The area of a square is one third the area of a triangle. If the base of the triangle and a side of the square are equal, what is the ratio of the height of the triangle to the side of the square ?.

Answer:

  b. Square the number of the next term, n

Step-by-step explanation:

You want to know the pattern of the sequence 1, 4, 9, 16, 25, ... and why it tells you the next number is 36.

Usually we look for a common difference or a common ratio when we're trying to identify a sequence as arithmetic or exponential. This sequence has neither, as the differences are 3, 5, 7, 9, and the ratios are 4, 9/4, 25/16.

Neither of these are constant sequences. However, we do notice that the sequence of differences has a common difference of 2. The fact that "second differences" are common (all the same) means the sequence can be described by a second-degree polynomial.

Looking at the sequence values, we see they are ...

  1 = 1², 4 = 2², 9 = 3², 16 = 4², 25 = 5²

so we expect the 6th term to be the square of 6, 6² = 36. This is in line with the predicted next number.

The pattern is ...

  square the number of the next term, n

The sector area is equal to: B. 54π yd².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θr²/2

Where:

Substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θr²/2

Area of sector = 240(π/180) × (9)²/2

Area of sector = 120(π/180) × 81

Area of sector = 54π yd².

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The correct statements regarding the ordered pairs are given as follows:

The general format of an ordered pair is given as follows:

(x,y).

The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.

The two pairs on this problem are given as follows:

(0,3) and (4,6).

Hence the numeric values are given as follows:

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The coordinates of the point is Q ( 22 , -24 )

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Measure the distance between the two end points, and divide by 2.

Let A ( x₁ , y₁ ) be the first point

Let B ( x₂ , y₂ ) be the second point

The midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Given data ,

Let the first point be represented as P ( -2 , 8 )

Let the second point be represented as Q ( x , y )

Now , the midpoint of P and Q is M ( 10 , -8 )

where , midpoint between P and Q is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Substituting the values in the equation , we get

10 = ( -2 + x ) / 2

Multiply by 2 on both sides of the equation , we get

-2 + x = 20

Adding 2 on both sides of the equation , we get

x = 22

And ,

-8 = ( 8 + y ) / 2

Multiply by 2 on both sides of the equation , we get

y + 8 = -16

Subtracting 8 on both sides of the equation , we get

y = -24

Hence , the coordinates of the point Q is Q ( 22 , -24 )

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The conversion of 5 mcg (micrograms) to mg (milligrams) is 0.005 mg.

This is because there are 1,000 micrograms in 1 milligram which is the conversion factor. Therefore, to convert micrograms to milligrams, you would divide the number of micrograms by 1,000.

Here is the step-by-step explanation for this conversion:

1. Start with the number of micrograms: 5 mcg
2. Divide the number of micrograms by 1,000 to convert to milligrams: 5 mcg / 1,000 = 0.005 mg
3. The result is the number of milligrams: 0.005 mg

So, 5 mcg is equal to 0.005 mg.

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45 pieces of 4 inch can the dressmaker cut from 5 of these rolls of ribbon.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

1 roll = 3 feet of ribbon

So, 5 rolls = 5 x 3 = 15 feet of ribbon

and, 1 foot = 12 inches

Then, 15 feet = 15 x 12 = 180 inches

The dressmaker has 180 inches of ribbon in total.

Now, the 4-inch pieces can the dressmaker cut from 5 of these rolls of

ribbon

= 180 / 4

= 45 pieces

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The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.

To find the percentage of 322 out of 450, we can use the following formula:

percentage = (part/whole) x 100

where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".

Using the formula mentioned above, we get:

percentage = (322/450) x 100

percentage = 0.7156 x 100

percentage = 71.56%

Therefore, percentage of 322 out of 450 is approximately 71.56%.

A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.

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The output of the function g(x) for the given input is 9.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is [tex]g(x)=3^{(\frac{x}{2} )}[/tex].

When we input 4 into g(x), we get

[tex]g(4)=3^{(\frac{4}{2} )}[/tex]

g(4)=3²

g(4)=9

Hence, the output is 9.

