Plan 1 costs $35 per month + $5 per gigabyte of extra data used
Plan 2 costs $50 per month + $2 per gigabyte of extra data used

Answers

Answer 1

The computation of the equation shows that the extra data that will be used to have the same amount will be 5 gigabytes.

How to compute equation?

Let the amount of extra data used be represented by x.

Plan 1 = 35 + (5 × x) = 35 + 5x

Plan 2 = 50 + (2 × x) = 50 + 2x

35 + 5x = 50 + 2x

Collect like terms

5x - 2x = 50 - 35

3x = 15

x = 15/3 = 5

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Related Questions

What quadrilaterals can you draw that have two sides with length 8 cm and two sides with length
5 cm?
Which of these quadrilaterals can have two sides with length
8 cm and two sides with length 5 cm?
Select all that apply.
OA. Trapezoid
OB. Square
OC. Parallelogram
OD. Rectangle
E. Kite

Answers

Answer:

C. parallelogram

D. rectangle

E. kite

Step-by-step explanation:

Cannot be the square because all sides are the same. A trapezoid can have two sides the same, but not two pairs of equal sides. The remaining shapes can have two pairs of equal length sides. see image.

Look at these equations.
9 = 7+ a
a + 8 = b + 5

Use both equations to work out the value of B ​

Answers

Answer:

B=5

Step-by-step explanation:

If 7 plus a equals 9 then a would equal 2.

2+8=b+5

10=b+5

Ask yourself what number plus 5 equals 10

B is 5 because 5 plus 5 is 10

The perimeter of a notebook is 28
inches. The area is 48 square inches.
What are the dimensions of the
notebook?

Answers

Area = length x width

Half the perimeter = length + width


half the perimeter = 14 inches.

Find 2 numbers when added together = 14 and when multiplied together = 48

6 + 8 = 14

6 x 8 = 48


the dimensions are 6 inches by 8 inches

What time is it on the clock?

Answers

Answer:

About 2:18

The minute hand points toward the [tex]\frac{1}{4}[/tex] marker, meaning that is 15 minutes.Count the other ticks, and that's 18.Since the hand is not exactly on the 3, that means it is 2:00

With this information, we can make a hypothesis or come to a conclusion that the clock says 2:18

A rectangle has an area of 91.7 square inches and a base of 13.1 inches. What is the height?

Answers

Answer:

7 inches

Step-by-step explanation:

The area of a rectangle A is equal to its length times its width (or base times height if you want to put it that way.)

Since A = b*h, h = A/b. Plugging in values gives you 91.7/ 13.1 = 7 inches.

So the answer is 7 inches.

A company is designing a new cylindrical water bottle. The volume of the bottle will be 176 cm ^3. The height of the water bottle is 7.8 cm. What is the radius of the water​ bottle? Use 3.14 for pi

Answers

Step-by-step explanation:

volume = 176 cm³

height = 7.8

radius = ?

pi = 3.14

volume of cylinder = πr²h

176 = 3.14 × r² × 7.8

176 = 24.492 × r²

176/24.4 = r²

7.21 = r²

√7.21 = r². ( Using long division )

r = 2.69 ( approx. )

Which geometric figure would be the best to model a suitcase?

Answers

Answer:

A rectangular prism would be best to model a suitcase

Step-by-step explanation:

Hope that helps!

Answer:

Rectangular Prism

Step-by-step explanation:

If you look at a suitcase, it resembles a rectangular prism quite well.

A function f is defined by f(x, y) = 3x2 – 4y. What is the value of
f(3, 2)?

Answers

Assuming the function is [tex]f(x,y)=3x^2-4y[/tex]

     --> then f(3,2) is: [tex]f(3,2) = 3(3^2)-4(2)=3*9-8=27-8=19[/tex]

Hope that helps!

Please answer soon
(-2 • -4)^2 = ?

Answers

Answer:

64

Step-by-step explanation:

(-2(-4))^2

8^2

64

hope that helps

A researcher is studying the relationship between the number of TVs owned by a family and the size of the family's electric bill. After collecting data, he finds that the relationship is best modeled by the equation B = 2.43T + 95.66, where B is one month's electric bill in dollars and T is the number of TVs owned by the family. Which of these is a good interpretation of the y-intercept of this model?

Answers

Answer:

Step-by-step explanation:

No choice is given but here is the general interpretation.

Y-intercept is where the plot crosses the y-axia at x=0. In this case, x is T which represents number of TVs owned by the family. T=0 meaning there is no TV and B = 96.66 is the one month's electric bill in dollars for all other appliances in the home.

