A side of the triangle below has been extended to form an exterior angle of 156°. Find the value of x.

The length of the PM is 6 if ABCD is congruent to MNOP.

When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.

More specifically, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions including translation, rotation, and reflection. This indicates that either object may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. If we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are then congruent. I'm allowed to turn the paper over.

Here  both the given figures are congruent figures. So, their shape and size must be equal.

Therefore from the two figures, PM=DA

So, PM=6

Therefore, the length of the PM is 6 if ABCD is congruent to MNOP.

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Answer:

x=29 and y=53

Step-by-step explanation:

let y=3x-34 be the first equation (1) and y=2x-5 be the second equation (2)

Using the elimation method, (1)-(2): 0=x-29

-x=-29

x=29

Substitute x=29 into (2),

y=2(29)-5

y=58-5

y=53

So, x=29 and y=53

[tex]\angle 1=150^{\circ}[/tex] (linear pair)

[tex]\angle 2=30^{\circ}[/tex] (vertical angles)

[tex]\angle 4=150^{\circ}[/tex] (linear pair)

[tex]\angle 5=83^{\circ}[/tex] (linear pair)

[tex]\angle 6=97^{\circ}[/tex] (vertical angles)

[tex]\angle 8=83^{\circ}[/tex] (linear pair)

To find the percent increase, we need to calculate the difference between the new tuition and fees and the old tuition and fees, and then divide this difference by the old tuition and fees and multiply by 100%.

The difference between the new tuition and fees of $14,402 and the old tuition and fees of $1411 is $14,402 - $1411 = $12,991.

The percent increase is: ($12,991/$1411) * 100% = 9.2 * 100% = 920%

Therefore, the percent increase in tuition and fees between the fall of 1996 and the fall of 2018 was 920%, rounded to the nearest tenth percent.

The snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t

What is a constant rate of change?

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Constant rate is also called uniform rate which involves something traveling at a fixed and steady pace or else moving at some average speed.

The snow started melting at a rate of 0.5 inches per hour and it is known that 3 hours after the storm ended, the depth of snow was down to 11 inches.

Snow melted in 3 hours = 0.5 * 3 = 1.5 inches

Thus;

The Initial depth of snow = 11 + 1.5 inches = 12.5 inches.

Now, depth of snow on Gabriella's lawn = Initial depth - 0.5(Number of hours)

Let S(t) be the depth of snow on  Gabriella's lawn, in inches, t hours after the snow stopped falling.

Hence, the snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t

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The remainder of 4 when f(x) is divided by x - 5 means that f(5) = 4

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

The function is given as

Polynomial = f(x)

Remainder = 4

The function is represented as

z(x)

This means that

x = 5 in f(x)

So, we add -5 to both sides of the equation

This gives

x - 5 = 0

Also, we have

A remainder of 4 when divided by x-5

So, when the equation in interpreted, it means

The remainder when f(x) is divided by x - 5 is  4

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The inequality for the value of y can be given as -1/8 < -2/3y, where y < 3/16.

Inequality shows relation between two expression which are not equal to each others.

Let the required number is y.

To find the inequality that represents the -1/8 is less than the product of -2/3 and number y.

The product of -2/3 and y = -2/3y

The inequality for the y can be written as,

-1/8 < -2/3y

Solve for the value of y,

1/8 > 2/3 y

3/16 > y

Or y < 3 / 16

The required inequality is -1/8 < -2/3y, where y < 3/16.

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Answer: y < 2

Step-by-step explanation:

The error occur from line 2 to line 3(optionB)

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation forms a straight line.

A linear equation can have one or two variables. For example 5 = y+ 3y is an example of linear equation with one variable and y = 5 +3x is an example of linear equation with two variables.

8x-4= 2(4x+1)-6

8x-4= 8x+2-6

8x-4= 8x-4

Therefore the error is made where the parentheses is been solved, 2 is to multiply both 4x and 1.

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Answer:

80 cards would have to sold before your average total cost per card falls to $10

Step-by-step explanation:

To find the number of cards you would have to sell to bring the average total cost per card down to $10, you can use the following formula:

number of cards = setup fee / (average total cost per card - cost per card)

Plugging in the values given in the problem, we get:

number of cards = $320 / ($10 - $6)

Solving this equation gives us:

number of cards = $320 / $4

Dividing 320 by 4 gives us a result of 80, so you would have to sell 80 cards before your average total cost per card falls to $10

Another approach is setting it up as y = mx+b

$10 = (320 + 6x) / x

Where x is the number of cards that you need to sell.

