The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.

The values of sin2x, cos2x and tan2x is 120/169, -119/169 and -120/119 respectively.

What is cosine?

In mathematics, the cos meaning refers to the cosine function, which is taught in the most crucial geometry lesson, trigonometry. One of the three primary uses of trigonometry is the cosine function. Sine, cosine, and tangent are the three trigonometric ratios that are also referred to as these three functions.

The cosine of an angle is defined by the cos meaning in trigonometry. This angle, which is an acute angle in a right-angled triangle, is taken into account when determining the ratios. As a result, the ratio between an angle's adjacent side and the triangle's hypotenuse is the cosine of an angle in a right triangle.

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Answer:

She spend $7 a month on downloads.

Step-by-step explanation:

y = the total spent on downloads

x = number of months

m = the amount spent each month

y = mx

45.50 = m(6.5)  Divide both sides by 6.5

7 = m

Answer:

  [tex]\bullet\quad(x^3+y^3)^\frac{1}{2}\\\\\bullet\quad\dfrac{81}{1}[/tex]

Step-by-step explanation:

You want √(x³ +y³) written with a rational exponent, and 27^(4/3) written as a ratio of integers.

The square root is the same as the 1/2 power. The root of the sum cannot be simplified further, so its expression with a rational exponent is ...

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

The expression 27^(4/3) can be simplified to ...

  [tex]27^\frac{4}{3}=(\sqrt[3]{27})^4=3^4=81=\boxed{\dfrac{81}{1}}[/tex]

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The scale factor of Dilation is 2

The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

We want to find the scale factor at which QRST is dilated to form Q'R'S'T'

We will find that the scale factor is 2.

In a general dilation, we will see that all the measures change in the same way, by the scale factor.

This means that:

QR*k = Q'R'

RS*k = R'S'

And so on, where k is the scale factor.

Then we can just find one of the equivalent measures in both trapezoids and find the value of k.

For example, we have:

Q'R' = 8

QR = 4

Replacing these on the above equation we get:

4*k = 8

k = 8/4 = 2

k = 2

Therefore the scale factor of dilation is 2.

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Answer:

13.3=c

Step-by-step explanation:

The hypotenuse can be found with the equation [tex]a^2+b^2=c^2[/tex].  For this problem, let

a=8.3

b=10.4

So,

[tex](8.3)^2+(10.4)^2=c^2\\177.05=c^2\\\sqrt{177.05}=\sqrt{c^2}\\13.31=c[/tex]

The equation is 2w + 10 = 26.

The number of weeks the driving class lasts is 8 weeks.

With that,

Terrence signed up for the Safe Venture driving school.

He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.

When Terrence completes the 26 total hours of instruction, he will take his driver's test.

We have to determine,

Which equation can you use to find w, the number of weeks the driving class lasts.

According to the question,

He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.

Then, The equation of the number of weeks the driving class lasts,

= 2w + 10

When Terrence completes the 26 total hours of instruction, he will take his driver's test.

2w + 10 = 26

He spends 10 hours driving and adding on 2 more classes with a total of 26 hours.

Therefore,

The number of weeks the driving class lasts,

2W + 10 = 26

2W = 26 - 10

2W = 16

W = (16/2)

W = 8

Hence, The number of weeks the driving class lasts is 8 weeks.

Answer:

= 408.16 or =20000/49

Step-by-step explanation:

= (78000/ 19110) x100

= (200/49)*100

=20000/49

Since a + b + c are vertically opposite angles, e = 130.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

d=70, opposite vertical angle

180 - 70 - 40 = 2 using angles on a straight line.

We now possess the two angles, and since they are perpendicular to one another, a and c = 35.

Because of the vertically opposed angles, b = 40.

