Lillie is saving up for a trip she is taking with friends during her break from school. If Lillie's current monthly net pay is $560.00 and her monthly expenses are $347.49, what percent of her net pay is left for savings? (2 points)
19%
23%
38%

If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which

x - 5 = r (x + 1)

==>   r = (x - 5) / (x + 1)

and

x - 2 = r (x - 5)

==>   r = (x - 2) / (x - 5)

Then

(x - 5) / (x + 1) = (x - 2) / (x - 5)

Solve for x :

(x - 5)² = (x - 2) (x + 1)

x ² - 10x + 25 = x ² - x - 2

-9x = -27

x = 3

It follows that the ratio between terms is

r = (3 - 5) / (3 + 1) = -2/4 = -1/2

Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by

a(n) = 4 (-1/2)ⁿ⁻¹

The sum of the first 12 terms - denoted here by S - is then

S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹

Solve for S :

S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]

(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]

==>   S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]

==>   3/2 S = 4 (1 - 1/4096)

==>   S = 8/3 (1 - 1/4096)

==>   S = 1365/512

Answer:

The domain and range remain the same.

Step-by-step explanation:

Hi there!

First, we must determine what increasing a by 2 really does to the exponential function.

In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).

Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).

The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.

The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.

I hope this helps!

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Answer:

  C.  2cos²(x)

Step-by-step explanation:

The relevant identities are ...

  cos(2x) = cos²(x) -sin²(x)

  cos²(x) = 1 -sin²(x)

__

Then the expression can be simplified to ...

  cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)

  = 2cos²(x)

9514 1404 393

Answer:

Step-by-step explanation:

The only factor outside parentheses that contain 2 terms is the factor 3/5. It can be distributed. (The correct response is shown.)

  3/5 can be distributed

__

The only like terms that reside on the same side of the equal sign are ...

  18 and -1

Answer:

Option B

Step-by-step explanation:

If the larger triangle (Preimage) is dilated by a scale factor 'k' to form the image triangle (small triangle),

Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the preimage}}[/tex]

                 k = [tex]\frac{3}{2.4}[/tex]

Therefore, Option B will be the correct option.

Answer:

x = -2

Step-by-step explanation:

x^2 + 4x + 4 = 0

quadratic formula:

-b +or- sqrt(b^2-4ac)/2a

-4 +/- sqrt ((-4)^2-4*1*4)/2*1

-4+/- sqrt(16-16) / 2

-4 +/- 0 / 2

-4/2

-2

Answer:

Step-by-step explanation:

11/20 = 55/100 = 55%

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Answer:

Step-by-step explanation:

In the US, a decimal point is represented by a period. This value is interpreted as an integer with no fractional part, so the fractional part is zero:

 12,963.00

__

Some other places, a comma is used to identify the beginning of the decimal fraction. In that form, this number has a fractional part that has 3 as its thousandths digit. The value of 3 is less than 5, so the number is simply truncated at the hundredths place.

  12,96

If the thousandths digit were 5 or greater, then 1 hundredth would be added to the truncated number.

Answer:

10 and 16, x+(x+6)=26

Step-by-step explanation:

Michelle has an age we don't know, so we put her age as x.

Yogi is 6 years older than her, so her age is x+6

Michelle=x

Yogi=x+6

we know both their ages equal 26. so we set it up as

x+(x+6)=26

combining like terms we get

2x+6=26

subtract 6 from both sides

2x=20

divide both sides by 2

x=10

now that we have the value for x, we plug it into their original ages

Michelle is 10, because her age is just x.

Yogi is 16, because her age is x+6

Expand the expression as

(s + 1)³/s ⁵ = (s ³ + 3s ² + 3s + 1)/s ⁵

… = 1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵

Then taking the inverse transform, you get

LT⁻¹ [1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵]

… = LT⁻¹ [1/s ²] + LT⁻¹ [3/s ³] + LT⁻¹ [3/s ⁴] + LT⁻¹ [1/s ⁵]

… = LT⁻¹ [1!/s ²] + 3/2 LT⁻¹ [2!/s ³] + 1/2 LT⁻¹ [3!/s ⁴] + 1/24 LT⁻¹ [4!/s ⁵]

… = t + 3/2 t ² + 1/2 t ³ + 1/24 t ⁴

Answer:

5 x 4 = 20.

Step-by-step explanation:

5 + 5 = 10

5 + 10 = 15

5 + 15 = 20!

Please mark brainliest!

