How do you figure out if the parabola is to the side or upward/downward?

Answers

Answer 1

Answer: patterns: vertical : y = a(x - h)² + k horizontal: x = a(y - k)² + h

Look at the patterns above and remember these key points.

1) if the x is squared, the parabola is vertical. It either opens up or down.
if the y is squared, the parabola is horizontal. It either opens left or right.

2) if a is positive, the parabola opens up or to the right.
if a is negative, the parabola opens down or to the left

3) the vertex is at (h,k). Be very careful. locations of h and k varies if the parabola is vertical or horizontal. its sign is also different in those positions

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Screen Shot 2023-10-12 at 6.57.17 PM

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Answer:

Screen shot 2016-12-25 at 8.01.34 AM

Step-by-step explanation:

Screen Shot titled,"Merry Christmas"

2. Which is larger?The common ratio, r , in a geometric sequence whose second term is
24 and whose fifth term is 1536
or
The common difference, d , in an arithmetic sequence whose fourth
term is 16 and whose seventh term is 31.

Answers

Answer:

The common difference d is larger than the common ratio r

Step-by-step explanation:

The common difference in the arithmetic sequence $d=u_(n)-u_(n-1)$

The nth term in the arithmetic sequence is $a_(n)=a+(n-1)d$ , where a is the first term

The common ratio in the geometric sequence $r=(u_(n))/(u_(n-1))$

The nth term in the geometric sequence is $a_(n)=a(r)^(n-1)$ , where a is the first term

Geometric sequence

∵ The second term is 24

∴ $u_(2)$ = 24

∵ $u_(2)=a(r)^(2-1)=ar$

- Equate it by its value

∴ ar = 24 ⇒ (1)

∵ The fifth term is 1536

∴ $u_(5)$ = 1536

∵ $u_(5)=a(r)^(5-1)=ar^(4)$

- Equate it by its value

∴ $ar^(4)$ = 1536 ⇒ (2)

Divide (2) by (1)

∴ $(ar^(4))/(ar)=(1536)/(24)$

- Divide up and down by ar

∴ r³ = 64

- Take ∛ for both sides

∴ r = 4

Arithmetic sequence

∵ The fourth term is 16

∴ $u_(4)$ = 16

∵ $u_(4)$ = a + (4 - 1)d

∴ $u_(4)$ = a + 3 d

- Equate it by its value

∴ a + 3d = 16 ⇒ (1)

∵ The seventh term is 31

∴ $u_(7)$ = 31

∵ $u_(7)$ = a + (7 - 1)d

∴ $u_(7)$ = a + 6 d

- Equate it by its value

∴ a + 6 d = 31 ⇒ (2)

Subtract equation (1) from equation (2) to eliminate a and find d

∵ (a - a) + (6 d - 3 d) = (31 - 16)

∴ 3 d = 15

- Divide both sides by 3

∴ d = 5

∵ r = 4 and d = 5

∴ d > r

∴ The common difference d is larger than the common ratio r

A social worker earns $760 gross pay. If he is married and claims 1 dependent, his state tax rate is 7%, and FICA is 7.65%, what is his net
pay?

Answers

I believe the net pay is $648.66.
$760×.07 for sales tax rate =53.20
$760×0.0765 for FICA= 58.14
(7.65÷100=0.0765)
now 760-53.20-58.14= 648.66

5/x+1 ÷ 6/3x+3 divide

Answers

Here is how to work that problem out. (check the picture)

3/12 and 5/x are equivalent ratios. Solve for x

Answers

The required value of x is 20.

What is proportion?

A proportion is an equation in which two ratios are set equal to each other. In simple words, equivalent fraction are called as proportions.

Now the given equivalent ratios is,

3/12 = 5/x

Cross multiply the ratios we get,

3*x = 5*12

Solve them we obtain,

3x = 60

now dividing both side by 3,

3x/3 = 60/3

Solve them we obtain,

x = 20

So the value of x = 20.

Hence, for equivalent ratios 3/12 and 5/x the valueof x is 20.

To learn more about proportions :

brainly.com/question/8099778

#SPJ2

3/12=5/x
1/4=5/x
times both sides by 4x aka cross multiply
1x=20
x=20

Compare and contrast the absolute value of a real number to that of a complex number.

Answers

The absolute value of a real number is a positive value of the number. Which means that the absolute value is the distance from zero of the number line. However, that of the complex numbers is the distance from the origin to the point in a complex plane.

The definition of complex, real and pure imaginary number is as follows:

$A \ \mathbf{complex \ number} \ is \ written \ in \ \mathbf{standard \ form} \ as:\n \n \ (a+bi) \n \n where \ a \ and \ b \ are \ real \ numbers. \ If \ b=0, \ the \ number \ a+bi=a \n is \ a \ \mathbf{real \ number}. \ If \ b\neq 0, \ the \ number \ (a+bi) \ is \ called \ an \n \mathbf{imaginary \ number}. \ A \ number \ of \ the \ form \ bi, \ where \ b\neq 0, \n is \ called \ a \ \mathbf{pure \ imaginary \ number}$

The absolute value of this number is given by:

$|a+bi|=\sqrt{a^(2)+b^(2)}$

So, the absolute value of a complex number represents the distance between the origin and the point in the complex plane. On the other hand, the absolute value of a real number means only how far a number is from zero without considering any direction.

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