Danielle owes $47.25 for text messaging in the month of June. If her text messaging plan costs $6 for the first 600 messages and 25¢ for each additional text message.
how many text messages did she send that month?

Answer:

All the zeroes of f(x) are x = 1, x = -1 + 4i and x = -1 - 4i.

Step-by-step explanation:

Given that f(x) = x³ + x² + 15x - 17

Now, we have to find all the zeroes of the function.

Given that x = - 1 + 4i is a zero of the function.

So, x = - 1 - 4i must be another zero of the function.

Therefore, (x + 1 - 4i)(x + 1 + 4i) will be factor of the function.

Hence,  (x + 1 - 4i)(x + 1 + 4i)

= x² + 2x + (1 - 4i)(1 + 4i)  

= x² + 2x + [1² - (4i)²]

= x² + 2x + 17

Assume that (x + a) is another factor of f(x).

Therefore, we can write f(x) = x³ + x² + 15x - 17 = (x + a)(x² + 2x + 17)

⇒ x³ + x² + 15x - 17 = x³ + (a + 2)x² + (2a + 17)x + 17a

Hence, comparing the coefficients we can write  

a + 2 = 1  

⇒ a = -1  

Therefore, f(x) =x³ + x² + 15x - 17 = (x - 1)(x² + 2x + 17)

So, all the zeroes of f(x) are x = 1, x = -1 + 4i and x = -1 - 4i (Answer)

Answer:

she used 3 on each

Step-by-step explanation:

255/85=3

Final answer:

To find two consecutive odd integers, we can set up an equation based on the information given and solve for the variables. In this case, the lesser integer is 15 and the greater integer is 17.

Explanation:

To find two consecutive odd integers, let's represent the lesser integer as 'x' and the greater integer as 'x+2'. According to the given information, 87 more than the lesser integer is six times the greater integer. Mathematically, we can represent this as: x + 87 = 6(x+2).

To solve this equation, we can simplify and solve for 'x': x + 87 = 6x + 12. Simplifying further, we get 5x = 75, which leads to x = 15. Therefore, the lesser integer is 15 and the greater integer is 17.

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We need to simplify the fraction, once done you solve it from there. It's the main step, when you're done figure out who made a mistake (if someone does) and fix it.

Here's a reminder on how to simplify a fraction,

Find a common factor of the numerator and denominator. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.

Divide both the numerator and denominator by the common factor.

Repeat this process until there are no more common factors.

The fraction is simplified when no more common factors exist.

Another method to simplify a fraction

Find the Greatest Common Factor (GCF) of the numerator and denominator

Divide the numerator and the denominator by the GCF

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Have an amazing day!

Answer:

The pattern is that the decimal point moves the same number of decimal points to the right as zeros the power of ten has.

Step-by-step explanation:

To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zero in the power of ten. Then go to the right the decimal point the same number of positions.

For example, 0.36 * 10 = 3.6. The multiplier 10 has one zero, so you move the decimal point in 0.36 one position to the right to get the product 3.6.

A second example, 0.36 * 100 = 36. The multiplier 100 has two zeros, so you move the decimal point in 0.36 two positions to the right to get the product 36.

So, the pattern is that the decimal point moves the same number of decimal points to the right as zeros the power of ten has.

Answer:

To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zero in the power of ten. Then go to the right the decimal point the same number of positions.

Step-by-step explanation:

Answer:

He has won 28 games.

Step-by-step explanation:

Since he wins 80% of the games he pitched, we need to find 80% of 35.

80% as a decimal is 0.8.

[tex]0.8 * 35 = 2.8[/tex]

Now we need to convert the product to a whole number.

[tex]2.8 * 10= 28[/tex]

80% of 35 is 28.

The baseball player won 28 games he pitched in.

The baseball pitcher won 28 games out of the 35 games he pitched by calculating 80% of the total games pitched.

