Use synthetic division to find the result when x4 - 11x³ +26x² + 10x + 28 is
divided by x - 7.

Based on the relation between two numbers considering their difference and multiple, the numbers are 50 and 250.

Let the one number be x. So, the other number, according to the information in question, will be 5x. Now representing the equation depending on the stated details -

5x - x = 200

Performing subtraction on Left Hand Side of the equation

4x = 200

Writing the equation again to find the value of x

x = 200/4

Performing division on Right Hand Side of the equation

x = 50

First number = 50

Another number = 50×5

Performing multiplication on Right Hand Side of the equation

Second number = 250

The two numbers according to multiple and difference are 50 and 250.

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The weighted mean of the mixture of recyclables would be (4 x $1 + 2 x $2) / 6 = $1.33.

To calculate the weighted mean of the mixture of recyclables, first identify the number of each material and their respective values. In this case, there are 4 items worth $1 each and 2 items worth $2 each. To calculate the weighted mean, multiply each item's value by the number of items and then divide by the total number of items

In this case,

4 x $1 + 2 x $2 = $6

and 6 items total, so the weighted mean is

$6 / 6 = $1.33.

This means that if compost is now worth twice as much, the weighted mean would be

(4 x $1 + 2 x $2) / 6 = $1.33.

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Answer:

r = 6

Step-by-step explanation:

6г - 17r = -66

-(17г - 6r) = -66

-11r = -66

-11r/(-1) = -66/(-1)

11r = 66

11r/11 = 66/11

r = 66/11

r = 6

Answer:

----------------------------------------

Simplify the expression in below steps:

Answer:

[tex]32-60i[/tex]

Step-by-step explanation:

Given expression:

[tex](2+\sqrt{-4})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Rewrite $\sqrt{-4}$ as $\sqrt{4 \cdot -1}$}:[/tex]

[tex]\implies (2+\sqrt{4 \cdot -1})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies (2+\sqrt{4}\sqrt{-1})(3 +5i)(-4-i)[/tex]

[tex]\implies (2+2\sqrt{-1})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Apply imaginary number rule} \quad \sqrt{-1}=i:[/tex]

[tex]\implies (2+2i)(3 +5i)(-4-i)[/tex]

Multiply:

[tex]\implies (6+16i+10i^2)(-4-i)[/tex]

[tex]\implies -24-6i-64i-16i^2-40i^2-10i^3[/tex]

[tex]\implies -24-70i-56i^2-10i^3[/tex]

[tex]\textsf{Apply imaginary number rule} \quad i^2=-1:[/tex]

[tex]\implies -24-70i-56(-1)-10(-1)i[/tex]

Simplify:

[tex]\implies -24-70i+56+10i[/tex]

[tex]\implies 32-60i[/tex]

Based on the provide system of linear equations, the solution is that there is no solution.

A system of linear equations refers to a collection of one or more linear equations involving the same variables. The solution to a system of linear equations refer to the point at which the lines representing the linear equations intersect. If the lines are parallel, they will never intersect hence, the system has no solution.

According to the provided information, the percentage of smokers in Russia is given by the equation 36x+100y=346 and the percentage of smokers in Poland is given by the equation 18x+50y=176. In order to determine the solution of the system of linear equations, multiply the Poland equation by 2 and subtract it from the Russian equation. Hence,

2*(18x+50y=176)

36x + 100y = 352

-(36x+100y=346)

0 = 6

It means the original equations are parallel. As both the variables are eliminated, the system has no solution.

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Answer:

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

Step-by-step explanation:

x=3y-1

x+1=3y

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

y=1/3x+1/3

Answer:

Sold:

adults: 375 tickets

student: 324 tickets

Step-by-step explanation:

a + s = 699       Eq. 1

a = s + 51          Eq. 2

a = adult tickets sold

s = student tickets sold

Replacing Eq. 2 im Eq. 1

(s+51) + s = 699

2s + 51 = 699

2s = 699 - 51

2s = 648

s = 648/2

s = 324

From Eq. 2

a = 324 + 51

a = 375

Check:

From Eq. 1:

a + s = 699

375 + 324 = 699

The person who mows the lawn in less time is given as follows:

Daniel.

