Write an equation in point-slope form of the line that passes through (-3, -2) and (2, -1).

The graph of the trigonometry function g(x) = 4 cos πx is plotted and attached,

The graph is made by picking some x values say 0, 0.5, 1, 1.5, 2 .... and solve for the output y.

For x = 0, y = 4 cos π * 0 = 4

For x = 0.5, y = 4 cos π * 0.5 = 0

For x = 1, y = 4 cos π * 1 = -4

For x = 1.5, y = 4 cos π * 1.5 = 0

For x = 2, y = 4 cos π * 2 = 4

Table of value

x     y

0     4

0.5  0

1      -4

1.5    0

2      4

The graph is plotted by tracing each x and y value and joining the intercepts to form a curve

It can be deduced that the amplitude of the graph is 4 and it completes a revolution in 2 units

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The height of the roof is 21 inches.

Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. In other terms, an isosceles triangle is a triangle with two congurrent sides.  

Here we have,

Tony is building a doghouse, and the front view of the roof is an isosceles triangle.  

As we consider, the front view as an isosceles triangle

Side of the triangle = 29 inches

Base of the triangle = 40 inches

When we draw a line along the height of the triangle, it will divide the base equally and forms two right-angle triangles.

Let 'x' be the height of the triangle  

If we apply the Pythagorean theorem,

=> 29² = 20² + x²  

=> 841 = 400 + x²

=> x² = 441

=> x² = (21)²    

Hight of the triangle = 21

Therefore,

The height of the roof is 21 inches.

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Find 10% of 50 by dividing 50 by 10. Then multiply the result by 4 is how to determine 40% of 50 which is denoted as option A.

This is referred to as the process of splitting a number or an amount into equal parts.

40% of 50 = 40/100 × 50 = 2000/100 = 20

Another method is finding the 10% of 50 by dividing 50 by 10 which will be 50/10 = 5. Then multiplying the result by 4 to get 20 which is why option A was chosen as the correct choice.

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The number of years after which the population of North Dakota equals the population of South Dakota is 150.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

North Dakota:

Population in 2012 = 0.3 million

Growth rate per year = 0.017 million

The population after x years.

= 0.3 + 0.017x

South Dakota:

Population in 2012 = 0.9 million

Growth rate per year = 0.013 million

The population after x years.

= 0.9 + 0.013x

Now,

The number of years after which the population is equal.

0.3 + 0.017x = 0.9 + 0.013x

Solve for x.

0.017x - 0.013x = 0.9 - 0.3

0.004x = 0.6

x = 0.6/0.004

x = 150

Thus,

After 150 years, the population will be the same.

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The difference between two natural numbers is greater than 6 and less than 11. The greater of the two numbers is 14. There are 5 possible values for the unknown number.

These integers that start at 1 and go all the way up to infinity are known as natural numbers or counting numbers. You can use numbers to count things, represent or exchange money, determine the temperature, tell the time, and many other things. Since they are used to count things, these numbers are known as "natural numbers." It may be 5 glasses, 6 books, 1 bottle, and so on while counting the objects. Thus, counting numbers is a different term for natural numbers. Natural numbers are a group of all whole integers other than 0. These numbers are crucial to daily interactions and communication.

Let's call the unknown number x. We know that:

x - 14 > 6 and x - 14 < 11

x > 20 and x < 25

Now we can see that there are 5 possible values for x: 21, 22, 23, 24 and 25.

Therefore, there are 5 possible values for the unknown number.

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Answer:

Step-by-step explanation: Inverse property of addition

Answer: D, 128 boxes

Step-by-step explanation:

There are 8 cutting machines that each cut 12 boxes every 3/4 minutes. 8x12=96. Divide that by 3 which is 32 boxes a 1/4 minute. Then multiply that by 4 to get a whole minute which is 128 boxes.

The image of point Q under a translation by 4 units to the right and 1 unit up is Q'(5, 5).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A point Q with coordinates (1, 4).

Now, The translation of point Q  4 units to the right and 1 unit up would be,

Q'(1 + 4, 4 + 1).

= Q'(5, 5).

