verizon's plan costs $75 per month and gives you unlimited talk, and 500 messages per month, and no dataplan. If you send more 500 text messages, on top of the $75 it will cost $.10 per text overage. Write the piecewise function for the following situation. If you send 800 text messages, then how much will your bill be?

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==>   a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C

Answer:

48 49 51 53 58

Step-by-step explanation:

48×2= 96 so 49 51 53 and 58 are greater hope this helps:)

Answer:

Fraction: 1/5

Decimal: 0.2

Step-by-step explanation:

Answer:

The scuba diver is at sea level.

Step-by-step explanation:

Hi there!

We're given that the scuba diver is 30 feet below sea level, and then she rises 30 feet.

This means she would be at sea level, not above or below.

You can think of it on a vertical ruler; the scuba diver starts at 0, goes down 30 units and goes back up 30 units. She will end up at 0 again, which in this case is sea level.

I hope this helps!

9514 1404 393

Answer:

  p = -3/4b -3/4

Step-by-step explanation:

Vectors are perpendicular when their dot product is zero.

  A·B = p(4) +b(3) -3(-1) = 4p +3b +3

We want this to be zero, so ...

  4p +3b +3 = 0

  4p = -3b -3

  p = -3/4b -3/4 . . . . the value of p that makes A⊥B

Answer:

hope it helps you........

Answer:

Step-by-step explanation:

Coordinates of Q and S are:

We need to find the coordinates of R such that:

Let R has coordinates (x, y):

The point is R(2, -2)

Answer:

2,-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

(16.2t+3.4u+2.9)cm

Step-by-step explanation:

A triangle is a plane shape that has three sides. The perimeter of a triangle is gotten by taking the sum of all the lengths of the three sides. Let the length of the three sides by s1, s2 and s3, the perimeter of the triangle will be expressed as;

P = s1+s2+s3

Given the side lengths

s1 = (8.1t-6.1)cm

s2 = (8.1t+7.1)cm

s3 = (3.4u+1.9)cm

Perimeter of the triangle = 8.1t-6.1+8.1t+7.1+3.4u+1.9

collect the like terms

P = 8.1t+8.1t+3.4u-6.1+7.1+1.9

P = 16.2t+3.4u+2.9

Hence the expression that represents the perimeter, in centimeters, of the triangle is  (16.2t+3.4u+2.9)cm

Answer:

243

Step-by-step explanation:

1 /3 x=81

Step 1: Multiply both sides by 3.

3*( 1 /3 x)=(3)*(81)

x=243

The value of x for the expression (1/3)x = 81 is 243.

An algebraic expression is consists of variables, numbers with various mathematical operations.

The given expression is,

(1/3)x = 81

To find the value of x,

Solve the expression,

(1/3)x = 81

x = 81 x 3

x = 243

The required value of x is 243.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ2

Answer:

B

Step-by-step explanation:

tan(30)=n/(5*sqrt(3))

=> n=5

Answer:

25

Step-by-step explanation:

4×25 =100

____________

Answer:

25

Step-by-step explanation:

4 × 25 = 100

100 ÷ 4 = 25

Hope this help :)

#Semangat_Belajar

Answer: trescientos ochenta mil doscientos diez es,pero te ayude

Answer:

A, B, C, and E

Step-by-step explanation:

A) -4 X-3 = 12

B) 6 x 2 = 12

C) -6 X-2 = 12

D) 3 X-4 = -12

E) 12 x 1 = 12

the expressions that have a value of 12 are :

A, B, C, and E

Answer:

Lets find

[tex]\\ \rm\longmapsto -4(-3)=12\checkmark[/tex]

[tex]\\ \rm\longmapsto 6(2)=12\checkmark[/tex]

[tex]\\ \rm\longmapsto -6(-2)=12\checkmark[/tex]

[tex]\\ \rm\longmapsto 3(-4)=-12\checkmark[/tex]

[tex]\\ \rm\longmapsto 12(1)=12\checkmark[/tex]

Answer:

6,400

Step-by-step explanation:

One yard equals 3 feet.

160/3=53.3333

120X53.3333=6400

Answer:

No

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 1 ← is in slope- intercept form

with slope m = 3

Calculate the slope using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2,4) and (x₂, y₂ ) = (4, 12) ← 2 ordered pairs from the table

m = [tex]\frac{12-4}{4-2}[/tex] = [tex]\frac{8}{2}[/tex] = 4

Parallel lines have equal slopes

The slope of these 2 lines are not equal , thus not parallel

9514 1404 393

Answer:

  104π in² ≈ 326.7 in²

Step-by-step explanation:

Put the given numbers in the surface area formula for a cylinder.

