Trigonometric Ratios

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case we have

268 = 2×86 + 2x = 172 + 2x

96 = 2x

x = 96/2 = 48 m

The process of find the x and y coordinates of the vertex of a parabola is y = -b/2a

Coordinates in math is known as  a number on the x-axis called an x-coordinate and a number on the y-axis called a y-coordinate.

Here we need to write down the process of finding the x and y coordinates of the vertex of a parabola.

The first step is to Get the equation in the form y = ax² + bx + c.

And then we have to calculate -b / 2a ad this is the x-coordinate of the vertex.

In order to find the y-coordinate of the vertex, then we have to simply plug the value of -b / 2a into the equation for x and solve for y.

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The graph of the function f(x) = −15|x−40|+8 will be a piecewise linear function.

Graph explain: What is it?

A graph is defined as a mathematical structure that connects a collection of points to express a specific function. A pairwise relationship between the objects is established using it. The edges that connect the graph's vertices (also known as nodes) are its vertices (lines).

It will be a V-shape, with the vertex at x = 40 and y = 8.

On the left side of the vertex, the function will be decreasing, representing Tyra moving away from home.

On the right side of the vertex, the function will be increasing, representing Tyra moving towards home.

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

Key features of the graph in the context of the situation:

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

The left side of the vertex represents the time period when Tyra is moving away from home, and the right side represents the time period when Tyra is moving towards home.

The slope of the graph on the left side of the vertex is negative, indicating that Tyra is moving away from home at a decreasing rate, while the slope of the graph on the right side of the vertex is positive, indicating that Tyra is moving towards home at an increasing rate.

The y-intercept is at 8, which means Tyra starts 8 miles away from home.

The graph is symmetric about the y-axis because for every time x on the left side of the vertex, there is a corresponding time on the right side of the vertex.

The graph is not a function because for every x value, there are two y values, one for when Tyra is moving away from home and one for when Tyra is moving towards home.

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I would be paid $310.4 for 32 hour of work at the same rate

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

We transform the mixed fraction into improper fraction and we have:

24 1/2 =

[(24*2) + 1)] /2=

[48+1] /2=

49/2

Calculating the amount of dollars paid for 1 hour worked:

Dollar per hour = Paid  / Hours worked

Dollar per hour = $236.64 / (49/2)

Dollar per hour = $236.64 * 2 / 49

Dollar per hour = $473.28/49

Dollar per hour = $9.70

Calculating the amount of dollars paid for 32 hours worked:

Paid (32h) = Dollar per hour * Hours

Paid (32h) = $9.70/h * 32 h

Paid (32h) = $310.4

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If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.

We have to prove that ∠A + ∠B + ∠C is equal to 180 degrees.

The measure of A = ∠1

B = ∠2

C = ∠3

Given, l || BC

We know that the alternate angles are equal in parallel lines.

∠2 = ∠4 -------------- (1)

∠3 = ∠5 -------------- (2)

Adding (1) and (2),

∠2 + ∠3 = ∠4 + ∠5

By adding ∠1 on both sides,

∠1 + ∠2 + ∠3 = ∠4 + ∠5 + ∠1

From the figure,

The sum of the angles at a point on a line is equal to 180 degrees.

∠4 + ∠1 + ∠5 = 180°

So, ∠1 + ∠2 + ∠3 = 180°

Therefore, ∠A + ∠B + ∠C = 180°

Thus, If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.

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The midpoint of the line segments with

1) (-4,-2), (3, 3) is ( -1/2 , 1/2).

2) (−1, −6), (−6, 5) is ( -7/2 , -1/2 ).

3) (2, 4), (1, −3) is ( 3/2 , -1/2).

In geometry, the midpoint is defined as the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. To determine the midpoint, just add the two X-values, then divide by 2 and add the two Y-values, then divide by 2. Mathematically, let (xm , ym) be coordinates of mid point of line segment ents with end points ( x₁, y₁) , (x₂, y₂). Then, xₘ =( x₁ + x₂)/2 and yₘ = ( y₁ + y₂)/2

We have , the line segments with coordinates

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

Midpoint = ( (-4 + 3)/2 , (-2 + 3/2) )

= ( -1/2 , 1/2)

2) (−1, −6), (−6, 5)

Midpoint = ( ( -6 +(-1))/2 , ( -6 + 5)/2)

= ( -7/2 , -1/2 )

3) (2, 4), (1, −3)

Midpoint = ((2 + 1)/2 , (4+(-3))/2)

= ( 3/2 , -1/2)

Hence, we got all midpoints for line segments.

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Complete question:

Geometry - Clark Midpoint and Distance Formulas

© 2011 Kuta Software LLC. All rights reserved.

Find the midpoint of the line segment with the given endpoints.

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

2) (−1, −6), (−6, 5)

3(2, 4), (1, −3)

The wrapping paper Marcus have left is 5 5 / 12 feet.

Marcus buys 7 3/4 feet of wrapping paper. He lets his sister use 2 1/3 feet of the wrapping paper to wrap a gift.