To calculate how many games a baseball pitcher won after knowing he won 80% of the 35 games he pitched, you can use a simple percentage calculation. First, convert 80% to a decimal by dividing 80 by 100, which equals 0.80. Then, multiply the total number of games (35) by 0.80 to find out the number of games won:

Number of games won = Total games pitched imes Win percentage

Number of games won = 35 imes 0.80 = 28

So, the pitcher won 28 games out of the 35 games he pitched.

Answer: Like terms

Example: 7x+9x are like terms because they both have an x with the same exponent of 1. We can combine them to get 7x+9x = 16x. This is like saying you have 7 boxes and you add on 9 boxes to get a total of 16 boxes.

Like terms are terms that have the identical variables and exponents. They can be combined or simplified in an expression. An example of like terms is 3x2 and 2x2 in the expression 3x2 + 2x2.

Terms that have the same variables with the same exponents on the variables are called like terms. In other words, like terms can be combined together because they have identical variable parts. For instance, in the expression 3x2 + 2x2, 3x2 and 2x2 are like terms because they both contain the variable x raised to the power of 2. Therefore, they can be simplified or added together, resulting in 5x2.

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The percent error in estimating the tree's height is 22%.

To find the percent error, follow these steps:

Calculate the absolute error: Absolute error = |actual value - estimated value|

In this case, absolute error = |58 ft - 45 ft| = 13 ft.

Calculate the percent error: Percent error = (absolute error / actual value) * 100%

Percent error = (13 ft / 58 ft) * 100% ≈ 22.41%

Round to the nearest percent: Round 22.41% to the nearest integer, resulting in 22%.

Therefore, the percent error in estimating the tree's height is 22%.

Complete question:

Find the percent error in each estimation. Round to the nearest percent.

You estimate that a tree is 45 ft tall. It is actually 58 ft tall.

Answer:

  7n +5

Step-by-step explanation:

For each person, the bread required is ...

  1 club + 2 regular sandwiches = 1(3 slices) + 2(2 slices) = 7 slices

Then for n people, 7n slices of bread are required.

In addition, there is one Dagwood sandwich requiring 5 slices of bread. The total is then ...

  7n +5 . . . . slices of bread required to fill the order.

Answer:

15n+5

Step-by-step explanation:

To determine the number of slices of bread needed to fulfill the deli's order for the company picnic, we need to calculate the total number of sandwiches required and then multiply it by the number of slices each type of sandwich contains.

Let's break it down step by step:

1. For each person attending the picnic, the company wants three sandwiches: one club sandwich and two regular sandwiches. So, for $n$ people, we have $3n$ sandwiches in total.

2. A club sandwich has 3 slices of bread, and a regular sandwich has 2 slices. Therefore, the number of bread slices required for $3n$ sandwiches can be calculated as follows:

- For the $3n$ club sandwiches, we need $3 \times 3n$ slices of bread, which is $9n$ slices.

- For the $3n$ regular sandwiches, we need $2 \times 2 \times 3n$ slices of bread, which is $6n$ slices.

3. In addition to the club and regular sandwiches, the company wants just one Dagwood sandwich, which has 5 slices of bread.

4. To find the total number of slices of bread needed, we add up the slices needed for each type of sandwich:

- $9n$ slices for the club sandwiches

- $6n$ slices for the regular sandwiches

- 5 slices for the Dagwood sandwich

Therefore, the total number of slices of bread required is $9n + 6n + 5$, which can be simplified to $15n + 5$.

So, the fully simplified expression for the number of slices of bread needed by the deli to fulfill the order for the company picnic is $15n + 5$.

The length of ramp is 8.9 meters approximately.

Given that, the entrance of the old town library is 2.3 feet above ground level.  

A ramp from the ground level to the library entrance is scheduled to be built.  

The angle of elevation from the base of the ramp to its top is to be 15º

We have to find the length of the ramp.

Let the length of ramp be “n” feet.

Now, if we observe there forms a right angle triangle with ramp as hypotenuse and height of entrance as opposite side for angle of elevation 15 degrees.

The diagram is attached below

In the figure,

AC = length of ramp

AB = height above ground level = 2.3 feet

angle of elevation = 15 degree

Then, we know that,

[tex]\sin \theta=\frac{\text {opposite side}}{\text {hypotenuse}}[/tex]

where θ is angle of elevation.

