To rotate triangle ABC 90 degrees clockwise about a point P, we can follow these steps:
Draw a line segment from each vertex of the triangle to the point P.
Measure the distance from each vertex to the point P and make note of the lengths.
Rotate each line segment 90 degrees clockwise by swapping the x and y coordinates and changing the sign of the new y-coordinate. For example, if a vertex has coordinates (x, y), the new coordinates after rotation will be (y, -x).
Use the new endpoints of the line segments to draw the new triangle, A'B'C'.
For example, suppose the coordinates of triangle ABC are A(1,2), B(3,4), and C(5,2), and the point of rotation is P(3,3). Then the distances from each vertex to the point P are:
AP = sqrt((3-1)² + (3-2)²) = sqrt(5)
BP = sqrt((3-3)² + (3-4)²) = 1
CP = sqrt((3-5)² + (3-2)²) = sqrt(5)
After rotating each vertex 90 degrees clockwise about P, we get:
A'(4,1)
B'(2,3)
C'(4,5)
Using these new coordinates, we can draw the new triangle A'B'C', which is the result of rotating triangle ABC 90 degrees clockwise about P.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C
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K Write the inequality represented by each graph, using the variable x. b. 50 51 52 53 54 ← 10 11 H 55 56 57 58 59 ++ 12 13 14 15 16 17 18 19
The inequality represented by the graph is 10 ≤ x ≤ 20.
What is inequality?Inequality is the unequal distribution of resources or opportunities among individuals or groups in a society. It can be measured in multiple ways, including income, wealth, access to education, health care, and political power. It is a major social problem, as it can lead to poverty, lack of opportunity, and even violence. The root causes of inequality are complex, but can include discrimination, unequal access to resources, and social and cultural norms. In order to address inequality, governments must create policies that provide access to resources for all individuals, regardless of their social, economic, or other backgrounds. Additionally, it is important to recognize that the effects of inequality are not limited to one group of people – everyone is affected by it in some way.
The graph shows that x must be a number between 10 and 20 (inclusive). This means that the value of x must be at least 10, but it cannot be greater than 20. This is because the graph shows that the values of x between 50 and 59 are not included in the range.
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The crafts store charges 49 cents for each of the first five yards of fabric and 30 cents for each additional yard. If you have $10.50, what is the greatest number of yards you could purchase?
Answer:
buy a maximum of 31.83 yards of fabric
Daniel earns $18. 50 an hour, with time-and-a-half for hours worked over 37 a week. His clock hours for a week are 9. 5, 8. 5, 10, 10, and 10. 75. How much is his weekly
To calculate Daniel's weekly pay, add his regular pay and overtime pay: Weekly pay = $1038.31.
To calculate Daniel's weekly pay, we need to determine his regular hours and his overtime hours.
Regular hours = 37 hours
Overtime hours = Total hours worked - Regular hours
Total hours worked = 9.5 + 8.5 + 10 + 10 + 10.75 = 49.75 hours
Overtime hours = 49.75 - 37 = 12.75 hours
Daniel's regular pay for 37 hours is:
$18.50/hour x 37 hours = $684.50
Daniel's overtime pay for 12.75 hours is:
$18.50/hour x 1.5 = $27.75/hour (time-and-a-half rate)
$27.75/hour x 12.75 hours = $353.81
Therefore, Daniel's weekly pay is the sum of his regular pay and overtime pay:
Weekly pay = $684.50 + $353.81 = $1038.31
Therefore, Daniel's weekly pay is $1038.31.
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Complete question:
Daniel earns $18.50 an hour, with time-and-a-half for hours worked over 37 a week. His clock hours for a week are 9. 5, 8. 5, 10, 10, and 10.75. How much is his weekly pay?
Rewrite cos 4x I'm terms of cos x.
Answer: Using the multiple angle formula for cosine, we have:
cos 4x = 2cos^2 2x - 1
Now we need to rewrite cos 2x in terms of cos x. Again, using the multiple angle formula for cosine, we have:
cos 2x = 2cos^2 x - 1
Substituting this expression into the previous equation, we get:
cos 4x = 2(cos^2 x)^2 - 1
Simplifying the expression further, we have:
cos 4x = 2(cos^4 x) - 1
Therefore, cos 4x can be written in terms of cos x as 2(cos^4 x) - 1.