The amount of wrapping paper Marcus have left can be calculated as follows:

The amount of wrapping paper Marcus have left is the subtraction of the paper used by the sister by the wrapping paper he had initially.

Hence,

wrapping paper Marcus have left = 7 3 / 4 - 2 1 / 3

wrapping paper Marcus have left = 31 / 4 - 7 / 3

wrapping paper Marcus have left = 93 - 28 / 12

wrapping paper Marcus have left = 65 / 12

Therefore,

wrapping paper Marcus have left = 5 5 / 12 feet

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Answer:40+4x

Step-by-step explanation:

1) distribute the 4 to each term

4(10+x)

40+4x

Isosceles Triangle Theorem: If two triangle sides are similar, then their corresponding angles must also be similar. The sides of a triangle that correspond to two angles that are congruent are also congruent.

According to the isosceles Angle Theorem, the angles in an isosceles triangle that face congruent sides are also congruent.

A triangle with two equal sides is said to be isosceles. Isosceles triangle is basically such triangle which have two sides equal in magnitude. It is to be noted that because two angles should also be equal because of the two equal sides.

Angles opposing two triangle sides are congruent if their two sides are as well.

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Answer:

327 miles

Step-by-step explanation:

Answer:

327.5 miles

Step-by-step explanation:

45 times 4.5 + 50 times 2.5 = 327.5

Answer:

y = 10 and x = 5

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5\sqrt{3} }{y}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

y × [tex]\sqrt{3}[/tex] = 10[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

y = 10

-----------------------------------

using Pythagoras' identity in the right triangle

x² + (5[tex]\sqrt{3}[/tex] )² = y² = 10²

x² + 75 = 100 ( subtract 75 from both sides )

x² = 25 ( take square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

The lengths of all three sides of the triangle are;

43.6 inches

52.3 inches

61.1 inches

The arcs are seen to be two times the angles and as such, the arc made by the 50° angle is 100° and then we see that the one made by the 60 degree angle given as 120°.

Formula for the circumference of a circle is;

C = 2πr

C = 50π inches

C = 157 inches

The arc made by the 50° angle is;

Arc length = 157*100/360

=  43.6 inches

The arc length made by the 60° angle = 157(120/360)

=  52.3 inches

The arc length made by the remaining 70° angle is;

Arc length = 157(140/360)

Arc length = 61.1 inches

Total arc length = 43.6 + 52.3 + 61.1

= 157 inches.

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Answer:

$389.5

Step-by-step explanation:

621/2 = 310.5 assuming they're equal therefore, it is stated that the table cost cost 79 less than the bench so we substract.

310.5 - 79 = 231.5

This is the cost of garden table, lets find the bench now.

621(both table and bench)-231.5(garden table)= 389.5 is the cost of the bench.

The revised form of the sentence would be as follows: Mark Twain, who was born in Florida, is one of America's most famous authors.

Nonrestrictive elements are sets of words that can be deleted from a statement without affecting its meaning.

A nonrestrictive element is nonessential because we don't need the information it provides. These elements are always separated with commas from the rest of the sentence to specify that they are not essential. If they were dropped, the meaning of the sentence would be left unchanged.

Mark Twain, is one of America's most famous authors. - In the above sentence the nonrestrictive element is a nonessential relative clause.

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Answer:

50%

Step-b50%y-step explanation:

Joint relative frequency

Answer:  y=17.3

refer to the image for the steps

According to Maths, in order to solve a system of linear equations by graphing, we must first graph both equations in the same coordinate plane and then locate the intersection of the two lines.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables. An illustration of a system of equations is the set of equations below.

2x - y = 12

x - 2y = 48

Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions,

There are numerous ways to solve any set of equations. We require at least two equations in order to solve a system of two-variable equations. Similar to this, we will need at least 3 equations to solve a system of 3 equations. Let's examine three approaches to solving a set of equations, presuming that they are linear equations in two variables.

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Answer:

90-99=86x45[80[

Step-by-step explanation:

Answer:

The function g(x) = √(x - 3) is defined for all real numbers x such that x - 3 ≥ 0, since the square root of a non-negative number is a real number.

Solving for x, we have:

x - 3 ≥ 0

x ≥ 3

Therefore, the domain of the function is D: [3, ∞).

Since the square root of a non-negative number is always non-negative, the range of the function is R: [0, ∞).

Therefore, the correct answer is: A. D: [3, ∞) and R: [0, ∞).

The ideal utilization would be $150but he can choose to borrow $1050

A credit card is a type of credit facility, provided by banks that allow customers to borrow funds within a pre-approved credit limit. It enables customers to make purchase transactions on goods and services.

Given here: Bob's credit limit is $3500 and he has a balance of $2200

Therefore available credit is equal to $3500-$2200=$1300

Thus if he spends more than $1300 then he goes over his limit.

But ideal utilization ratio is 30% and therefore 30%×3500=$1050

Thus ideal credit usage would be = 3500-1050

                                                        =2450

Then $2450-$2200=150

Hence, The ideal utilization would be $150but he can choose to borrow $1050

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The value of x for the given angles is 23

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. The angles that result from a transversal crossing of two lines in pairs can be successive internal angles, matching angles, or alternate angles.

