Polynomial Factor Theorem is the subject.
I only need this exercise to finish and I'm very tired, please help.​

Answer:

Step-by-step explanation:

You want the missing length EG and the corresponding value of x in isosceles triangle DEF with midline GH of length 6 parallel to base DF of length 12.

The length of segment GH is half the length of segment DF (6/12 = 1/2), so we know that corresponding sides EG and ED have the same ratio:

  EG/ED = 1/2

  2EG = ED . . . . . . . . . . . . multiply by 2·ED

  2(x -5) = (x-5)+9 . . . . . . substitute given values

  2x -10 = x +4 . . . . . . . . simplify

  x = 14 . . . . . . . . . . . . . add 10-x

Then the length of EG is ...

  EG = 14 -5 = 9

The model shows that there are 10 pieces that are each 0. 2 ft long.

From the given model, we see that Devin cut the ribbon in equal proportions. The number of proportions can be found by summing the different sections on the ribbon.

This number comes to 10 sections which means that Devin cut the ribbon into 10 pieces.

The length of each of these pieces is:

= Length of entire ribbon / Number of pieces

= 2 / 10

= 0. 2 ft long

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38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.

The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:

d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]

There are points that correspond to each vertex in the polygon:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:

d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }[/tex] ≤ b r/≥ d=[tex]\sqrt{(8-(-2)^{2})+(7-11)^{2} }[/tex]  ≤b r/≥

d=[tex]\sqrt{116}[/tex]

There are points that correspond to each vertex in the polygon:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So, using the distance formula and the vertex positions of side PT, we can determine its length:

P  = (-2, 11)

T  = (8, 7)

The length of PT is [tex]\sqrt{116}[/tex]

The other 4 sides are handled in the same way, and the results are as follows:

TS = [tex]\sqrt{49}[/tex]

SR = [tex]\sqrt{50}[/tex]

RQ = [tex]\sqrt{61}[/tex]

QP = [tex]\sqrt{40}[/tex]

You may calculate the perimeter by adding all the sides:[tex]\sqrt{116}[/tex]+[tex]\sqrt{49}[/tex]+[tex]\sqrt{50}[/tex]+[tex]\sqrt{61}[/tex]+[tex]\sqrt{40}[/tex] = 38.97

The solution is 39 units if you round off.

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Answer:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

Step-by-step explanation:

Given exponential function:

[tex]f(x)=P(1+r)^x[/tex]

Replace f(x) with y:

[tex]y=P(1+r)^x[/tex]

Divide both sides by P:

[tex]\dfrac{y}{P}=(1+r)^x[/tex]

Take natural logs of both sides:

[tex]\ln \left(\dfrac{y}{P}\right)=\ln (1+r)^x[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)=x \ln (1+r)[/tex]

Divide both sides by x:

[tex]\dfrac{1}{x}\ln \left(\dfrac{y}{P}\right)=\ln (1+r)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)^{\frac{1}{x}}=\ln (1+r)[/tex]

Raise both sides to power of e:

[tex]\large\text{$e^{\ln \left(\frac{y}{P}\right)^{\frac{1}{x}}}=e^{\ln (1+r)}$}[/tex]

[tex]\textsf{Apply the power law}: \quad e^{\ln x}=x[/tex]

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}=1+r[/tex]

Subtract 1 from both sides:

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1=r[/tex]

Therefore, the equation to find r is:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

Answer:all integers

Step-by-step explanation:

the correct is all integers

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }[/tex]

The correct answer is x² - 7x - 18 = (x - 9)(x + 2)

Hope it helps. If you have any query, feel free to ask.

Answer:

a₅ = 48

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] and a₁ = 3 , then

a₂ = - 2a₁ = - 2(3) = - 6

a₃ = - 2a₂ = - 2(- 6) = 12

a₄ = - 2a₃ = - 2(12) = - 24

a₅ = - 2a₄ = - 2(- 24) = 48

According to the information, we can infer that the number of customers that buy package 1 is 16 customers.

To calculate how many customers buy package 1 we have to identify some important information such as:

To calculate this value, we have to divide 40 in 100, and then we have to multiply the result by 40.

According to previous information, the number of customers that buy package 1 is 16 customers. So, 24 customers buy package 2, 3 or 4. If we have to identify exactly how many buy an specific package we have to make the same procedure. For example package 3.

40 / 100 = 0.4

0.4 * 15 = 6

So, 6 customers buy package 3.

Note: This question is incomplete because there is some information missing. Here is the complete information:

TASK

Calculate how many customers buy package 1.

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Therefore, the number of seats for each aircraft is 752, 688, and 1224.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

Let x be the number of seats for the second aircraft.

The first aircraft has x + 64 seats.

The third aircraft has 2x - 152 seats.