Step-by-step explanation:
Two pipes can fill a tank in 12 minutes & 15 minutes respectively. If first pipe is changed with a pipe having twice of its radius while second with a pipe having half of second’s radius. Now the tank will be filled in:
The tank will be filled in 6 minutes with the new pipes.
How to calculate how long it will take the tank to be filledLet the capacity of the tank be C.
Then the rate at which the first pipe can fill the tank is C/12 per minute, and the rate at which the second pipe can fill the tank is C/15 per minute.
If the first pipe is changed with a pipe having twice of its radius, then the rate at which the new pipe can fill the tank is (2C)/12 = C/6 per minute.
If the second pipe is changed with a pipe having half of second’s radius, then the rate at which the new pipe can fill the tank is (1/2)C/15 = C/30 per minute.
Let t be the number of minutes it takes to fill the tank with the new pipes. Then we have:
(C/6 + C/30)t = C
Simplifying this equation, we get:
5Ct/30 = C
Multiplying both sides by 30/5C, we get:
t = 6 minutes
Therefore, the tank will be filled in 6 minutes with the new pipes.
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At Cheapmore supermarket, 1 litre of fruit juice cost R25 and 1,5 litres cost R34. Which juice is cheaper. Show your calculations.
In 2016, the mean score on the AP Statistics exam was 2. 80, with a standard deviation of 1. 35. The mean score on the AP Calculus exam was a 2. 86, with a standard deviation of 1. 55. What is the combined mean and standard deviation for these exams?
Mean, 2. 83; standard deviation, 0. 2
Mean, 5. 66; standard deviation, 2. 9
Mean, 5. 66; standard deviation, 2. 055
Mean, 2. 83; standard deviation, 2. 9
Mean, 5. 66; standard deviation, 4. 225
the combined mean and standard deviation for these exams will be Mean, 5. 66; standard deviation, 2. 055.
Combined mean=5.66
Combined standard deviation = 2.06
Combined mean= (MXa+ n×Xb)/(m+n)
Combined mean =2.80+2.86=5.66
Combined mean= sqrt(1.55)^2+(1.35)^2)
Combined deviation = 2.06
The mean is the number you get by separating the amount of a bunch of values by the quantity of values in the set.
Conversely, the middle is the center number in a bunch of values when those values are organized from littlest to biggest.
The mode of a bunch of values is the most often rehashed esteem in the set.
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Which situation can be represented by 11+ 6.5p ≤ 89?
A Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
The answer of the given question based on the inequality equation the answer is given below,
What is Equation?An equation is mathematical statement that asserts equality of two expressions. It typically includes of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division
The situation that can be represented by 11+ 6.5p ≤ 89 is:
a) Napoleon is the buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at most $89. What is p,
To solve for p, we can follow these steps:
11 + 6.5p ≤ 89 (subtract 11 from both sides)
6.5p ≤ 78 (divide both sides by 6.5)
p ≤ 12
Therefore, Napoleon can buy at most 12 shirts if he wants to spend at most $89.
b) None of the given situations can be represented by the inequality 11 + 6.5p ≤ 89 when p represents the number of shirts Napoleon can buy. This is because the inequality implies that the total cost of buying p shirts at $11 each and mailing them for $6.50 is no more than $89, which is not consistent with the given information about the cost of the shirts and mailing.
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Which three of these number add up to 180, 128 90 34 80 56
The three numbers which add up to 180 are 90, 34 and 56.
To find the sum of three numbers as 180, we simply add the three numbers together.
In this case, the numbers are given as 128, 90, 34, 80 and 56;
We see that the three numbers whose sum is 180 are 90, 34 and 56,
Let 90 represents one quantity, 34 represents another quantity, and 56 represents yet another quantity.
When we add these three quantities together, we get the total sum of all three quantities, which is 180.
Therefore, the numbers 90, 34 and 56 adds up to 180.
