A square a triangle and a parallelogram are used to form the figure shown. What is the area of the figure in square feet?
A) 213.04
B) 210.64
C) 231.04
D) 207

The given expression is proved.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have.

tan∅/(1+ sec∅)

=(sin∅/cos∅)/(1+ sec∅)                  [tan∅=(sin∅/cos∅)]

=(sin∅/cos∅)/(1+1/cos∅)

=sin∅/1+cos∅

multiplying both numerator & denominator by 1-cos∅, we get,

=sin∅(1-cos∅)/ sin^2∅

=(1-cos∅)/sin∅

=cosec∅ - cot∅

Hence, The given expression is proved.

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The quadrilateral is most specifically a square since all the sides of the quadrilateral are equal and have 90°

A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the quadrilateral be represented as ABCD

Now , the measures of the sides of the quadrilateral are

The measure of side AB = measure of side BC

And , the measure of side AB = measure of side AD

So , all the 4 sides of the quadrilateral are same so it is a square

And the measures of angles are 90° each

Therefore , the quadrilateral is a square

Hence , it is a square

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If the two cars collide and couple, then their final velocity will be 1.91 meters per second.

According to the principle of momentum conservation, movements are only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never generated nor destroyed inside a problem domain.

The conservation of momentum is given as,

m₁u₁ + m₂u₂ = (m₁ + 2₂)v

Car 1 is moving at a speed of 7 m/s and weighs 3000 kg. Car 2 is not moving and weighs 8000 kg.

3,000 x 7 + 8,000 x (0) = (3,000 + 8,000) x v

21,000 + 0 = 11,000v

v = 21,000 / 11,000

v = 1.91 meters per second

If the two cars collide and couple, then their final velocity will be 1.91 meters per second.

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The start point the graph of a function of this form is (h, k)

From the question, we have the following parameters that can be used in our computation:

f(x) = a√(x - h) + k

The domain is given as

x ≥ h

This means that the initial x value is h

From the question, we have the following parameters that can be used in our computation:

f(h) = a√(h - h) + k

Evaluate

f(h) = k

Hence, teh initial point is (h, k)

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By calculating , The value of x we get is  5 as a final resultant.

What is trapezoid ?

A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.

Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that

180=110+17x-15

70=17x-15

85=17x

x=5

Therefore, By calculating , The value of x we get is 5 as a final resultant.

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The speed of Petra will be 0.55 mile/minute.

What exactly is speed?

The definition of speed is:

The pace at which an object's location changes in any direction.

Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.

Formula for Speed

The speed formula is shown below:

s=d/t

Where,

s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.

Now,

As given petra jogs 60 miles in 110 minutes

then in one minute she will jog =60/110 mile

=0.5454 mile/min

Hence,

           The speed of Petra will be 0.55 mile/minute.

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Answer:

A = w*6

Step-by-step explanation:

W = A/6

Multiply both sides by 6 using the multiplication property of equality.

A = W*6

or

A = W x 6

Hope this helps!

The expression equivalent to 5x +10y -15 by taking the common factor is 5(x + 2y - 3).

What is taking out common factors?

The takeout of the common factor is the procedure, ab + ac = a(b + c). Think about how the expression 5x + 10 gets factored. The common factor 5, which was previously in front of the brackets, has been removed.

Figuring out what to multiply to create an expression. It is comparable to "splitting" an expression into numerous smaller expressions.

Given, the expression is 5x + 10y -15

So, 5x +10y -15 = 5x + 5*2y - 5*3

                         = 5(x + 2y - 3)

Hence, the required answer is 5(x + 2y - 3).

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The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-

E = 3h(n) + 2g(n)

E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)

E = 12n + 6 + 2n³ + 10 -4n

E = 2n³ + 8n + 6

Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.

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㏒Answer:

Step-by-step explanation:

Based on the recipe for making green slime, 3 cups of water is not enough to make a double recipe of green slime.

