use an addition or subtraction formula to simplify the equation. cos(θ) cos(2θ) + sin(θ) sin(2θ) = √2/ 2

Using the slope and y - intercept, the linear function that models this problem is y = -33.333x + 68.32

A system of linear equation is a set of at least two linear equations containing the same set of variables. Linear equations use only polynomial coefficients and the operations of addition, subtraction, multiplication and division. The solutions to a linear equation system are the values of the variables which make all the equations true.

To solve this problem, we have to define our variables and set our system of linear equations.

Let;

Using the data given, we can find the slope and y - intercept of a linear function that represents this.

slope (m) = y₂ - y₁ / x₂ - x₁

m = 64.99 - 59.99 / 0.10 - 0.25

m = -33.333

Using the slope in the slope-intercept form of a linear equation

y = mx + c

Taking one point;

59.99 = -33.333(0.25) + c

c = 68.32

The linear equation can be written as;

y = -33.33x + 68.32

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Answer: The relation between the time it will take Rashid to make the trip, t, and the speed at which he slows down, v, can be determined by using the formula:

distance = speed * time

We know that Rashid travels 240 km from Abu Dhabi to Sharjah and that he originally drove at 120 km/h for 2 hours. So, we can write the equation:

240 = 120 * 2

Now, if Rashid slows down by v km/h, then the new speed is (120 - v) km/h and the new time, t, can be determined by substituting the new speed and distance into the equation:

240 = (120 - v) * t

So the relation shows that t = (240 / (120 - v))

This relation shows that the time, t, it will now take Rashid to make the trip is directly proportional to the speed, v, at which he slows down. As Rashid slows down, the time taken to make the trip will increase, and as he speeds up, the time will decrease.

Step-by-step explanation:

Answer: y = 1/4x +1

Step-by-step explanation:

First, we can find the midpoint of the line segment using the average of x and y coordinates of the endpoints:

M(x,y) = ((-2 + (-6))/2 , (-9 + 7)/2)

M(x,y) = (-4, -1)

To find the slope of the perpendicular bisector, we have to take the negative reciprocal of the slope of the line segment which is (y2-y1)/(x2-x1) = (7-(-9))/(-6-(-2)) = -16/4 = -4

Slope of the perpendicular bisector = -1/slope of the line segment = -1/(-4) = 1/4

Now we can use the point-slope form to find the equation of the line:

y - y1 = m(x - x1)

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

y = 1/4x +1

so the equation of the perpendicular bisector of the line segment whose endpoints are (-2,-9) and (-6,7) is y = 1/4x +1

Answer: The first graph

Step-by-step explanation:

Graph the absolute value using the vertex and a few selected points.

Hope this helps !

A. The quotient is given as follows: 60.9 miles / 3.5 hours.

B. The exact distance that she rode in one hour is of: 17.4 miles.

The measures in this problem are obtained considering the relation between velocity, distance and time.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

The parameters for this problem are obtained as follows:

Hence the average velocity is obtained as follows:

v = d/t

v = 60.9/3.5

v = 17.4 miles per hour.

This means that the exact distance that she rode in one hour is obtained as follows:

17.4 = d/1

d = 17.4 miles.

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Answer:

Step-by-step explanation:

Answer: 22.5

Step-by-step explanation: To get a percentage of a number you multiply the number you want the percentage of (125), and multiply it by your percent in decimal form. So basically the equation went like this: 125 x 0.18 = 22.5. Another example of this would be if you wanted to find 60 percent of 20. You would just take 60 and put it in decimal form and multiply. 20 x 0.60 = 12. Hope this helps!

Answer:

The y-intercept of -5x+7y=8 is (0,8/7)

Step-by-step explanation:

The y-intercept of a linear equation is the point where the graph of the equation crosses the y-axis. In this equation, when x = 0, the equation becomes 7y = 8, so the y-intercept is (0, 8/7).

Answer:I hope this helps

Step-by-step explanation:

-5x+7y=8

To find the -intercept, substitute x=0 something like this

-5 times 0+7y=8

Solve the equation for Y which is something like

y=8/7 this your answer for the y intercept.

Answer:

4/3 as an exponent is 4 to the 3rd power ( so four with a three right above it a little)

Step-by-step explanation:

The solution for the given system of equations would be (6, 6).

What is the system of equations?

A system of equations is a set of two or more equations that are solved simultaneously. Each equation in the system contains one or more variables, and the goal is to find the values of the variables that satisfy all the equations in the system.

y = -1/6x + 7

y = 2x - 6

To graph the equations y = -1/6x + 7 and y = 2x - 6, we can follow these steps:

Plot the y-intercepts of the equations: The y-intercept is the point where the line crosses the y-axis. For the equation y = -1/6x + 7, the y-intercept is (0,7), and for the equation y = 2x - 6, the y-intercept is (0,-6).