- KanaKittyKat

Answer:

5 x 4 = 20

5 + 5 + 5 + 5 = 20

Answer:

72°

Step-by-step explanation:

[tex] m\angle \: 6 = m \angle \: 8 \\ (corresponding \: \angle s) \\ m\angle \: 8 = 72 \degree \\ \therefore \: m\angle \: 6 = 72 \degree \\ \\ m\angle \: 14 = m \angle \: 6 \\ (corresponding \: \angle s) \\\therefore \: m\angle \: 14 = 72 \degree [/tex]

Answer:

[tex]\frac{BC}{DC}=\frac{AC}{EC}[/tex]

[tex]\frac{20-x}{x} =\frac{21}{7}[/tex]

[tex]\frac{20-x}{x} =3[/tex]

[tex]20-x=3x[/tex]

[tex]4x=20[/tex]

[tex]x=5[/tex]

[tex]So, CD=5[/tex]

OAmalOHopeO

Answer:

y=3/4x+19/4

Step-by-step explanation:

y=mx+c

4=3/4*-(1)+c

4=-3/4+c

c=4+3/4

c=19/4

y=3/4x+19/4

Answer:

In the direction you are going,

Explanation:

We know that the tangent to  {x[t], y[t]} are  {x'[t], y'[t]}. Since  {x'[t], y'[t]} are tangents at  {x[t], y[t]}, we know that the tangent at a point is always parallel to the direction of the function at that point and in the direction of the function. So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in my direction of motion as I move along the curve.

So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in the direction you are going.

Answer:

37.8+52.2=90

Step-by-step explanation: x + (x + 14.4) = 90

2x + 14.4 = 90

2x = 75.6

x = 37.8  (one angle)

And (x + 14.4) = 52.2 (other angle).

Answer:

A. 2.04 seconds

B. 5.92

C: 1.48 -  0.4 = 1.08 seconds    

Step-by-step explanation:

~~~~~~~~~~~~~~~~~~~~~

USE THIS TO GET "B"

the f(-b/2a) is the highest point,

the vertex of the parabola [-b/2a, f(-b/2a)] will give you the time

and height of the highest point

~~~~~~~~~~~~~~~~~~~

USE THIS TO GET "A"... you will get two answers one will be negative

ignore that one , the positive one is the time to hit the ground

if you factor the equation (use the quadratic formula) you will get

the "zeros" that is where the ball is on the ground...

~~~~~~~~~~~~~~~~~~~~~~~

THIS IS FOR PART "C"

if you set the equation equal to 4.5 meters and factor that for the "zeros" you will get the two times that the ball is at that height.. subtract the two times for the duration

Answer:

No

Step-by-step explanation:

Let's look at an example

24

24 is divisible by 6   24/6 = 4  

24 is divisible by 8   24/8 = 3

24 is not divisible by 48  24/48 = 1/2  which is not an integer

Answer:

The time required is 60.3 days.

Step-by-step explanation:

initial amount, No = 0.3 g

rate, r = 1.15 % per day = 0.0115 per day

final amount, N = 0.15 g

Let the time is t.

[tex]N = No e^{-rt}\\\\0.15 = 0.3 e^{-0.0115 t}\\\\0.5 =e^{-0.0115 t}\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days[/tex]

Answer:

I believe it's A

Step-by-step explanation:

I'm not sure sorry if its wrong

Answer:

30%

Step-by-step explanation:

you just add 10% and 20%

Hope it helps c:

Zelina scored 32% higher on the third quiz than on her first quiz.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

Given that:-

From the given data we will see that:-

1 ) Zelina scored 10% higher on her second quiz than on her first quiz.

SQ = 1.10 FQ

2 ) On her third quiz, Zelina scored 20% higher than on her second quiz

TQ = 1.20SQ

From the above to expression solve for the first quiz:-

TQ = 1.20 x  1.10 FQ

TQ = 1.32FQ

Therefore Zelina scored 32% higher on the third quiz than on her first quiz.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ2

9514 1404 393

Answer:

  f(x) = -4(x +7)(x +1)

Step-by-step explanation:

The x-intercepts tell us that m=-7 and n=-1. We can use the given point to find 'a'.

  f(-4) = 36

  a(-4+7)(-4+1) = 36

  a = 36/-9 = -4 . . . . divide by the coefficient of 'a'

Filling in the known values, ...

  f(x) = -4(x +7)(x +1)

Answer:

[tex]{ \bf{ log_{a}(U) = x}} \\ { \boxed{ \tt{ {a}^{x} = U}}} \\ \\ { \bf{ log_{a}(V) = y}} \\ { \boxed{ \tt{ {a}^{y} = V }}}[/tex]

Answer:

1) x+y=-2

x=-2-y

2) x-y=-8

substitude value of x

(-2-y)-y=-8

-2-2y=-8

-2y=-6

y=3

Substitute value of y in 1

x=-2-3

x=-5

Brainliest please~

Answer:

Mean = 35.56

Median = 35.5

Step-by-step explanation:

Given the data:

16 25 24 19 33 25 34 46 37

33 42 40 37 34 49 73 46 45

Reordered data :

16, 19, 24, 25, 25, 33, 33, 34, 34, 37, 37, 40, 42, 45, 46, 46, 49, 73

The mean = ΣX / n

n = sample size ; ΣX = sum of values

The mean = 658 / 18

The mean = 36.56

The Median = 1/2(n+1)th term

1/2(18+1)th term = 1/2(19)th term = 9.5 term

Median = (9th + 10th) / 2 = (34 + 37) / 2 = 35.5