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The given question is incomplete, the complete question is
Which three of these number add up to 180? 128, 90, 34, 80, 56.
Hi please help 100 points+brainliest ( it is supposed to be answered like an expenecial function )
1. The table shows the Total Expenses y (in dollars) of the College or University for year 2020-2021 and 2021-2022. Mine it's 21,211
a) Write a function that represents the Total Expenses y (in dollars) of that College or University you would like to attend after t years.
b) Use the function to estimate the Total Expenses your first year of school. *This year (t) is not the same for everyone since there are 8th graders to 11th graders in the class.
c) Sketch a graph (by hand) to model your function.
d) Identify the y-intercept and asymptotes of the graph. Find the domain and range of your function. Then describe the end behavior of the function.
Answer:
a) The Total Expenses y (in dollars) of the College or University for t years can be modeled by an exponential function of the form:
y = ab^t
Where "a" is the initial amount and "b" is the growth rate.
b) Using the given data, we can find the value of "a" by plugging in the first year's data into the equation:
y = ab^t
21211 = a * b^0
a = 21211
Thus, the function representing the Total Expenses y (in dollars) of the College or University after t years is:
y = 21211b^t
c) The graph of the exponential function will be an upward-sloping curve that starts at the point (0, 21211) and grows at a rate determined by the value of "b".
d) The y-intercept of the graph is (0, 21211), which represents the initial expense at the start of the first year. The function has no asymptotes. The domain of the function is all real numbers, while the range of the function is y > 21211. As t approaches infinity, the function grows without bound, which means the end behavior is that the expenses continue to increase exponentially over time.
Determine if 0. 68 is rational or irrational and give a reason for your answer
0.68 is a rational number because it can be expressed as a ratio of two integers (17/25).
0.68 is a rational number because it can be expressed as a ratio of two integers.
To see this, we can convert 0.68 to a fraction by placing the decimal value over a denominator of 1 followed by the number of decimal places (two in this case):
0.68 = 68/100
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor,
which is 4:
68/100 = 17/25
Thus, 0.68 can be expressed as the ratio of two integers (17 and 25) and is therefore a rational number.
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1. Explain what Marc did in steps 4 and 5.
2. Why did he do this?
3. Create your own radical equation and explain how to solve it.
4. Is there an extraneous solution to your equation?
A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7
Explaining step 4 and 5, and why it is doneFrom the question, we have the following parameters that can be used in our computation:
The solution to a radical equation
In step 4 and 5, we have
x = ∛5 * 5 * 5 * 5
x = 5∛5¬ * 5¬ * 5¬ * 5
The above steps are carried out because it would simplify the radical expression to its simplest form
The reason it is done is to have the value of x in its simplest form
Create a radical expression
Here's an example of a radical equation:
√(x + 2) = 4 - x
Square both sides
x + 2 = 16 - 8x + x^2
Evaluate the like terms
x^2 - 9x + 14 = 0
Factor the quadratic equation
(x - 2)(x - 7) = 0
Solve for x:
x = 2 or x = 7
Is there an extraneous solution to your equation?For x = 2:
√(2 + 2) = 4 - 2
√4 = 2
2 = 2
This is true, so x = 2 is a valid solution.
For x = 7:
√(7 + 2) = 4 - 7
√9 = -3
3 = -3
This is not true, so x = 7 is not a valid solution.
So, there is an extraneous solution
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Basketball
30%
(A)
(B)
(C)
(D)
Tennis
36⁰
300
360
720
900
Cricket
35%
If 180 students played football, how many
students are in the group?
Football
Proportionately, if 32% represent students who played football, and the total number of them is 180, the total students in the group is 563.
What is proportion?Proportion is the ratio of two quantities equated to each other.
Proportion is a fractional value and we represent proportional values as between zero and one.
Basketball Tennis Cricket Football
Percentage 30% 3% 35% 32% (100 - 30 - 3 - 35)
The number of
students 169 17 197 180 (32% of 563)
The number of students who played football = 180
Proportionately, if 32% = 180, 100% representing the total number of students in the group = 563 (180/0.32).
