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This is College Algebra.

Note that if Triangle PQR is similar to Triangle XYZ, and  If PQ = n + 2, QR = n - 2, and XY = n²- 4, then the value of YZ, in terms of n is: (n-2)²

Where triangle PQR is similar to triangle XYZ, then;

PQ/QR =XY/YZ

Given

PQ = n + 2,

QR = n - 2 and

XY=n² - 4,

Substitute

n+2/n-2 = n²-4/YZ

n+2/n-2 = (n+2)(n-2)/YZ

1/n-2 = n-2/YZ

Cross multiply

YZ = (n-2)(n-2)

YZ = (n-2)²

Hence the value of YZ in terms of n is (n-2)²

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Answer: 49

Step-by-step explanation:

78 subtracted by 29 equals 49

Answer:

Step-by-step explanation:

78-29

49

Jerry scored 49 points

The equation of the line that passes through (6,-3) and is parallel to the line y = -2/3 x + 5  is y = - 2 / 3 x + 1.

The equation of a line can be represented in slope-intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through (6,-3)  and is parallel to y = -2/3 x + 5.

Parallel lines have the same slopes.

Therefore, the slope of the line is - 2 / 3.

Hence, let's find the y-intercept of the line using (6, -3).

Therefore,

y = - 2 / 3 x + b

-3 = - 2 / 3 (6) + b

-3 = -12 / 3 + b

b = -3 + 4

b = 1

Therefore, the equation of the line is y = - 2 / 3 x + 1.

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There are two solutions to the given equation 3x + 4y = 12.

Finding two solutions for the equation 3x + 4y = 12

Putting the value of x = 0 in equation 3x + 4y = 12

⇒3(0) + 4y = 12

⇒ 4y = 12

⇒y = 3

Thus, (0, 3) is a solution to the equation 3x + 4y = 12

Putting the value of y = 0 in the equation 3x + 4y = 12

Thus,

⇒3x + 4(0) = 12

⇒3x = 12

⇒x = 4

Thus, (4, 0) is a solution to equation 3x + 4y = 12

Therefore, (0, 3) and (4, 0) are two solutions to the equation 3x + 4y = 12.

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The intensity of earthquakes is measured on the Richter scale. It is a device which compares earthquakes.

Earthquake strength is measured using instruments such as the Richter scale. The Richter scale was invented in the 1930s to help us understand the magnitude and intensity of earthquakes measured by seismographs. Ground surveillance equipment. Standard scale. This is a logarithmic scale measuring a factor of 10. It is measured using information collected by seismographs. It has a base 10 logarithmic scale.

Mathematically, If M is magnitude and I is intensity of earthquake then formula,

M = log(I/Iₛ)

where, Iₛ --> standard intensity

The strength of an earthquake is measured or estimated by two things: amplitude and energy..

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Complete question:

How is the intensity of an earthquake measured ?

A limit in mathematics is a point at which a function approaches the output for the specified input values.

The idea of the limit of a geometric net expands the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals.

Limit is said to be exits when f(x) = [tex]\lim_{h \to 0\0} f(h-x) = \lim_{h \to0 \0} f(h+x)[/tex]

It means that when f(x) = L.H.L = R.H.L

LHL means left hand limit and RHL means right hand limit.

Some Property of limits are as follows

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The formula for finding the base of an isosceles triangle is Base = 2 x (Area) / (Height)

An isosceles triangle is a particular kind of triangle in which the lengths of the two sides are equal. This indicates that the two base angles' lengths are similar (congruent means that they are of the same measure). The third side is referred to as the base, and its opposite angle is referred to as the vertex angle. The legs are the two sides that are of equal length.

The formula for finding the base of an isosceles triangle is - Base = 2 * (Area) / (Height). Where the Area is the total area of the triangle, and "Height" is the height of the triangle as measured from the base to the apex (or the point opposite the base).

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Answer:

5 days to make a house for both of them

Answer: 6/5 days

Step-by-step explanation:

If a worker can make a house in 2days, it can make 1/2 of the house in 1 day.

Similarly, the other worker can make 1/3 of the house in 1 day.

So, in 1 day, together, they will make 1/2 + 1/3 = 5/6 of the house.

So, it will take them 6/5 days to complete the house together.

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Answer:

-5x + 13

Step-by-step explanation:

Difference = subtraction

[tex](-2x+9) - (3x-4)\\-2x - 3x + 9 + 4\\-5x + 13[/tex]

Answer: 12 attendees can attend the corporate team-building event, with a budget of $48.

How to calculate event cost?

step1:

First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4

11÷11=1

So for every 1 attendee it is $4.

Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12

And whatever you do to one number you have to do for the other.

Step2:

so  $4*12= $48

So for every 12 attendees it costs $48.