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The VAT percentage of a mobile price is tagged Rs 5,000 with a 12% discount and adding a certain percentage of VAT reaches Rs 4,972 is a 13% VAT Percentage.

The solution to the problem is as follows:
Step 1: Find the price of the mobile after the discount. The discount is 12% of the original price, which is Rs 5,000. So, the discount amount is:
12% of Rs 5,000 = (12/100) * 5000 = Rs 600

Step 2: Subtract the discount amount from the original price to get the price after the discount:
Rs 5,000 - Rs 600 = Rs 4,400

Step 3: Now, we need to find the VAT percentage that was added to the price after the discount to get the final price of Rs 4,972. Let the VAT percentage be x%. Then the equation is:
Rs 4,400 + x% of Rs 4,400 = Rs 4,972

Step 4: Simplify the equation and solve for x:
4400 + (x/100) * 4400 = 4972
4400 + 44x = 4972
44x = 4972 - 4400
44x = 572
x = 572/44
x = 13

Therefore, the VAT percentage is 13%.

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Answer:

The drama club receives $9 for each ticket they sell.

Step-by-step explanation:

The total amount of money the drama club receives from selling 108 tickets is the difference between the total amount collected and the amount donated to the school.

Total amount collected = 108x + 972

Amount donated to the school = 108x

Amount received by the drama club = (108x + 972) - 108x = 972

Therefore, the drama club receives a fixed amount of $972 for selling 108 tickets.

To find how much money the drama club receives for each ticket sold, divide the total amount received by the number of tickets sold:

972/108 = $9

Therefore, the drama club receives $9 for each ticket they sell.

Answer:

69

Step-by-step explanation:

The prime factorization of P is given as follows:

C. 2³ x 3² x 7.

The number P in this problem is defined as follows:

P = 14 x 36.

Hence we must obtain the prime factorization of each number in this problem, as follows:

Then the prime factorization of the multiplication is given as follows:

14 x 36 = 2 x 7 x 2² x 3² = 2³ x 3² x 7.

Meaning that the correct option is given by option C.

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The value of the discriminant for the equation "2x² + 5x + 3"  is 1 , and the it has 2 real and rational roots .

The Discriminant of a quadratic equation of the form of ⇒ "ax² + bx + c" is calculated  by the expression "b² - 4ac"  .

the values of the variables "a", "b" and "c" ; for quadratic equation "2x² + 5x + 3" ,

the value of  a is = 2, b is = 5, and c is = 3.

substituting values ;

So , the discriminant is ⇒ b² - 4ac

⇒ 5² - 4×2×3  ;

⇒ 25 - 24

⇒ 1

Since , the discriminant is (1)positive, which means that the equation has 2 real roots. and since, discriminant is a perfect square, that means the roots are rational numbers.

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The given question is incomplete , the complete question is

Find the value of the discriminant for the equation 2x² + 5x + 3 , and then describe the number and type of roots for the equation .

Triangles that are similar are A and C because they have equal angles and the sides have the same scale dimensions.

To identify equal triangles we must look at the dimensions of the triangles, especially their angles and the lengths of their sides. Based on the above, we can infer that the triangles that are similar are triangle A and triangle C.

This is because both triangles have angles of 23°, 67°, and 90°. Additionally, a scale is stored between the length of its sides.

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1. Adjacent angles and  1 degree is missing angle.

3. Complementary angles are  missing angle is 177 degrees.

4. Adjacent angles and missing angle is 10 degrees.

5. Adjacent angles and missing angle is 104 degrees.

6. Adjacent angles and missing angle is 10 degrees.

6. Vertical angles and missing angle is 57 degrees.

an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

1. The angles are Adjacent

54+10x+16=180

10x=180-70

x=1

So the unknown angle is 10+16=26 degrees.

3. The angles are complementary

22+4x=90

4x=68

Divide both sides by 4

x=17

So, the angle is 4(17)=68 degrees

4. The angles are Adjacent

110+7x=180

7x=70

x=10,  the other angle is 7(10)=70 degrees

5. The angles are Adjacent

72+x+4=180

x=104

The other angle is 104+4=108 degrees.

