If A is an obtuse angle in a triangle and sin A is 5/13, calculate the exact value of sin 2A

Answer : [tex] 5m^4n^3[/tex]  and [tex] 15m^2n^2[/tex]

Greatest common factor of  [tex] 5m^2n^2 [/tex]

If we are able to factor out [tex] 5m^2n^2 [/tex] from each option then that would be our answer.

Lets check with each options

(a)[tex] m^5n^5 [/tex], we cannot take out 5.

(b)[tex] 5m^4n^3 [/tex], We can take out common factor and it can be written as [tex] 5m^4n^3=5m^2n^2(m^2n) [/tex]

(c) [tex] 10m^4n [/tex], we cannot take out n^2 because we have only 'n'

(d) [tex] 15m^2n^2[/tex], We can take out common factor and it can be written as [tex] 15m^2n^2=5m^2n^2(3) [/tex]

(e) [tex] 24m^3n^4 [/tex], we  cannot take out 5 because we have 24

So answer is (b)  and (d)

Answer:  The below graph shows the given situation.

Step-by-step explanation:

Let x represents the number of week, and y represents the total balance in the account after x weeks.

Since, initially the amount in the account = $ 270

According to the question,

Every week $80 is saved.

Thus, the total saving in x weeks = 80 × x = 80x

Since the total amount in x weeks = Initial amount + total saving.

⇒ y = 80x + 270

Which is the equation of line that shows the given situation.

x-intercept of the line is (-27/8,0)

y-intercept = (0,270)

If x=1 y = 350

If x=2 y= 430

If x=3 y =510

Thus, the points of the line are (1,350), (2,430), (3,510)

Hence we can draw the graph with help of above information.

Answer:

9

Step-by-step explanation:

Answer:

the graph is stretched horizontally to 1/3 the original width

Step-by-step explanation:

the graph is also reflected and translated but those are rigid transformations and this is asking about the non rig transformations

So basically the answer would be 86%

Answer:

The value of the equation for [tex]d_2[/tex] is [tex]d_2=\frac{2A}{d_1}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]A=\frac{1}{2}d_1d_2[/tex]  

We need to solve the equation for [tex]d_2[/tex].

Multiply both the sides by 2.

[tex]2A=2\times \frac{1}{2}d_1d_2[/tex]

[tex]2A=d_1d_2[/tex]

Divide both sides by [tex]d_1[/tex].

[tex]\frac{2A}{d_1}=\frac{d_1d_2}{d_1}[/tex]

[tex]d_2=\frac{2A}{d_1}[/tex]

Hence, the value of the equation for [tex]d_2[/tex]is [tex]d_2=\frac{2A}{d_1}[/tex].

The slope of the line passing through points J (0,0) and K (-2,8) is calculated using the slope formula and results in a slope of -4.

The question asks to calculate the slope of the line passing through points J (0,0) and K (-2,8). The slope of a line is found by the formula

slope = (y'' - y') / (x'' - x'), where (x', y') and (x'', y'') are the coordinates of two distinct points on the line. Substituting the given points into this formula gives us

slope = (8 - 0) / (-2 - 0) = 8 / -2 = -4.

A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. The main difference is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.

A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. However, there are some key differences between the two.

Tilt Level: A tilt level, also known as a tilting level, is a type of level that utilizes a compensator mechanism to maintain a level plane even when the instrument itself is not level. This compensator allows for accurate measurements and eliminates the need for manually leveling the instrument each time.

Dumpy Level: A dumpy level, on the other hand, is a more traditional type of level that requires manual leveling before each use. It consists of a telescope mounted on a tripod, and the instrument is adjusted using leveling screws to ensure that it is perfectly horizontal. The dumpy level does not have a compensator like the tilt level, so the instrument needs to be leveled manually to obtain accurate measurements.

In summary, the main difference between a tilt level and a dumpy level is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.

According to given question, 12 divided by 144140 is approximately 0.000083158.

To divide 12 by 144140, simply perform the division:

12 ÷ 144140 ≈ 0.000083158

So, 12 divided by 144140 is approximately 0.000083158.

Division is a mathematical operation used to distribute a quantity or a number of items into equal parts. It involves finding out how many times one number (called the divisor) can be subtracted or taken away from another number (called the dividend) until there is nothing left or the subtraction cannot be done anymore.

The result of the division is called the quotient, and it represents the number of equal parts or groups that the dividend can be divided into by the divisor. In the division expression "a ÷ b," where "a" is the dividend and "b" is the divisor, the quotient is represented by "a/b."

For example, in the division 12 ÷ 3:

12 is the dividend (the total quantity to be divided).

3 is the divisor (the number of equal parts to divide the dividend).

The quotient is 4, as 12 can be divided into 4 equal parts of size 3.

Division is the opposite operation of multiplication. If you have two numbers, the product of their multiplication can be divided by one of the numbers to get the other number. For example, 12 × 3 = 36, and 36 ÷ 3 = 12.

To know more about division here

https://brainly.com/question/28119824

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Answer:

a)  2 red lights

b) SD = 1.26

c) mean = 10, SD = 1.26

Step-by-step explanation:

a) The number of red lights she expects to hit by day can be gotten by calculating the mean of the distribution.