One recipe of green slime requires 1 pint of water, which is equal to 2 cups.

In order to make a double recipe, you would need to double the amounts of all the ingredients, including the water.

So, for a double recipe of green slime, you would need:

4 cups of water (2 cups per recipe)

1/2 cup of cornstarch (1/4 cup per recipe)

Green food coloring

Therefore, Rosa would need to measure out 4 cups of water to make a double recipe of green slime for the class project.

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The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:

2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person

So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

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The scenarios can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful in

E) As the number of calls made by a cell phone increases, the cell phone bill amount increases.

We anticipate that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Given:

We can see from Option A that the opposite may not be true, as an increase in the risk of lung cancer may not always be accompanied by an increase in the number of cigarettes smoked each day.

Now, second it is clear that the opposite may not be true because an infant's age may not necessarily increase along with his or her height.

Now, third also acknowledges that a rise in traffic is not always accompanied by an increase in pollution in a city.

Fourth, a rise in water density does not always imply an increase in the amount of salt present in the water.

Only in Option E do we find a potential reverse reliance because a rise in phone bill amount does typically correspond to a rise in cell phone call volume.

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Answer:

Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0), which is not in the given options, so none of the options are the correct answer.

The solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 75x + 0.55y = 125.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Substitute x=0, 1, 2, 3, 4, 5,....

When x=0

75(0)+0.55y=125

0.55y=125

y=125/0.55

y=227

When x=1

75(1)+0.55y=125

0.55y=50

y=50/0.55

y=91

When x=2

75(2)+0.55y=125

0.55y=-25

y=-25/0.55

y=-45.45

Therefore, the solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

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Answer:

360

Step-by-step explanation:

Every 1/2pi is 90 degrees.

Going down the list...

1/2pi is 90

pi is 180

3/2pi is 270

2pi is 360

Answer: To find the limit of the expression 3√x-1/x-1 as x approaches 1, we can use L'Hopital's Rule. L'Hopital's Rule is a method for finding the limit of indeterminate forms, such as 0/0 or ∞/∞, by taking the derivative of the numerator and denominator.

In this case, the expression is of the form 0/0, so we can use L'Hopital's Rule:

lim 3√x-1/x-1 = lim (3/2)((x-1)^(1/2)) / 1 = 3/2

So the limit of the expression 3√x-1/x-1 as x approaches 1 is equal to 3/2.

Step-by-step explanation:

Answer:

689.85 liters

Step-by-step explanation:

1 gallon =  about 3.78 liters

182.5 gallon = ? liter

We take  

182.5 times 3.78 = 689.85 liters

So, 182.5 gallons is about 689.85 liters

The interest to be paid is $99

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Simple Interest = P×R×T/100

where P is the principal,

R is the rate

and T is the time

P = $900

R = 11%

T= 1

I = 900× 11/100

I = $99

therefore the interest to be paid is $99

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Reason: Split the angle 155 in half to get 155/2 = 77.5

The volume of the cylinder is 72π cubic centimeters.

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.

The formula for the volume of a cylinder is:

V = Bh

where B is the area of the base of the cylinder, and h is the height of the cylinder.

In this problem, the cylinder has a diameter of 6 centimeters, which means the radius is 3 centimeters. The area of the base of the cylinder is therefore:

B = πr²

B = π(3 cm)²

B = 9π cm²

The height of the cylinder is given as 8 centimeters. Therefore, we can use the formula for the volume of a cylinder to find the volume V:

V = Bh

V = (9π cm²)(8 cm)

V = 72π cubic centimeters

Therefore, The volume of the cylinder is 72π cubic centimeters.