Draw the lines: Starting from the y-intercepts, use the slope of the lines to draw the lines. The slope of the first equation is -1/6 and the slope of the second equation is 2.

Find the x-intercept: The x-intercept is the point where the line crosses the x-axis. For the equation y = -1/6x + 7, the x-intercept is (-42,0) and for the equation y = 2x - 6, the x-intercept is (-3,0)

Locate the point of intersection: The point of intersection of the two lines is the solution of the system of equations. The point of intersection for the given equation is (3,1).

Label the axes and the lines: Label the x- and y-axes, and give the lines descriptive names or equations.

Now draw the graph, we get

Hence, the solution for the given system of equations would be (6, 6).

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Answer:

Option D

Step-by-step explanation:

Remember that the sum of all angles in ANY triangle is 180 degrees. Also, remember that an acute triangle has angles that are all less than 90 degrees. So not only do our options have to add up to 180 degrees, but they also have to be less than 90 degrees in order for the triangle to be acute.

We can immediately exclude options A, B, and C because all three options have angles greater than 90 degrees, which means the triangle isn't acute.

Your answer is option D or "70, 80, 30." Since...

70 + 80 + 30 = 180
70 < 90
80 < 90
30 < 90

Hope this helps.

Ann and Byron set up shop 35 meters apart on one side of a creek, with the height of the cliff on the other side of the stream being 106.73 meters.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

consider the triangles ABC and ACD

from the figure

∠DAC = 36°

∠CAB = 68°

AD = 35 m

we have to find the height of the cliff i.e. he length BC

i.e. the length BC

cosθ = adjacent side / hypotenuse

cos36° = 35 / AC

AC = 43.21 m

tan68° = BC / 43.21

BC = 43.21 * 2.47 = 106.73 m

Ann and Byron set up shop 35 meters apart on one side of a creek, with the height of the cliff on the other side of the stream being 106.73 meters.

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Answer:20

Step-by-step explanation: 5+5+5+5

Answer:

4 times 5 is equal to 20.

Step-by-step explanation:

Answer:

80 %

Step-by-step explanation:

Christine enjoyed 44 out of the 55 movies she watched.

This can be represented as

44/55 movies. This fraction simplified is 4/5 or 80 %

Given that segment BD bisects segment AC, the value of x is 5.8 units.

If the corresponding sides and/ or internal angles of two shapes have some  common properties, then it can be said that the shapes are similar. Though similarity does not mean congruency.

Given that segment BD bisects segment AC, the value of x can be determined by comparing the sides of triangles ABD and BCD.

Thus, we have;

x/ 7 = 14/ 17

17x = 7 * 14

     = 98

17x = 98

x = 98/ 17

  = 5.76

x = 5.8 units

Thus to the nearest tenth, the value of x is 5.8 units.

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It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.

Now, According to the question:

We know that:

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

We have the sides:

4 , 7 and 8

4 + 7 > 8

It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.

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Answer:

Step-by-step explanation: v = 1/3π[tex]r^{2}[/tex]h

[tex]\frac{1}{3}[/tex]π([tex]1.5^{2}[/tex]) x 15

[tex]\frac{1}{3}[/tex]π x 2.25 x 15

=35.34291

Answer:undefined

Step-by-step explanation:

Since ​14​ is equivalent to 8x, that number must be 14 ÷ 8. Then ​14 ÷ 8 = x, because of the inverse relationship between multiplication and division.

There are 4 basic mathematical operations which are addition, subtraction, division and multiplication.

Multiplication and division are inverse operations because multiplication undoes division and also division undoes multiplication.

We want to find the quotient of 14 and 8. This is expressed as 14 ÷ 8.

Now, we are told to consider that some number times 8 equals ​14. Let the number be x and as such we have;

8x = 14

Now, since 14 is equal to 8x, then that number must be gotten by using the inverse relationship by multiplying both sides by 1/8 to get;

x = 14/8

Finally, ​14÷8 = x because of the inverse relationship between multiplication and division.

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The cost of admission for an adult is $10 and for a child is $6

The cost of each ride for an adult is $1.50 and for a child is $1

The adult will spend $10 for admission + $1.5 x 7 rides = $17.5

The child will spend $6 for admission + $1 x 7 rides = $13

The adult spent $17.5 - $13 = $4.5 more than the child.

The system of equations 12x + 51y = 156 and -8x - 34y = -104 has infinitely many solutions

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Given the equation:

12x + 51y = 156

Dividing by 3:

4x + 17y = 52       (1)

Also:

-8x - 34y = -104

Dividing by 2:

-4x - 17y = -52    (2)

To solve both equation by elimination, add equation 1 and 2:

0 = 0

The equation has infinitely many solutions

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According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

The smallest polygon with three sides and three interior angles is a triangle.