[tex]\begin{array}{l}{\sin 15^{\circ}=\frac{2.3 \text { feet }}{n \text { feet }}} \\\\ {\rightarrow 0.2588=\frac{2.3}{n}} \\\\ {\rightarrow n=\frac{2.3}{0.2588}} \\\\ {\rightarrow n=8.8865}\end{array}[/tex]

Hence, the length of the ramp is 8.9 meters approximately.

The acceleration rounded off to the nearest 100th is: -2.14 m/s^2

Step-by-step explanation:

Acceleration can be defined as the change in velocity over time.

The acceleration is negative in case of slowing down as the velocity goes from a higher value to lower value.

The formula for acceleration is:

[tex]a=\frac{Change\ in\ velocity}{time}\\a=\frac{v_f-v_i}{t}\\Here,\\v_f\ is\ final\ velocity\\v_1\ is\ initial\ velocity\\t\ is\ time[/tex]

Given

v_f = 230 m\s

v_i = 245 m\s

t = 7

Putting the values

[tex]a=\frac{230-245}{7}\\=\frac{-15}{7}\\=-2.14\ ms^{-2}[/tex]

Hence,

The acceleration rounded off to the nearest 100th is: -2.14 m/s^2

Keywords: Velocity, Acceleration

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Answer:

Step-by-step explanation:

2x -2+5=13

2x +3 =13

2x = 13-3

2x = 10

x = 10/2

x = 5

(9 + 2i)(9 − 2i)=85

The square of an imaginary number i is always -1. i.e. i²=-1

So according to asked question,

(9+2i)(9-2i)

using the algebric identity (a+b)(a-b)=a²-b²

where a=9 , b=2i

=(9)²-(2i)²

=9²-(4*i²)    

=81-4i²

if we want to simplify the following expression    

=81-(4(-1))                  where i²=-1

=81+4

=85

Therefore (9 + 2i)(9 − 2i)=85

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Ron worked for 3.25 hours and the total payment is $29.25 for 11.25 hours of combined work, which equates to an hourly wage of $2.60. Therefore, Ron should receive $8.45.

To calculate Ron's share of the $29.25 payment for removing garden gnomes, we first need to determine the total amount of time worked by all three individuals. Since Steve and Jerry worked 4 hours each and Ron was 45 minutes late, Ron worked 3 hours and 15 minutes, or 3.25 hours. We can convert 45 minutes to a decimal by dividing 45 by 60, which gives us 0.75, and since Ron was late by that duration, we subtract it from 4 hours (4 - 0.75 = 3.25).

Total hours worked by all = (Steve's hours + Jerry's hours + Ron's hours) = 4 + 4 + 3.25 = 11.25 hours.

To find the hourly rate, we divide the total payment by the total hours worked: $29.25 / 11.25 hours = $2.60 per hour. Finally, we multiply Ron's hours worked by the hourly rate to find his share: 3.25 hours * $2.60 per hour = $8.45.

Answer: Dominant. The answer is dominant.

Answer:

yes

Step-by-step explanation:

In order to be a function, x values should not be repeated.

For example. (0,2) and (2, 2) would work.

(0,2) and (0,8) would not because there are two values for 0.

In this case, each x-value (0, 2, 7, and 9) are only used once so it is a function

Answer:

yes

Step-by-step explanation:

For this relation to be a function

Each value of x from the domain ( values on left ) must map to exactly one value of y in the range ( values on right )

Here

0 → 11

2 → 9

7 → 4

9 → 2

This is the case here thus represents a function

Final answer:

To solve the problem, three equations can be used: 25 ÷ 5 = ?, 5 × ? = 25, and 25 ÷ ? = 5.

Explanation:

The correct equations to help solve the problem are:

To find the number of lettuce plants in each row, you need to divide the total number of lettuce plants, which is 25, by the number of rows, which is 5. So the first equation, 25 ÷ 5 = ?, will give you the answer. The second equation, 5 × ? = 25, can also be used to find the number of lettuce plants in each row by solving for the missing value. Finally, the third equation, 25 ÷ ? = 5, can be used as an alternative way to find the number of lettuce plants in each row.