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A home has a replacement value of $324,000. What is the amount of the insurance if the
coverage is:
a. 100% of the replacement value?
b. 90% of the replacement value?
c. 80% of the replacement value?
Answer:
a) $324,000
b) $291,600
c) $259,200
Step-by-step explanation:
The percentage of the replacement value represents how much of the house will be insured.
a) 100% of 324000 = 1.00 * 324000 = $324,000
b) 90% of 324000 = 0.9 * 324000 = $291,600
c) 80% of 324000 = 0.8 * 324000 = $259,200
suppose that all conditions are met. compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer. group of answer choices (0.341, 0.559) (0.45, 0.5) (0.394, 0.506) (0.4, 0.45)
None of above options are correct.
To compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer:
Follow these steps:
STEP 1: Determine the sample proportion (p) and sample size (n).
STEP 2:Calculate the standard error (SE) using the formula
SE = √(p(1-p)/n).
STEP 3: Determine the critical value (z) for a 95% confidence level
(1.96 for a two-tailed test).
STEP 4: Calculate the margin of error (ME) using the formula
ME = z * SE.
STEP 5: Find the confidence interval by adding and subtracting the margin of error from the sample proportion:
CI = (p - ME, p + ME).
Unfortunately, without the sample proportion (p) and sample size (n), it's not possible to compute the confidence interval.
However, once you have these values, you can follow the steps above to find the 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer.
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hi need help i eill give you many points like a lot help due soon
Answer:
E
Step-by-step explanation:
To solve this question we have to count which one of the options have five red square and which of the options have 7 blue squares.
By looking at the options we can see that E is the only one that matches the requirements!
We have to be careful that we are looking for 5 red squares and not 5 blue squares as our answer would be wrong.
We can find this out in the question, we see that in the question it says red and blue defining that red goes first. This is why we consider red to be 5 and blue to be 7
Hope this helps, have a lovely day! :)
XY=8 and YZ=4 find XZ
If XY = 8 and YZ = 4, the length οf XZ is 4√5 cm.
What is the Pythagοrean theοrem?The Pythagοrean theοrem states that in a right-angled triangle, the square οf the length οf the hypοtenuse (c) is equal tο the sum οf the squares οf the lengths οf the οther twο sides (a and b) c² = a² + b².
We can use the Pythagοrean theοrem tο find the length οf the hypοtenuse XZ οf the right-angled triangle XYZ.
In this case, X is the right angle, sο XY is the adjacent side and XZ is the hypοtenuse. YZ is οn the οppοsite side. We are given that XY = 8cm and YZ = 4cm.
So, we have:
XZ² = XY² + YZ²
XZ² = 8² + 4²
XZ² = 64 + 16
XZ² = 80
Taking the square root of both sides, we get:
XZ = √80 = √(16 × 5) = √16 × √5 = 4√5
Therefore, the length of XZ is 4√5 cm.
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Complete question:
If XY=8 and YZ=4 find the length XZ
Find the value of the variable 7x + 19
Answer:
Step-by-step explanation:
7x+19=0
7x=-19
x=-19/7 ---> This is your final answer!
Plug in the x we found to see if the expression is correct:
7(-19/7)+19=0
-19+19=0
So our x value is correct!
Which is the solution set of the compound inequality 3.5x-10>-3 and 8x-9 <39?
-2
-2
2
2
Answer:
OPTION C: 2 < x < 6
Step-by-step explanation:
3.5x - 10 > -3
Adding 10 to both sides:
3.5x > 7
Dividing by 3.5:
x > 2
8x - 9 < 39
Adding 9 to both sides:
8x < 48
Dividing by 8:
x < 6
Therefore, the solution set of the compound inequality is:
2 < x < 6
A person makes $1800 per month, but 1/3 of that amount goes to her rent. What two numbers can you multiply to find out how much she has after playing her rent?
The two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.
Explain about the fraction of number?Part of an entire unit is represented by a fraction. A fraction's numerator is the number at the top, and its denominator is the number at the bottom. Hence, the numerator of the fraction 3/5 is 3 and the denominator is 5.Total income of person: $1800 per month.