To obtain who mows the lawn in less time, we calculate the hourly rates for each person, applying the proportion, which is the division of the amount of area mowed by the time needed.

Daniel can mow 15,000 ft³ in 3/4 = 0.75 hours, hence his hourly rate is calculated as follows:

Daniel hourly rate = 15000/0.75 = 15000 x 4/3 = 20,000 ft² per hour.

Bronwyn can mow 12,000 ft² in hour, hence her rate is of:

12,000 ft² per hour.

20,000 > 12,000, hence Daniel can mow the law in less time, as he has a higher rate.

The missing sentence is of:

"Bronwyn can mow 12,000 ft² in hour".

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Answer:

 Rs 1400

Step-by-step explanation:

You want the monthly installment payment if the balance of a Rs 34500 purchase after a 6500 deposit earns 10% simple interest and is paid in 24 months.

The outstanding balance is ...

  Rs 34500 -6500 = Rs 28000

The interest on this balance for 24 months is ...

  I = Prt

  I = Rs 28000(0.10)(2) = Rs 5600

The monthly payment will be 1/24 of the total due:

  (28000 +5600)/24 = 1400

Each monthly installment will be Rs 1400.

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The general solution will be:

[tex]$$y(x)=e^{-x / 28}\left(c_1 \cos \left(\frac{\sqrt{55}}{28} x\right)+c_2 \sin \left(\frac{\sqrt{55}}{28} x\right)\right)+x^2-5 x-23$$[/tex]

[tex]$$14 y^{\prime \prime}+y^{\prime}+y=x^2-3 x$$[/tex]

Consider the homogenous equation [tex]$14 y^{\prime \prime}+y^{\prime}+y=0$[/tex]

The auxiliary equation is [tex]$14 m^2+m+1=0$[/tex]

[tex]m=-\frac{1}{28}+i \frac{1}{28} \sqrt{55}[/tex]

The homogenous solution is

[tex]$$y_c(x)=e^{-x / 28}\left(c_1 \cos \left(\frac{\sqrt{55}}{28} x\right)+c_2 \sin \left(\frac{\sqrt{55}}{28} x\right)\right) \text {. }$$[/tex]

Consider the non-homogenous de [tex]$14 y^{\prime \prime}+y^{\prime}+y=x^2-3 x$[/tex] by using the method of undetermined coefficients

consider [tex]$y_p=A x^2+B x+C \Rightarrow y_p^{\prime}=2 A x+B \Rightarrow y_p^{\prime \prime}=2 A$[/tex]

by plugging the values in [tex]$14 y^{\prime \prime}+y^{\prime}+y=x^2-3 x$[/tex]

[tex]$$\begin{aligned}& 28 A+(2 A x+B)+A x^2+B x+C=x^2-3 x \\& \Rightarrow x^2(A)+x(2 A+B)+28 A+B+C=x^2-3 x\end{aligned}$$[/tex]

On comparing both sides we get

A=1.

2A+B =-3

=>B=-3-2A

=>B=-5

28A+B+C=0

=>C=-28A-B

=>C=-23

by plugging the values [tex]y_p=x^2-5 x-23[/tex].

The general solution will be:

[tex]$$y(x)=e^{-x / 28}\left(c_1 \cos \left(\frac{\sqrt{55}}{28} x\right)+c_2 \sin \left(\frac{\sqrt{55}}{28} x\right)\right)+x^2-5 x-23$$[/tex]

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The lengths of the segments SH is 16, HM is 8, TH is 8, HR is 12,

TD = 12 and ER = 18.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a centroid divides a line segment in the ratio of 2 : 1 from vertices

to the other side.

Given, ΔSTR, H is the centroid EH = 6, DH = 4, and SM = 24.

SH = (2/3)×24 = 16.