6.  92+x+78=180

x=10

The unknown angle is 10 degrees.

7. The angles are vertical.

72=x+15

x=57 degrees.

Hence,  

1. The angles are Adjacent and missing angle is 1 degrees.

3. The angles are complementary and missing angle is 177 degrees.

4. The angles are Adjacent and missing angle is 10 degrees.

5. The angles are Adjacent and missing angle is 104 degrees.

6. The angles are Adjacent and missing angle is 10 degrees.

6. The angles are Vertical and missing angle is 57 degrees.

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4 ounces is equal to 0.25 pounds. Since 1 pound is equal to 16 ounces, to convert ounces to pounds, you need to divide the number of ounces by 16. So, 4 ounces divided by 16 equals 0.25 pounds.

One pound is equivalent to 16 ounces. To convert 4 ounces to pounds, you need to divide 4 by 16. This gives the result of 0.25 pounds, since 4 ounces is one-quarter of a pound. The conversion factor between ounces and pounds is useful when working with small weights, as ounces are commonly used to express small quantities of weight, while pounds are used for larger quantities. Knowing the conversion factor can help in many situations, such as when cooking, measuring ingredients or mailing a package, where it may be necessary to convert between different units of weight.

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Answer:

bvalue = 7

rise = 0 run can be any number besides 0 since slope is 0 (and slope = change in y/change in x)

another point : (1,7)

Step-by-step explanation:

Answer: In summary, all integers can be classified as either positive, negative, or zero.

Step-by-step explanation:

There are three types of integers: positive integers, negative integers, and zero.

Positive integers: Positive integers are numbers greater than zero, such as 1, 2, 3, 4, and so on.

Negative integers: Negative integers are numbers less than zero, such as -1, -2, -3, -4, and so on.

Zero: Zero is an integer that is neither positive nor negative. It is the only integer that is neither positive nor negative, and it is often referred to as the "origin" on a number line.

In summary, all integers can be classified as either positive, negative, or zero.

Answer: The three types of integers are Zero (Neutral Integers), Negative Integers, and Positive Integers.

Step-by-step explanation:

Negative Integers are the ones that has a value less than zero, examples of these are -7, -8, -9.

Positive integers, on the other hand. Are the ones that has a value more than zero, examples of these are 10, 11, 12, 13.

Note: The key difference between Negative Integers and Positive Integers is that a negative integer has a "-" sign, while a positive integer does not.

Zero are the neutral integers which means that it's the integer that's in the middle of the positive and negative integers, it has neither a positive sign or a negative sign.

Another note: Integers do not include fractions or decimals, only whole numbers.

The perimeter first figure that is made of a square and equilateral triangle is 52 cm.

What exactly are squares?

A square is a two-dimensional planar shape with four equal sides and four 90-degree angles. The features of a rectangle are similar to those of a square, but the distinction is that a rectangle has just its opposing sides equal.

A square's most significant qualities are

The diagonal of a square is divided into two isosceles triangles.

Square area=(side)²

Square perimeter=4*side

Now,

For first figure given that

sides of square are 14 cm in length

and length of side of equilateral triangle are=5 cm

but for finding perimeter of the figure only 3 sides of square and 2 sides of triangle are needed.

So, perimeter=3*14+2*5

=42+10

=52 cm

hence,

         The perimeter first figure 52 cm.

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The solutions to the inequality are (-5, -3), (-3, 4), (0, -4), (0, 0), (1, 1), (2, 2)

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

graph of y = 3x - 4

Express properly

y = 3x - 4

From the graph, we have the following ordered pairs on the shaded region

(-5, -3), (-3, 4), (0, -4), (0, 0), (1, 1), (2, 2)

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The Morse Fall Scale (MFS) is a standardized tool used to assess a patient's risk of falling. It is used by healthcare professionals in a variety of clinical settings, including hospitals, long-term care facilities, and home care.