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Answer:None

Step-by-step explanation:

Answer: 1.5 dollars

Step-by-step explanation: 24 times 1.5 is 36

Answer: 3/2 or 1.5 dollars per cupcake

Step-by-step explanation:

Use ratios:

$36 : 24 cupcakes

Divide by 24 on each side:

$36/24 : 1 cupcake

36/24 = 3/2 or 1.5 dollars per cupcake

The relative frequency for Point 3 will be 28.57 and cumulative frequency will be 28.

What is relative and cumulative frequencies?

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

To calculate the relative frequency two things must be known:

Number of total events/trials

Frequency count for a category/subgroup.

Relative frequency = subgroup frequency/ Total frequency

Cumulative frequency-

In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on. Frequencies that are obtained this way are known as cumulative frequency (c.f.).  

Now,

For Relative frequency

subgroup frequency for point 3=8

Total frequency = 28

Therefore,

Relative frequency=8/28

=2/7

=0.2857

Relative frequency=28.57 (upto two decimal points)

For cumulative frequency,

add all the subgroup frequency and that will be 28.

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Answer:

We can use algebra to solve this problem. Let's call the unknown number x.

We are given that 10% of x is 40, so we can write that as:

x * 10% = 40

x * 0.1 = 40

We are also given that 55% of x is 220, so we can write that as:

x * 55% = 220

x * 0.55 = 220

We can now use these two equations to solve for x.

From the first equation, x = 40 / 0.1 = 400

We can substitute that value of x into the second equation to check if it's true.

400 * 0.55 = 220

Now, we have the value of x, we can use it to find 65% of that number.

x * 65% = x * 0.65 = 400 * 0.65 = 260

So, 65% of that number is 260

Answer:

260

Explanation:

Formulate: 220+40

----------------------/\  You should know the answer by now

Answer: only y=3x+4 is a function

Step-by-step explanation:

vertical line test. basically a function has to have one output (y) for every input (x)

Answer:

$7.50

Step-by-step explanation:

The price of a hot dog today is $0.75 * (1 + 220%) = $2.38.

In another 45 years, the price will be $2.38 * (1 + 220%) = $7.50.

The measure of angle FAB is 13x6°-3° = 78°-3°=75°.

An angle is a figure formed when two straight lines, or rays, intersect at a single point. There are many different types of angles, including acute angles, obtuse angles, right angles, reflex angles, and straight angles. Angles are measured in degrees, with a full rotation being 360 degrees.

We know outer angle of a triangle is equal to the sum of the two opposite interior angles
So, from triangle ABC,
13x - 3 = 3x + 2 + 55°
So, 13x - 3x = 57° + 3°
So, 10x = 60°
So, x = 60°/10 = 6°
So, Angle FAB = 13 x 6° - 3° = 78° - 3° = 75°

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Answer:

In real world context, h(10) would represent the height of the balloon above the ground. To find the value of h(10), substitute t with 10 in the equation

height = 210-15t

height = 210-15(10)

height = 210-150

height = 60

The quadratic equation represented by the table is

y = x² + 6x - 9.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is a quadratic function in tabular form as -

(x)   :   1     2   3   4

f(x)  :   -2  -5  -6  -5

The general form of a quadratic function is -

y = ax² + bx + c

For the point (1, - 2), we can write -

- 2 = a + b + c

For the point (2, - 5), we can write -

- 5 = 4a + 2b + c

For the point (3, - 6), we can write -

- 6 = 9a + 3b + c

Now, let's assume that -

a = x

b = y

c = z

Now, we can write the equations as -

- 2 = x + y + z             ... (1)

- 5 = 4x + 2y + z          ... (2)

- 6 = 9x + 3y + z           ... (3)

Subtracting Eq(1) from Eq(2) -

4x + 2y + z - (x + y + z) = - 5 + 2

4x + 2y + z - x - y - z = - 3

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

Subtracting Eq(2) from Eq(3) -

9x + 3y + z - (4x + 2y + z) = - 6 + 5

5x - y = - 1                          ... (5)

From the graph, we get -

x = 1

y = 6

Then, we can write {z} as -

- 2 = x + y + z

z = - 2 - x - y

z = - 2 - 1 - 6

z = - 9

So, we get -

x = 1

y = 6

z = - 9

Now, we can write -

a = x = 1

b = y = 6

c = z = - 9

So, we will get the quadratic equation as -

y = x² + 6x - 9

Therefore, the quadratic equation represented by the table is

y = x² + 6x - 9.

