Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2. which word describes their measures?

The required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

Given that,

The endpoints of the circle's diameter (-2, -1) and (4,7).
The equation of the circle is to be determined.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r².

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

Center of the circle(h, k) = (-2 + 4)/2 ,(-1+7)/2
                                  = 1  , 3
Radius of the circle,
[tex]r^2 =\sqrt{(1+2)^2+(3+1)^2}\\r^2 =\sqrt{9+16} \\r^2 = 25[/tex]

Equation of the circle with center (1, 3)
[tex]r^2 = (x - 1)^2 + (y-3)^2[/tex]
[tex]25 = (x - 1)^2 + (y-3)^2[/tex]

Thus, the required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

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The current value of the stock is $53.413455.

To find the current price of stock:

Stock’s current price: 53.41 dollars

First, we determine the stock's value using the CAPM model.

Then, Ke = 0.085 + 1.3(0.045).

The current value of the future dividends must now be known:

The next dividends, which are at perpetuity will be solved using the dividend growth model:

In this case, dividends will be:

Return will be calculated using the CAPM and g = 7%.

plug this into the Dividend grow model,

Finally, it's crucial to remember that these statistics were calculated for the present year.

We must bring them to the present day using the present value of a lump sum:

We add them and get the value of the stock, 53.413455

Therefore, the current value of the stock is $53.413455.

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Answer:

71

Step-by-step explanation:

The regression linear function, in slope-intercept form, is given by:

y = -0.07x + 14.5

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points are given as follows:

(0, 14.7), (1, 14.5), (2, 14.4), (3, 14.1), (4, 14), (5, 14.1), (6, 14.1), (7, 14.2), (8, 14), (9, 13.8), (10, 14).

Inserting these points into a calculator, the regression linear function, in slope-intercept form, is given by:

y = -0.07x + 14.5

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Answer:

y = -0.07x + 14.5

Step-by-step explanation:

This is a telescoping sum. The K-th partial sum is

[tex]S_K = \displaystyle \sum_{k=1}^K \left(\frac1{\sqrt{k+1}} - \frac1{\sqrt{k+3}}\right) \\\\ ~~~= \left(\frac1{\sqrt2} - \frac1{\sqrt4}\right) + \left(\frac1{\sqrt3} - \frac1{\sqrt5}\right) + \left(\frac1{\sqrt4} - \frac1{\sqrt6}\right) + \left(\frac1{\sqrt5} - \frac1{\sqrt7}\right) + \cdots \\\\ ~~~~~~~~+ \left(\frac1{\sqrt{K-1}} - \frac1{\sqrt{K+1}}\right) \\\\ ~~~~~~~~+ \left(\frac1{\sqrt K} - \frac1{\sqrt{K+2}}\right) + \left(\frac1{\sqrt{K+1}} - \frac1{\sqrt{K+3}}\right)[/tex]

[tex]\displaystyle = \frac1{\sqrt2} + \frac1{\sqrt3} - \frac1{\sqrt{K+2}} - \frac1{\sqrt{K+3}}[/tex]

As [tex]K\to\infty[/tex], the two trailing terms will converge to 0, and the overall infinite sum will converge to

[tex]\displaystyle \sum_{k=1}^\infty \left(\frac1{\sqrt{k+1}} - \frac1{\sqrt{k+3}}\right) = \lim_{k\to\infty} S_k = \boxed{\frac1{\sqrt2} + \frac1{\sqrt3}}[/tex]

By the limit comparison test, the expression √[1 / (1 + 1 / k)] - √[1 / (1 + 3 / k)] has a limit, then the expression [1 / √(k + 1)] / [1 /√k] -  [1 / √(k + 3)] / [1 /√k] has a limit and the series ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)] is convergent.

