A. What are the coordinates of R’ if R (-2, 7) is dilated around the origin with k=3?
B. What are the coordinates of T’ if T (4,-1) is dilated by a scale factor of ½ with R as the center of the dilation?

Answer:

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Answer:

x+(x+5)=28

Step-by-step explanation:

girls(g)should be equal to x

boys(b) will therefore be x+5

x+(x+5)=28

Answer:

  (x, y) = (-√3/2, 1/2)

Step-by-step explanation:

The terminal point for that angle can be read from a unit circle chart.

On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...

  (x, y) = (-√3/2, 1/2)

The value of 'y' is 32. 5 degrees . Option B

It is important to note that If two chords intersect inside a circle,

The measure of the angle formed is half the sum of the measure of the arcs intercepted by the angle and its vertical angle

From the diagram, it is shown that the both the chords at 'y' and the angle '65' intersect in the circle

We then have that;

[tex]y = 65[/tex] × [tex]\frac{1}{2}[/tex]

[tex]y = 65[/tex] × [tex]0. 5[/tex]

y = 32. 5 degrees

We can see that the value of 'y' in the given figure is 32. 5 degrees which is half the angle at the vertex of the intersecting chords.

Thus, the value of 'y' is 32. 5 degrees . Option B

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Answer:

Step-by-step explanation:

slope-- 1/2

y intercept-- -4

Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.

Given that angle ADE ≅ angle ABC, we also know that:

Angle EAD ≅ CAB.

Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.

Thus, the ratios that are equal to each other would be:

AE/EC = AD/DB.

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Answer: 1

Step-by-step explanation:  It's subtraction and add ion look at the right side

The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

Substituting a = x + y/2 and b = x - y/2 in this, we get:

cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],

or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],

or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:

cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.

Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

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The provided question is incorrect. The correct question is:

"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."

Solving a system of equations, we can see that:

Let's define the variables:

With the given information, we can write:

P*8h = D

C*7h = D

C = 2*P - 144mi/h

So we have a system of 3 equations, where D is the distance in the problem.

With the first and second equations we can write:

P*8h = D = C*7h

Isolating P, we get:

P = C*(7/8)

Now we can replace that in the last equation:

C = 2*P - 144mi/h

C = 2*C*(7/8) - 144mi/h

And now we can solve that for C.

C - 2*(7/8)*C = - 144mi/h

C*(1 - 14/8) = -144mi/h

C*(8/8 - 14/8) = - 144mi/h

C*(6/8) = 144mi/h

C = (8/6)*144mi/h = 192mi/h

Now that we know the speed of the commercial jet, we can find the speed of the private jet.

P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h

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Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.

A proportion is a mathematical measure that compares two variables or numbers.

Proportions can be stated in percentages or ratios, as decimals or fractions.

Content of 16-ounce bag of nuts = 60% chocolate-covered nuts

Content of first bag = 50/50 plain and chocolate-covered nuts

Content of second bag = 80% chocolate-covered nuts

A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.

Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.

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Is Bob correct?

Answer:

It is a rational number.

Step-by-step explanation:

A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.

Hi :)

Below is the difference between rational & irrational numbers

Evidently,

Let's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]

Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.

Thus

[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

The answer is Pedro.

Answer: 3 loops

Step-by-step explanation: The loop is 1.2 miles, and the total walk is 3.6 miles. You want to find out how many laps are in the 3.6 miles. This can be found using division. 3.6/1.2= the number of 1.2 mile laps inside the 3.6 mile walk, which is 3 laps. hope this helped!

See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1

From the question, the given parameters are:

Amplitude, A = 5

Vertical shift, D = -1

Period, T = 4

A cosine function is represented as:

f(x) = A cos(B(x + C)) + D

Where

Amplitude = A

Period = T

Horizontal shift = C

Vertical shift = D

Since the horizontal shift is not stated in the question, we can assume that the horizontal shift is 0

i.e. C = 0

So, the equation of the cosine function becomes

f(x) = A cos(Bx) + D

Calculate the value of B using

B = 2π/T

So, we have:

B = 2π/4

Evaluate

B = π/2

So, we have:

f(x) = A cos(π/2x) + D

Substitute the known values of A and D in the above equation

f(x) = 5 cos(π/2x) - 1

Next, we plot the graph of the cosine function on a graphing tool

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Answer:

1/6 p - 4/5 or -4/5 + 1/6p They both mean the same thing.

Step-by-step explanation:

You have two sets of like terms.  You have 2 terms that have the variable p as part of the term and you have 2 terms with no variable that are called constants.

-2/3p + 5/6p  Are two terms that you want to combine.  We need common denominators to add.  The common denominator would be 6, so we will make an equivalent fraction with -2/3 with 6 as the denominator.

-2/3 = -4/6  We just multiple the top (numerator) and the bottom (denominator of the first fraction (-2/3) by 2 to the get the second faction (-4/6).  Now we can add the 2 terms with p together.

-4/6p + 5/6p  The denominators stays the same (6) and we add the numerators -4 + 5 = 1,  So our p term is 1/6p

Now we have to combine the constant terms of 1/5 and - 1.  Another name for -1 is 5/5.  We are going to use this form so that our denominators are the same.

1/5 - 5/5 = -4/5

Based on the amount that both Salesmen A and B earn per sale, the number of sales they both had was 12 sales.

Sales commission is a key aspect of sales compensation. It's the amount of money a salesperson earns based on the number of sales they have been able to make.

We are told that;

Salesman A gets $65 per sale.

Salesman B gets $300 and $40 per sale.

Assuming the number of sales to take them both to the same amount is x, the relevant formulas would be:

65x = 300 + 40x

Rearranging gives;

65x - 40x = 300

25x = 300

x = 300/25

x = 12 sales

The amount that salesman A earned is = 65 * 12 = $780

The amount that salesman B earned is = 300 + (40 * 12) = $780

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[tex]f(x) = 2 {}^{x} \\ g(x) = f(x + 2) = 2 {}^{x + 2} \\ g(x) = 2 {}^{x + 2} =2 {}^{x} .2 {}^{2} = 4.2 {}^{x} [/tex]

[tex]a.b {}^{x} = > horizontal \: asymp \: y = 0[/tex]

[tex]4.2 {}^{0} = 4 = > vertical \: int \: (0,4)[/tex]

[tex]a.b {}^{x} = > x ∈ \: ] -∞ , ∞ [[/tex]

The horizontal asymptote of the function f ( x ) = 2ˣ is y = 0 and the y-intercept is ( 0 , 4 )

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be denoted as f ( x )

Now , the value of f ( x ) is

f ( x ) = 2ˣ   be equation (1)

The y-intercept of the function is when x = 0

So , when x = 0

f ( 0 ) = 2⁰

f ( 0 ) = 1

So , the y-intercept of the function is at ( 0 , 4 )

And , when the function f ( x ) is tending to zero , the horizontal asymptote is y = 0

Therefore , the horizontal asymptote is y = 0

The domain of the exponential function is { -∞ < x < ∞ }

Hence , the horizontal asymptote of the function f ( x ) = 2ˣ is y = 0

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The sales last year of the company is 5617

The given parameters are:

Company sales = 6740

Percentage increase = 20%

The sales of the company last year (x) to date is calculated as:

Company sales = (1 + Proportion) * Last year sales

Substitute the known values in the above equation

6740 = (1 + 20%) * x

Evaluate the sum

6740 = 1.2 * x

Divide both sides by 1.2

x = 5617

Hence, the sales last year is 5617

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The odds in favor of them winning is 20%

From the information given, we have that the probability of them winning the next game is 80%

P( winning) = 80% = 0. 8

The odds against them winning is given as;

1 - probability of winning

We have;

= 1 - 0. 8

= 0. 2

The odds in favor of them winning is simply the probability of them losing;

= 0. 2 × 100

= 20%

Thus, the odds in favor of them winning is 20%

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The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

From the complete question, we understand that Mr. A wants to plays the game until he wins

This means that

He might win at the first game and he might win after n attempts

So, the values of X are

X = 0, 1, 2, 3, 4.......n

Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

The probability of x is represented as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, the probability that X = n is:

P(n) = nCn * p^n * (1 - p)^(n - n)

Evaluate the exponent

P(n) = nCn * p^n * 1

Evaluate the combination expression

P(n) = 1 * p^n * 1

This gives

P(n) = p^n

Hence, the probability that X = n is p^n

The distribution satisfies PMF conditions because

The expected value E(x) is calculated using

E(x) = n * p

So, we have:

E(x) = np

Hence, the value of E(x) is np

The variance V(x) is calculated using

V(x) = √n * p * (1 - p)

So, we have:

V(x) = √np(1 - p)

Hence, the value of V(x) is √np(1 - p)

The memoryless property of X is that each probability of X is independent

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The cost to rent each chair is $1.5 and cost to rent each table is $6.5

From the question, we are to determine the cost to rent each chair and each table

Let c represent chair

and

t represent table

From the given information,

The total cost to rent 5 chairs and 3 tables is $27

That is,

5c + 3t = 27 ------------ (1)

Also,

The total cost to rent 2 chairs and 12 tables is $81

That is,

2c + 12t = 81 ---------- (2)

Now, solve the equations simultaneously

5c + 3t = 27 ------------ (1)

2c + 12t = 81 ---------- (2)

Multiply equation (1) by 2 and multiply equation (2) by 5

2 × [5c + 3t = 27 ]

5 × [2c + 12t = 81 ]

10c + 6t = 54        ------------- (3)

10c + 60t = 405   ------------- (4)

Subtract equation (4) from equation (3)

10c + 6t = 54        

10c + 60t = 405

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

-54t = -351

t = -351/-54

t = 6.5

Substitute the value of t into equation (2)
2c + 12t = 81

2c + 12(6.5) = 81

2c + 78 = 81

2c = 81 - 78

2c = 3

c = 3/2

c = 1.5

∴ The cost of chair is $1.5 and cost of table is $6.5

Hence, the cost to rent each chair is $1.5 and cost to rent each table is $6.5

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Answer:20.00

Step-by-step explanation: next time include the table but i managed to find it anyway

The third decile is 58.

Decile is a statistical term that divides the data into groups of ten. The third decile is the third group of the data set.

Third decile = 3/10 x (n + 1 )

3/10 x 16 = 4.8th term  = 58

Answer:

26 units^2

Step-by-step explanation:

the area of a kite is (d1 * d2)/2

d1 = 2 + 2 = 4

d2 = 6 + 7 = 13

4 * 13 = 52

52 / 6 = 26

26 units^2 is your answer

Answer: 26

Step-by-step explanation:

The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.

Let

For instance,

if the size of the first application is 297 MB

Size of the second application= x - 3.45 mb

= 297 MB - 3.45 MB

= 293.55 MB

Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB

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Answer: B. (-1, -5)

Step-by-step explanation:

Given equations

2x + y = -7

x - y = 4

Concept

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]

Convert into matrix

[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

Calculate the inverse of the matrix

[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]

Solve by multiplying the inverse of the matrix

[tex]A*A^{-1}=A^{-1}*A=I[/tex]

[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]

Simplify by multiplication

[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]

Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

this just means that the first function with input value x = 0 is calculated. that result becomes the input value x for the second function. and that result becomes the input value x for the 3rd function. and that result is then our result.

to answer a and b we only need to look at the main operation of each function :

the first one uses only basic multiplication and subtraction.

the second one uses squaring.

the third one is a 1/x operation.

a.

since the final result is a negative number (-31), the second function with the square operation cannot be last.

because a square operation always delivers a positive result.

+a × +a = +a²

-a × -a = +a²

remember, for a square operation we multiply the same number by itself. therefore we cannot mix signs like -a × +a, because then they would not be the same numbers anymore.

b.

since the initial input value is 0, the third function (1/x) cannot be the first, because 1/0 is not defined.

c.

because of the "large" -32 term in the first function I guess that this will be the last one to create such a low negative result of -31.

since 1/x cannot be first, (x - 2)² is then first. that makes 1/x second, and (4x - 32) third, as mentioned.

let's try :

x = 0

(x - 2)² = (0 - 2)² = (-2)² = 4

x = 4

1/x = 1/4

x = 1/4

4x - 32 = 4×1/4 - 32 = 1 - 32 = -31

hurrah ! we are correct !

Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion estimate and the sample size are given as follows:

p = 0.45, n = 437.

Hence the mean and the standard error are:

The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (0.42 - 0.45)/0.0238

Z = -1.26

Z = -1.26 has a p-value of 0.1038.

2 x 0.1038 = 0.2076.

0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

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If the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.

Given that height in t seconds is shown by h(t)=52t-16[tex]t^{2}[/tex].

We are required to find the time after which the ball will attain its maximum height.

The maximum height is the y coordinate of vertex of the parabola. Then we can use the following value of t.

h(t)=52t-16[tex]t^{2}[/tex]

Differentiate with respect to t.

dh/dt=52-32t

Again differentiate with respect to t.

[tex]d^{2}h/dt^{2}[/tex]=-32t

Because tim cannot be negative means the height is maximum.

Put dh/dt=0

52-32t=0

-32t=-52

t=52/32

t=1.625

Hence if the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.

Question is incomplete as the right and complete equation is

h(t)=52t-16[tex]t^{2}[/tex] .

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Area equals Length times Width.

since the width of this equation is 5 units Longer then its Length

W = L + 5

To put this area in a equation we could say

L(L+5)=A
Simplify the equation, L^2 + 5L = A.