  SA = 2πr(r +h)

  SA = 2π(4 in)(4 in +9 in) = 104π in² ≈ 326.7 in²

Answer:

326.73

Step-by-step explanation:

You just have to plug this into the cylinder surface area formula, which is [tex]A=2\pi rh+2\pi r^{2}[/tex]. So solving this would be [tex]A=2\pi (4) (9) +2\pi (4)^{2}[/tex]. You can simply put that into your calculator, and you'll get 326.72564, which rounds to 326.73. Make sure to read your problem carefully in case it specifies what number to round to though.

Answer:

100 km

Step-by-step explanation:

Speed = distance/time

=> Speed × time = distance

=> Distance = speed × time

=> Distance = (40 km/h) × 2.5 hours

=> Distance = 100 km.h/h

=> Distance = 100 km

Answer:

x = 7

Step-by-step explanation:

2x - 8 = 6              (Given)

2x - 8 + 8 = 6 + 8  (Add 8 on both sides)

2x = 14                  (Simplify)

2x/2 = 14/2           (Divide 2 on both sides)

x = 7                      (Simplify)

Answer:

29, 35, 41

Step-by-step explanation:

sequence is in the difference of 6

Step-by-step explanation:

There is 7 blocks that measure is 12.0-12.2

11 blocks that measure 12.2 to 12.4

18 blocks that measure 12.4 to 12.6

10 blocks that measure 12.6-12.8

4 blocks that measure 12.8 to 13.0

We can't find a mean by with Intervals so let find the midpoint of each interval,

12.1, 12.3, 12.5, 12.7, 12.9.

Add up the products and divide them by 50

[tex]\frac{623.6}{50} = 12.472[/tex]

Standard Deviation is

0.23( it is alot of steps so I use a calculator to save time).

The interqualtie range is 0.4

Answer:

-16200

Step-by-step explanation:

162×(-92)+(162)×(-810)×3

Step-by-step explanation:

[tex](162 \times ( - 92) + 162 \times ( - 5 \times - 162) \times 3 = (-14904 + 162 )\times( 810 \times 3) = (-14904+ 162) \times (2430) = - 14742\times 2430 = 378,756

Answer: 30 degrees

This is the minimum amount of rotation.

Why this value? Well because 360/12 = 30

Consider a triangle with 3 sides. Specifically I mean an equilateral triangle. We can rotate it 120 degrees to have it line up with itself. Now notice that 360/3 = 120.

For a square, we can rotate it 90 degrees and we can say 360/4 = 90

So the general rule is that the minimum angle of rotation is 360/n, where n is the number of sides. This rule only works for regular polygons. Regular polygons have the same side length and the same angle measure (the side and angle measure won't necessarily be equal).

So going back to this 12 sided dodecagon, we have n = 12 and 360/n = 360/12 = 30 as the minimum angle of rotation. Each 30 degree rotation will have the polygon match up perfectly with its old image. The preimage and image will be identical.

Answer:

height =10

[tex] \frac{4}{5} h + 2 = h \\ h - \frac{4}{5} h = 2 \\ \frac{1}{5} h = 2 \\ h = 2 \times 5 = 10[/tex]

Answer:

1. Y

2. YX , YZ

3. X

4. XZ

Answer:

[tex]\frac{y^7z^3}{x}[/tex]

Step-by-step explanation:

When variables have negative exponents, switch their positions.

[tex]\frac{x^{-1}y^7}{z^{-3}}=\frac{y^7z^3}{x}[/tex]

Step-by-step explanation:

5-3a-1+2a

5-1-3a+2a

4-1a

Answer:

x = -5 ​

Step-by-step explanation:

3+X=-2 ​

Subtract 3 from each side

3-3+X=-2-3

x = -5 ​

Answer:

-5

Step-by-step explanation:

1 Subtract 3 from both sides.

x=-2-3

2 Simplify -2 -3 to -5

x=-5

Let lebgth be x

[tex]\\ \rm\Rrightarrow Perimeter=2(L+B)[/tex]

[tex]\\ \rm\Rrightarrow 2(x+\dfrac{3x}{4})=140[/tex]

[tex]\\ \rm\Rrightarrow 2\left(\dfrac{4x+3x}{4}\right)=140[/tex]

[tex]\\ \rm\Rrightarrow 2\left(\dfrac{7x}{4}\right)=140[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{14x}{4}=140[/tex]

[tex]\\ \rm\Rrightarrow 14x=140(4)[/tex]

[tex]\\ \rm\Rrightarrow 14x=560[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{560}{14}[/tex]

[tex]\\ \rm\Rrightarrow x=40[/tex]

Answer:

D. [tex] 5.1[/tex]

Step-by-step explanation:

[tex] \frac{ - 44.288 - 31.6}{ - 3.1(6 - 1.2)} [/tex]

➡️ [tex] \frac{ - 75.888}{ - 3.1 \times 4.8} [/tex]

➡️ [tex] \frac{24.48}{4.8} [/tex]

➡️ [tex] = 5.1[/tex]