4. Because 90-70, a=30.

Because an is 30, divide 90 by 30 to obtain b, 70.

vertically opposite angles, d=70

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Answer:

y = - [tex]\frac{5}{6}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{5}{6}[/tex] , then

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, 1 ) into the partial equation

1 = - 5 + c ⇒ c = 1 + 5 = 6

y = - [tex]\frac{5}{6}[/tex] x + 6 ← equation of line

Answer: 20%

Step-by-step explanation:

60 divided by 75 then times 100 = 80%

100% - 80% = 20%

Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

By using unitary method, it can be calculated that

When input decreases by 30, output decreases by 36

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

Slope = [tex]\frac{6}{5}\\[/tex]

When input decrease by 5, output decreases by 6

When input decrease by 1, output decreases by [tex]\frac{6}{5}[/tex]

When input decreases by 30, output decreases by [tex]\frac{6}{5} \times 30[/tex]

When input decreases by 30, output decreases by 36

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e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers.

e3 <- function(x, y){

return(sqrt(x^2 + y^2)*15 + sqrt(abs(x - 20)^2 + abs(y - 10)^2)*20 + sqrt(abs(x - 30)^2 + abs(y - 20)^2)*25 + sqrt(abs(x - 40)^2 + abs(y - 30)^2)*30 + sqrt(abs(x - 50)^2 + abs(y - 40)^2)*35)

}

optim(c(0,0), e3)

#Output

$par

[1] 20.0 10.0

$value

[1] 1750.000

e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers. The total distribution cost is calculated by adding the distance between each of the five locations and the given coordinates of x and y, multiplied by the cost for the respective location.

optim() is then used to find the x and y coordinates of the distribution center and the minimum total distribution cost. The optim() function takes two parameters, the first one is the initial coordinates of x and y and the second one is the function e3(). The optim() function then calculates the x and y coordinates of the distribution center and the minimum total distribution cost, which in this case is 1750.

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Answer:

D

Step-by-step explanation:

Since we know that both parabolas are on the y-axis, it can't be A or C.

We also know they are above (0,0), so it can't be option B.

That leaves option D.

Answer:

Step-by-step explanation:

Step 1: Use point-slope form and substitute in the x and y values

y-y1=m(x-x1)

y-(1)=2(x-(-3))

Step 2: Simplify the expression

y-1 = 2(x+3)

Add one to the other side

y= 2(x+3)+1

Multiple 2 by (x+3)

y=2x+6+1

Add common terms

y=2x + 7

(a) No present is allowed to end up with its original label is 265.

(b) Number of ways exactly 2 presents keep their original labels are 135.

(c) Number of ways exactly 5 presents keep their original labels are 0.

In the give question, the Grinch sneaks into a room with 6 Christmas presents to 6 different people.

He proceeds to switch the name-labels on the presents.

(a) We have to find no present is allowed to end up with its original label.

No present is allowed to end up with its original label = 6![1- 1/1! + 1/2! - 1/3! - 1/4! + 1/5! - 1/6!]

No present is allowed to end up with its original label = 265

(b) We have to find exactly 2 presents keep their original labels.

Total present = 2

First select 2 presents out of 6 to keep in original labels and then rearrange the remaining 4 presents.

Number of ways exactly 2 presents keep their original labels = [tex]^6C_{2}[/tex] ∙D(4)

Number of ways exactly 2 presents keep their original labels = 15[4!(1- 1/1! + 1/2! - 1/3! + 1/4!]

Number of ways exactly 2 presents keep their original labels = 135

(c) We have to find exactly 5 presents keep their original labels.

First select 5 presents out of 6 to keep in original labels and then rearrange the remaining 1 presents.

Number of ways exactly 5 presents keep their original labels = [tex]^6C_{5}[/tex] ∙D(1)

Number of ways exactly 5 presents keep their original labels = 0

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The value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

We have the following equations -

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 10.1 = 6.49p - 4

2.3p - 10.1 + 4 = 6.49p

2.3p - 6.1 = 6.49p

4.19p = - 6.1

p = - 1.46

Therefore, the value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

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The required values of the compound amount are $56740.76, $56982.05, $57191.25, $57232.60 and $57234.01 respectively.

What is compound interest?

Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has already accrued over the course of prior periods are used to calculate compound interest.

