AABC ~ AQRS
Find the missing side length, m.
R
B
3/
A
C
1
m = [?]
m
5
S

Answer: Look at step-by-step explanation

Step-by-step explanation:

1) When a polynomial f(x) has a factor x - y, then f(y) = 0, hence

[tex]2^{3}[/tex] - 3 × [tex]2^{2}[/tex] + 2a + b = 0

8 - 12 + 2a + b = 0

2a + b = 4

2) When a polynomial f(x) is divided by x - y, then f(y) = the remainder, hence

(A) When divided by x - 1

[tex]1^{3}[/tex] - 3 × [tex]1^{2}[/tex] + a + b = 1 - 3 + a + b = a + b - 2

(B) When divided by x - 3

[tex]3^{3}[/tex] - 3 × [tex]3^{2}[/tex] + 3a + b = 27 - 27 + 3a + b = 3a + b

The rate of increase in stock price is $ 0.10 per hour.  

To calculate the rate of increase we need to know the increased amount per given time period

In this problem, we will calculate the stock price per given hour from that will calculate the rate of increase in a given situation.

Here we have

The price (in dollars) of a stock tracked from noon to three on a given day is shown by the function f(t) = 0.1(t - 2)³ + 6 where t is in hours.  

Take t = 1

=> f(1) = 0.1(1 - 2)³ + 6

= 0.1(-1)³ + 6

= 0.1(-1) + 6

= - 0.1 + 6

= 5.9

Take t = 2

=> f(2) = 0.1(2 - 2)³ + 6

= 0.1(0)³ + 6

=  6

Take t = 3

=> f(3) = 0.1(3 - 2)³ + 6

= 0.1(1)³ + 6

= 0.1 + 6

= 6.1

The rate rate of increase = f(3) - f(2) = 6.1 - 6 = 0.1 ≅ $ 0.10

Therefore,

The rate of increase in stock price is $ 0.10 per hour.

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Answer: 28.

Step-by-step explanation:

If 40% of the teachers in attendance at the school staff meeting were first-year teachers, that means 28 of the teachers in the meeting were first-year teachers.

Answer:

28

Step-by-step explanation:

We first would need to figure out what %10 of 70 is.

%10 of 70 is equal to 7.

Now that we have this answer, we can multiply 7 by 4 to get the number of teachers.

7 × 4 = 28

28 first year teachers were in the meeting.

The given expression can be simplified using the arithmetic operation as 0.00080987.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The given problem can be written in terms of expression as,

42 ÷ 51860

It can be solved as follows,

The number of digits in 51860 is 5 and in 42 is 2.

In order to divide the two numbers, the dividend should be greater than the divisor.

Therefore, multiply both 42 and 51860 by 10000 to obtain,

(42 × 10000) ÷ (51860 × 10000)

⇒ 420000 ÷ (51860 × 10000)

Now, first divide  420000 by 51860 to get,

420000 ÷ 51860 = 8.0987

Then, divide 8.0987 by 10000 to get,

8.0987 ÷ 10000 = 0.00080987

Hence, the required result of the given expression is 0.00080987.

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Answer:

D

Step-by-step explanation:

it is a regular pentagon.

so, all side lengths are equal, and also all cross connections between corners are equal.

that makes TR parallel to PQ.

and that makes SPQ an isoceles triangle (both legs are equally long). and the smaller triangle S to x to the angle to the right of x is similar to SPQ, which means they have the same angles.

so, the triangle interior angle at P = the triangle interior angle Q = y.

and they must be the same as the bottom 2 interior angles of the small triangle.

x and the angle right to x are equal too, as they are the triangle exterior (supplementary) angles to the bottom 2 interior angles of the small triangle.

we know that the sum of all angles of the internal trapezoid (PQ to x and its right neighbor) is 360.

and based on the EqualLogic found above these angles are

2×x + 2×y = 360°

x + y = 180°

In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.

There are many different types of equations, such as linear, quadratic, cubic, etc.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side).

Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol in the sentence, it is not an equation.

Hence, In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.

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Complete question-

Using the equation y = 2/3 x - 5, describe how to create a system of linear equations with an infinite number of solutions.

Answer:

d = {-10, 0, 3, 7, 8}

Step-by-step explanation:

the domain is the set of x values in a function

Answer:

Step-by-step explanation:

1000-520=480

480/6=80

x+6+520=1000 (-6)

x+514=1000

x=486

The elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.

A division is a process of splitting a specific amount into equal parts.

