on a unit circle, the terminal point of theta is (0, - 1) what is tan theta?
A. 1
B. Undefined
C. -1
D. 0

The measure of angle < APD = 98°. That is option D

Angle APB = 62°

Angle DPC = 102°

But length AD = BC

Therefore, angle APD = BPC

Also, the angle at a point = 360°

The sum of the angles given = 102 + 62 = 164°

The remaining angle = 360 - 164 = 196°

Therefore angle APD = 196/2 = 98°

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Answer:

x = 4

Step-by-step explanation:
1.Distribute

2. Subtract 2 from both sides
3. Simplify
4. Divide both sides by same factor

5. Simplify
x = 4

Answer: 4

Step-by-step explanation:

We have to try getting x by itself to solve for it. Since we have two sides that are equal to each other, we can add, subtract, multiply, and divide anything on both sides to try to isolate x.

[tex]2(x+1)=10[/tex]

We can first divide the left side and the right side by 2. This would remove the 2 being multiplied on the outside.

[tex]\frac{2(x+1)}{2}=\frac{10}{2}\\x+1=10\div 2\\x+1=5[/tex]

Now, we have a + 1 on the left side that we need to remove to get x by itself. If we are adding something, we can remove that by subtracting the same thing. Hence, we can subtract 1 from both sides to remove the + 1.

[tex]x+1=5\\x+1-1=5-1\\x+0=4\\x=4[/tex]

After all that simplifying, we get that x equals 4.

Answer:

$9600 saving / year

Step-by-step explanation:

1/5 of $21000 = 21000 / 5 = $4200 / month on rent

3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)

1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month

total savings/month = salary/month - rent/month - food/month - other expenses/month

total savings/month = 21000 - 4200 - 9000 - 7000

total savings/month = $800

BUT the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)

800 x 12 = $9600

the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year

the solution of the system of linear equations is:

x = 6/11

y = -4/11

Here we have the system of equations:

To solve the system, we can see that y is already isolated in both sides, then we get:

(-5/2)*x + 1 = 3x - 2

Now we can solve this for x:

(-5/2)*x + 1 = 3x - 2

2 + 1 = 3x + (5/2)*x

3 = (6/2)*x + (5/2)*x

3 = (11/2)*x

(2/11)*3 = x

6/11 = x

To get the value of y, we evaluate any of the lines in x = 6/11

y = 3*(6/11) - 2 = 18/11 - 2 = 18/11 - 22/11 = -4/11

Then the solution of the system of linear equations is:

x = 6/11

y = -4/11

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The account be worth in 7 months is 375.725 .

Amount (A) is the total money paid back at the end of the time period for which it was borrowed. The total amount formula in case of simple interest can also be written as: A = P(1 + RT)

Here, A = Total amount after the given time period.

Given that,

P = $350, R = 1.05%, T = 7 month

The simple interest equation uses "t" as years, but is just cycles, using an APR rate.

now, if we never mind "t" as years and just use it as an interest cycle, then we can say the rate is 1.05% and the period is 7 cycles.

A = P(1 + RT)

   = 350(1+1.05%×7)

   = 350(1+0.0105×7)

   = 350(1+0.0735)

   = 350×1.0735

A  = $375.725

Hence, The account be worth in 7 months is 375.725 .

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Answer:

You can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°

Step-by-step explanation:

The above is a cyclic quadrilateral.

A Cyclic quadrilateral is having all the vertices of a quadrilateral ( four sided figure) inside a circle, that is a quadrilateral inscribed in a circle.

To find either x or y, we should note:

The sum of opposite angles of a cyclic quadrilateral is 180° or Angles in opposite segment are supplementary.

Therefore,

2x + 2x + 4= 180

4x = 180 - 4

4x = 176

x = 44°

To find y

3y + 8 + y = 180°

4y = 180 - 8

4y = 172

y = 43°

Therefore, you can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°

Answer:  te correct answer is A

Step-by-step explanation:

He has $50,000 more in assets than in liabilities.

Answer:

1. He has $50,000 more in assets than in liabilities.

Step-by-step explanation:

Last option, (-2,6) where the lines intercept / cross over each other.

Hope this helps!

The slope of the scenario is calculated as: -250.

Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).