Herein we have a series that involves radical components. First, we simplify the expression given:

∑ [1 / √(k + 1) - 1 / √(k + 3)] = ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)]

The convergence of the series can be proved by the limit comparison test, where each component of the subtraction of the series is compared with a series that is convergent. We notice that both 1 / √(k + 1) and 1 / √(k + 3) resembles the expresion 1 /√k. Then, we have the following subtraction of ratios:

[1 / √(k + 1)] / [1 /√k] - [1 / √(k + 3)] / [1 /√k]

√k / √(k + 1) - √k / √(k + 3)

√[k / (k + 1)] - √[k / (k + 3)]

Then, by using the limit property for rational functions we find the following result for n → + ∞:

√[1 / (1 + 0)] - √[1 / (1 + 0)]

√1 - √1

1 - 1

0

By the limit comparison test, the expression √[1 / (1 + 1 / k)] - √[1 / (1 + 3 / k)] has a limit, then the expression [1 / √(k + 1)] / [1 /√k] -  [1 / √(k + 3)] / [1 /√k] has a limit and the series ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)] is convergent.

The statement is incomplete and complete form cannot be found, therefore, we decided to determine if the series is convergent or not.

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Step-by-step explanation:

4.6 hrs is 46over 10 which is

13 over 5 or 2 and 3over 5

Answer: B) -8

Step-by-step explanation:

We add 12 both sides

Add −18 and 12 to get −6.

Multiply both sides by 3/4 by the reciprocal of 3/4.

Express a -6 x (3/4) as a single fraction.

Multiply −6 and 4 to get −24.

Divide −24 by 3 to get −8.

Answer: Option "2" is correct. ✅

Answer:

- (2x^2 - 13x + 6)

The above expression is in brackets and a negative sign is outside of the brackets. This means that when expanding the expression, we have to multiply each number with the negative sign (each number would switch their signs to the opposite one). Therefore, 2x^2 becomes -2x^2, -13x becomes 13x and 6 becomes -6.

Answer: 180 meters

Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.

The average number of miles he will ride each day to meet his goal is 6.6 miles

He wants to ride his bicycle 30.4 miles this week.

He has already ridden 4 miles.

He rides 4 more days.

Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:

let

x = number of miles driven

Hence, the equation can be represented as follows;

4x + 4 = 30.4

Therefore,

4x + 4 = 30.4

4x + 4 - 4 = 30.4 - 4

4x = 26.4

x = 26.4 / 4

x = 6.6

Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles

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The number set(s) that - 10 belong to are rational numbers, integers and real numbers. Option C, D and E

A rational number can be defined as a number expressed as the ratio of two integers, where the denominator is not be equal to zer0

- 10 can be written as = 1/ 10

Integers are whole number that could be positive, negative and even zero

- 10 is a negative whole number

Real numbers are numbers with continuous quantity that can represent  distance along a number line

-10 can represent distance along a number line.

Thus, the number set(s) that - 10 belong to are rational numbers, integers and real numbers. Option C, D and E

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Answer: C. - √2

Step-by-step explanation:

Given requirements from the question

Find the exact value of sec 135°

Convert into common trigonometric expression

sec = secant

secx = 1 / cosx

Therefore, sec 135° = 1 / (cos 135°)

Find the reference angle

135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.

Since 135° is in the second quadrant, its reference angle will be

                                         180° - 135° = 45°

However, we need to consider the positive and negative.

In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.

Therefore, when the value of cosine is in QII, it is negative.

The reference angle = - (1 / cos 45°)

Determine the final value

Given that the reference angle = - (1 / cos 45°)

cos 45° = 1 / √2

Therefore:

sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) = [tex]\boxed{-\sqrt{2} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.

The formula for finding the number of arrangement is given as;

Permutation = [tex]\frac{n!}{n - r!}[/tex]

Where;

From the question given, we can deduce that

n = 12 people

r = 2, because they must come next to each other and is taken as 2

We then have,

Permutation = [tex]\frac{12!}{12 - 2!}[/tex]

Permutation = [tex]\frac{12!}{10!}[/tex]

Permutation = 132 ways

This is to tell us that the number of ways to arrange the people is 132 ways

Thus, the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.

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The weight of the package is 12 ounces

The given parameters are

Total amount = $2.76

Domestic rate = $.23 per ounce

The equation to determine the weight of the package is represented as:

Weight = Total amount/Domestic rate

Substitute the known values in the above equation

Weight = 2.76/.23

Evaluate the quotient

Weight = 12

Hence, the weight of the package is 12 ounces

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The correct option is B.