Solving for x, we get:

$10x = 320 + 6x

4x = 320

x = 80

The following are the actions she could take to solve the quadratic equation: 2(x² + 6x + 9) = 18 + 3.

Following is the determination of the quadratic equation's solution;

2x² + 12x - 3 = 0

2x² + 12x = 3

Divide equation by 2.

x² + 6x = 3/2

Add both of the equation's sides after squarely multiplying the x-coefficient by half:

(x + 3)² = 3/2 + 3²

x² + 6x + 9 = 9 + 3/2

2(x² + 6x + 9) = 18 + 3

Thus, in order to calculate the quadratic equation, she could follow these steps: 2(x² + 6x + 9) = 18 + 3.

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By using linear equation, it can be calculated that

New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3

New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Equation of line : x + 3y = -3

Putting y = 1

x + 3 [tex]\times[/tex] 1 = -3

x = -3 - 3

x = -6

Putting y = 2

x + 3 [tex]\times[/tex] 2 = -3

x + 6 = -3

x = -3 - 6

x = -9

New solutions (-6, 1) and (-9, 2)

New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3

New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3

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The equations representing the proportional relationships between two variables:

In this problem we find three cases of tables showing proportional relationships between two variables. Proportional relationships are represented by equations of the form:

y = k · x

Where:

Each table represents a proportional relationship if and only if each pair of variables has one and same proportionality factor. After a quick inspection, we find the following features:

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Answer:

Yes it is

Step-by-step explanation:

The triangle has a value of x=22°.

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles.

Having three sides, a triangle is a form. Each kind of triangle has a unique name. The size of the angles and side lengths determine what kind of triangle it is (corners). Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.

The sum of all the angles in a triangle must be °

120° + (x+16)° + x° = 180°

2x + 136° = 180°

2x = 180° - 136°

2x° = 44°

x = 22°

The triangle has a value of x=22°.

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The value of x in the quadratic equation using mathematical operations is  4±√19

To solve this problem, we have to use some mathematical operations to find the value of x.

In this process, we have to remove the square root and solve for x. This will eventually result to a quadratic equation

In the equation given;

√(2x - 6) = x - 3

Square both sides

(√(2x - 6)² = (x - 3)²

This will eliminate the square root

2x - 6 = (x - 3)²

Open the bracket on the right hand side

2x - 6 = x² - 6x - 9

Collect like terms

x² - 6x - 9 - 2x + 6 = 0

x² - 8x - 3 = 0

Solving for x

x = 4±√19

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The solutions to the x and w variables are x = 2097153 and w = (6)⁻²/⁵

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

1/7log(x - 1) = 3log(2)

3 ln(w + 6) = 5 ln(6)

Solving the equation (1), we have the following equation

1/7log(x - 1) = 3log(2)

Multiply both sides of the equation by 7

So, we have the following representation

log(x - 1) = 21log(2)

Apply the power rule of logarithm

log(x - 1) = log(2)²¹

By comparison, we have

x - 1 = (2)²¹

Evaluate the exponent

x - 1 = 2097152

So, we have

x = 2097153

Solving the equation (2), we have the following equation

3 ln(w + 6) = 5 ln(6)

Multiply both sides of the equation by 1/3

So, we have the following representation

ln(w + 6) = 5/3 ln(6)

Apply the power rule of logarithm

ln(w + 6) = ln(6)³/⁵

By comparison, we have

w + 6 = (6)³/⁵

So, we have

w = (6)⁻²/⁵

Hence, the solutions are x = 2097153 and w = (6)⁻²/⁵

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Answer:

2   (the first choice)

Step-by-step explanation:

This is a matrix of size 3 rows and 5 columns  (3 x 5)

Any element of the matrix can be reference by row and column number

C₃₂  refers to the element in the 3rd row, 2nd column which is 2

Answer:

121.23

Step-by-step explanation:

48.49/0.4 = 121.225

121.225 rounding into nearest hundredth = 121.23

Answer:

inverse proportion

Step-by-step explanation:

2=k240/16

To find the equation of the normal to the given curve at the point (-1,1), you can use the following steps:

Rewrite the given equation in the form "y = mx + b," where m is the slope of the curve and b is the y-intercept.

