Monday: P.S. 2- Algebraic Expressions
Problem and Effort:
Simplify the following
expression given the
variables m = 4, n = -3,
and p = -3
√e
m+n²-p
Correct Answer:

The ratio used to find the measurement of angle x is given as follows:

cos(x) = 40/68.

The three trigonometric ratios are defined as follows:

For angle x, we have that:

Hence the ratio is given as follows:

cos(x) = 40/68.

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The number in question is the magic sum of the square. The outcome is the same as if you multiply the three integers in each column together and then add the three products: 8, times 3, 4, 1, 5, 6, 7, and 2 equals 225. This quantity is known as the magic square product.

The term "integer" refers to any number that is not zero, a positive natural number, or a negative integer denoted by a minus sign. Because they are diametrically opposed to their positive counterparts, negative integers are additive.

When representing a group of numbers in mathematical notation, the blackboard bold mathbb Z or boldface Z are frequently used. The word "integer" is pronounced "IN-tuh-jer" and refers to a whole number that can be positive, negative, or zero.

A few examples of integers are -5, 1, 5, 8, 97, and 3,043. Non-integer numbers include the figures -1.43, 1 3/4, and 3.14.

The integers are a collection of all whole numbers and their antipodes. Decimal points and fractions are not included in the set of integers. The numbers 2, 5, 0, 12, 244, 15, and 8 are examples.

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Answer: 240 ft²

Step-by-step explanation:

Break the diagram into a rectangle and triangle:

Area of Rectangle + Area of Triangle = Total area of Wall

(20x10) + 1/2(20 x 4) = Area of wall

200 + 40 = Area of wall

240 ft² = Area of wall

Hare Krishna :)

The solution of the given system of linear equations is (1, -1)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given is a system of linear equations, x - 3y = 4 and y = -3x + 2, we need to find the point which is the solution of the system,

The linear equations are :-

x-3y = 4...(i)

y = -3x+2....(ii)

Put eq(ii) in eq(i)

x-3(-3x+2) = 4

x+9x-6 = 4

10x = 10

x = 1

Put x = 1 in eq(ii)

y = -3+2

y = -1

Therefore, the solution point is (1, -1)

We can find the solution point by graphing method also, we will plot the graph of the lines and the line where intersects is the solution point is (1, -1) [attached]

Hence, the solution of the given system of linear equations is (1, -1)

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The complete question is (Multiple Choice Worth 2 points)

(Systems of Linear Equations MC)

Which point is a solution of the system of linear equations?

x - 3y = 4

y = -3x + 2

A) (9,0)

B) (-5, 8)

C) (1, 1)

D (1, -1)

Maximum number of hours per day that first smokestack can operate 12.5 hours and for second smokestack is 7 hours.

According to the question a  factory has two smokestacks:

Let first smokestack take x  number of hours per day

and second smokestack take y number of hours per day

The rate of particle pollution produced is 12 kg/h for the first smokestack

and rate of particle pollution produced is 32 kg/h for the second.

A local pollution control board has ordered that the factory produce no more than 374 kg of particle pollution per day.

so, equation becomes 12x + 32y = 374

also the first smokestack operates 2 hours longer than 1. 5 times as long as the second.

so, x = 2 + 1.5y

putting value of x in other equation

12(2 + 1.5y) + 32y = 374

24 + 18y + 32y = 374

50y = 350

y = 7 hours

x = 2 + 1.5(7) = 12.5 hours

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Answer:

x = 40.5

Step-by-step explanation:

SQ is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is

[tex]\frac{PS}{RS}[/tex] = [tex]\frac{PQ}{RQ}[/tex] ( substitute values )

[tex]\frac{20}{18}[/tex] = [tex]\frac{45}{x}[/tex] ( cross- multiply )

20x = 18 × 45 = 810 ( divide both sides by 20 )

x = 40.5

Step-by-step explanation:

9-3 =6

So we have 6 dollars for 3 bracelets

Which means each bracelet costs 2 dollar each

So 9x-3x=6x

Answer:

3/4 hour-72

1 hour- 92

Step-by-step explanation:

3/4-

24 x 3= 72

1-

24 x 4 =92

Answer:

It will take Richard 12 minutes to type 720 words.

Step-by-step explanation:

720 ÷ 60 = 12

Answer:

D.) QIII

Step-by-step explanation:

Because 1.2 radians is in between 7π/6 and 5π/4

The statistical method that is used for identifying the cost behavior is  (e) Least Squares regression method .

The Least Squares Regression method is defined as a statistical technique that is used to determine the relationship between two variables, which are , "the cost" and its "corresponding activity level" .

This method also involves plotting data points on a scatter diagram and fitting a straight line to data points.

The line that best fits data is line that minimizes sum of squared vertical distances between the data points and the line, this is why it is called the Least Squares regression method.

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The given question is incomplete , the complete question is

A statistical method for identifying cost behavior is the:

(a) Scatter diagram method

(b) High low method

(c) Composite method

(d) CVP charting method

(e) Least Squares regression method

The multiply of 45 and 23 is = 1035  we calculate this by simple multiplication method.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

And here we have 2 number 1st is 45 and 2nd is 23 so here we will multiply

    4  5

 x  2 3

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

  1 3 5

  9 0 x

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

1 0 3 5

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

final ans is 1035

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By inspection, the following products which are multiples of 30 are:

This is referred to as a number that may be divided by another a certain number of times without a remainder.

The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D  were chosen as the correct choice.

