If θ i an angle in tandard poition and it terminal ide pae through the point (-9,-1), find the exact value of tan theta implet radical form

The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7

A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle

angle Z = 180-(90+51)

angle Z= 180- 141= 39°

using trigonometry ratio

tan51 = 27/XY

XY= 27/tan51

XY= 27/1.2

XY= 21.9

using Pythagoras theorem

XZ²= 21.9²+27²

XZ²= 1208.6

XZ= √1208.6

XZ= 34.7

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1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

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Answer:

[tex]x=1.45[/tex]

Step-by-step explanation:

[tex]2\left(x-4 \frac{1}{2} \right)=-6.1 \\ \\ 2\left(x-\frac{9}{2} \right)=-6.1 \\ \\ 2x-9=-6.1 \\ \\ 2x=2.9 \\ \\ x=1.45[/tex]

The reduced form of the fraction would be 2.8/2.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

Given that a/b is a fraction and when it is divided by 100 it will result in 0.014.

So we can write,

            [tex]\frac{\frac{a}{b} }{100}=0.014\\\\ \frac{a}{b}=0.014*100\\\\\frac{a}{b}=1.4\\[/tex]

Now 1.4 can be written as

       a/b = 2.8/2

Hence, the reduced form of the fraction would be 2.8/2.

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Answer:

Website A is cheaper by 29 cents

Step-by-step explanation:

A

49.95 + 4.39 = 54.34

B

47.68 + 6.95 = 54.63

54.63 - 54.34 = 0.29

Answer:

the difference is 0.29 cents

website A is cheaper

Step-by-step explanation:

(47.68 + 6.95) - (49.95 + 4.39)

54.63 - 54.34 = 0.29

The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.

What is angle bisector?

An angle bisector is the ray or line segment that divides the angle into two equal parts.

Since the segment BD bisects angle ABC hence,

∠ABC = ∠ABD+∠DBC               ..... (1)

Also, since segment BD bisects angle ABC hence,

∠ABD = ∠DBC

Use this fact in equation (1)

∠ABC = ∠ABD+∠ABD

∠ABC =2 ∠ABD

Now, substitute values and use algebriac multiplication.

7x = 2(3x+25)

7x = 6x+50

7x - 6x= 50

x=50

Now, substitute the value of x in the expression of ∠ABD.

∠ABD = 3x+25

∠ABD = 3(50)+25

∠ABD = 100

Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.

Hence, the measurement of angle DBC is 100°.

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the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm

Given the data in the question;

F = 11100 N

l₀ = 310 mm = 0.31 m

E = 207 GPa = 207 × 10⁹ N/m²

Δl = 0.38 mm = 0.0005 m

So, lets assume the deformation is elastic;

d₀ = √(  [4l₀F] / [πEΔl] )

we substitute

d₀ = √(  [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )

d₀ = √( 10123.2 / 172787595.947 )

d₀ = √( 5.85875 × 10⁻⁵ )

d₀ = 0.007654 m

d₀ = ( 0.007654 × 1000 )mm

d₀ = 7.65 mm

Therefore, required diameter is 7.65 mm

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The blanks are filled as below

Collinear points are those that are situated along a single straight line.

Collinear points are those that are on a line either close to or far from another point, it can be more than two points.

While coplanar points imply lying on the same plane

In the diagram,

E, F, and G are collinear points

D, B, E, F, and G are coplanar points

A, B, and C are another collinear points

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Answer:

103

Step-by-step explanation:

angle 1 and angle 5 are the same as each other.

We can write the given statement as inequality as -

-(x/9) < 12

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.

Reversal property : If (a > b) then (b < a) and  if (a < b) then (b > a).

Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).

The general equation of a straight line is y = mx + c

Other possible equations of lines are -

We have the following statement -

"the quotient of a number and three minus twelve is less than 12".

We can write the inequality as -

-(x/9) < 12

Therefore, we can write the given statement as inequality as -

-(x/9) < 12

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Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)

From the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.

The given expression is

18 + 24

First, we will determine the greatest common factor of 18 and 24

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Thus,

The greatest common factor is 2 × 3 = 6

Now, we will write the expression using the greatest common factor and the distributive property

18 + 24

6(3 + 4)

Hence, the expression is 6(3 + 4)

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Answer: It is A

Step-by-step explanation:

The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(x) = 4x² - 1. and g(x) = 2x - 1.

Now, g(f(2)) is the output of f(2) is the input of g(x).

∴ f(2) = 4(2)² - 1.

f(2) = 15.

Now, g(f(2)) = 2(15) - 1.

g(f(2)) = 29.

Also given,

f(x) = x² and g(x) = x - 1.

Now, 2.f(g(x)).

2.f(g(x)) = 2.f(x- 1).

2.f(g(x)) = 2(x - 1)².

2.f(g(x)) = 2(x² - 2x + 1).

2.f(g(x)) = 2x² - 4x + 2.

2.f(g(x)) = 2x² - 2x - 2x + 2.

2.f(g(x)) = 2x(x - 1) - 2(x - 1).

2.f(g(x)) = (x - 1)(2x - 2).

There is no restriction to the domain of this quadratic function.

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According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

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The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, perimeter =2(x-2+5)

= 2(x+3)

= 2x+6 units

Area of a rectangle =length × width

= (x-2) × 5

= 5x-10 square units

Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

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The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)

In this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:

cos 3x / (sin x · cos x)

Second, use trigonometric formulas:

cos (x + 2x) / (sin x · cos x)

(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)

cos 2x / sin x - sin 2x / cos x

csc x · cos 2x - sec x · sin 2x

The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.

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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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A) The number of pounds that the beverage cans are recycled in an hour is 119772 pounds

B) The number of tons that the beverage cans are recycled in an average day is 2397 ton

C) The number of Kilograms that the beverage cans are recycled in a day is 57528000 kg

The pound is the main unit of sterling, and the term "pound" is frequently used to refer to British currency in general, which is often qualified in foreign contexts as the British pound or the pound sterling.

In 2002 about 34 beverages can weigh one pound.

In one minute 113204 beverage cans are recycled.

In one hour, 60 minutes number of beverage cans recycled=113204×60

=6792240

34 beverage cans weight 1 pound

1 beverage cans weight=1/34 pounds

A) 6792240 beverage can weigh=1

=(1/34)(6792240) pound

=119771.765 pound

≈119772 pound

B) So, In 24 hours, no. of pounds recycled

=119772×24 pound

=119772×24×0.0005 ton

=2397.26 ton

≅2397 ton in one day.

C) So, In 24 hours, no. of tons recycled

=2397×24 ton

=2397×24×1000 kg

=57528000 kg

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Answer:

-3x, where x is the number of yards lost on the first play.

Step-by-step explanation:

The length of the segment connecting (-4, 3) and (-5,2) is 1.4.

The length of a line segment can be measured by measuring the distance between its two endpoints.

Therefore, the length of the segment connecting (-4, 3) and (-5,2) can be found as follows:

length of the segment = √(2 - 3)² + (-5 + 4)²

length of the segment = √(-1)² + (-1)²

length of the segment = √1 + 1

length of the segment = √2

length of the segment = 1.41421356237

length of the segment = 1.4

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Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

What is unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

According to the given question:

Gianna can wash 6 cars in 2 hours

Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.

Gianna's rate of washing cars is 3 cars per hour

Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.

Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

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The number of runs up and runs down for the preceding data is 5.

Runs up refers to the number of observations that are higher than the number of observations before them.

Runs down refers to the number of observations that are lower than the number of observations before them.

As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.

Therefore,

Runs up = 2nd + 4th + 6th observations

             = 3

As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down

Therefore,

Runs down= 3rd +5th observations

                 =2

Therefore,

Runs up + Runs down  =3+2

                                        =5

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On solving the given problem, The value of the median of the distribution is closest to 5.

In order to visualize data, a histogram is used. The width and area of each rectangle in the histogram are proportional to the class interval and data frequency, respectively.

When a dataset is sorted in either ascending or descending order, the median is the value that appears in the middle of the dataset.

Ascending numbers are listed in the following order:

2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9

Median is -  5

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Standard form of ellipse has equation [tex]\frac{y^2}{a^2} +\frac{x^2}{b^2} =1[/tex] where, a and b are the halves of the length of major and minor axis respectively.

Given that,

Length of major axis(2a)=6.

So

a=6/2

 =3

Length of minor axis(2b)=4.

So

b=4/2

 =2

Putting in equation of standard ellipse. We get

[tex]\frac{y^2}{3^2} +\frac{x^2}{2^2} =1[/tex]

After simplifying

4y² + 9x² = 36

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The Height of trees are equal after 4 years and the height is 54 inches.

A linear equation is a equation which draws straight line on the plot

when plotted.

Given,

Height of tree A at the time of planting = 38 inches

Height of tree B at the time of planting = 22 inches

Each year  tree A grow = 4 inches

Each year  tree B grow = 8 inches

Let's make an equation for the height of the trees,

H = 38 +4t

H = 22+8t

Now the time when height of both the trees will equal

38 + 4t = 22 + 8t

4t = 16

t = 4

Hence , After 4 years the height of both the trees will equal and the height of both the trees after 4 years will be 54 inches.

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Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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