Given function

B=2.43T+95.66

Now

Compare to slope intercept form y=mx+b

Slope=m=2.43Y intercept=b=95.66

Here y intercept may be the fixed charge .

Can anyone help me with this one Question on volume The diameter of a cylinder is 1 yd. The height is 12 yd. Find the volume of the cylinder.

Answers

Answer:

9.42 cube.yd

Step-by-step explanation:

Volume of cylinder= πr^2h

3.14 × 0.5 × 0.5 × 129.42 cube.yd

this question is too hard

Answers

Answer:

27 children

Step-by-step explanation:

For every 9 children, there are 4 adults. Those numbers added together equal 13. Now, if we divide the total number of adults and children by 13, we will get the number of how many groups there are of 9 kids and 4 adults.

39 / 13 = 3

There are 3 groups of 9 kids and 4 adults, which means to find the total number of children, we have to multiply 3 by 9.

3 * 9 = 27

Therefore, there are 27 children total. I know this was probably really confusing, but I hope it helped in some way! Have a lovely day!! :)


Identify the initial amount in the following exponential function: y = 2.3(1.32)

Answers

The initial amount is y = 3.036

HELP PLEASE!! 20 Points!! Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.

Answers

Answer:

my answer was wrong

Which is an equivalent fraction for
?
A
12\frac{1}{2}
2
1


B
26\frac{2}{6}
6
2


C
46\frac{4}{6}
6
4


D
32\frac{3}{2}
2
3

Answers

Answer:

I believe the answer is C

Step-by-step explanation:

Briefly describe a predatory/prey boom bust graph.

Answers

Answer:

This can lead to cyclical patterns of predator and prey abundance, where prey increase in number and then, with abundant food, predator number increases ...

Step-by-step explanation:

Charles buys 60 packs of pens.
There are 14 pens in each pack.
Each pack costs £4.50.
Charles sells each pen for 70p but he only manages to sell
2
3
of the pens.
How much profit did he make?

Answers

Answer:

£122

Step-by-step explanation:

Total no. of pens :- 60× 14= 840

Cost of all pens :- £270

Total no. of pens sold :- 560

Cost of those pens :- £392

Profit = £122

Charles made a profit of  £122, By selling (2/3)rd of his pens.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Charles buys 60 packs of pens and there are 14 pens in each pack.

If each pack costs £4.50.

So, The Total cost is,

=  £(60×4.50).

=  £270.

The total number of pens is,

= (14×60).

= 840, And he manages to sell (2/3) of it which is,

= (2/3)×840.

= 560.

Now, The total money made by him is,

= 540×0.7.

=  £392.

Therefore, The profit he made is  £(392 - 270) =  £122.

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differentiate the following with respect to x

irrelevant answers will be reported​

Answers

Answer:

[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}[/tex]

Step 2: Differentiate

Apply Derivative Rule [Product Rule]:
[tex]\displaystyle y' = \big[ e^{x^2 + 7} \big]' \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = e^{x^2 + 7} (x^2 + 7)' \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Addition/Subtraction]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Trigonometric Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \cos (3x + 4) (3x + 4)' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Addition/Subtraction]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules [Basic Power Rule + Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{\big[ \csc (5x) \big] '}{2\sqrt{\csc (5x)}}[/tex]Apply Trigonometric Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{- \csc (5x) \cot (5x) (5x)'}{2\sqrt{\csc (5x)}}[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Multiplied Constant]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{-5 \csc (5x) \cot (5x)}{2\sqrt{\csc (5x)}}[/tex]Rewrite:
[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]

∴ we have found the derivative of the function.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

To find the derivative of the function [tex]\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}[/tex] with respect to [tex]\displaystyle\sf x[/tex], we'll use the chain rule and product rule.

Let's break down the function into its individual parts:

[tex]\displaystyle\sf u= e^{x^{2}+7}[/tex]

[tex]\displaystyle\sf v= \sin(3x+4)[/tex]

[tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex]

Now, let's differentiate each part separately:

Using the chain rule, the derivative of [tex]\displaystyle\sf u= e^{x^{2}+7}[/tex] is:

[tex]\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}[/tex]

Using the chain rule, the derivative of [tex]\displaystyle\sf v= \sin(3x+4)[/tex] is:

[tex]\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)[/tex]

To differentiate [tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex], we can rewrite it as [tex]\displaystyle\sf w= (\csc(5x))^{1/2}[/tex]. Using the chain rule, the derivative of [tex]\displaystyle\sf w[/tex] is:

[tex]\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)[/tex]

Simplifying the derivative [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Now, using the product rule, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] can be calculated as follows:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}[/tex]

Substituting the values of [tex]\displaystyle\sf \dfrac{du}{dx}[/tex], [tex]\displaystyle\sf \dfrac{dv}{dx}[/tex], and [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further, we have:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Write a numerical expression to represent the phrase.

the difference of 4 cubed and 25

Answers

Hello!