Rent amount = 1/3 * income
Remaining amount : 1 - 1/3 = 2/3 of income
So,
Remaining amount = 2/3*1800
Remaining amount = 1200
Thus, the two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.
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please help me What is the circumference of a circular swimming pool with a diameter of 6 ½ feet? 0 20 -/-/ 099/ 0 6 1/1 0 71/1/2 .ft. (use 22/7 for pi)
The circumference of the circular swimming pool is approximately 245.04 inches.
What connection exists between a circle's diameter and circumference?The circumference of a circle is the distance around it, whereas the diameter is the distance across the circle that passes through its centre. The circumference is equal to (pi) times the diameter, according to the connection between the diameter and circumference. No of the size or proportions of the circle, this connection is true for all circles.
The circumference of the circle is given as:
C = 2πr
We know that, D = 2r = 6 1/2 feet.
6 ½ feet = 6.5 × 12 inches = 78 inches
Substituting the values we have:
C = π × 78 inches = 245.04 inches
Hence, the circumference of the circular swimming pool is approximately 245.04 inches.
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A. Jace collected data on the distances electric vehicles can travel on one charge. He wants to show the average distance and the range an electric vehicle can travel on one charge.
Choose and make an appropriate display of the data
b. Jace wants to compare the range and shape of his electric-vehicle data to related data he collected on gas-powered vehicles. Choose and make appropriate data displays
A box-and-whisker plot is the appropriate data display for Jace's electric-vehicle data and gas-powered vehicle data, and it will give him a visual representation of the difference between the two datasets.
The appropriate data displays for Jace's electric-vehicle data and gas-powered vehicle data would be a box-and-whisker plot. This type of plot is a graphical representation of the five-number summary of a dataset. The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. It can be calculated using the following formulas:
Minimum = smallest value
Q1 = 25th percentile (the value below which 25% of the data lies)
Median = 50th percentile (the value below which 50% of the data lies)
Q3 = 75th percentile (the value below which 75% of the data lies)
Maximum = largest value
Using these formulas, Jace can calculate the five-number summary for his electric-vehicle data and his gas-powered vehicle data. He can then use these values to create a box-and-whisker plot that compares the range and shape of each dataset. The box-and-whisker plot will give him a clear visual representation of the difference between the two datasets. By comparing the range and shape of the two datasets, Jace can get a better understanding of the difference between the electric-vehicle data and the gas-powered vehicle data. From there, he can draw conclusions about the differences between the two vehicle types.
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a standard number cube has six sides labeled 1 through 6. think about rolling a number cube one time.is it more likely that the cube will show a multiple of 2 or a multiple of 3?
Answer:
Multiple of 2
Step-by-step explanation:
There are six possible outcomes when rolling a standard number cube labeled 1 through 6. Out of these six possible outcomes, there are three outcomes that are multiples of 2 (2, 4, and 6) and two outcomes that are multiples of 3 (3 and 6).
Therefore, it is more likely that the cube will show a multiple of 2 than a multiple of 3. The probability of rolling a multiple of 2 is 3/6 or 1/2, while the probability of rolling a multiple of 3 is 2/6 or 1/3.
Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion. Which of the following pieces of information could help you determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle?
Please answer this question. Giving out BRAINLIEST.
The information that could be used to determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle is given as follows:
b) The number of fluid ounces in 8 small and 4 medium bottles of lotion.
How to obtain the amounts?The amounts are obtained with a system of equations, for which the variables are given as follows:
Variable x: amount in a small bottle of lotion.Variable y: amount in a medium bottle of lotion.Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion, hence:
6x + 4y = 93.
With 8 small and 4 medium bottles, the equation is given as follows:
8x + 4y = t.
Hence we can subtract the first equation by the second to obtain the value of x, then we replace and obtain the value of y, meaning that the correct option is given by option b.
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Jasper and corey have saved up a total of $78. 0. Jasper has saved 6 dollars more then twice as much as corey. How much has cory saved?
Corey has saved $24 and Jasper has saved $54.
Let x be the amount of money Corey has saved.