Step-by-step explanation:

Your equation is:

[tex] \frac{x}{8} + 3 = 7[/tex]

[tex] \frac{x}{8} = 4[/tex]

[tex]x = 32[/tex]

The student's question involves solving the algebraic equation x/8 + 3 = 7 to find the value of the unknown variable x. The solution to the equation is x = 32.

The question asks us to solve an equation involving the unknown variable, which is a common type of problem in algebra. According to the question, 'Three more than the quotient of a number and 8 is equal to 7'. This can be translated into the equation x/8 + 3 = 7, where x is the number we are trying to find.

To solve for x, we need to isolate it on one side of the equation. We start by subtracting 3 from both sides of the equation:

Next, we multiply both sides of the equation by 8 to solve for x:

Therefore, the unknown number is 32.

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height:length

1:2

x feet: 5 feet

You know the length and the ratio of the dimensions. From the ratio you know that the length is twice the height. So height = 5/2 = 2.5 ft.

Answer:

81

Step-by-step explanation:

Answer:

20% peanuts are there in the mixture of nuts.

Step-by-step explanation:

Total weight of the mixture =25 lbs(10+15)

In the 25 lbs mixture of nuts, 68 % is peanuts, therefore finding the total weight of peanuts.

68 % of 25 lbs= 17 lbs.

There is a total 17 lbs of peanuts in the mixture .

15 lbs of peanuts was exclusively added, therefore the rest 2 lbs must have come from the mixture of nuts.

Therefore, there is a total of 2 lbs of peanuts in 10 lbs of mixture of nuts.

[tex]\frac{2}{10} *100[/tex] =20 %

20% peanuts are there in the mixture of nuts.

Answer:

It is not a function because there is a maximum.

Step-by-step explanation:

With 12 as the maximum it will not go on forever and functions do.

The amount of time a car is parked is not a function of parking cost since the cost of parking cannot exceed the maximum amount of  $12 no matter how long the car is parked in the lot.

Given:

the rate of cost of parking in a lot, R = $3 per hour

maximum cost of parking in a lot, C = $12

To explain:

The cost of parking in a lot can be calculated as;

Cost = cost rate x time

let the time = t

Cost = 3t

        Cost = 3 x 1 = $3

        Cost = 3 x 2 = $6

        Cost = 3 x 3 = $9

        Cost = 3 x 4 = $12

        Cost = 3 x 5 = $15  

(notice, $15 has exceeded $12, but the maximum cost has to be $12)

Thus, time is not a function of cost of parking since the maximum cost cannot exceed $12 no matter how long the car is parked in the lot.

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Answer:

The vertex of the function is (2, -3).

Step-by-step explanation:

Given:

[tex]y=x^{2}-4x+1[/tex]

So, to find the vertex of the function we will get the equation in the form:

[tex]y=ax^{2} +bx+c[/tex]

[tex]y=1x^{2}+(-4)x+1[/tex]

So, [tex]a=1,b=-4,c=1[/tex]

Then, we calculate the x-coordinate of the vertex:

[tex]x=\frac{-b}{2a}[/tex]

[tex]x=\frac{-(-4)}{2\times1}\\x=\frac{4}{2}[/tex]

[tex]x=2[/tex]

And now, we get the [tex]y[/tex] value of vertex of the function:

[tex]y=1x^{2}-4x+1[/tex]

[tex]y=1\times 2^{2}+(-4)\times (2)+1[/tex]

[tex]y=1\times 4-8+1[/tex] (when the opposite signs multiply the result is negative)

[tex]y=4-8+1[/tex]

[tex]y=-3[/tex]

Therefore, the vertex is at [tex](x,y)=(2,-3)[/tex].