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The tables with their equations are

From the question, we have the following parameters that can be used in our computation:

Tables and equations

Table (a)

Here, we notice that:

The output is the reciprocal of the input

This is represented as

y = 1/x

Table (b)

Here, we notice that:

The output is the square root of the input

This is represented as

y = √x

Table (c)

Here, we notice that:

The output is the cube of the input

This is represented as

y = x³

Table (d)

Here, we notice that:

The output is the same as the input

This is represented as

y = x

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The solution is, the equation is y=2/3x.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

here, we have,

so the line is in slope intercept form

y=mx+b, m=slope and b=y intercept

we know the slope so just solve for b

y=2/3x+b

subsitute

3 for x and 2 for y

2=2/3(3)+b

2=2+b

subtract 2 from both sdies

0=b

so the equaiton is

y=2/3x+0 or just simply

y=2/3x

here is the graph

just input values for x and get y values exg

x=3 y=2

x=6 y=4

x=0 y=0

x=-3 y=-2

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Answer:

Step-by-step explanation:

To simplify the expression, we need to divide -3x^9 + 2x^8 - 8 by x^4.

The procedure is as follows:

Divide -3x^9 by x^4: -3x^9 / x^4 = -3x^5

Divide 2x^8 by x^4: 2x^8 / x^4 = 2x^4

Divide -8 by x^4: -8 / x^4 = -8x^-4

Combine the results from steps 1-3: -3x^5 + 2x^4 - 8x^-4

Note that the exponent of x in each term is either positive or zero. We can't simplify the expression further since we can't simplify the exponents any more.

Answer:

c) [tex]10x<7z[/tex]

Step-by-step explanation:

[tex]5x<3y \implies 10x<6y \\ \\ \therefore 10x<6y<7z \implies 10x<7z[/tex]

52s represents the cost for the snowboard times s days.

What is an expression ?

An expression consists of one or more numbers or variables along with one more operation.

Given :

expression : 52s + 10

Since it represents , total cost to rent a snow board for s days plus the fee for the helmet

Therefore , 52 is the cost of the snowboard rental per day.

s represents the day(s) that the equipment is rented out.

Hence , 52s represents the cost for the snowboard times s days.

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Given question is incomplete , the complete question is given below:

At the ski shack customers can rent skis snowboards boots and poles by the day. josh rents a snowboard and a helmet. The expression 52s + 10 represents the toatak cost to rent a snow board for s days plus the fee for the helmet what dose the term 52s represent​

The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:

Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )

Midpoint = ( (-2-6)/2 , (-9+7)/2 )

Midpoint = (-4,-1)

Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (7 - (-9)) / (-6 - (-2))

Slope = 4

The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.

Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:

y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.

Plugging in the values we found, we get:

y - (-1) = (-1/4)(x - (-4))

y + 1 = (-1/4)(x + 4)

y + 1 = (-1/4)x - 1

y = (-1/4)x - 2

Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.

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A structure may lack structural integrity if it experiences overloading and material degradation.

A structure may lack structural integrity if it experiences:

Overloading, where the loads placed on the structure exceed its design capacity, leading to failure of some structural components or members.

Material degradation, where the structural materials lose their strength and stiffness over time due to environmental factors such as corrosion or excessive temperature.

ii. The basic types of structural systems are:

Frame Structures, where the structural components are arranged in a series of interconnected frames that can resist lateral and gravity loads. Examples include steel frames and concrete frame structures.

Load-Bearing Wall Structures, where the structural components are arranged in a series of interconnected walls that bear the weight of the structure and transfer loads directly to the foundation. Examples include masonry and concrete walls.

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The company can expect to find 125 defective flashlights in a production run of 12,500. The correct option  is B, 125.

Flashlight can be defined as a portable, battery-operated device used for illumination. It typical unit consists of one or more dry cell batteries arranged in a line inside a battery compartment that forms the handle of the light.

Assuming the proportion of defective flashlights remains the same, the number of defective flashlights in a production run of 12,500 would be:

(5/500) x 12,500 = 125

Therefore, the company can expect to find 125 defective flashlights in a production run of 12,500. The answer is option B, 125.

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