An angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2) What is the exact value of cos(120)

The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.

Given that,

vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)

vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)

(x,y) ; (x, y-8)

ABCD is reflected across the line y=4 to get the quadrilateral EFCD.

Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.

Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.

Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).

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If f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.

Given that f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 and we are required to find the inverse if the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have corresponding value of y.

The given function is as under:

f(-1)=-21,

f(0)=-9,

f(1)=3

f(2)=15

In the inverse of the function the value of x becomes the value of y and the value of y becomes the value of x. So the inverse of the function is as under:

p(-21)=-1,

p(-9)=0,

p(3)=1,

p(15)=2

Hence if f(-1)=-21,f(0)=-9,f(1)=3,f(2)=15 then the inverse of function f(x) is p(-21)=-1,p(-9)=0,p(3)=1,p(15)=2 which is option d.

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The numerator in the fixed asset turnover ratio is sales.

To determine the fixed Asset Turnover ratio, the subsequent components are used: fixed Asset Turnover = sales / common fixed property.

The fixed asset turnover ratio exhibits how green an employer is at generating sales from its current fixed assets. A higher ratio implies that control is the usage of its fixed property extra efficiently.

Within the retail region, an asset turnover ratio of 2.5 or greater can be considered good, even as a business enterprise in the software region is much more likely to intention an asset turnover ratio it is among zero.25 and 0.5.

We can now calculate the constant asset turnover ratio by dividing the internet revenue for the yr through the average constant asset balance, which is equal to the sum of the modern-day and earlier duration balance divided through two.

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The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

Given that?

First, we determine the length of side c using the law of cosines.

c = √( a² + b² - 2ab( cosC ) )

We substitute in our values

c = √( 20² + 13² - 2×20×13( cos 139° ) )

c = √( 400 + 169 - 520( cos 139° ) )

c = √( 569 + 392.44898 )

c = √961.44898

c = 31 cm

Next, we find Angle A, using the law of cosines.

A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]

We substitute in our values

A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 )  ]

A = cos⁻¹[ ( 169 + 961 - 400) / 806]

A = cos⁻¹[ 730 / 806]

A = cos⁻¹[ 0.9057 ]

A = 25°

The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

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Hi! ❄

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The eccentricity of the conic section below is 1, since the given conic section is a parabola, and any parabola's eccentricity is 1.

Hope that made sense !!

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[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]

The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)

Herein we have an equation that models the height of the ball as function of time, we need to evaluate the expression for t = 3 s to find the required height:

s(3) = - 4.9 · (3 s)² + 19.6 · (3 s) + 58.8

s(3) = 73.5 m

The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)

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The average rate of change is -5 per month

The interval is given as:

July to December

From the graph, we have:

July = 110

December = 30

The average rate of a function over the interval (a, b) is calculated as:

Rate = [f(b) - f(a)]/[b - a]

So, we have:

Rate = (30 - 110)/(December- July)

This gives

Rate = (30 - 110)/(12 - 7)

Evaluate

Rate = -16

Hence, the average rate of change is -5 per month

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Answer:

12.11069457

Step-by-step explanation:

You start by using sin(48) = 9/x
You then multiply both sides by x to give you

xsin(48) = 9

you then divide both sides by sin(48) to get x by itself

x = 9/sin(48)

this gets you

x=12.11069457

Answer:

√(3 , √(π , 2

Step-by-step explanation:

ascending order

The stores that will be in the sample are - 00, 02, 05, 08, 11, 14, 17, 20, 23.

What comprises the sample?

An analytical subset of a larger population is referred to as a sample in statistics. A sample are used in research so that it can be done quickly and with more manageable data. However, obtaining such a sample may be costly and time-consuming. Randomly generated samples do not have significant bias if they are large enough.

Stores in the Sample

Since it is given that the sample is made up of every third store, starting from the first retail store. The stores have been numbered systematically from 00 to 23.  Since a systematic sampling is done, after picking the first store, the third store will be picked, that is, 02, and then 05, and so on till 23.

Thus, the following retail stores will be present in the sample,

00, 02, 05, 08, 11, 14, 17, 20, 23

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Answer:

Below in bold.

Step-by-step explanation:

Using the Pythagoras theorem:

Distance from the origin after  1 move = √(1^2 + 2^2) = √5.

So after 2016 distance is 2016√5 units.

This = 4507.9 units to the nearest tenth,

Answer:

They can type 825 words in 25 minutes.

Step-by-step explanation:

First, we need to find how many words they can type per minute. To do that, we need to divide 495 by 15.

[tex]495 \div 15 = 33[/tex]

Now, we know how many words per minute, and the question is how many words they can type in 25 minutes. So to find our answer, we need to multiply 33 by 25, since 33 is how many words in one minute.

[tex]33 \times 25=825[/tex]

So now we know our answer: 825 words in 25 minutes.

The length of side AC = 5 units

Missing sides of a right triangle can be solved using the Pythagoras theorem

From the given question

Length of side AB = 3 units

Length of side BC = 4 units

The length of side AC is calculated below

[tex]AC^2=AB^2+BC^2\\\\AC^2=3^2+4^2\\\\AC^2=9+16\\\\AC^2=25\\\\AC=\sqrt{25}\\\\AC=5[/tex]

Therefore, the length of side AC = 5 units

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Complete Question

The length of side ab is 3 units. the length of side bc is 4 units. the length of side ac is .......... units.

The equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank is g = 3h + 3; 12 gallon

Check all equation

g = 18 – 2h; 18 gallons

= 18 - 2(3)

= 18 - 6

= 12

g = 18 – 2h; 16 gallons

= 18 - 2(3)

= 18 - 6

= 12

g = 3h + 3; 30 gallons

= 3(3) + 3

= 9 + 3

= 12

g = 3h + 3; 12 gallon

= 3(3) + 3

= 9 + 3

= 12

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The commission earned are R41123.17, R47931.67 and R15024.09

The VAT included prices are given as:

R271 800,00; R316 800,00 and R99 300,00.

The VAT rate is 12.36%.

So, the price before VAT is calculated as:

VAT included = Price without VAT * (1 + 12.36%)

This gives

VAT included = Price without VAT * 1.1236

So, we have:

Price without VAT = VAT included/1.1236

For the three cars, we have:

Price without VAT = R271 800.00/1.1236 = R241901

Price without VAT = R316800.00 /1.1236 = R281951

Price without VAT = R99300.00/1.1236 = R88377

Hence, the prices of the cars before VAT was added are R241901, R281951 and R88377

This is calculated as:

Commission = Price * 17%

So, we have:

Commission = R241901 * 17% = R41123.17

Commission = R281951 * 17% = R47931.67

Commission = R88377 * 17% = R15024.09

Hence, the commission earned are R41123.17, R47931.67 and R15024.09

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The measure of angle C is obtained as 35 degrees

Give that;

b^2 = a^2 + c^2 - 2ac Cos B

a = 29

c = 24

B = 101 degrees

b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]

b^2 = 841 + 576 + 266

b = 41 cm

Now;

b/sinB = c/sinC

bsinC = csinB

sinC = csinB/b

sinC =  24 * sin 101/41

C = sin-1(24 * sin 101/41)

C = 35 degrees

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Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

According to the statement

We have given that the two rectangles EFGH and ABCD and we have show that the these rectangles Are dilation at origin or not.

So, According to the given diagram

Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation of rectangle at the origin.

Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.

The scale factor could be calculated by the ratio of the sides of the image to the pre-image rectangle.

According to the diagram In Rectangle ABCD:

Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).

Now consider rectangle EFGH:  

Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).

Hence the scale factor is becomes from these values is:

EF/AB = EH/AD = FG/BC = HG/DC = 4/3.

Hence the scale factor becomes 4/3.

Also

∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°

( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).

So, Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

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A conclusion which can be derived from these random samples is that: B. the students in grades 11 and 12 scored higher than the students in grades 9 and 10.

A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Based on the information provided for these samples, we can logically conclude that the students in grades 11 and 12 scored higher than the students in grades 9 and 10 because a median score of 86 is greater than a median score of 79.

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The system of equation which represent the scenario is;

x + y = 42

x + y = 420.13x + 0.18y = 6.66

let

x + y = 42

x + y = 420.13x + 0.18y = 6.66

Therefore, the equation which represent the problem is;

x + y = 42

0.13x + 0.18y = 6.66

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Answer:

y = [tex]-\frac{4x-5}{2}[/tex]

Step-by-step explanation:

Step 1: Switch sides

5 - 2y = 4x

Step 2: Subtract 5 from both sides

5 - 2y - 5 = 4x - 5

Step 3: Simplify

-2y = 4x - 5

Step 4: Divide both sides by -2

[tex]\frac{-2y}{-2} = \frac{4x}{-2} - \frac{5}{-2}[/tex]

Step 5: Simplify

y = [tex]-\frac{4x-5}{2}[/tex]

[tex] \frac{5}{6} \: of \: a \: number \: is \: 180[/tex]

[tex] \frac{1}{6} \: is \: 5 \: times \: less \: than \: \frac{5}{6} \\ \frac{1}{6} = \frac{180}{5} = 36[/tex]

Initially, as x increases, y decreases.

The slope of the graph is equal to 1 for all x between x=0 and x=3.

Starting at x=3, the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5.

For x between x=0 and x=4, the function value y decreases then increases to 0.

For x between x=4 and x=8, the function value y increases and decreases to 0.

From the graph, initially the it goes down when x increases up-to the x value 3. After that from x value 3 to 5, the graphs goes up. After that from the x value 5 it goes down to zero.

The slope of the line is the measurement of inclination of that line from the positive x-axis. It can be calculated by the following formula.

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of the graph between x=0 to x=3

[tex]Slope=\frac{-3-0}{3-0}=-1[/tex]

The slope of the graph between x=3 to x=5

[tex]Slope=\frac{3-(-3)}{5-3}=3[/tex]

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The equation that could be used to find how many gallons Erin would need to drive 92 miles is 92 = 23g (option c)

The first step is to determine the gallons needed to drive 1 mile. To do this, divide the  6 gallons by 138 miles. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Gallons needed for 1 mile = 6/138

In order to determine the gallons needed for 92 miles, multiply the ratio gotten in the previous step by 92

(6/138) x 92 = 4 gallons

The option that gives 4 gallons is : 92 = 23g

g = 92 / 32 = 4

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The standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.

Dispersion is measured by variance. A metric called a "measure of dispersion" is used to assess how variable data are concerning an average value. There are two sorts of data: grouped and ungrouped. Data is referred to as grouped data when it is presented as class intervals. On the other hand, it is referred to as ungrouped data if it comprises just individual data points. For both types of data, the sample and population variances may be calculated.

The variance of the provided data is obtained by taking the square of the standard deviation. The standard deviation is used to determine how widely distributed the data points are about the mean. In other words, the standard deviation is used to determine how observations in a data collection deviate from the mean. While the standard deviation has the same unit as the population or the sample, variance is represented in square units.

In the question, we are asked to find the standard deviation, if the variance is 0.01545.

We know that Variance = (Standard Deviation)².

This gives us:

Standard Deviation = √Variance,

or, Standard Deviation = √0.01545,

or, Standard Deviation = 0.12429802894 ≈ 0.1243.

Thus, the standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.

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Answer:

y= -1/3x + 1

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y= -1/3x + 1

Answer:27 < AB < 81

Step-by-step explanation:

Answer:

27 < AB < 81

Step-by-step explanation:

in a triangle the sum of any 2 sides must be larger than the third side.

that must be true for every pair of sides you pick.

simply because, if that is not fulfilled, the third side would be too long, and the other 2 sides cannot connect to the endpoints of the third side.

so,

AC + CB = 81 must be longer than AB. otherwise the triangle cannot "close".

AC + AB = 27 + AB must be longer than CB = 54.

so, AB must be longer than 27.

CB + AB = 54 + AB must be longer than AC = 27. but that is always true, as CB alone is already larger.

so only the other 2 conditions need to be true.

hence the answer.

Using a system of equations, it is found that 10,000 children attended the park that day.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The attendance at the amusement park is 30,000 attendees, hence:

c + a = 30,000, which is the first equation in matrix form.

Then:

a = 30,000 - c

The cost of attending an amusement park is $10 for children and $20 for adults. The total money earned by the park is $500,000, hence:

10c + 20a = 500,000, which is the second equation in matrix form.

Since a = 30,000 - c, we replace:

10c + 20a = 500,000

10c + 20(30000 - c) = 500,000

10c = 100,000

c = 10,000.

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