Graph the line has a slope of 1/4 and includes the point (-2,0)

Find an exact value.

leonid [27]

Answer:

(√2 - √6) / 4

C. square root of two minus square root of six divided by four.

Step-by-step explanation:

sine of negative eleven pi divided by twelve.

We have :

sin(-11π/12)

sin((4 - 15)π / 12) = sin(4π/12 - 15π/12)

sin(4π/12 - 15π/12) = sin(π/3 - 5π/4)

Recall:

Angle difference formula:

sin(A - B) = sinAcosB - sinBcosA

Hence,

sin(π/3 - 5π/4) = sin(π/3) cos(5π/4) − sin(5π/4) cos(π/3)

From trigonometry:

sinπ/3 = √3/2

cos5π/4 = -√2/2

sin5π/4 = -√2/2

cos π/3 = 1/2

(√3/2) (-√2/2) − (-√2/2) (1/2)

-√6/4 - -√2/4

-√6/4 + √2/4

√2/4 - √6/4

(√2 - √6) / 4

7 0

3 years ago

A proper unbiased coin was tossed 10 times for 3 trials, giving TTHHTHTTHH, TTTTTHHHHH, and THTHHHTTH (T = Tails; H = Heads). Wh

nadya68 [22]

Theoretical probability is what, theoretically, the probability should be, regardless of data. Because there are only two options, the probability for getting heads on each toss should be 50%. For the total thirty tosses, theoretically, the coin should land on heads fifteen times, or five per trial, which is determined solely on the number of options.

Experimental probability is what the probability was based on the given data. In the first trial, head was scored 5 times, or 5/10, or 50%. This was repeated in the second and third trials. So, based purely on the data, the probability of the coin landing on heads was also 50%.

I hope this helps!
~Chrys

5 0

3 years ago

Read 2 more answers

Write two equivalent rates for 3 breads made in 45 minutes.

Alex777 [14]

Answer:

1/15 ; 6/90

Step-by-step explanation:

$\frac{3}{45}=\frac{1}{15} \\\\\frac{3}{45}=\frac{3*2}{45*2}=\frac{6}{90}$

7 0

3 years ago

The sum of 2 times p and 2 is 48. What is p?

yaroslaw [1]

Answer:

p = 23

Step-by-step explanation:

2p + 2 = 48

-2 -2

2p = 46

/2 /2

p = 23

Hope this helps and I hope u have an Amazing day!!

8 0

3 years ago

Look at the system of equations below.

Annette [7]

Answer:

Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.

Step-by-step explanation:

Let us consider the system of equation below.

$4x-5y=3$

$3x+5y=13$

Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.

Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Adding Equation 1 and Equation 2

$4x-5y+3x+5y=3+13$

$7x=16$

$x=$ $\frac{16}{7}$

Putting $x=$ $\frac{16}{7}$ in Equation [1]

$4x-5y=3$ $......[1]$

$y=$ $\frac{43}{35}$

Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.

For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Solving the equation 2 for x variable

$3x=13-5y$

$x=\frac{13-5y}{3}$

Plugging $x=\frac{13-5y}{3}$ in equation [1]

$4(\frac{13-5y}{3}) -5y=3$

$y = \frac{43}{35}$

Putting $y = \frac{43}{35}$ in Equation 2

$3x+5y=13$ $......[2]$

$x = \frac{16}{7}$

So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.

Similarly, using graphing method, it would take a certain time before we identify the solution of the system.

Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.

Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

Keywords: substitution method, system of equations, elimination method

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4 0

3 years ago

Graph the line has a slope of 1/4 and includes the point (-2,0)￼

Graph the line has a slope of 1/4 and includes the point (-2,0)