Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?

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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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°).

C=(-4,-4)

E = (4,-2)

-4 +4 = 0/2 =0

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

(0,-3)

Answer:

A. definition of perpendicular bisector

Step-by-step explanation:

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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.

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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:  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]

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:

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.

The margin of error can be calculated using the t statistic. The formula for margin of error is given as:

Margin of error = t * s / sqrt (n)                                 ---> 1

Where,

t = the t score based on the given confidence level and degrees of freedom

n = number of samples = 21

s = standard deviation = 7.1

Degrees of freedom = n – 1 = 21 – 1 = 20

Based on the standard probability tables for t, the t score is:

t = 0.860

Substituting into equation 1:

margin of error = 0.860 * 7.1 / sqrt (21)

margin of error = 1.33

The range is:

range = 30.1 ± 1.33

range = 28.77, 31.43

Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.

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]