Paul caught 3 pike and 1 salmon

The total number of fish the three boys caught is 16

Solution:

According to question,

Mike caught 1 pike and 4 salmon

Charlie caught 5 pike and 2 salmon

Paul caught half the number of pike that both Charlie and Mike caught combined, and 1 less salmon than Charlie caught

Pike caught by Paul = half of number of pike that both charlie and mike caught combined = [tex]\frac{1}{2} (5 + 1) = 3[/tex]

Salmon caught by Paul = 1 less salmon than Charlie caught = 2 - 1 = 1

Thus, Paul caught 3 pike and 1 salmon

Total of numbers Pike caught by three boys are  

5 + 1 + 3 = 9 pikes

Total of numbers salmon caught by three boys are  

4 + 2 + 1 = 7 salmons

Hence , the total number of fish caught are

9 + 7 = 16 fishes  

Answer: 90 millimeters

Step-by-step explanation: To convert centimeters to millimeters, multiply centimeters by 10. 9x10=90.

Answer:

7 )

x =  [tex]\frac{3\sqrt{2} }{2}[/tex]

[tex]y= 3[/tex]

8 )

[tex]x=6\sqrt{6}[/tex]

[tex]y= 9\sqrt{2}[/tex]

Step-by-step explanation:

7  )                                 8)

In Δ ABC                                      In Δ XYZ            

∠ C = 45°                                          ∠ X = 60°

∠ A = 90°                                           ∠ Y = 90°

[tex]AC= \frac{3\sqrt{2} }{2}[/tex]             [tex]XY= 3\sqrt{6}[/tex]

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45°  ......Angle sum property of a triangle i.e 180°

∴  Δ ABC is an Isosceles Triangle

∴ AC = AB = x =  [tex]\frac{3\sqrt{2} }{2}[/tex]

Now appplying Trignometry identity we get

[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2}  }{2}\\\\y= 3[/tex]

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30°  . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

[tex]\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}[/tex]

[tex]\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\  y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}[/tex]

Now,

[tex]\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}[/tex]

Answer:

Neither

Step-by-step explanation:

Parallel lines have equal slopes.

Clearly the lines are not parallel.

The product of the slopes of perpendicular lines equals - 1

2 × [tex]\frac{1}{2}[/tex] = 1 ≠ - 1

Thus the lines are not perpendicular.

Lines with Slope 1 = 2 and Slope 2 = 1/2 are neither parallel nor perpendicular.

To determine whether the two lines represented by Slope 1 = 2 and Slope 2 = 1/2 are parallel, perpendicular, or neither, we must consider the relationship between their slopes. Two lines are parallel if they have the same slope. In contrast, two lines are perpendicular if their slopes are negative reciprocals of each other (the product of their slopes is -1). In this case, since the slopes are different and their product (2 * 1/2) equals 1, not -1, the lines are neither parallel nor perpendicular.

Answer:

Slope: 2y- int: −6

Explanation:

We can easily find the slope and

y -intercept of this line by converting it to slope intercept form

y=mx + b, with slope m and a

y- intercept of b.

Let's subtract

8x

from both sides to get

−4y=−8x+24

Next, we divide all terms by

−4 to get y=2x−6

Now that our equation is in this form, we see that our slope is

2, and our y -intercept is −6.

-Hope this helps you

Creating parallel and perpendicular lines involves understanding that parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. A line that is neither parallel nor perpendicular to a given line simply has a slope that does not meet these conditions.

Given the lines in your question, you're asked to create a parallel, perpendicular, and neither parallel nor perpendicular line. Let's consider the first line: y = 3x.

1) A line parallel to y = 3x will have the same slope, so the equation of such a line can be y = 3x + b. You can choose any value for b, as it shifts the line up or down but doesn't change its slope.

2) A line perpendicular to y = 3x would have a slope that is the negative reciprocal of 3, which is -1/3. So, such a line can be represented by the equation y = -1/3x + b. Again, any value of b will work.

3) A line that is neither parallel nor perpendicular to y = 3x could have any slope that's not equal to 3 or -1/3. For instance, the line y = 2x + b is neither parallel nor perpendicular to y = 3x.

Do the same for all the remaining lines by understanding these principles.

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