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12 attendees can attend the corporate team-building event, with a budget of $48.

step1:

First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4

11÷11=1

So for every 1 attendee it is $4.

Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12

And whatever you do to one number you have to do for the other.

Step2:

so  $4*12= $48

So for every 12 attendees it costs $48.

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According to the Science and Technology Desk Reference, a US fuel gallon weighs 6.1 pounds. The weight of gasoline may be slightly influenced by the quality of the fuel.

This year, high demand for crude oil and limited supply drove up gas prices. There are other international forces at play even though the Federal Reserve has increased interest rates five times so far in 2022 and plans to do so again soon to push prices down.

|0.1 | 11.8|\s| 1 | 118|\s|10 | 1180|

When you can travel 118 miles on 1 gallon, that is equivalent to a ratio of 1:18.

Just solve for the remaining ratios, 0.1: 11.8; 10: 1180.

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The complete question is

The table shows the distance a small motor scooter can travel using one gallon of gasoline. complete the table to find the number of miles the scooter can travel for other amounts of gasoline.

| Gallons | Miles |

| 0.1 | *Ans* |

| 1 | 118 |

| 10 | *Ans* |

The inequality  |x+9|<7 can be written as -16<x<-2.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

we have the inequality:|x+9|<7

By Definition of Absolute Value.

-(x+9)<7 and x+9<7

-x-9<7

-x<16

x>-16..(1)

and

x+9<7

x<-2...(2)

-16<x<-2

Hence, the inequality  |x+9|<7 can be written as -16<x<-2.

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Answer:

The expression (√2 – √3) (√2 – √3) simplifies to 2 - 2√6 + 3, which can be further simplified to 3 - 2√6.

Answer:

25% sugar syrup means in a mixture of 100g sugar syrup, sugar should be 25g

so, when sugar is 25g , mixture is 100g

when sugar is 1g, mixture is 100/25 = 4g

when sugar is 15g, mixture is 15*4 =60g

So, amount of water to be added=60-15= 45g

Step-by-step explanation:

La fórmula para multiplicar dos números decimales es la misma que para multiplicar números enteros.

Primero, muestra los números en forma de dígitos y coloca un punto decimal entre los números. Luego, multiplica los dígitos del número de la izquierda a la derecha, como si fueran números enteros. Después, añade los resultados, teniendo en cuenta la regla de los puntos decimales. Por último, contar el número de dígitos que hay después del punto decimal, y coloca el punto decimal en el resultado.

En este caso, se multiplican los números 9.7 y 0.08. Primero, se muestran los números en forma de dígitos: 9.7 y 0.08. Luego, se multiplican los dígitos de la izquierda a la derecha, como si

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Answer: $11.25

Hope this helps :)

Step-by-step explanation:

45 * .25 = 11.25

25 out of 100

When using percentages, remember that they are only a number out of 100. This makes it easy to find its decimal. When finding the discount price of a number, multiply it by the percentage as a decimal.

The standard form equation of the  circle which has an area  A=36π and a center of (-4,0),  (x+4)² + y² = 36. So Option A is correct

In mathematics, the circle is a two dimensional rounded figure which has no corner edges.

Area = [tex]\pi r^{2}[/tex]

Perimeter = [tex]2\pi r^{}[/tex]

Standard form = (x - a)² + (y - b)² = r²

Given that,

A circle has an area of A=36π

And a center of (-4,0)

The area of a circle for radius r is,

Area =  [tex]\pi r^{2}[/tex]

[tex]\pi r^{2}[/tex]   = 36π

[tex]r^{2}[/tex]     = 36

r   = 6

here,

a  = -4

b  = 0

Now,

Standard equation,

(x -(-4))² + (y - 0)² = 6²

(x+4)² + y² = 36

Hence, The standard form is  (x+4)² + y² = 36

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A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. It is formed by combining two congruent trapezoids, which results in a quadrilateral with two pairs of opposite sides that are parallel and equal in length. All four angles of the parallelogram are also equal.

1. Draw the two congruent trapezoids.

2. Line up the two trapezoids, making sure that the corresponding sides are parallel and the same length.

3. Connect the two trapezoids with lines to form the parallelogram.

4. Check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length.

A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. To make a parallelogram, two congruent trapezoids are combined. This can be done by lining up the two trapezoids, making sure that the corresponding sides are parallel and the same length. Then, the two trapezoids can be connected with lines to form the parallelogram. It is important to check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length. If these criteria are met, then the shape is a parallelogram.