HM = 8.

As DH = 4 hence TH = 8.

As EH = 6, HR = 12.

TD = (DH + TH) = 12.

ER = 6 + 12 = 18.

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Answer:

215

Step-by-step explanation:

218+212/2

Answer:

[tex]14 \frac{1}{8}[/tex]

Step-by-step explanation:

112 goes into 8 14 times, there is then 1/8 leftover

To find the percentage of girls in class A, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

14 / 20 * 100 = 70%

To find the percentage of girls in class B, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

15 / 25 * 100 = 60%

Thus, the percentage of girls in class A is 70%, and the percentage of girls in class B is 60%.

a and C of the two-member frame=Ax=-300N,Ay=300N, cx=300n, cy=300N.

momentum  of all forces  about A is
=-600x1.5+Cxx3=0

cx=900/3=300n
cx=300n.

momentum of all forces about c is
-600x1.5-AXx3=0                  
Ax=-900/3=-300n
Ax=-300n

forces in Ab components is
600x1.5-Ayx3=0
ay=300n

momentum of all forces about b

600x1.5-ayx3-cyx3+cxx3=0
900-900-900+cxx3=0
cxx3=900
cx=300n

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[tex]x^{2} + y^{2} = t^{2}[/tex] represent the correct graph which is the first figure graph.

Equations with Parameters If x and y are continuous functions of t on an interval I, the equations x = x(t) and y = y(t) are referred to as parametric equations, and t is also known as the parameter. The graph of the parametric equations is the set of points (x, y) obtained as t varies over the interval I.

Since x = tsint

And z= tcost

We have a circle in the x-z plane a

[tex]x^{2} + z^{2} = t^{2}[/tex]

Now, as y = t

The graph will be a helix with movement along the y-axis. Furthermore, the circle made on the x-z plane will have a variable radius since the radius is equal to t which by itself is changing.

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All four measures of the angles are mentioned in the figure.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

If the measure of the angle is more than the right angle that is 90°. Then the angle is known as the obtuse angle.

Move the yellow dabs to make the portions cross. Allow the convergence to be called point V. Cause the lines to cross so that point ∠SVT is a harsh point under 135°.

Let the measure of the angle ∠SVU be 'x' which is greater than 45°. Then the measure of the angle ∠SVT will be '180 - x'.

All four measures of the angles are mentioned in the figure.

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Answer:

To find the new price after a discount, you can use the formula: new price = original price * (1 - discount rate). In this case, the new price would be $28 * (1 - 0.25) = $28 * 0.75 = $<<28*0.75=21>>21. So the new price, rounded to the nearest cent, would be $21.

Step-by-step explanation:

If the congruence statement ABCA = AFGA is true, then the following must also be true:

B = G, since corresponding angles are congruent

AB = FG, since corresponding sides are congruent

C = F, since corresponding angles are congruent

Thus, the complete congruence statement is ABCA = AFGA, where B = G, AB = FG, and C = F.

Answer:[tex]x+8\geq 40[/tex]

Step-by-step explanation:

[tex]x+8\geq 40[/tex]

subtract 8 from both sides  to isolate x

[tex]x\geq 32[/tex]

You must spend 32 more dollars to receive three free songs.

The overall price considering the percentages is decreased.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

In stores, online, in commercials, and in the media, you can see percentages practically anywhere. Understanding what percentages signify is a crucial skill that could help you save time and money and raise your employability.

Let us suppose mary bought that antique clock for 100$.

So now in the first year its value is increased by 30% which is 100+30 = 130$ after the 1 st year.

Now the clock price is 130$

So now in the second year its value is decrease by 30% which is 130- 39 = 91 $

So the overall clock price has been decreased by $9 since mary bought it.

The overall price considering the percentages is decreased.

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Answer:

b

Step-by-step explanation:

Infer from domain and range

Answer:

39.95m

Step-by-step explanation:

To find the side length of a regular 36-gon with a given area and apothem, we need to use the formula for the area of a regular polygon and the formula for the apothem of a regular polygon.