5 pound

The number (5.3) after Decimal is <5 so it round off to 5.

It is the same to round a number to one decimal place as to the nearest tenths. At this instance, it is known which numeral is in the hundredths position. When the number in the hundredths place is higher than or equal to 5, the tenths digit is raised by one unit.

A typical rule of thumb is to glance at the digit immediately to the right of the place value you want to round to and make your choice. For instance, rounding 5.1837 to the closest hundredth would result in 5.18 (because 3<5), whereas rounding 5.184 to the nearest thousandth would result in 5.184 (because 7>5).

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I understand that the question your are looking for is:

A scale measured a 4.5-pound brick as weighing 5.3 pounds. which measurement is more accurate but less precise than 5.3 pounds?

A. 4.98 pounds

B. 5 pounds

C. 5.52 pounds

D. 6 pounds

The value of λ = 8s + 6

The zeroes of a function f(x) are the values of x at which f(x) = 0.

Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.

Since we require λ,

So, let f(x) = 2 - 8x + λ.

At x = a, f(x) = 0.

So, substituting the value of x = a into f(x), we have

f(a) = 2 - 8a + λ

Since f(a) = 0, we have

2 - 8a + λ = 0   

2 + λ = 8a  (1)

Also, x = s, f(x) = 0.

So, substituting the value of x = s into f(x), we have

f(s) = 2 - 8s + λ

Since f(s) = 0,we have  

2 - 8s + λ = 0

2 + λ = 8s  (2)

Since a - s = 2

Making a subject of the formula, we have

⇒ a = s + 2

So, substituting the value of a into equation (1), we have

2 + λ = 8a  (1)

2 + λ = 8(s + 2)  (1)

2 + λ =  8s + 16

- 14 + λ = 8s   (3)

Adding equation (2) and (3), we have

-14 + λ = 8s   (3)

+

2 + λ = 8s     (2)

-12 + 2λ = 16s

2λ = 16s + 12

Dividing through by 2, we have

2λ/2 = (16s + 12)/2

λ = 4(4s + 3)/2

λ = 2(4s + 3)

λ = 8s + 6

So, the value of λ = 8s + 6

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The image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)

The coordinate point is given as:

P = (-3, 2)

The translation is given as

T<2,1>

The translation can be represented as:

(x, y) = (x + 2, y + 1)

So, we have the following equation

P' = (-3 + 2, 2 + 1)

Evaluate the sum

P' = (-1, 3)

Hence, the image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)

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The correct option regarding the outliers of the data-set is given by:

The greatest value, 78, is the only outlier.

The IQR for this problem is:

IQR = 37 - 13 = 24.

Hence the bounds for outliers are:

The options are:

Hence the correct option is that only 78 is an outlier.

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The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;

[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]

From the given information, we have;

According to the ratio of corresponding sides of similar triangles, we have;

[tex] \frac{x}{z} = \mathbf{\frac{BD}{QD} }[/tex]

[tex] \frac{y}{z} = \frac{BD}{ BQ} [/tex]

Which gives;

[tex] \mathbf{\frac{y}{z}} = \frac{BD }{ BD - Q D} [/tex]

[tex] \frac{z}{y} = \frac{BD - QD }{ BD } = 1 - \frac{Q D }{ BD}[/tex]

QD × x = BD × z

BD × z = (1 - QD/BD) × y = y - (QD × y/BD)

Therefore;

BD × z = y - (QD × y/BD)

BQ × y = y - (QD × y/BD)

BQ × y = y - (z × y/x) = y × (1 - z/x)

(1 - z/x) = BQ

BD × z = y × (1 - z/x)

BD = (y × (1 - z/x))/z

Therefore;

QD × x = y × (1 - z/x)

(BD-BQ) × x = y × (1 - z/x)

(BD-(1 - z/x)) × x = y × (1 - z/x)

BD = (y × (1 - z/x))/x + (1 - z/x)