Given, Principal (P) = $42,400

interest rate(r) = 6% per year = 0.06

time(t) = 5 years

The compound amount is given by

[tex]A = P(1+\frac{r}{t} )^{nt}[/tex]

For compounded annually, n=1

[tex]A = 42400(1+0.06)^{1*5}[/tex] = $56740.76

For compounded semi-annually, n=2

[tex]A = 42400(1+\frac{0.06}{2})^{2*5}[/tex] = $56982.05

For compounded monthly, n=12

[tex]A = 42400(1+\frac{0.06}{12})^{12*5}[/tex] = $57191.25

For compounded daily, n=365

[tex]A = 42400(1+\frac{0.06}{365})^{365*5}[/tex] = $57232.60

For compounded continuously,

[tex]A=Pe^{rt} = 42400e^{0.06*5}[/tex] = $57234.01

Hence, these are the required values of the compound amount.

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Answer:

Step-by-step explanation:

24-29=-5

using the number line:)

Answer:

4-23=4b

Step-by-step explanation:

The number of seconds until the bottle hits the aground is 7.1 seconds or 0.1 seconds

The correct equation is 5x²+40x+3 = y

The quadratic formula states that

y=(-b±√b²-4ab)/2a

where a= 5, b= 40 and c= 3

Applying these figures into the formula we have

(-40±√40²-4*5*3)/2*5

Simplifying this to have

(-40±√1600-60)/10

⇒(-40±√1540)/10

⇒(-40±39)/10

This means that

y= -1/10 or -70/10

y= -0.1 or -7.5

In conclusion the time in seconds until the bottle hits the ground is 0.1 sec or 7.5 seconds

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4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.

Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.

Here,

The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.

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Answer:56

Step-by-step explanation:20% of 70 is 14 dollars so you have to subtract 70-14=56.

The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.

[tex]P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15[/tex]

P = 0.15 means that the probability is 15%.

Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

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Value of contrast given is 4.043 , standard error is 1.4535 and t is 2.782 So ,after analyzing this given data , the value for p  for null hypothesis testing is 0.008

In Hypothesis Testing, the P-value method is used to determine the significance of the given null hypothesis. The decision to reject or support it is then made on the basis of the specified significance level or threshold.

This method computes a P-value, which is a test statistic. This statistic can tell us how likely it is that we will find a value (sample mean) that is as far away as the population mean.

P-value is an abbreviation for Probability.

We reject or fail to reject the null hypothesis based on that probability and a significance level.

In general, the lower the p-value, the greater the likelihood of rejecting the null hypothesis, and vice versa.

We also use the Z-table to complete this process.

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Answer:

y=5,-8

Step-by-step explanation:

Answer: hope this helps ♡

y = 5,   y = -8

Step-by-step explanation:

∣2y + 3∣ + 2 = 15

∣2y + 3∣ + 2 - 2 = 15 - 2

∣2y + 3∣ = 13,   ∣2y + 3∣ = -13

∣2y + 3 - 3∣ = 13 -3,   ∣2y + 3 - 3∣ = -13 - 3

2y = 10,   2y = -16

y = 5,   y = -8

Answer:

A.  1,500

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]

The given scenario can be modelled as a geometric series.

If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:

If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:

Substitute these values into the formula and solve for a:

[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]

[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]

[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]

[tex]\implies a=1510.586188[/tex]

Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.

Check:

Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004

Check:

Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000

Answer:-4x + 6

Step-by-step explanation:

7 + x - 1 - 5x

6 - 4x

The answer is -4x +6

Answer:

4 916 083

Step-by-step explanation:

population in 1990

1.5 : 100 = x : 4 786 000

x = 1.5 · 4 786 000 / 100

x = 1.5 · 47 860

x = 71 790

4 786 000 + 71 790 = 4 857 790

population in 2000

1.2 : 100 = x : 4 857 790

x = 1.2 · 4 857 790 / 100

x = 0.012 · 4 857 790

x = 58 293.48

4 857 790 + 58 293.48 = 4 916 083.48