A triangle is a three-sided polygon that consists of three vertices, three sides, and three angles. Three types of triangles—scalene, isosceles, and equilateral—can be distinguished based on the length of their sides.

It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the size of its angles. A triangle's internal angles add up to 180 degrees. Two more terms—altitude and triangle median—are introduced to you in this essay.

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Hence option b is the correct option i.e The sample mean's sampling distribution will be roughly normal.

The appropriate response to the question about Sampling Distributions is The sample mean will have a sampling distribution mean that is identical to the population mean.

The sampling distribution must then resemble the normal distribution as the sample size grows.

According to this, if the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or any other distribution.

A bell-shaped, symmetrical distribution known as a normal distribution has fewer observations the farther out from its center.

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Graph of g(x) = (1/2)ˣ i.e. Graph of f(x) = 2x reflected over the y-axis is drawn below.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.

f = {(a, b)| for all a ∈ A, b ∈ B}.

Given, the function

f(x) = (2)ˣ

g(x) = (1/2)ˣ

g(x) is the graph of f(x) reflected over y- axis.

The rule of reflection over y-axis:

(x, y) → (-x, y)

Thus, when a graph gets reflected over y-axis it means that horizontal components are additive inverse of the original horizontal components.

Therefore the graph of g(x) = (1/2)ˣ is as follows.

Hence, below is the graph of g(x) = (1/2)ˣ that is graph of f(x) reflected over y- axis.

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The surface area of the square pyramid is B)61.25[tex]cm^2[/tex]

What is surface area of square pyramid?

The term "square pyramid" also refers to a polyhedron having a square base and four triangular faces. Where the four faces come together is known as the apex. The pyramid's faces connect the base and the tip. The calculation for the square pyramid's surface area adds the areas of the four triangular faces and the base.

Here the given measures are base = 3.5 cm and height = 7cm.

Now using surface area formula then

Surface area of the square pyramid = Base area + 2bl square unit.

Base area = 3.5 × 3.5 = 12.25[tex]cm^2[/tex]

=> Surface area = 12.25+ 2×3.5×7

=> Surface area = 12.25+49

=> Surface area = 61.25[tex]cm^2[/tex]

Hence the surface area of the square pyramid is B)61.25[tex]cm^2[/tex]

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An inverse function or  anti function is defined as a function, in which the graph can be  reverse into another function. hence commonly , if any type of function “f” takes x to y then, the inverse of “f”  function will take y to x.  hence  the function is represented as ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1} and F^{-1}[/tex].

let us assume that  f and g are inverse functions, then the condition for  f(x) = y if and only if g(y) = x

when the graph is represented in an original function which has to be  one-to-one function in order  to assure that its inverse is an function. A function is said to be a one to one function only if  function of every second element corresponds to the first value .

The graph of function is  the inverse of a function which  reflects two things, that is , one represents the  function and second represents the inverse of the function, over the line y = x. This line in the graph passes through the origin and which  has slope value  equal to 1 and represented as;

y = f-1(x)     which is equal to     x = f(y)

This relation is basically  similar to y = f(x), which tells that  graph of f but the part of x and y are reversed here. So if we have to draw the graph of f-1, then we have to manipulate the positions of x and y in coordinate axes.

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If in rectangular park that is 63 yards by 16 yards, a dog began in the northwest corner and ran south along the length of the park and Finally, the dog ran back to the northwest corner. The dog ran 65 yards.

Distance can be defined as how far an object is from another object.

Using the Pythagoreans theorem to find the distance

c² = √a² + b²

Let plug in the formula

c² = √63² + 16²

c² = √3,969 + 256

c = √4,225

c = 65 yards

Therefore the distance is 65 yards.

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Answer:

  p:q:r = 12:15:10

Step-by-step explanation:

Given p:q = (2/3):(5/6) and q:r = (3/4):(1/2), you want p:q:r.

We can turn each ratio into a ratio of integers by multiplying by the least common denominator.

  p:q = 4:5 . . . . . . . multiply the given ratio by 6

  q:r = 3:2 . . . . . . . multiply the given ratio by 4

Now, we need to have q be represented in each ratio by the same number. That number will be the least common multiple of its representations in these ratios: LCM(5, 3) = 15.

Multiplying the first ratio by 3, we have ...

  p : q = 12 : 15

Multiplying the second ratio by 5 gives ...

  q : r = 15 : 10

Now, we can write the ratio of interest:

  p : q : r = 12 : 15 : 10

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