Find the slope of the curve at the point (-1,1). This can be done by taking the derivative of the equation and evaluating it at x = -1.

The slope of the normal line at the point (-1,1) is the negative reciprocal of the slope of the curve at that point. Calculate this value.

Use the point-slope formula to write the equation of the normal line in the form "y - y1 = m(x - x1)," where (x1, y1) is the point (-1,1) and m is the slope of the normal line.

Substitute the values for x1, y1, and m into the point-slope formula to obtain the final equation of the normal line.

For example, if the given equation is 2x^2 + 2y^2 - 4x + 4y = 12, you can follow these steps:

Rewriting the equation in slope-intercept form, we get: y = -x + 2

Taking the derivative of the equation, we get: y' = -1

The slope of the normal line is the negative reciprocal of the slope of the curve, which is 1/-1 = -1

Using the point-slope formula, we get: y - 1 = -1(x + 1)

Substituting the values into the point-slope formula, we get: y - 1 = -1x - 1

Thus, the equation of the normal line at the point (-1,1) is y - 1 = -1x - 1.

The value of mixed fraction 1(1/5) using fifths is 6/5.

How may a number be written as a mixed number?

As an illustration, we convert 7/3 into a mixed fraction form by using the instructions provided.

[tex]1\frac{1}{5}[/tex]  = [(5 * 1) + 1]/5

= (5 + 1) / 5

= 6/5

Hence, The value of mixed fraction 1(1/5) using fifths is 6/5.

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Answer:

Step-by-step explanation:

B

Answer:

3 ln(abs ln(7x)) +C

Step-by-step explanation:

Do not forget to add the absolute value!

a) The function in vertex form is; y = -16(x - 3.5)² + 198

b) The maximum height if the arrow is; 198 feet

c) The time that it takes the arrow to hit the ground is; 16 seconds

We are given the function as;

y = -16t² + 112t + 2.

where;

y is the height (in feet) of an arrow

t is the time in seconds after it is shot from a bow

This is the equation of a vertical parabola open downward

The vertex is a maximum

The general form of a  quadratic equation in vertex form is;

y = a(x - h)² + k²

where (h, k) is the vertex coordinate

a) y = -16t² + 112t + 2

This is in standard form and using completing the square, we can write in vertex form as;

y = -16(x - 3.5)² + 198

b) The vertex is the point (3.5, 198)

The maximum height of the arrow represents the y-coordinate of the vertex of the function

Thus, the maximum height of the arrow is 198 feet

c) We know that when the arrow hits the ground, the value of y is equal to zero. Thus, at y= 0, we have;

-16(x - 3.5)² + 198 = 0

Rearranging gives;

(x - 3.5)² = (198/16)

(x - 3.5) = ±√(198/16)

(x - 3.5) = ±12.375

x = 12.375 + 3.5

x = 15.875 ≈ 16 seconds which is the time it will take to hit the ground.

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The sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 95% confidence. Assume that s = 13 based on earlier studies is 40.58.

Making use of the given data to determine the sample size.

Sample size (n) =?

The confidence level = 95% or 0.95

Z-score for 95% confidence interval  =1.960

Using this formula

Margin of error = Zα/2 × α/√n

Solving for n

4 =   1.960 × 13/√n

√n = 6.37

n = 40.58

Therefore the sample size is 40.58.

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Answer:

the expression is constant, which means it can be rewritten with a factor of x⁰.

The degree is the largest exponent on the variable.

0

15 green marbles are there among 56 marbles.

A bag contains 56 marbles, so Total marbles =56.

In That, There are Green and red marbles contained in a ratio of 3:4.

Now we have to assume that

Let 3x = the number of green marbles and 4x = the number of red marbles

By using the ratios and the total we can know how many green and red marbles are there in a bag. so the formula is:

ax+bx=t-------(1)

a and b are ratios of given marbles

t is the total number of marbles

x is to find the value

substituting the values in the above equation we get

3x + 4x =35

7x = 35

x = 5

substitute the x value in 3x we get:

Green: 3x = 15

Therefore,15 green marbles are present among 56 marbles

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Answer:

False

A sphere is 3 dimensional.