Given lines m and n, where m ║ n

and t intersect at both the lines as shown in the figure,

so line t works s transversal,

and angles,

(8x - 27)° and (7x - 4)°

both the angles are at the bottom of the line and same side so they are corresponding angles,

and corresponding angles for any transversal are equal,

(8x - 27)° = (7x - 4)°

8x - 27 = 7x - 4

8x - 7x = -4 + 27

x = 23

Hence the value of x is 23.

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The 2nd step when solving for systems of equations using the elimination method is explained below.

Equations in math is defined as a mathematical statement that shows that two mathematical expressions are equal.

Here we need to find the steps to the 2nd step when solving for systems of equations using the elimination method.

Here first we need to find Enter the equations.

And then multiply each equation by a number to get the lowest common multiple for one of the variables.

And then add or subtract the two equations to eliminate that variable .

Now we have to substitute that variable into one of the equations and solve for the other variable.

Finally we have to check by substituting your answer into one of the equations,

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The statement with the correct value is C. 9

Simple substitution is a topic which are mathematical expressions with variables whose value/s has been given. Thus it is just required to solve the question by simple substitution of the given value in the expression. Example, given that a = 2, determine the value if a + 6.

This can be solved by substituting 2 for a in the question, so that;

a + 6 = 2 + 6

          = 8

Therefore, it can be deduced from the given question that;

-2z + 1, but z = -4

Thus,

-2z + 1 = -2(-4) + 1

          = 8 + 1

          = 9

To complete the statement, the correct value is 9. Option C.

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Answer:8534.46

Step-by-step explanation:

The depreciated value of the bike after 12 years is $8534.46

Depreciated value is the minimum amount that an asset is worth after depreciation.

Given that, the value of a motorcycle is depreciating by 2.8% each year, the bike was purchased for $12,000,

We know that, the depreciation value is given by,

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = rate

n = years or time

Therefore,

A = 12000(1-0.028)¹²

A = 12000(0.972)¹²

A = 8534.46

Hence, the depreciated value of the bike after 12 years is $8534.46

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When the diagonal of a rectangle splits the rectangle into two producing angles 30 - 60 - 90 the sides of the rectangle is

Area of a rectangle is solved to get 191 square in

The problem is solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The shape describes a right triangle of

opposite = width

adjacent = length

hypotenuse = diagonal

The dimensions are calculated using SOH and CAH

sin 30 = opposite / hypotenuse

sin 30 = width / 21

width = 21 * sin 30

width = 10.5

For the length

cos 30 = adjacent / hypotenuse

cos 30 = length / 21

length = 21 * sin 30

length = 18.19

Area of a rectangle = length * width

Area of a rectangle = 18.19 * 10.5

Area of a rectangle = 190. 995

Area of a rectangle = 191 square in

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The characteristics of parallel lines:

1) Parallel lines lie in the same plane

2) The parallel lines  never intersect each other.

3) The slopes of parallel lines are equal.

We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.

Parallel lines are always equidistant from each other.

Also, the parallel lines are coplanar.

Mathematically, the parallel lines are represented by the symbol, ‘||‘.

If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.

Also, the slopes of parallel lines are equal.

Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are parallel to each other then m₁ = m₂

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Answer:

Step-by-step explanation:

Part A:

The graph of the function g(x) = |x - 7| is a V-shaped graph that opens upwards and has a vertex at x = 7. The vertex is the midpoint of the graph and occurs at the value of x where the absolute value changes from positive to negative. The domain of the function is all real numbers and the range is all non-negative numbers.

Part B:

The transformation from f(x) to h(x) occurs by shifting the graph of the parent function up by 2 units along the y-axis. In other words, every y-coordinate in the graph of f(x) is increased by 2 in the graph of h(x). The vertex of the parent function is (0,0) and is shifted to (0,2) in the transformed function. The range of h(x) is all non-negative numbers greater than or equal to 2.

The final graph is given below in the image.

The equation is [tex]y = -\frac{3}{4}x - 2[/tex]

The graph of a linear equation in two variables is a line (that's why they call it linear).

If you know an equation is linear, you can graph it by finding any two solutions

(x1,y1) and (x2,y2)

plotting these two points, and drawing the line connecting them.

You can find two solutions, corresponding to the x-intercepts and y-intercepts of the graph, by setting first x=0 and then y=0.

To graph the line [tex]y = -\frac{3}{4}x - 2[/tex] we are going to take advantage of the fact that its y-intercept is -2 when x = 0, so our first point is (0,-2). To find our second point, we are going to find the x-intercept; to do it, we are going to set y = 0 and solve for x:

[tex]y = -\frac{3}{4}x - 2\\0 = -\frac{3}{4}x - 2\\2 = -\frac{3}{4}x \\x = -\frac{8}{3}[/tex]

Now, we have our second point (0, -8/3), we just need to join the 2 points with a straight line.

The final graph is given below in the image.

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A square's side to perimeter ratio is one to four.

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