First, "the difference" of 2 numbers means you subtract these numbers.

Then, 4 cubed is written as follows:

Subtract:

4³-25

[If necessary] Evaluate:

64-25

39

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

a parabola has focus of (5 2) and directrix y=0.where is the parabola's vertex

Answers

keeping in mind that the vertex will be half-way between the directrix and the focus point, in this case the directrix is below the focus point, meaning is a vertical parabola, Check the picture below.

Solve the system of equations below. Thankyou!

Answers

Answer:

x = - 9

y = 5

Step-by-step explanation:

EQ1 + EQ2

Substitute the value of X in either EQ1 or EQ2

-7y-4x=1.............eqn 1
7y-2x=53..........eqn 2
Add both eqns
-6x=54
x=54/-6
x=-9
Sub for x in eqn 1
-7y-4(-9)=1
-7y+36=1
-7y=1-36
-7y=-35
y=-35/-7
y=5
:x=-9 and y=5

Solve for x.
32
(2x - 12)°

Answers:
x = 35
X= 51
x = 80
x = 96

Answers

51 I thinks that’s the correct answer

which expression is equavilent to the epression -3(4x - 2) - 2x?

A. -8x
B. -16
C. -14 - 2
D. -14 + 6

Answers

Answer:

D

Step-by-step explanation:

-3(4x - 2) - 2x

-12x + 6 -2x

-14x + 6



Angle FGH is a right angle.
The measure of angle JGH is 50.
The measure of angle FGJ is
What is the value of x?

Answers

Answer:
since its a triangle then angles have to be 90 (the right angle) and 50 (which is given)
180-90-50 = 40
Answer = 40

Step-by-step explanation:

Manny has 36 coins in
his piggybank.
3 of the coins are silver dollars.
• The remaining coins are dimes (10€), quarters (25€) and nickels (5¢).
• There is an equal number of dimes, quarters and nickels.
How many nickels does Manny have?

Answers

Answer:

q=50

d=22

Step-by-step explanation:

Will choose Brainliest.
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.

How many more cookies will Jessica have than Martha?

If x represents the number of cookies Jessica started with, complete the statements below.

The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.

Answers

That part is total cookies as per algebraic formula x^2-(a+b)x+ab=0

Hence

The inequality is

[tex]\\ \rm\rightarrowtail x^2-30x+224>=0[/tex]

[tex]\\ \rm\rightarrowtail (x-14)(x-16)>=0[/tex]

[tex]\\ \rm\rightarrowtail 14\leqslant x\leqslant 16[/tex]

Solution range

[14,16]

Atleast means the range

16-142

Atleast 2 more than Martha

After measuring the heights of 7 people, they have an average height of 156cm. after
measuring the heights of 8 people they have an average height of 158cm. how tall is
the 8th person?

Answers

Answer:

8th Person = 172 cm tall

Step-by-step explanation:

( a + b + c + d + e + f + g )/7 = 156

a + b + c + d + e + f + g = 1092 total size

----------------------------------------------------------

now they measured 8 people (a + b... g) + h, but we know the total size of the other 7 = 1092

a + b + c + d + e + f + g + h

( 1092 + h )/8 = 158

1092 + h = 158*8

h =  1264 - 1092

h = 172

-----------------------------------

the 8th person is 172 cm tall

Use the example above and determine the fraction of total interest owed. After the fourth month of a 12 month loan, the numerator is: {(n + ) + (nt ) + (n + ) + (n + and the denominator is: {(n) + (n + 1) + ... + (n + )} Therefore, the fraction is numerator/denominator (to the nearest tenth) = %.​

Answers

Answer:

Step-by-step explanation:

The picture does not show the example which will help in determining whether it is simple or compound interest calculation.

Based on what is shown, the answer is:

the numerator is: {(n + 11) + (n + 10) + (n + 9 ) + (n + 8) = 4n + 38;

and the denominator is: {(n) + (n + 1) + ... + (n + 11) = 12n + 66.

Therefore, the fraction is numerator/denominator:

= (4n + 38) / (12n + 66)

In this case n=1, the fraction = 42/78 =  0.53846

= 53.85%

Find the area of the figure below. You may assume all sides are perpendicular.


Multiple answer choice

23

19

27

17

Answers

Answer:

I think the answers is 27, just add all of those squares.

the standard form of a linear equation is the form ______________

Answers

Answer:

Ax+By=C

Step-by-step explanation:

:)

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