:

D = 36.7 feet

Step-by-step explanation:

Diagonal of a Rectangle

Given a rectangle of width W and length L, its diagonal can be calculated as the hypotenuse of a triangle of legs W and L as follows:

\(D=\sqrt{W^2+L^2}\)

The dimensions of the living room are 32 feet by 18 feet, thus the diagonal is:

\(D=\sqrt{32^2+18^2}\)

\(D=\sqrt{1024+324}=\sqrt{1348}\)

D = 36.7 feet

Answer:

D

Step-by-step explanation:

0.0000058102 can be rounded to 0.000006.

5 x 10^-5 = 0.00005

6 x 10^-5 = 0.00006

5 x 10^-6 = 0.000006

6 x 10^-6​ = 0.000006

The closest answer to the estimate is option D.

Answer:

ggttttttttttttt

Step-by-step explanation:

A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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Answer:

Step-by-step explanation:

L=2W+4

P=2(L+W), using L from above makes this

P=2(2W+4+W)

P=2(3W+4)

P=6W+8

6W=P-8

W=(P-8)/6, since we are told P=26

W=(26-8)/6

W=18/6

W=3 cm, and since L=2W+4

L=2(3)+4

L=6+4

L=10 cm

So the dimensions of the envelope with a perimeter of 26cm is 3cm by 10cm

The lines L1 and L2 are skew, which means they do not intersect and are not parallel. Skew lines are non-intersecting lines that lie in different planes and never meet.Thus the answer is DNE (does not exist).

To determine if two lines are parallel or intersecting, we can compare their direction vectors. The direction vector of L1 is ⟨-9, 6, -12⟩, and the direction vector of L2 is ⟨6, -4, 8⟩. If the direction vectors are scalar multiples of each other, the lines are parallel. If they are not parallel and their planes do not coincide, the lines are skew. In this case, the direction vectors are not scalar multiples, indicating that the lines are skew.

To find the point of intersection between two lines, we need to set the corresponding coordinates equal to each other and solve for the variables. However, when we set the equations for L1 and L2 equal, we end up with inconsistent equations that have no solution. Therefore, the lines do not intersect, and the point of intersection does not exist.

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Answer:

Olivia spent 129 minutes or 2:15 doing all the homework

Step-by-step explanation:

Answer: 47.4 or -42.6/negative

Step-by-step explanation: i tried my best

The parent function is,

The graph is stretched horizontally when x is replaced by kx where k is less than 1.

Thus, option (B) is the correct solution as x is replaced by x/2 in the F(x) to get G(x).

The red curve represents F(x) and the blue one represents G(x).

which measure of center can you most accurately estimate from this information: Median

The median divides the data into equal-sized groups. So approximately 50% of the data is above the median and approximately 50% of the data is below the median.

Calculating the median

The median is the value in a data set, implying that half of data focuses have a value more modest or equivalent to the median and half of data focuses have a value higher or equivalent to the median.

For a little data set, you first count the quantity of data focuses (n) and organize the data focuses in expanding request. Assuming the quantity of data focuses is lopsided, you add 1 to the quantity of places and separation the outcomes by 2 to get the rank of the data point whose value is the median.

The rank is the place of the data point after the data set has been organized in expanding request: the smallest value is rank 1, the second-smallest value is rank 2, and so forth.

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the complete question is:

The dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. The data is divided into equal-sized subgroups with 25% of the adults in each subgroup.

Which measure of center can you most accurately estimate from this information?

1. mean

2. median

Answer:

neither terminating nor repeating.

Step-by-step explanation:

The set of irrational numbers is the set of numbers whose decimal representations are neither terminating nor repeating.

Rational numbers are numbers which can be written in the form of \(\dfrac{a}{b}\)where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Irrational numbers are those real numbers, which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers means, natural numbers are not irrational.

The set of irrational numbers is the set of numbers whose decimal representations are neither terminating nor repeating.

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Answer:

Step-by-step explanation:

227.07

Answer:

2010 miles.

Step-by-step explanation:

Victoria fell asleep 13% into the trip. if 261=13%, then you want to know how many miles in 1%. so you divide 261 by 13 and get 20.1 so you know one percent of the trip is 20.1 miles, so if you want to know 100% of the trip, then you multiply 20.1 by 100, to get 2010.

Answer:

The answer would be 27

Step-by-step explanation:

You need to multiply 9 to both sides. Please mark me brainliest.