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The value of ∠4 in the given transversal line image is; 85°

Corresponding angles are defined as the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

In this question, we see that ∠3 is a corresponding angle to 95°. Thus;

∠3 = 95°

Now, ∠4 forms a straight line with ∠3 and as such they will sum up to 180 degrees as sum if angles on a straight line sums up to 180 degrees. Thus;

∠4 = 180 - 95

∠4 = 85°

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The five number summary is the minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and the maximum.

To give the smallest interval that we know contains the 30th percentile, we would take the 25th percentile and the 30th percentile. So, the smallest interval that we know contains the 30th percentile would be [25th percentile, 30th percentile].

The smallest interval that contains the 30th percentile is [25th percentile, 30th percentile], which is found using the five number summary (minimum, first quartile, median, third quartile, and maximum).

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The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).

The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.

When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒  (x + a, y + b).

The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.

Therefore, the correct transformation used is  (b) (x, y) → (x+5, y+3).

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The given question is incomplete , the complete question is

A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?

(a) (x, y) → (x-5, y-3)

(b) (x, y) → (x+5, y+3)

(c) (x, y) → (x-3, y-5)

(d) (x, y) → (x+3, y+5)

Answer:

Step-by-step explanation:

... good luck

The answers are given as follows:

2
a)

A = 8

b = 10

x = 118°

y = 62°

b)

a = 8

b = 15

y = 50

x = 100°

3)

(a)

∠2 = 25°

∠3 = 65°
∠4 = 65°
∠5 = 90°

(b)

since SL = 10,
i) LT  10
ii) TM = 10

iii) SM = 10

4)

a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°

If FA = 27, then LO = 13.5

The above are resolved using the properties of Parallelograms; Rhombus, and Rectangle

Since the above answers are justified by the qualities or properties of :

Parallelograms; Rhombus, and Rectangle, lets look at them one by one.

2
a)

A = 8 - opposite sides of a parallelogram are equal in length

b = 10 -opposite sides of a parallelogram are equal in length

y = 62° - opposite angles of a parallelogram are of equal measure.

x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2

= 118°

3)

(a) Here we have a Rhombus.

∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2

∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]

(b)

since SL = 10,
i) LT  10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal

iii) SM = 10 - All sides of a Rhombus are equal


4) Here we have a Rectangle.

a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ =  90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)

If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,

LO = FA/2

LO = 27/2

LO = 13.5

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Answer: D and C

Step-by-step explanation:

To get the value of a market basket you would add up the cost of each year so

2019 market basket = 2.50 + 1.00 + 3.75 = 7.25

2020 market basket = 2.25 + 3.00 + 4.50 = 9.75

2021 market basket = 3.00 + 3.25 + 5.00 = 11.25

now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135

CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155

The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.

What is meant by the speed of an object?

A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.

The formula of speed = Distance covered /Time taken

Given,

Distance travelled = 10 miles

Time taken to travel 10 miles = 20 minutes

Speed = Distance/ time = 10/20 = 0.5miles/min

Now given the speed remains constant throughout the journey.

So the distance travelled in 3 hours = 3 * 60 = 180 minutes

Distance = speed * time = 0.5 * 180 = 90 miles.

Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.

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Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is equal to the total change in the function's output divided by the total change in the input over the interval. In other words, it is the slope of the secant line that connects the two points on the function defined by the interval.

If the function is represented by y = f(x), the average rate of change of the function over the interval [-4, -3] can be calculated as:

Δy / Δx = (f(-3) - f(-4)) / (-3 - (-4))

So, to calculate the average rate of change, you would need to know the values of the function f(x) at x = -3 and x = -4. If you provide the equation for the function f(x), I can help you find the average rate of change.

The equation connecting y and x when y is directly proportional to x and y = 30 when x = 6 is y = 5x.

If y is directly proportional to x, we can write the equation in the form:

y = kx

where k is the constant of proportionality.

To find k, we can use the values of y and x given:

y = 30, x = 6

When we enter these values into the formula above, we obtain:

30 = k * 6

Solving for k, we get:

k = 30/6 = 5

Therefore, the equation connecting y and x when y is directly proportional to x is:

y = 5x

When two variables are directly proportional, it means that when one variable increases or decreases, the other variable changes in the same proportion. In this scenario, we are given that y is directly proportional to x and we are also given a specific point on the line, (6, 30). Using this information, we can solve for the constant of proportionality k and write the equation connecting y and x as y = kx, where k is 5.

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The exponential equation is y=2,642(2.5)ˣ. x represents the number of days.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

Given that a video was released to the public, it already had 2,642 views.

One day later, the number of views increased to 3,963.

The number of viewers after one day is ( 3,963 + 2,642 ) = 6,605

Assume that the exponential function y = a(b)ˣ represents the number of viewers. x represents the number of days.

Putting x = 0 and  y = 2,642 in y = a(b)ˣ:

2,642 = a(b)⁰

a = 2,642

Putting x = 1 and  y = 6,605 in y = a(b)ˣ:

6,605 = a(b)¹

Putting a = 2,642:

6,605 = 2,642(b)¹

b = 6,605/2,642

b = 2.5

Therefore, an exponential equation is y=2,642(2.5)ˣ.

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Answer:

[tex]\sqrt{106}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]

The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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Answer:

C 11

Step-by-step explanation:

you have 1 less penny than dimes which is 10 pennies

you have 2 less nickels than dimes which is 9

11+10+9=30

The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.

What is a linear equation?

This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.

Let the plane speed be 'P' and the wind speed be 'W'.

We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.

So, we get an equation as

P + W = 158       ...(1)

Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.

So, we get another equation as

P - W = 112       ...(2)

Now, on adding the equations we get,

⇒P + W + P - W = 158 + 112

⇒2P = 270

⇒P = 135

Now substituting the value into either equation, we get

⇒P + W = 158

⇒135 + W = 158

⇒W = 23

Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.

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