The MFS was first developed in 1987 by Dr. Morse and her colleagues as a way to identify patients at high risk for falls and to implement fall prevention measures. The MFS is a quick and simple tool that assesses six different risk factors for falls. These risk factors include history of falling, secondary diagnosis, ambulatory aids, intravenous therapy, gait, and mental status. The MFS assigns points to each risk factor based on the severity of the risk, with a maximum score of 125. Patients who score higher on the MFS are considered to be at higher risk for falls and require more intensive fall prevention interventions. The MFS is useful for healthcare professionals in identifying patients at risk for falls and in developing an individualized fall prevention plan. The MFS is also useful in measuring the effectiveness of fall prevention interventions by allowing healthcare professionals to track a patient's progress over time. However, it is important to note that the MFS is only one tool in a comprehensive fall prevention program and should not be used in isolation.

In summary, the Morse Fall Scale is a standardized tool used to assess a patient's risk of falling. It is a simple and quick tool that assesses six different risk factors and assigns points based on the severity of the risk. The MFS is useful in identifying patients at risk for falls and in developing an individualized fall prevention plan.

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The boolean expression that is true if the value of x is equal to zero is:

x == 0

Let's us first learn about Boolean expression.

A boolean expression is an expression that evaluates to either true or false. It can be created using comparison operators, such as == (equal to), != (not equal to), < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to). These operators compare two values and return a boolean result.

In this question, the double equal sign (==) is the comparison operator for equality in many programming languages, and it returns true if the values on both sides are equal, and false otherwise.

So in this case, the expression "x == 0" would return true if x is equal to zero, and false otherwise.

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Answer:

Step-by-step explanation:

The sum of the interior angles in a polygon can be calculated using the following formula:

(n - 2) * 180 degrees

where n is the number of sides in the polygon.

To understand why this formula works, let's consider a single interior angle in the polygon. Each interior angle is split into two equal angles that form a straight line. The sum of these two angles is 180 degrees. Now, if we look at all the interior angles in the polygon, we can see that they are divided into (n - 2) pairs of angles that form straight lines. This means that the sum of all the interior angles in the polygon is (n - 2) * 180 degrees.

For a hexagon, which has 6 sides, we can plug in n = 6:

(6 - 2) * 180 = 4 * 180 = 720 degrees

So, the sum of the interior angles in a hexagon is 720 degrees.

Answer:exp(1)

Step-by-step explanation:

Answer:

40m deep = 500 kPa.

+10m deep = +100 kPa

50m deep = 600 kPa

60m deep = 700 kPa

( It never stops ! )

Explantion:

The depth affects the entire water pressure, not the other way around, and thus the depth is a independant variable and the water pressure is most likely a dependant variable.

Fact:

100 kPa every 10 meters, or 10 kPa per meter.

0m deep = 100 kPa. Add 10 kPa for every meter. ( and so on )

kPa = 100 + (10x the depth in meters)

Using the variables given, p = 10d + 100.

Answer:

Step-by-step explanation:

The change in temperature over the three hours is -12 - 0 = -12 degrees. To find the change in temperature per hour, divide the total change by the number of hours:

-12 / 3 = -4 degrees per hour

So, the change in temperature per hour is -4 degrees. The answer is -4.

Answer:

it's x,-6y is ur answer If I'm correct

Step-by-step explanation:

I want to say Marisella. Here's my argument.

5 seats in the front row, so 5/20. Before the first person enters, 5 seats are open making it 5/20.

Once the first person sits.. now there are 4 spots in the front and only 19 total seats left, making it 4/19

The largest angle for which it would be appropriate to use the small angle approximation for cosine is 15 degrees

We know that basic trigonometric identities are the primary trigonometric ratios of sine, cosine, and tangent that are defined in a right triangle but at the same time these ratios have numerous applications, but their most important application is finding unknown sides and angles in a right triangle.

Small Angle approximation can be said to be the approximation that can be used to find a more simplified formula for each of the three primary ratios. This process is called a small-angle approximation or applying the small-angle approximation theorem.

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