Given the points:

(4, 7,000) = (x1, y1)

(6, 6,500) = (x2, y2)

Plug in the values

Slope (m) = (6,500 - 7,000) / (6 - 4)

Slope (m) = (-500) / (2)

Slope (m) = -250

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Answer:

Below in bold.

Step-by-step explanation:

Standard form is Ax + By = C

where A, B and C are integers  and A must be positive.

So the first 2 are already in standard form but the last 2 can be converted to standard form by multiplying each term by -1:

-12x+3y=27

= -1*-12x + -1*3y = -1*27

12x - 3y = -27   is the answer.

The last one is:

24x + 12y = -60.

The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.

About the Distribution of Data:

The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.

The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.

Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.

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Answer:

Given,

y=x³ ,0≤x≤2

We have to find the surface area of the surface by rotating the curve about the x axis.

For rotation about the x axis, the surface area formula is given by-

s=2π∫ᵇₐ y√1+(y)² dx

y=x³

y'=3x²

By rotating the curve y=x³ about the x axis in the interval [0,2]

s=2π∫₀²(x³)√1+(3x²)² dx

let u=1+9x⁴

du=36x³dx

dx/36x³

Substituting u and du in the integral,

s= 2π∫₀²(x³)√u du/36x³

s= 2π∫₀²√u du

s= 2π/36.2/3[u.3/2]₀²

s= π/27[(145)³/²-(1)³/²]

s= π/27 [1746.03-1]

s= π/27 [1745.03]

s= 64.67π

s= 64.67(3.14)

s=203.06 square units.

therefore, the exact surface area is 203.06 square units.

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Answer:

      In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.                       

         Given:    y=3x, for x is in [1,125] about the y axis.

                                            y=x³ ,0≤x≤2

Lets find the surface area of the rotating curve,

Finding surface area for rotation along x-axis,

                                    s=2π∫ᵇₐ y√1+(y)² dx

                                     y=x³

                                     y'=3x²

By rotating the curve y=x³ about the x axis in the interval [0,2]

                           s=2π∫₀²(x³)√1+(3x²)² dx

                          Assuming  u =1+9x⁴

                                           du=36x³dx

                                               =dx/36x³

Substituting respective values of u and du in the integral,

                              s= 2π∫₀²(x³)√u du/36x³

                              s= 2π∫₀²√u du

                              s= 2π/36.2/3[u.3/2]₀²

                              s= π/27[(145)³/²-(1)³/²]

                              s= π/27 [1746.03-1]

                              s= π/27 [1745.03]

                              s= 64.67π

                              s= 64.67(3.14)

                              s=203.06 square units.

hence, the surface area is 203.06 square units.

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Answer:

6 days

Step-by-step explanation:

if they are writing at 5,000 words per 6 hours, we divide 120,000 by 5,000 and then multiply by 6: 120,000/5,000 = 24, 24*6 = 144 total hours

There are 24 hours in a day: 144/24 = 6

The category of the function f(x) shown in the graph is a (B) linear function.

To find which type of function describes f(x):

How do determine the graph?

Therefore, the category of the function f(x) shown in the graph is a (B) linear function.

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The complete question is given below:
Which type of function describes f(x)?

(A)exponential

(B) linear

(C) logarithmic

(D) polynomial

(E) rational

Answer:

7

Step-by-step explanation:

The length of the arc can be calculated via a simple proportion:

2 pi r : 360° = x : 45°

Where r is the radius of the circumference and x the length of the arc we want to know. Isolating the x:

x = (2 pi r : 360) * 45 = (2 pi * 9 : 180) * 45 = 18 pi : 360 * 45 = 18pi : 8 = 7

The maximum value of P = x + 6y subject to the constraints is 9

The objective function is given as:

P = x + 6y

The constraints are given as:

2x + 4y ≤ 10

x + 9y ≤ 12

x≥0 y≥0

Rewrite 2x + 4y ≤ 10 and x + 9y ≤ 12 as equations

2x + 4y = 10

x + 9y = 12

Divide 2x + 4y = 10  through by 2

x + 2y = 5

Subtract x + 2y = 5 from x + 9y = 12

x - x + 9y - 2y = 12 - 5

Evaluate the difference

7y = 7

Divide by 7

y = 1

Substitute y = 1 in x + 2y = 5

x + 2(1) = 5

Solve for x

x = 3

So, we have

(x, y) = (3, 1)