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Answer:

A = 811.84 centimeters squared

Step-by-step explanation:

I cut the shape in half (two trapezoids)

I did the area for one trapezoid:

A = 22.3+46.5/2 (11.8)

A = 68.8/2 (11.8)

A = 34.4 (11.8)

A = 405.92 centimeters squared

Since this is only half of the shape, I multiplied the area by 2.

A = 405.92 (2)

A = 811.84 centimeters squared

The expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

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Answer:

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Step-by-step explanation:

On solving the provided question, we can say that form an equation = area of the figure = x = 1/2*9*9 + 6*18 = 40.5 + 48 = 88.5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

to find the area

we have to form an equation =

area of the figure = x = 1/2*9*9 + 6*18 = 40.5 + 48 = 88.5

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The simplest form of monomial rational expressions are

17. 4x,         18. xy²,        19. 2xy      

20. 3xy,      21. 3x²y⁶,    22. 13x⁶ y

23. 8x⁶y²,   24. 19x⁹y⁵,   25. 5y

26. -5x¹¹y⁴,  27. -8x⁵y³.

A polynomial with only one term is called a monomial. An algebraic expression known as a "monomial" has a single term but can also include several variables and a higher degree.

Given Monomial Rational expressions can be solved as follows

17.  [tex]\frac{4x^{2} y^{3} }{xy^{2} } = \frac{4 \times x \times x \times y \times y \times}{x \times y\times y} = 4\times x[/tex]  

=>  [tex]\frac{4x^{2} y^{3} }{xy^{2} } = 4x[/tex]  

18.  [tex]\frac{2x^{4}y^{3} }{2x^{3} y } = \frac{2 x^{3} \times x\times y^{2} \times y }{2x^{3} y}[/tex]  

=>  [tex]\frac{2x^{4}y^{3} }{2x^{3} y } = x y^{2}[/tex]    

19.  [tex]\frac{8x^{2} y^{2} }{4xy} = \frac{2xy (4xy)}{4xy}[/tex]  

=>  [tex]\frac{8x^{2} y^{2} }{4xy} = 2xy[/tex]  

20.  [tex]\frac{6x^{3} y^{4} }{2x^{2} y^{3} } = \frac{3xy (2x^{2} y^{3} )}{2x^{2} y^{3} }[/tex]  

=>  [tex]\frac{6x^{3} y^{4} }{2x^{2} y^{3} } = 3xy[/tex]  

21.  [tex]\frac{12x^{6} y^{8} }{4x^{4} y^{2} } = \frac{3x^{2} y^{6} (4x^{4} y^{2})} {4x^{4} y^{2} }[/tex]

=> [tex]\frac{12x^{6} y^{8} }{4x^{4} y^{2} } = 3x^{2} y^{6}[/tex]  

22. [tex]\frac{26x^{9} y^{5} }{2x^{3} y^{4} } = \frac{13x^{6} y (2x^{3} y^{4})}{2x^{3} y^{4}}[/tex]  

=>  [tex]\frac{26x^{9} y^{5} }{2x^{3} y^{4} } = 13x^{6} y[/tex]  

23.  [tex]\frac{80x^{12}y^{9} }{10 x^{6}y^{7} } = \frac{8x^{6}y^{2}(10 x^{6}y^{7})}{10 x^{6}y^{7} }[/tex]  

=>  [tex]\frac{80x^{12}y^{9} }{10 x^{6}y^{7} } = 8x^{6}y^{2}[/tex]  

24.  [tex]\frac{95x^{18}y^{7} }{5x^{9}y^{2} } = \frac{19x^{9}y^{5}(5x^{9}y^{2}) }{5x^{9}y^{2} }[/tex]  

=>  [tex]\frac{95x^{18}y^{7} }{5x^{9}y^{2} } = 19x^{9}y^{5}[/tex]    

