Find an equation for the sphere with center and passing through the point

Solve for x:* 8 – 2(3x + 5) = 0

IRINA_888 [86]

8-2(3x+5)=0
8(-6x-10)=0
-48x-80=0
-48x=80
x= -8/5 or -1.6

4 0

3 years ago

Rewrite with only sin x and cos x. (3 points) cos 2x + sin x

ArbitrLikvidat [17]

Answer:

I think its option 2

7 0

3 years ago

Please help ASAP I am in desperate need

Vlad1618 [11]

Answer:

x = 9

TH = 12

Step-by-step explanation:

since TM is half of HM, the equation is:

2(21 - x) = 3x - 3

42 - 2x = 3x - 3

45 = 5x

x = 9

TH = 21 - x

TH = 21 - 9

TH = 12

8 0

3 years ago

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

1 year ago

Triangle FGH is translated using the rule (x,y) > (x+3,y-1). What are the coordinates of H ?

Masteriza [31]

Answer: $H'(4,-3)$

Step-by-step explanation:

For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".

A Translation is defined as a transformation in which the figure is moved a fixed distance in a fixed direction. In this kind of transformatiosn the size and shape do not change and the figure is not flipped.

In this case you know that the Pre-Image is the Triangle FGH.

You can identify in the picture that its vertex H has these coordinates:

$H(1,-2)$