Given,

An elevator in the Seattle Space Needle can rise 100 meters in 50 seconds,

We need to find the elevator's rate of travel in meters per second and in seconds per meter

To find in meter per second we just need to divide 100 by 50 seconds

100/50=2 m/s

To find in seconds per meter we just need to divide 50 by 100

50/100=1/2s/m

Hence, the elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.

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The required zeros of the function y=(x-3)(x + 2)(x-2) is given as 3, -2, and 2. Option C is correct.

Here,
Zero of the function are the values of x, for a function for which the function gives y = 0,
So let y = 0,   - - - - - -(1)

Put y = (x-3)(x + 2)(x-2) in equation 1
(x-3)(x + 2)(x-2) = 0
Equating each parenthesis step by step with zero,
x - 3 = 0     ; x + 2 = 0     ;   x - 2 = 0  
    x  = 3     ;     x  = -2    ;        x = 2

So the values that came out are 3, -2, and 2, are said to be zeros of the given function,

When we substitute any value in the function then y becomes zero such as,
Put x = 3 in function,

y = (3-3)(3+2)(3 - 2)
y = (0)(5)(1)
y = 0

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82.5 million was the profit the year before the profit decreased 20% to 66 million from one year to the next

What does profit means ?

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

Any profits generated are returned to the company's owners, who can decide whether to keep the money for themselves, pay dividends to shareholders, or reinvest it in the company.

Entire revenue less total costs equals profit.

Companies report gross profit, operational profit, and net profit for accounting purposes (the "bottom line").

Investors are drawn to profitable businesses because these businesses either distribute their earnings as dividends to shareholders or invest them back into the business, which raises stock value.

According to the question Company lost 20% from its profit and it reached to 66 million that means

let X be the total profit of the year

X - loss percent = 66 millions

X - X (20/100) = 66 million

X-0.2X = 66 million

0.8X = 66 million

X= 66/0.8 million

X = 82.5 million

So, 82.5 million was the profit the year before

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The subject of a random event is covered in the mathematical field of probability.

Statistics is a field of mathematics that deals with gathering, analyzing, interpreting, and presenting vast amounts of numerical data.

Given,

Probability;-

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

Statistics;-

Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.

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Answer:

Q-(1,1)       L-(1,-2)       G-(4,-4)

Step-by-step explanation:

becuase

Answer:30,000 meters

Step-by-step explanation:

Answer:

30km

Step-by-step explanation:

to find 10% you divide 100km by 10= 10km

to find the full 30% simply divide 10% by 3 which will give you 30km.

Considering the climate of the North Pole, Alaska, we have seen that the change in the Temperature is 13°F and 14 °F respectively on the 1st and last day of the month respectively.

From records, we know that Alaska usually has an average low temperature of 9°F and an average high temperature of 22°F in January.

However In February,  Alaska's temperature usually ranges from an average low temperature of 12°F to an average high temperature of 26°F.

Thus, we can find the change in Temperature:

On 1st day of January , the Change in temperature is;

ΔT = Highest Temperature - lowest temperature

ΔT = 22°F - 9°F

ΔT = 13°F

On the 1st day of February, and then the last day of January, the change in temperature is;

ΔT= Highest Temperature -  lowest temperature

ΔT = 26°F -  12°F

ΔT = 14 °F.

The hardest part will be to take take care of the animals since most of the animals only require a warm, secure, as well as protected area to reside in addition to sufficient food, drink, and exercise.

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Answer:

Start with 60 fliers

post 1/4 of fliers so 60*.25=15

60-15=45 left

post 1/5 of remaining so 45*.20=9

45-9=36 left

Step-by-step explanation:

Last week: (had 60) (used 1/4)= (60)(1/4)= 15. So, you used 15.

You have 60-15=45 left. This is how many you have to start the week.

This week: (had 45) (used 1/5)= (45)(1/5)= 45/5=9. So, you used 9.

This means that you have 45-9= 36 left.

Mary Still did not post 60 fliers.

Total fliers Mary was having = 96

Fliers she posted last week = 1/6 = 0.16

Fliers left with Mary after posting 1/6 part last week

= 96 x 0.16

= 16

Fliers left with Mary after the posting of 1/6 of them

= 96 - 16

= 80

Now the new remaining number of fliers with Mary = 80

Fliers she posted this week = 1/4 = 0.25

Fliers left with Mary after posting 1/4 part this week

= 80 x 0.25

= 20

Fliers left with Mary after the posting of 1/4 of them this week

= 80 - 20

= 60

Therefore, the fliers that Mary still did not post = 60

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Answer:

if you want the volume of the outer cube with the other cube in it, it would be 48. if you want it without the cube its 120. the inside cube is 72.