Then, we know that Jasper has saved $6 more than twice as much as Corey, which can be expressed as:
J = 2x + 6
We also know that the total amount saved by both Jasper and Corey is $78, so we can set up another equation:
J + x = 78
Now we can use these equations to solve for x, which will give us the amount of money Corey has saved:
J + x = 78 (substitute J = 2x + 6)
(2x + 6) + x = 78
3x + 6 = 78
3x = 72
x = 24
Therefore, Corey has saved $24.
To check this answer, we can substitute x = 24 into the equation we found for J:
J = 2x + 6
J = 2(24) + 6
J = 54
So Jasper has saved $54.
We can verify that $24 + $54 = $78, which matches the total amount saved by both Jasper and Corey.
In summary, Corey has saved $24 and Jasper has saved $54. It's important to remember to set up equations to represent the given information in a problem and to check our answers to make sure they are reasonable and match the given information.
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A circle has a radius of 14 feet. Find the exact area in feet squared (meaning
leave your answer as pi)
Answer:
196pie
Step-by-step explanation:
A store sells packages of comic books with a poster write a linear function in the form Y equals MX plus B that represents the cost Y of a package containing any number of comic books X suppose another store sells a similar package modeled by a linear function with one with initial value $7. 99 which store has a better deal explain one poster +6 comics $12. 75 or one poster and 13 comics $19. 75
The cost of a package containing x comic books and a poster is given by the equation y = 0.91x + 7.08.
Let's start by using the information given to form two equations. Let x be the number of comic books and let y be the cost of package.
From the first sentence, we can form the equation:
y = 7.99 + 2x
From the second sentence, we can form the equation:
y = 16.99 + 11x
Now we can use these equations to find the linear function rule that models the cost of a package containing any number of comic books.
First, we can set the two equations equal to each other since they both represent the cost of a package:
7.99 + 2x = 16.99 + 11x
Solving for x, we get:
9x = 9
x = 1
Now that we know that 1 comic book costs $4, we can substitute that value into either of the original equations to find the cost of a package with a poster and 1 comic book:
y = 7.99 + 2(1) = 9.99
So a package with a poster and 1 comic book costs $9.99.
Finally, we can use the slope of the line to find the linear function rule that models the cost of a package containing any number of comic books. We know that the slope is the change in y over the change in x, or:
m = (16.99 - 7.99)/(11 - 2) = 0.91
So the linear function rule is:
y = 0.91x + 7.08
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The given question is incomplete, the complete question is:
A store sells packages of comic books with a poster. A poster and 2 comics cost $7.99. A poster and 11 comics cost $16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Five friends each bought a shirt and a pair of shoes. The table shows the cost of the tems. The expression 5(x+24) shows the total amount of money they spent. Expand the expression using the Distributive Property
Answer:
5x+120
Step-by-step explanation:
5(x) + 5(24)
5x+120
Technetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function T where T (d) = 100(2)^-2 is the percent of Technetium-99m remaining d days after the tests. Write an expression that represents the number of days until only 5% remains.
The expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.
The given function [tex]T(d) =[/tex] [tex]100 \cdot 2^{-2d}$[/tex]represents the percent of Technetium-99m remaining d days after the test.
To find the number of days until only 5% remains, we need to solve the following equation:
[tex]$100 \cdot 2^{-2d} = 5$[/tex]
Dividing both sides by 100, we get:
[tex]$2^{-2d}$[/tex] [tex]= 0.05[/tex]
Taking the natural logarithm of both sides, we get:
[tex]$\ln{(2^{-2d})}$[/tex] = [tex]ln(0.05)[/tex]
Using the logarithmic identity log(base a)(bⁿ) = nlog(base a)(b), we can simplify the left side as:
[tex]-2d \cdot ln(2) = ln(0.05)[/tex]
Dividing both sides by -2 ln(2), we get:
[tex]d = ln(0.05) / (-2 \cdot ln(2))[/tex]
Using a calculator, we get:
[tex]d = 3.79[/tex]
Therefore, the expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.
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Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
b. $3,840
c. $2,088
d. $1,740
The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.
.
To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.
Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740
Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).
Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.
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