Simplifying each side of the equation results in x2 − 3x − 4 = x2 − 5x + 6. Find the solution: x + 2 3x − 1 x − 2 = x − 3 3x

Answer:  The required ratio is [tex]\dfrac{12}{13}.[/tex]

Step-by-step explanation:  In the given triangle, we are to find the ratio of sinθ.

We know that

in a right-angled triangle, the ratio sine of an angle is given by the length of the perpendicular divided by the length of the hypotenuse.

For the given right-angled triangle, we get

[tex]\sin\theta=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin\theta=\dfrac{36}{39}\\\\\\\Rightarrow \sin\theta=\dfrac{12}{13}.[/tex]

Thus, the required ratio is [tex]\dfrac{12}{13}.[/tex]

Answer:

1. 19.2

Step-by-step explanation:    

Please find the attachment.

Since we know that radius is perpendicular to tangent of a circle. So AB will be perpendicular to BC at c and DC is perpendicular to CB at C.

Now we will construct a perpendicular line to radius AB at point E from the center of our small circle. Since we have two right angles at point B and C so we will also have right angles at point E and D as well.    

Length of CD is is 7 so length of BE will be 7 as well and length of EA will be 10-7=3. Length of DE will be equal to length BC that is 19.

Now we have formed a right triangle and now we will use Pythagoras theorem to find the length of AD.  

[tex](AD)^{2}=(DE)^{2}+(EA)^{2}[/tex]    

Upon substituting our values in above formula we will get,

[tex](AD)^{2}=(19)^{2}+(3)^{2}[/tex]

[tex](AD)^{2}=361+9[/tex]

[tex](AD)^{2}=370[/tex]

Upon taking square root of both sides of our equation we will get,

[tex]AD=\sqrt{370}[/tex]  

[tex]AD=19.2353840616713448\approx 19.2[/tex]

Therefore, the length of AD will be 19.2 and 1st option is the correct choice.

Answer:

60 odd numbers

Step-by-step explanation:

A normal dice has 6 different sides numbered from 1 to 6, each side has the same probability of appearing when you roll the dice, i.e., in the long run each number will appear 1/6 of the times. We have three different odd numbers in a normal dice each will appear 1/6 of the times in the long run. Therefore, in the long run we hope to get 3/6 = 1/2 of the times an odd number and rolling the dice 120 times will produce about 120(1/2) = 60 odd numbers.

Answer: B. 36

Step-by-step explanation: Trust me!

The correct answer is C: Rhombus. This is how you find your answer: desmos.com because you just plant in the ordered pair into the program and it plots out the shape for you. The only thing you need to know is your shapes and you should be set.

Answer: [tex]sec \theta[/tex].

Step-by-step explanation: Given expression : [tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex]

We know,

[tex]sec \theta = \frac{1}{cos \theta}[/tex]

[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]

Substituting those values in given expression, we get

[tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex] =[tex]\frac{sin \theta\ \frac{1}{cos \theta} } {cos \theta\ \frac{sin \theta}{cos \theta} }[/tex]

= [tex]\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}[/tex]

Crossing out [tex]sin \theta \ cos \theta[/tex] from top and bottom, we get

=[tex]\frac{1}{cos \theta }[/tex]

= [tex]sec \theta[/tex].

Answer:

The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is  [tex]\sec\theta[/tex]

Step-by-step explanation:

Given: Expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]

We have to writ the given expression in simplified form.

Consider , The given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]

Since, we know,

[tex]\sec\theta=\frac{1}{\cos\theta}[/tex]

and  [tex]\tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]

Substitute, we have,

[tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}=\frac{\sin\theta \cdot\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{\sin\theta}{\cos\theta} }[/tex]

Simplify, we have,

[tex]=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }[/tex]

Simplify further, we get,

[tex]=\frac{1}{\cos\theta}=\sec\theta[/tex]

Thus, The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is  [tex]\sec\theta[/tex]

The given system of equations, x - 2y = 2 and x - 2y = -2, are parallel lines and do not intersect, thus there is no common solution to the system.

In mathematics, to find the solution to a system of equations, we generally try to find the values of variables that satisfy all the equations in the system. When looking at the given equations: x - 2y = 2 and x - 2y = -2, we can see that there is something strange. These two equations are equivalent to each other, meaning they represent the same line. This is due to the fact that both equations have the same coefficients for the x and y variables (1 and -2 respectively). So, if two lines are equivalent, they are essentially the same line. This means there are infinitely many solutions which satisfy this system of equations, since all points on the line satisfy both equations. However, if two lines have the same coefficients but different constants (the numbers without the variables), as in our case, then they are parallel and do not intersect, indicating that there's no solution for the system of equations. Therefore, this system of equations has no solution.

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Answer:

-7

Step-by-step explanation:

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Answer:

-7

Step-by-step explanation:

We are given that   a function

[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]

We have to find the minimum value of y.

We know that range of sin x is [-1,1].

[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]

[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]

[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]

[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]

[tex]-7\leq y\leq 3[/tex]

Maximum value of y=3

Minimum value of y=-7

Hence, the minimum value of given function =-7

C=(-4,-4)

E = (4,-2)

-4 +4 = 0/2 =0

-4+-2 = -6/2 = -3

(0,-3)

Answer:

Step-by-step explanation:

The prefix Pre stands for before and algebra is math so pre algebra is informing you about what you will be learning before it actually happens.

Algebra is math for ninth graders that if you fail makes you have to take it until you pass it.

Three other ordered pairs with θ between −360° and 360° that name the same point as (3, 135°) are (−243, −45°), (−177, −15°), and (315, 495°).

The ordered pairs (−243, −45°), (−177, −15°) and (315, 495°) all name the same point as (3, 135°) with θ between −360° and 360°.

To find these ordered pairs, you can add or subtract 360° to the given angle of 135° while keeping the x-coordinate constant at 3.

For example, you could subtract 360° from 135° to get −225° and combine it with the x-coordinate of 3 to get the ordered pair (3, −225°).

volume = 4/3 x PI x r^3

 in terms of pi. multiply r^3 x 4/3 = 18432PI

surface area = 4pir^2

in terms of pi multiply r^2 x 4 = 2304PI

Answer:

A. definition of perpendicular bisector

Step-by-step explanation:

I JUST TOOK THE TEST!!!!!!

Answer:

The correct option is a) perpendicular bisector definition.

Step-by-step explanation:

Given :

Triangle QPT is similar to triangle QRT.

[tex]\rm SP \cong SR[/tex]

To find : Why [tex]\rm PT \cong RT[/tex]

Solution :

According to perpendicular bisector definition -

Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment. Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

Therefore, [tex]\rm PT \cong RT[/tex]

Hence option a) is correct.

For more information, refer the link given below

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Answer:

The correct statement is:

On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.

Step-by-step explanation:

We are given a data of 11 gardens as:

2   9    1    23    3    7    10    2    10    9     7

Now on removing the outlier i.e. 23 (since it is the very large value as compared to other data points) the entries are as follows:

x         |x-x'|        

2          4              

9          3              

1           5              

3          3              

7           1                

10         4              

2           4              

10          4              

9           3              

7            1              

Now mean of the data is denoted by x' and is calculated as:

[tex]x'=\dfrac{2+9+1+3+7+10+2+10+9+7}{10}\\\\x'=\dfrac{60}{10}\\\\x'=6[/tex]

Hence, Mean(x')=6

Now,

∑ |x-x'|=32

Now mean of the absolute deviation is:

[tex]\dfrac{32}{10}=3.2[/tex]

This means that , On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.