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Answer:

13

Step-by-step explanation:

Since a = 3,  10 x 3 = 30

5c = 5 x 2 = 10

2c = 2 x 2

Now we have 30 - 3 - 10 - 4

30 - 3 = 27 - 10 = 17 - 4 = 13

13 is our total

Answer:

[tex] \sf \: 10a - 3 - 5c - 2c = 13[/tex]

Step-by-step explanation:

Given expression,

→ 10a - 3 - 5c - 2c

Now we have to use,

→ a = 3

→ c = 2

Let's solve the expression,

→ 10a - 3 - 5c - 2c

→ 10(3) - 3 - 5(2) - 2(2)

→ 30 - 3 - 10 - 4

→ 30 - 3 - 14

→ 30 - 17

→ 13 => final value

Therefore, the answer is 13.

The graph of a linear equation is always a straight line.

Linear equations in two variables, for example, are known when they have two variables in them. A, B, and C are constants in the generic linear equation in two variables, which is written as axe + by + c = 0.

Simply assume a set of values for x and compute the corresponding set of values for y to discover the graph of axe + by + c = 0. We now possess a set of coordinates (x, y). Now connect the spots on the graph. A straight line will be generated on the graph.

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Answer:

x = 2, y = 7

Step-by-step explanation:

y - 3x = 1    |*2

2y - x = 12

2y - 6x = 2

2y - x = 12   | - Ist equation

2y-x-2y+6x = 12-2

5x = 10

x = 2

Insert x to first equation:

y - 3*2 = 1

y = 7

Answer:

B = 162

Step-by-step explanation:

B/9 = 18

(9) B/9 = 18(9)

B = 162

Answer:

b = 162

Step-by-step explanation:

Given statement,

→ b divided by 9 = 18

Forming the equation,

→ b/9 = 18

Now the value of b will be,

→ b/9 = 18

→ b = 18 × 9

→ [ b = 162 ]

Hence, value of b is 162.

We can solve for log bases without a calculator by using  logarithmic formulas and identities.

A logarithm is basically a mathematical operation which is able to determine how many times a particular number, which is known as the base, will be multiplied by itself to reach the other number. We can solve for log bases even without a calculator.

For example, we need to find the value of log 128 to the base 8, which we can write as log₈28.

We know that,

[tex]log_{a} b^{x} = 1/b(log_{a}x)[/tex]

[tex]log_{a} x^{b} = b(log_{a}x)[/tex]

Using this property of logs,

log₈128 = log₂³2⁷

7/3 (log₂2)

Another property is,

[tex]log_{a}a = 1[/tex]

Using this property of logs,

⇒ 7/3(log₂2) = 7/3×1

=7/3

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

x= 48.19° .

An angle is a shape in Euclidean geometry comprised of two rays, known as the sides of the loop, that diverge at the apex of both the angle and the vertex, which is situated in the middle. It is possible for two rays to combine to generate an angle inside the plane they are located in. An angle also comes from the collision of two planes. They are known as dihedral angles. There are many options for arranging two line ray with end points in two dimensions to form an angle.

Here,

Given : A right angle triangle,

Where we have to find the value of x angle

thus,

Using trigonometric ratios:

=> Cos x = 18/27

=> Cos x = 6/9

=> Cos x = 2/3

=> x = Cos⁻¹ (2/3)

=> x = 48.19°

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

x= 48.19° .

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The rate at which the temperature of the compound rose was 0.75 degrees per hour.

Temperature is a measure of how hot or cold an object or environment is. It is measured in degrees on the Celsius, Fahrenheit, or Kelvin scales. Different objects and environments have different temperatures. For example, the temperature of the human body is usually around 37°C (98.6°F). The temperature of boiling water is 100°C (212°F). The temperature of a winter day can be much colder than the temperature of a summer day.

To solve this problem, divide 1 1/4 degrees by 1 2/3 hours, which equals 0.75 degrees per hour. Therefore, the rate at which the temperature of the compound rose was 0.75 degrees per hour.

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the area of the triangle RMC will be 116.44 unit²

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. There are different types of triangles such as isosceles, right-angled, equilateral etc.

The sum of all angles of triangle = 180

In Triangle RMC, RM = 19. MC = 27. and CMR = 27°.

Area is = A*B*sin(M)/2

= 19*27*sin(27)/2

=116.44856

Hence the area of the triangle RMC will be 116.44 unit²

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Class range of 9 can be calculated, this can be shown through below illustrations :Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.

To know the maximum and minimum values in the data set, which are 90 and 45, respectively.

Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.

Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.

The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.

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Answer:

Step-by-step explanation:

Class range of 9 can be calculated, this can be shown through below illustrations:Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.

To know the maximum and minimum values in the data set, which are 90 and 45, respectively.

Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.

Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.

The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.

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Answer:

y = 40x

Step-by-step explanation:

Answer:

Step-by-step explanation:

z°=180°-79°=91°

(3x+13)°=79°, so x=22°