Step-by-step explanation:

Answer:

48 mm³

Step-by-step explanation:

Outer prism:

5 mm by 4 mm by 6 mm

V = LWH = 5 × 4 × 6 mm³ = 120 mm³

Inner prism:

4 mm by 3 mm by 6 mm

V = LWH = 4 × 3 × 6 mm³ = 72 mm³

Difference:

120 mm³ - 72 mm³ = 48 mm³

In the drawing, the length of the living room is 3 millimeters.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters.

The living room is 6 meters long in real life and assuming in the drawing it is x millimeters.

∴ 1 : 2 : : x : 6.

1/2 = x/6.

x = 6/2.

x = 3.

So, In drawing it is 3 millimeters.

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A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension.

The partial results :

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Answer:

G = -32

Step-by-step explanation:

Thus, the scale factor by which he increased his screen size is 3:2

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given, the pixel of Mike's old calculator = 96 pixel

His new calculator has pixels = 144 pixel

Scale by which it increased = New pixels/Old pixel

= 144p/96p

= 3:2

Thus, the scale factor by which he increased his screen size is 3:2

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Option D, The equation that satisfy the situation is  y - 12 = 1.50(x-6).

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is "m" and which passes through the points (x 1, y 1). The equation of a straight line can be expressed in several ways. Point slope shape is one of them. Y - Y 1 = m(x - X 1) is the equation for the point slope form, where (x1, y1) is a randomly chosen point on the line and m is the slope of the line.

The slope of the line is 1.5

The Point through which the equation will satisfy is (6,12)

Therefore the equation of the line in Point-Slope form is

y - y1 = m ( x- x1)

⇒ y - 12 = 1.50 ( x  - 6)

Option D, The equation that satisfy the situation is  y - 12 = 1.50(x-6).

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Answer:  -2 < x < 1

Step-by-step explanation:

Answer:

After the first translation, the coordinates of the vertices of the triangle will be X (3,-13), Y (0,-8), Z (-7, 1). After the second translation, the coordinates of the vertices will be X (5,-7), Y (2,-2), Z (-5, 7).

The final translation rule that maps the pre-image to the final image is a translation of 2 units right and 6 units up. This can be written as a translation rule of the form (x, y) -> (x + 2, y + 6).

Step-by-step explanation:

After the first translation the coordinates are:

After the second translation the coordinates are:

The final translation rule is:

or

Therefore, the linear speed of the wheel on a bike is approximately 0.9π miles per hour.

The pace at which an object travels a specific distance in a predetermined amount of time is known as linear speed. By dividing the distance traveled by the time it takes to cover that distance, it may be used to determine how rapidly an item is travelling in a straight line. For instance, if a car moves 100 meters in 10 seconds, its linear speed is 10 meters per second. Linear speed is distinct from average speed, which takes into account any variations in velocity or direction throughout the duration of a voyage. Linear speed is also distinct from tangential speed, which is the pace at which an item travels along a circular route. Physics' fundamental idea of linear speed.

How to solve?

C=2πr,

C=2π(19)=38π.

linear speed of v=(38π/60)*5280=33.6π feet per second.

final speed of v=(33.6π/3600)*60=0.9π miles per hour.

Therefore, the linear speed of the bike is approximately 0.9π miles per hour.

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If each unit on the grid represent 25 feet, then the perimeter of the factory is 1000 feet

Each unit on the grid represent 25 feet

The length of the side w1 = 3 × 25

= 75 feet

The length of the side N1 = 13 × 25

= 325 feet

The length of the side E1 = 7 × 25

= 175 feet

The length of the side S1 = 5 × 25

= 125 feet

The length of the side W1 = 4 × 25

= 100 feet

The length of the side S2 = 8 × 25

= 200 feet

The perimeter of the factory = 75 + 325 + 175 + 125 + 100 + 200

Add the terms together

= 1000 feet

Therefore, the perimeter of the factory is 1000 feet

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The number of songs and games Jenna bought is 9.5 and 2.5 respectively.

let

x + y = 12

1.99x + 3.99y = 18.88

From (1)

x = 12 - y

Substitute into (2)

1.99x + 3.99y = 18.88

1.99(12 - y) + 3.99y = 18.88

23.88 - 1.99y + 3.99y = 18.88

- 1.99y + 3.99y = 18.88 - 23.88

2y = -5

y = -5/2

y = 2.5

Substitute into (1)

x + y = 12

x + 2.5 = 12

x = 12 - 2.5

x = 9.5

Therefore, Jenna bought 9.5 songs and 2.5 games.

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Answer: 4

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]3^2 + x^2 = 5^2\\\\9+x^2=25\\\\x^2=16\\\\x=4[/tex]