BQ + QD = (1 - z/x) + (y × (1 - z/x))/x

BD = BQ + QD

(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z

(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z

Dividing both sides by (1 - z/x) gives;

y/x + 1 = y/z

Dividing all through by y gives;

(y/x + 1)/y = (y/z)/y

Therefore;

[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]

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We can rewrite the given time as:

First, remember that:

60s = 1 min

Then to write that amount in minutes, we just need to divide by 60, so we get:

(4.22x10^17)/60  mins=  7.03x10^15 mins

Now, remember that:

1 hour = 3600s

Then to get the time in hours, we need to divide by 3600:

(4.22x10^17)/3600 h = 1.17x10^14 hours.

Similarly, you can change to any time unit that you want, for example:

1 day = 24*3600 s

Then the time in days is:

(4.22x10^17)/(24*3600) days = 4.88x10^12 days.

And so on.

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The expectancy theory that could be phrased as the above question is based on the element called expectancy.

In this question,

Expectancy theory proposes that an individual will behave or act in a certain way because they are motivated to select a specific behavior over others due to what they expect the result of that selected behavior will be.

To make the connection between motivation, effort and performance, expectancy theory has three variables: Expectancy, Instrumentality and Valence.

Expectancy theory consists of three basic components:

(1) The employee's expectancy that working hard will lead to his or her desired level of performance;

(2) The employee's expectancy that working hard will thus ensure that rewards will follow; and

(3) Whether or not the employee's perception that the outcome of working hard is worth the effort or value associated with hard work.

VIE expectancy theory is often formulated using the equation MF (motivational forces) = V (valence) x I (instrumentality) x E (expectancy).

From the definition, the probability that, "if i do a good job, that there will be some kind of outcome in it for me" is comes under the element expectancy(E).

Hence we can conclude that the expectancy theory that could be phrased as the above question is based on the element called expectancy.

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The balance after 8 years is $22,942.67

We know that the savings account earns 15% annually, and the initial deposit is $7500, then the balance as a function of time in years is:

B = $7500*(1 + 15%/100%)^t

B = $7500*(1.15)^t

The balance after 8 years is what we get when we evaluate the above function in t = 8, so we get:

B = $7500*(1.15)^8 = $22,942.67

So the correct option is the last one.

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i really hate how we actually have to type something.

Answer:

 A. 3x^2y(4x2 + 3xy - y^2)

Step-by-step explanation:

 -12(x^4)y - 9x³y² + 3x²y³

 -3x²y(4x² + 3xy - y²)

60 ÷ 30 = 2

and

90 ÷ 30 = 3

---> 60/90 = 2/3

❄ Hi there,

the way 60/90 becomes 2/3 is this:

[tex]\sf{\dfrac{60\div30}{90\div30}=\dfrac{2}{3}}[/tex]

That's it!

❄

This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.

From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.

Let 1 = IMO

Let 0 = IPho.

Therefore, the number of arrangement will be:

0011

0110

1100

1010

0101

1001

Therefore, the number of arrangement will be 6.

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The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3

The quadratic equation is given as:

y = -x^2 + 4x - 1

Differentiate the above quadratic equation.

This is done with respect to x by first derivative

So, we have:

y' = -2x + 4

Set the derivative to 0

-2x + 4 = 0

Subtract 4 from both sides of the equation

-2x + 4 - 4 = 0 - 4

Evaluate the difference in the above equation

-2x = -4

Divide both sides of the above equation by -2

x = 2

Rewrite as

h = 2

Substitute 2 for x in the equation y = -x^2 + 4x - 1

y = -2^2 + 4 *2 - 1

Evaluate the equation

y = 3

Rewrite as:

k = 3

A quadratic equation in vertex form is represented as:

y = a(x - h)^2 + k

So, we have:

y = a(x - 2)^2 + 3

In the equation y = -x^2 + 4x - 1, a = -1

So, we have:

y = -(x - 2)^2 + 3

Hence, the vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3

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Answer: A, C, and D

Step-by-step explanation:

          A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.

✓ A. 0.032

✗ B. 0.999...

✓ C. 0.525

✓ D. 0.75