Substitute (x, y) = (3, 1) in P = x + 6y

P = 3 + 6 * 1

Evaluate

P = 9

Hence, the maximum value of P = x + 6y subject to the constraints is 9

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Answer:

±5

Step-by-step explanation:

-5k²+20k-30

if u look at the equation ±5 are the greatest common factors so we ±5(±k²±4k±6)

Answer:

is 54, 45, 36, 27, 18

Step-by-step explanation:

Recursive formulas give us two pieces of information:

1. The first term of the sequence

2. The pattern rule to get any term from the term that comes before it

In the formula given,

n is any term number

f(n) is the nth term

This means

f(1) is the first term

f(f-1) is the term before the nth term

To find the first five numbers in this arithmetic sequence, we know the formula has given us these two pieces of information:

1. The first term is 54

2. The rule to get any term from its previous term is -9

So, we know the sequence for this formula is 54, 45, 36, 27, 18 because starting off with 54, then minus 9 from every sum gives us the following equations

54-9=45

45-9=36

36-9=27

27-9=18

Answer:

y-9=-4(x+2)

Step-by-step explanation:

The point-slope formula is:

y-y1=m(x-x1)

m=-4 and use the point (-2, 9)

                                       x1    y1

Plug in the information.

y-9=-4(x+2)

This is the equation written in point-slope form using the point (-2, 9).

Hope this helps!

It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

According to the question

Gregory can mow the family's lawn in 3 hours, she mows at a rate of 1/3 of the lawn per hour(1/3 lawn/hour)

Jennifer can mow it in 4 hours, which means her rate is 1/4 lawn/hour.

Together , their rates are 1/3 + 1/4.

This equals 7/12 lawns/hr.

We want to know how many hours they have to mow in order to mow 1 lawn.

This can be represented by the equation : [tex]\frac{7}{12} \times x = 1[/tex]

To solve for x, we would divide both sides by 7/12.

This leaves us with x = 12/7 which is 1.714.

Convert 1.714 to minutes by multiplying 60.

This gives you a final answer of about 1 hour 43 minutes.

Hence, It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

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Answer:

3; 1

Step-by-step explanation:

when there are six spots we can see that there are 2 eyes

so

divide both sides by 2

6:2

6 / 2 : 2 / 2

3 : 1

that is your answer

Kathy has 22 more Euros than British pounds.

Linear equation is an algebraic equation that is a representation of the straight line. Linear equations are composed of variables and constants. These equations are of first-order, that is, the highest power of any of the involved variables i.e. 1. It can also be considered as a polynomial of degree 1. Linear equations containing only one variable are called homogeneous equations. The corresponding variable is called the homogeneous variables.

For instance,

300 / 2 = 150 dollars.

150 /1.64 = 91.46 British pounds

150 /1.32 =113.64 Euros

113.64 - 91.46 =22.18 ≅ 22

Thus Kathy has 22 more Euros than British pounds.

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Option (a) Sample

Sample is the research that analyzes a portion of an entire population.

A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.

By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.

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Answer:

Confidence Level z*-value

90% 1.645 (by convention)

95% 1.96

98% 2.33

99% 2.58

Step-by-step explanation:

the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.

Answer:

  b.  18

Step-by-step explanation:

The perpendicular bisector of a chord is a diameter of the circle. Conversely, if the diameter is perpendicular to a chord, it also bisects it.

  BC = BP +PC

  BC = 2×BP . . . . . . . BP = PC

  BP = BC/2 = 36/2 = 18 . . . . . . . divide by 2; substitute given values

The length of segment BP is 18 units.

The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.

In a quadratic equation ax² + bx + c = 0

when (b² - 4ac) exists a perfect square only then we can factorize the equation.

In the given equation x² - 8x - 12 we have to determine the value of

b² - 4ac

From the equation, we get b = -8 and c = -12

b²- 4ac = (-8)² - 4(1)(-12)

= 64 + 48 = 112

Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.

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Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the given angle is as follows:

[tex]\theta = \frac{5\pi}{4}[/tex]

It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:

[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]

The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:

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Answer:

The measure of the reference angle is 45 degrees

tan(theta) = 1

Step-by-step explanation: