Megan's text messaging plan costs $15 for the first 500 messages and 5¢ for each additional text message. If she owes $21.55 for text messaging in the month of May, how many text messages did she send that month?

The solutions of the equation are x = 15 and -20

The equation is given as

the absolute value quantity two fifths times x plus 1 end quantity minus 7 equals 0

Rewrite properly as

|2/5x + 1| - 7 = 0

Add 7 to both sides of the equation

|2/5x + 1| = 7

Remove the absolute bracket

2/5x + 1 = 7 and 2/5x + 1 = -7

This gives

2/5x = 6 and 2/5x = -8

Multiply both sides by 5/2

x = 15 and -20

Hence, the solutions of the equation are x = 15 and -20

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Answer:

x = 15 and -20

Step-by-step explanation:

Answer:

  y = -3

Step-by-step explanation:

You want the solution to the absolute value equation | y-4 | = | y+10 |.

The absolute value function ...

  f(x) = | x |

is piece-wise defined as ...

  [tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge 0\end{cases}[/tex]

That is, the function is defined differently for argument values less than 0.

The above observation regarding the absolute value function means the nature of the given equation changes where the absolute value arguments are zero. Those values are ...

  y -4 = 0   ⇒   y = 4

  y +10 = 0   ⇒   y = -10

In other words, the points y = -10 and y = 4 divide the domain of the equation into three parts. The behavior will be different in each of those parts.

To solve the equation, we must examine each region of the domain for possible solutions.

When y < -10, both of the absolute value functions change the sign of their argument. Then the equation is ...

  -(y -4) = -(y +10)

Adding y to both sides of this equation gives ...

  4 = -10 . . . . . false

This means there is no solution to the equation in the region y < -10.

When -10 ≤ y < 4, the absolute value function |y -4| changes the sign of its argument, but the other function does not. In this region, the equation becomes ...

  -(y -4) = (y +10)

  -6 = 2y . . . . . . . . . add y-10 to both sides

  -3 = y . . . . . . . . divide by 2. This value is in the region -10 ≤ y < 4.

The solution to the equation is y = -3.

When 4 ≤ y, neither absolute value function changes the sign of its argument. In this region the equation becomes ...

  y -4 = y +10

Subtracting y from both sides of this equation gives ...

  -4 = 10 . . . . . false

This means there is no solution to the equation in the region 4 ≤ y.

__

Additional comment

The first attached graph shows the given equation rewritten as two functions. The solution is where those functions have equal values: the point(s) where the graphs intersect.

We often find it more convenient to rewrite equations like this to the form f(x) = 0. Here, that might mean we define ...

  f(x) = |y -4| -|y +10|

Then the solution is found on the graph at the x-intercepts. The graph in the second attachment shows this solution, and clearly shows the changes in behavior at x = -10 and x = 4.

Answer:  27. 10 < x < 20

29. 10 < x < 20

Step-by-step explanation:

Answer:

The school should buy 39 packages.

Step-by-step explanation:

3198 notebooks

82 notebooks = 1 package

3198÷82 = 39

(Eg: you have 4 notebooks and there are 2 in each package. How many packages are there?  4÷2 = 2   So 2 packages)

Answer:  Choice 2

invalid. The inner circle is plants, and the outer circle is those with cells.

=========================================================

Further Explanation:

If we throw a dart at random, and we land in the inner circle (plants), then we automatically land in the outer circle (has cells).

Now imagine the dart landed in the "has cells" circle, but outside the smaller circle. This could be stuff like animal cells, bacteria, etc. So just because something has cells it does not automatically make it a plant. Saying "an iris has cells" is not enough info to be able to tell it's a plant or not. This means the conclusion of "irises are plants" is shaky at best.

This is why the overall argument structure is invalid.

For more information, check out the concept of "affirming the consequent" which is a common fallacy people make.

Answer: 1/10

Step-by-step explanation:2 * 1/5 is 2/5 and 1*3/10 is 3/10 and when you subtract them you get 1/10

Answer:9/10

Step-by-step explanation:get 2 1/5 into a improper fraction thats 11/5 then multiply by to for the common demontor thats 22/10

get 1 3/10 into a improper fraction 13/10

then minus 22-13 thats 9

then bring in the bottom 9/10 hope that helps

Answer:

spam

Step-by-step explanation:

spam spam spam

Answer:

=========================

Area equation of a rectangle

Answer:

Length = 88.9 cm

Step-by-step explanation:

Formula we use,

→ A = L × W

Then the value of its length is,

→ A = L × W

→ 8712 = L × 98

→ L = 8712/98

→ L = 88.8979591837

→ [ L = 88.9 cm ]

Hence, the length is 88.9 cm.

The required solution would be 46 for a given problem (1).

The required solution would be 1 for a given problem (2).

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

We have been given that A * B= A·B + 1 and A □ B = A + B/2,

⇒ 3 *[(7 □ 3) □ (3*4)].

⇒ 3 *[(7 + 3/2) □ (3·4 + 1)].

⇒ 3 *[(17/2) □ (13)].

⇒ 3 *[17/2 + 13/2].

⇒ 3 *[30/2].

⇒ 3 * 15.

⇒ 3·15 + 1

⇒ 46

We have been given that * represents an operation defined by a*b= a^b +b,

find (1*2)*3.

⇒  a∗b = aᵇ + b

∴ (1 ∗ 2) ∗ 3 = (1²) ∗ 2 =  (1) ∗ 2 = (1)³ = 1

Therefore, the required solution would be 46 for a given problem (1) and

the required solution would be 1 for a given problem (2).

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Step-by-step explanation:

9/32 or 0.28125

hehhehehehehehhehehehe

Answer:

Hello,

Step-by-step explanation:

[tex]\dfrac{\dfrac{3}{8} }{\dfrac{3}{4} } =\dfrac{0.375}{0.75}=\dfrac{375}{750} =\dfrac{1}{2} =0.5\\\\--------------------------------\\\\\dfrac{\dfrac{3}{8} }{\dfrac{3}{4} }=\dfrac{3}{8} * \dfrac{4}{3} \\\\\\=\dfrac{4}{8}\\\\=\dfrac{1}{2}\\\\=0.5\\[/tex]

Answer:

i think the question might be wrong.

The Fuel efficiency rate in miles per gallon is;  104.67 MPG

Let the initial amount of gallons be x

Now, after driving for 263 miles, you have 11 gallons of gas left in your tank.

Now, you continue driving and after driving 314 miles, you have 8 gallons left. This means that number of gallons used to drive 314 miles = 11 - 8 = 3 gallons

Therefore the Fuel efficiency rate which is in miles per gallon is;

MPG = 314/3

MPG = 104.67 MPG

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To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = [tex]σ^{2} =\frac{Sigma(xi-m)^{2}}{n}[/tex]

Now here we need to verify ∑x and ∑[tex]x^{2}[/tex].

∑x = 21+19+15+32+27

     = 114

and ∑[tex]x^{2}[/tex] = [tex]21^{2} +19^{2} +15^{2} +32^{2} +27^{2}[/tex]

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=[tex]\sqrt{Variance}[/tex]

                                     = [tex]\sqrt{45.2}[/tex]

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Answer:

8 with 6

Step-by-step explanation:

Answer:

x + 8 = 53

Step-by-step explanation:

x + 8 = 53

8 more than x is x + 8 because ur adding 8 more to x. And that is equal to 53 because it literally says IS EQUAL to 53. therefore.

to solve isolate x by subtracting 8 from both side so:

x = 53-8

x = 45

The average annual wage of workers in the country will be at least $68400 in the year 2023 and after , the correct option is option (B) .

In the question it is given that

model of the average annual wage (y) = 2286x + 38620   ...(i)

where x = number of years after 2010,

It is also given that the average annual wage(y) must be at least 68,400 .

which means y ≥ 68400

Substituting value of y from equation (i) we get  ,

2286x + 38620 ≥ 68400

Simplifying the inequality further we get ,

2286x ≥ 68400 - 38620

2286x ≥ 29780

x ≥ 29780/2286

x ≥ 13.02 ≅ 13

Hence , the average annual wage will more than the specified value from the year, 2010+13 = 2023 .

Therefore , the average annual wage of workers in the country will be at least $68400 in the year 2023 and after , the correct option is option (B) .

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Using the relation between velocity, distance and time, the distances are given as follows:

A. d = 13/3 miles.

B. d = 4.25 miles.

C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).

Velocity is distance divided by time, that is:

v = d/t.

Hence the distance is:

d = vt.

In item a, considering the time in hours, we have that:

v = 13, t = 20/60 = 1/3.

Hence:

d = 13/3 miles.

In item b, we have different definitions, then:

d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).

d = 15/12 + 15/5

d = 4.25 miles.

For item c, we have that:

d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).

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Answer:

You can flip the second fraction and multiply the fractions so 3/5 * 15/3 = 3

Step-by-step explanation:

Answer:

12.5 %

Step-by-step explanation:

There are 8 total sections, and only one of them is yellow. So if we spun it eight times, the possibility of getting yellow is one time. As a result, 1/8 is 12.5%

Answer:

$3,108.08 per month

Step-by-step explanation:

Calculator shows the answer as 3,108.0833 with the 33 repeating.  Rounding to the nearest cent (100ths place) gives $3,108.08

Answer:

11. 6

13. 73

15. 588

17. 139

19. 18

21. 18

23. 8

Step-by-step explanation:

To solve these equations, you simplify each expression. You also use the order of operations.

Answer as a fraction:  x = 1/2

Answer in decimal form:  x = 0.5

Work Shown:

4x+9 = 11

4x = 11-9

4x = 2

x = 2/4

x = 1/2

x = 0.5

Explanation: I subtracted 9 from both sides (step 2). Then I divided both sides by 4 to fully isolate x (step 4)

29 parcels can be made from 290 magazines and books

The given parameters are

1 parcel = 6 magazines and 4 books

This can be rewritten as:

1 parcel = 10 magazines and books

For 290 magazines and books, we  have

x = 290 magazines and books

This means that

x = 290 magazines and books

1 parcel = 10 magazines and books

Cross multiply

x * 10 = 290 * 1

This gives

x = 29

Hence, 29 parcels can be made from 290 magazines and books

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The rocket will take a time of approximately 2.686 seconds to hit the ground.

The height of the rocket (h), in feet, is modelled by a quadratic equation, which is used to model free fall motion, that is, the motion of an object solely due to action of gravity. In this problem we must look for the time when the rocket hits the ground:

- 16 · t² + 40 · t + 8 = 0

(t - 2.686) · (t + 0.186) = 0

Only the first root offers a realistic solution, for time is a non-negative variable. The rocket will take a time of approximately 2.686 seconds to hit the ground.

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The addition equation to represent the problem represented on the number-line is given by [tex]-5+8=3[/tex].

The number line is a visual representation of the real numbers along a straight line. Every point on a number-line contains a real number.

The integers that we see on this number line represents the round scores of the game Luis is playing.

At the beginning of second round Luis's team has a score of -5 , but he scored 8 points in the second round.

So the addition equation for representing this particular situation is given by :

Score in round 1 + points scored by Luis in round 2= Score in round 2

So the addition equation :

[tex]-5+8=3[/tex]

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Answer: y=-37/2

Step-by-step explanation:

y=9x/8 + (-1/2)

y=9x/8 - 1/2

y=9(-16)/8 - 1/2

y=9*(-2) - 1/2

y=-18 - 1/2

y=-(18 + 1/2)

y=-(18 + 1/2)*2/2

y=-(36 + 1)/2

y=-37/2

Venn diagram{image attached},2000 people didn't cast their vote and 1000 votes are not valid in the election

Given that In a municipal election, two candidates, A and B, ran for the position of Mayor, and 25000 people voted. Voters were supposed to vote for only one candidate. A received 12000 votes, B received 10,000 votes, and 1000 cast votes for A and B both.

Number of votes for A=12,000

Number of votes for B=10,000

1000 cast votes to Both A and B, these votes are not valid because each one is supposed to vote only for one.

Therefore, the number of votes not valid is 1000

Total people cast vote= sum of votes for every party

Total people cast vote=12,000+10,000+1000

Total people casted vote=23,000

Therefore, Venn diagram{image attached},2000 people didn't cast their vote and 1000 votes are not valid in the election

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