[tex]E(X) = \sum xP(x)[/tex]

[tex]E(X) = (0*0.05) + (1*0.25) + (2*0.35) + (3*0.15) + (4*0.15) + (5*0.15)\\E(X) = 2.25[/tex]

Since the number of lights cannot be a decimal, she expects to hit 2 lights each day

b)

Variance, [tex]V(X) = \sum(x- \mu)^{2} P(x)[/tex]

[tex]V(X) = [(0-2.25)^{2}*0.05] + [(1-2.25)^{2}*0.25] + [(2-2.25)^{2}*0.35] + [(3-2.25)^{2}*0.15] + [(4-2.25)^{2}*0.15] + [(5-2.25)^{2}*0.05][/tex]

V(X) = 0.253 + 0.391 + 0.022 + 0.084 + 0.459 + 0.378

V(X) = 1.587

Standard Deviation, [tex]SD = \sqrt{V(X)}[/tex]

[tex]SD = \sqrt{1.587}[/tex]

SD = 1.26

c) In a 5 day work week, the commuter is expected to hit an average of 5* 2 red lights, i.e. mean = number of red lights hit per day * number of days

mean = 2 * 5

mean = 10

The standard deviation will not change, SD = 1.26

The simplified form of each expression is as follows:

[tex]A. \( 729 \times 33 \) simplifies to \( 3^6 \times 33 \) B. \( 3 \times 33 \) simplifies to \( 3 \times 3 \times 11 \) or \( 3^2 \times 11 \). C. \( 729 \times 29 \) simplifies to \( 3^6 \times 29 \). D. \( 3 \times 29 \) simplifies to \( 3 \times 29 \).[/tex]

To simplify these expressions, we recognize that 729 is a power of 3, specifically [tex]\( 3^6 \)[/tex], and that 33 and 29 are prime numbers. Therefore, we can express each product in terms of its prime factors.

A. For the expression [tex]\( 729 \times 33 \)[/tex] , we know that 729 is [tex]\( 3^6 \)[/tex] and 33 is a prime number. Thus, the simplified form is [tex]\( 3^6 \times 33 \)[/tex].

[tex]B. For the expression \( 3 \times 33 \), we can further break down 33 into \( 3 \times 11 \), since 33 is the product of these two prime numbers. Therefore, the simplified form is \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \).[/tex]

[tex]C. For the expression \( 729 \times 29 \), similar to expression A, 729 is \( 3^6 \) and 29 is a prime number. Hence, the simplified form is \( 3^6 \times 29 \).[/tex]

[tex]D. For the expression \( 3 \times 29 \), both 3 and 29 are prime numbers, so the expression is already in its simplest form and cannot be simplified further. Thus, the simplified form remains \( 3 \times 29 \).[/tex]In summary, the simplified forms are:

[tex]A. \( 3^6 \times 33 \) B. \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \) C. \( 3^6 \times 29 \) D. \( 3 \times 29 \)[/tex]

Final answer:

To calculate the total charges for the cable installation, multiply the hourly rate of $30.00 by the 8.5 hours spent ($255.00) and add the $50.00 service charge, resulting in total charges of $305.00.

Explanation:

The task requires us to calculate the total charges based on the cable installer's hourly rate and a service charge. The installer charges $30.00 per hour and there's an additional $50.00 service charge. To find the total cost for 8.5 hours of work, we multiply the hourly rate by the number of hours and then add the service charge.

Calculation: Total charges = (Hourly rate × Number of hours) + Service charge = ($30.00 × 8.5 hours) + $50.00

Step 1: Calculate the hourly charge
Hourly charge = $30.00 × 8.5 = $255.00

Step 2: Add the service charge
Total charges = $255.00 + $50.00 = $305.00

The total charges for the cable installation service will be $305.00.

Answer:

[tex]\text{Area of sphere is }484\pi units^2[/tex]

Step-by-step explanation:

Given the radius of sphere 11 units

we have to find the surface area of sphere

Radius=11 units

As area of sphere can be calculated as

[tex]\text{Area}=4\pi r^2[/tex]

[tex]=4\pi (11)^2=484\pi units^2[/tex]

[tex]\text{Area of sphere is }484\pi units^2[/tex]

Answer:

Answer is option c

Step-by-step explanation:

Given that the cost, c(x), for a taxi ride is given by c(x) = 2x + 4.00, where x is the number of minutes.

We find that whenever 1 minute increases cost increases by 2 dollars.

Hence rate of change of cost with respect to minute of taxi ride = 2 dollas

i.e. this is of the form y=mx+b where

m =2 is the slope or rate of change and

b = 4 is the fixed charge even for 0 minute.

Thus option C is right

the solution to the system of equation is (5, -T

From equation 1;

x = -1 - 3y

Substitute x = -1-3y into equation 2

x + y = 3

-1-3y + y = 3

-1 -2y = 3

-2y = 4

y = -2

Since x + y = 3

x = 3 + 2

x = 5

Hence the solution to the system of equation is (5, -2)