The total number of seats for all aircraft is x + (x + 64) + (2x - 152) = 1900.

Therefore, 3x = 2064, so x = 688.

The first aircraft has 688 + 64 = 752 seats.

The third aircraft has 2(688) - 152 = 1224 seats.

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Answer:

(a)  See attachment.

(b)  12:23

Step-by-step explanation:

A bearing is the angle (in degrees) measured clockwise from north.

To mark the position of J on the given map:

(See attachment).

Given:

Convert 9600 meters into kilometers by dividing by 1000:

⇒ 9600 m = 9600 ÷ 1000 = 9.6 km

[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]

Therefore:

[tex]\sf Time=\dfrac{Distance}{Speed}[/tex]

Substitute the given distance and speed into the formula to calculate the time it took Kendra to walk from K to L:

[tex]\implies \sf Time=\dfrac{9.6\;km}{4.5\;km/h}=2.133333...\;hours[/tex]

Convert 2.133333.. into a mixed number:

[tex]\implies \sf 2.133333...=2\frac{2}{15}\;hours[/tex]

To find the number of minutes in 2/15ths of an hour, multiply 2/15 by 60:

[tex]\implies \sf \dfrac{2}{15} \times 60=\dfrac{120}{15}=8\;minutes[/tex]

Therefore, it took Kendra 2 hours and 8 minutes to walk from K to L.

If Kendra left at 10:15:

[tex]\implies \sf 10:15 + 2\;hours = 12:15[/tex]

[tex]\implies \sf 12:15 + 8\;minutes=12:23[/tex]

Therefore, Kendra arrived at L at 12:23.

The equation of the line in point-slope form is obtained as y = -2x + 4.

What is the point-slope form?

Point-slope is the general form of a linear equation which is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

The line passes through point (x1,y1) = (0,4)

The slope of the line is m = -2.

The formula for point-slope form of equation is -

y-y1=m(x-x1)

Substituting the values in the equation -

y - 4 = -2(x - 0)

y - 4 = -2x

y = -2x + 4

Therefore, the equation is obtained as y = -2x + 4.

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Answer:

4,7

Step-by-step explanation:

4,7

Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given : Sue covered 2.4 km distance and

bike wheel rotated 1225 times.

Thus,

To find the value of diameter of the wheel

=>2400=2πr*1225

=> 2400/2 = πr*1225

=> 1200 = πr*1225

=>r=31

Diameter = 2*31 = 62cm

Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

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Answer:  48 square inches

Step-by-step explanation:

To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.

area of triangle L x W = 6x4=24

area of rectangle LxW =6x4=24

24+24=48

Answer:

что там а? я даже не знаю hehe

The gallons of ice cream 4 machines can make is 650 gallons.

Two ice cream machines make a total of 320 gallons in a certain amount of time.

Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:

Therefore,

If 2 ice cream machine = 320 gallons

4 ice cream machine = ?

cross multiply

Hence,

gallons of ice cream made by 4 machines = 320 × 4 / 2

gallons of ice cream made by 4 machines = 1280 / 2\

Therefore,

gallons of ice cream made by 4 machines = 640 gallons

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The sequence of 100, 25, 6.25, 1.5625 is geometric.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.

In essence, we multiply the numbers together and calculate their n[tex]th[/tex]root, where n is the total number of data values.

A succession of shapes are used to create geometric patterns.

Because the pattern is governed by a rule, patterns created from shapes are comparable to patterns created from numbers.

The dimensions, perimeter, area, surface area, volume, etc. of geometric shapes are determined using geometry formulas.

Mathematics' branch of geometry examines the connections between points, lines, angles, surfaces, solids' measurements, and qualities.

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The model -3/4+5/12 on the number line is attached in the image below

Generally, A image of a graded straight line is what is known as a number line, and its purpose in elementary mathematics is to serve as a visual representation of real numbers. A number line is the name for this kind of diagram.

It is a widely held belief that a real number may be allocated to each point on a number line, as well as the inverse, which states that a real number can be assigned to each point on a number line.

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Answer:

A represents f(x) and B represents g(x)

Step-by-step explanation:

choose a value for x, substitute , say x = 1 into both f(x) and g(x) , then check the values obtained on the graph.

f(x) = 100 × [tex](\frac{3}{5}) ^{1}[/tex] = 100 × [tex]\frac{3}{5}[/tex] = 20 × 3 = 60

thus (1, 60 ) is a point on the graph of f(x)

the point (1, 60 ) is on graph A

g(x) = 100 × [tex](\frac{2}{5}) ^{1}[/tex] = 100 × [tex]\frac{2}{5}[/tex] = 20 × 2 = 40

thus (1, 40 ) is a point on the graph of g(x)

the point (1, 40 ) is on graph B

Answer:

- 8, - 6, - 4, - 2, 0

Step-by-step explanation:

the term- to- term rule

[tex]u_{n+1}[/tex] = [tex]u_{n}[/tex] + 2

means that to find a term in the sequence you add 2 to the previous term.

given u₃ = - 4 , then

u₄ = u₃ + 2 = - 4 + 2 = - 2

u₅ = u₄ + 2 = - 2 + 2 = 0

to find the first 2 terms, rearrange the rule as

[tex]u_{n+1}[/tex] = [tex]u_{n}[/tex] + 2 ( subtract 2 from both sides )

[tex]u_{n+1}[/tex] - 2 = [tex]u_{n}[/tex] , that is

[tex]u_{n}[/tex] = [tex]u_{n+1}[/tex] - 2

this allows for a term to be found by subtracting 2 from the next term, so

a₂ = a₃ - 2 = - 4 - 2 = - 6

a₁ = a₂ - 2 = - 6 - 2 = - 8

the first 5 terms are then : - 8, - 6, - 4, - 2, 0

The interest paid at the term end will be $5400.

What is interest and its types(Simple and compound interest)?

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

​The formula for these are

Simple Interest= P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

​

Compound Interest=P×(1+r)^t−P

where:

P=Principal amount

r=Annual interest rate

t=Number of years interest is applied

​

Here,

Interest rate will be risk percentage + LIBOR

i.e.4.8%

Hence, the interest can be found by using formula for simple interest

Therefore,

SI=P*r*t

=$450000*0.048*0.25               (Time is 3 month or  0.25 years.)

SI (Interest paid)=$5400

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The interest paid at the end of the 3-month loan term for a loan amount of $450,000 with a business risk percentage of 2.0% and a LIBOR rate of 2.8% would be $5,040.

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Therefore , the solution of the given problem of elevation comes out to be

X = 21.23°.

When it is between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.

Here,

Given :  tan X = P/ B

tan X = 68 / 175

X  = tan⁻¹ (68 /175)

X = 21.23

Therefore , the solution of the given problem of elevation comes out to be

X = 21.23°.

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Answer:

y = 4[tex]x^{2}[/tex]

Step-by-step explanation:

Your inputs (x's): are -1,0,1,2,3,4   if you plug them into the equation, you get the matching outputs given in the order pairs

input -1 (x value)

y = [tex]4x^{2}[/tex]

y = 4[tex](-1)^{2}[/tex]

y = 4(1)

y = 4

(-1,4)

input 0 (x)

y = [tex]4x^{2}[/tex]

y = [tex]4(0)^{2}[/tex]

y 4(0)

y = 0

(0,0)

input 1 (x)

y = [tex]4x^{2}[/tex]

y = [tex]4(1)^{2}[/tex]

y = 4(1)

y = 4

(1,4)

input 2 (x)

y = [tex]4x^{2}[/tex]

y = [tex]4(2)^{2}[/tex]

y = 4(4)

y = 16

(2,16)

input 3 (x)

y = [tex]4x^{2}[/tex]

y = [tex]4(3)^{2}[/tex]

y = 4(9)

y = 36

(3, 36)

input 4 (x)

y = [tex]4x^{2}[/tex]

y = [tex]4(4)^{2}[/tex]

y = 4(16)

y = 64

(4,64)

The population of Australia in 2018 was 24.909 million.

Given: The population of Sydney in 2018 = 5.48 million

           This population of Sydney is equal to 22 % of the total population of Australia.

To find: Total population of Australia

Solution:

According to the Question,

Total population of Australia * 22% = total population of Sydney

Total population of Australia * 22/100  = 5.48 million

                                                                = 5.48 million * 100/22

                                                                = 24.909 million (approx.)

Hence, the population of Australia in 2018 was 24.909 million.

The total population of Australia in 2018 was 24.90 million.

A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured.

Given that, the population of Sydney was 5.48 million, which was 22% of the total population of Australia.

We need to find the total population of Australia.

Let the total population of Australia be y.

Therefore,

y × 22% = 5.48

y = 5.48 × 100/22

y = 24.90

Hence, the total population of Australia in 2018 was 24.90 million.

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Using multiplication operation, the TRUE statement about the number of kilograms of dog food in the bag is A. There are approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/25.

The number of kilograms of dog food in the bag is determined using the multiplication operation.

The multiplication operation is one of the basic mathematical operations, including addition, subtraction, and division.

The multiplication operation involves multiplying the multiplicand by the multiplier to get a result called the product after the equal sign.

The pounds of dog food in a bag = 25 pounds

Approximately 2.2 kilograms = 1 pound

The number of kilograms = 25 x 2.2

= 55 pounds

Thus, Option A is correct since 1/2.2 equals 55/25, based on the multiplication operation.

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