25.  [tex]\frac{200x^{3}y^{8} }{40x^{3}y^{7} } = \frac{5y (40x^{3}y^{7}) }{40x^{3}y^{7}}[/tex]  

=>   [tex]\frac{200x^{3}y^{8} }{40x^{3}y^{7} } = 5y[/tex]  

26.  [tex]\frac{- 15x^{17} y^{13} }{3x^{6} y^{9} } = \frac{-5x^{11}y^{4} (3x^{6} y^{9} )}{3x^{6} y^{9} }[/tex]  

=>  [tex]\frac{- 15x^{17} y^{13} }{3x^{6} y^{9} } = -5x^{11}y^{4}[/tex]  

27.  [tex]\frac{-64x^{8}y^{10} }{8x^{3}y^{7} } = \frac{ -8x^{5}y^{3} (8x^{3}y^{7} )}{8x^{3}y^{7} }[/tex]  

=> [tex]\frac{-64x^{8}y^{10} }{8x^{3}y^{7} } = -8x^{5}y^{3}[/tex]  

Therefore,

The simplest form of monomial rational expressions are

17. 4x,         18. xy²,        19. 2xy      

20. 3xy,      21. 3x²y⁶,    22. 13x⁶ y

23. 8x⁶y²,   24. 19x⁹y⁵,   25. 5y

26. -5x¹¹y⁴,  27. -8x⁵y³.

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The respective exterior angles are 155°, 55°, 150°

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: The angles of the triangle as 30°, 25°, and 125°

We know that sum of an exterior angle is the sum of the two non-adjacent angles

Thus we have ∠DBC= 30+125=155°

∠ECA=30+25=55°

∠FAD=25+125=150°

Hence, The respective exterior angles are 155°, 55°, 150°

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On solving the provided question, we can say that the equation is, y = -48.3 ÷ (-7)=​48.3/7 = 6.9

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

the equation is, y = -48.3 ÷ (-7)=​48.3/7 = 6.9

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The number of terms in the sequence is 10.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

First term = -10

Last term = 26

Sum of all the terms = 80

We need to find how many terms are in the sequence.

Now,

Sum of n terms of an arithmetic sequence = n/2 x (First term + Last term)

So,

80 = (1/2)n (-10 + 26)

2 x 80 = n x 16

n = 10

Thus,

The value of n is 10.

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Answer:

[tex]\frac{281}{6}[/tex] or 46 [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

First lets find out the parentheses. ( The first thing we always do ):

89+9=98 ( Lets keep this aside )

Now lets find out what is : [tex]12^{2}[/tex] =

12 x 12 = 144.

Now lets add 144+98 = 242

Now subtract 78 from 242 =

164

Now lets add 398 =

562.

Now divide it by 12.

[tex]\frac{281}{6}[/tex] or 46 [tex]\frac{5}{6}[/tex]

The relationship between x and y in the equation y = x + 6. the relationship is Linear because the value of y is can be represented in a straight line

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Given the equation:

y = x + 6

This is a linear equation.

The slope (rate of change) is 1 and the initial value (y intercept) is 6

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The common difference will be equal to 3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression. A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Given that the data for the arithmetic sequence is a₁= -10, an = 26, Sn = 80, and the total number is n = 13.

The common difference will be calculated as,

an = a₁ + d ( n - 1 )

26 = -10 + d ( 13 - 1 )

d = 36 / 12

d = 3

Hence, for the arithmetic progression, the common difference is 3.

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A thermometer's accurate reading of the air's average temperature for a specific time frame, typically a day, a month, or a year.

The temperature for a month as a whole is known as the mean monthly temperature. The thermometer used to record it is well exposed. The average daily temperature for the month is added up and divided by the total number of days in the month to determine the mean monthly temperature.

By adding up the daily mean temperatures for each day of the month, multiplying that total by the number of days in the month, and then subtracting that result, you can find the mean monthly temperature. Add up the 31 mean daily temperatures for January, for instance, and divide the result by 31.

The average air temperature over a specific time period, typically a day, a month, or a year, as measured by an accurately exposed thermometer. In climatological tables, the average temperature is typically determined for each.

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