The formula for the area of a regular polygon is given by:

A = (1/2) * a * p

where A is the area of the polygon, a is the apothem of the polygon, and p is the perimeter of the polygon.

The formula for the apothem of a regular polygon is given by:

a = r * cos(180/n)

where a is the apothem of the polygon, r is the radius of the polygon, and n is the number of sides of the polygon.

In this case, we are given that the area of the 36-gon is 164,592 square meters, the apothem of the 36-gon is 228.6 m, and the number of sides of the 36-gon is 36.

We can use these values to solve for the side length of the 36-gon. First, we can use the formula for the area of a regular polygon to solve for the perimeter of the 36-gon:

A = (1/2) * a * p

164,592 = (1/2) * 228.6 * p

164,592 = 114.3 * p

p = 1438.3

Next, we can use the formula for the apothem of a regular polygon to solve for the radius of the 36-gon:

a = r * cos(180/n)

228.6 = r * cos(180/36)

r = 561.8

Finally, we can use the formula for the perimeter of a regular polygon to solve for the side length of the 36-gon:

p = n * s

1438.3 = 36 * s

s = 39.95

Therefore, the side length of the 36-gon is 39.95 meters.

Product ab has a value of 18 and is shaped like a regular hexagon.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

Let the side of the hexagon be 2.

so the radius of the circle is sqrt(3),

area of hexagon=sqrt(3) * 2 * 3

= 6 sqrt(3)

area of circle is pi (sqrt(3))^2 = 3 pi

3 pi / 6 sqrt(3) = sqrt(3)/ 6

3 * 6 = 18

The value of product ab is 18 which is in the shape of a regular hexagon.

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Answer:

31

Step-by-step explanation:

7, 10, 12, 16, 19, 22, 25, 28, 31

Adding by 3

Hope this works

30ft high above the ground is the lamp.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

BC⊥AD and DE⊥AD

∠ABC = ∠ADE(=90°)

Also,∠A=∠A

ΔABC ΔADE (AA similarity)

AB/AD = BC/DE

40/(200 + 40) = 5ft/DE

DE = 5ft×6 = 30ft

Hence, 30ft high above the ground is the lamp.

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The airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.

Function : In mathematics, 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

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is that an airplane pilot is planning a flight to Hawaii. In his flight plan, he will include fuel estimates for the trip.

Assume that the distance of Hawaii from the initial location of pilot is [D] miles. If the amount of fuel burnt per miles is [x] liters/miles. Let the total amount of fuel needed to reach Hawaii is [y] liters. Than, his estimates should include and follow the given relation as -

y > [D][x]

Therefore, the airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.

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The radius of the sector of area 135π is 15.

A sector is a geometric figure bounded by two radii and the included arc of a circle.

To calculate the radius of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the radius of the sector is 15.

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The angles that satisfy the trigonometric equation 4 · cos 2x + cos x - 3 = - 5 · cos x - 8 are described below:

In this problem we find a trigonometric equation involving both cos 2x and cos x, we need to simplify the expression such that only cos x is present. This can be done by means of trigonometric formulas. First, write the entire expression:

4 · cos 2x + cos x - 3 = - 5 · cos x - 8

Second, use trigonometric formulas to eliminate cos 2x:

4 · (2 · cos² x - 1) + cos x - 3 = - 5 · cos x - 8

8 · cos² x  - 4 + cos x - 3 = - 5 · cos x - 8

8 · cos² x + 6 · cos x + 1 = 0

Third, use the quadratic formula to find all possible roots:

cos x₁ ≈ - 1 / 4, cos x₂ ≈ - 1 / 2

Fourth, use inverse trigonometric functions to determine all possible angles between 0° and 360°:

Case 1: - 1 / 4

x₁₁ ≈ 104.5°, x₁₂ ≈ 255.5°

Case 2: - 1 / 2

x₂₁ = 120°, x₂₂ ≈ 240°

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