The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function over the x-axis, shifting it left by 3 units, and down by 2 units.
To reflect a quadratic function over the x-axis, we need to multiply the function by -1. Let's assume that our original quadratic function is f(x).
After reflecting the function over the x-axis, we get the new function g(x) = -f(x).
To perform a horizontal shift left 3 units, we need to replace x with (x + 3) in the function g(x). This gives us the new function h(x) = g(x + 3) = -f(x + 3).
Finally, to shift the function down 2 units, we need to subtract 2 from the entire function h(x).
Note that the order of the transformations is important. We first reflect the function over the x-axis, then shift it horizontally, and finally shift it vertically.
Hence,
The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function
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the state narcotics bureau must form a 5-member investigative team. if it has agents from which to choose, how many different possible teams can be formed?
the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).
Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.
Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).
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Kendra surveyed 100 people who own a dog or a cat, or both. Of those surveyed, 15 own both a dog and a cat, and the number of people who own a dog is four times the number of people who own a cat. How many people surveyed own a cat?
Answer:
17 people surveyed own a cat.
Step-by-step explanation:
Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.
d = 4c
d + c + 15 = 100
4c + c + 15 = 100
5c + 15 = 100
5c = 85
c = 17
Check:
The number of dog owners is 4 * 17, or 68.
68 + 17 + 15 = 100
It takes Shawn 35 minutes by car to get to his grandma’s. The nearest parking area is a 4 minute walk from her apartment. One week, he realized that he spent 5 hours and 12 minutes traveling to her apartment and then back home. How many round trips did he make to visit his grandma?
Shawn made 4 round trips to visit his grandma.
How to calculate Travel Time?The travel time is the amount of time it takes to travel from one location to another. The specific method for calculating travel time depends on the mode of transportation being used. Here are some general guidelines for calculating travel time:
Estimate the distance between the starting location and the destination.Determine the average speed or pace of travel. This will depend on the mode of transportation being used.Calculate the travel time by dividing the distance by the speed or pace. This will give you the estimated travel time in hours.Let's start by converting the total travel time to minutes:
5 hours and 12 minutes = 5 × 60 + 12 = 312 minutes
Let's call the number of round trips that Shawn made "x".
For each round trip, Shawn has to travel to his grandma's apartment and then back home. The total time for each round trip is:
time per round trip = time to get there + time to get back + time to walk to/from parking
time per round trip = 35 + 35 + 4 + 4 = 78 minutes
So the total travel time for all of the round trips is:
total travel time = time per round trip x number of round trips
312 = 78x
Solving for "x", we get:
x = 312/78 = 4
Therefore, Shawn made 4 round trips to visit his grandma.
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question 4
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
∠ B = 121°
Step-by-step explanation:
ABCD is a cyclic quadrilateral
• opposite angles sum to 180°
∠ B and ∠ D are opposite angles , then
∠ B + 59° = 180° ( subtract 59° from both sides )
∠ B = 121°
Brianna’s parents built a swimming pool in the backyard. Brianna days that the distance around the pool is 120 feet. Is she correct? Explain why or why not. 40ft 20ft
Brianna is correct, the distance around a rectangular pool with dimensions of 40 feet by 20 feet is 120 feet, which can be calculated by adding up the lengths of all four sides: (40 + 20 + 40 + 20) feet = 120 feet.
Brianna is correct, the distance around a rectangular pool with dimensions of 40 feet by 20 feet is indeed 120 feet. To calculate the distance around the pool, we need to add up the lengths of all four sides, which are equal in length. In this case, the length and width of the pool are both 40 feet and 20 feet, respectively. So, to find the distance around the pool, we add up these four lengths:
40 feet + 20 feet + 40 feet + 20 feet = 120 feet
Therefore, the total distance around the pool is 120 feet.
To determine the distance around the pool, Brianna needs to measure the length and width of the pool. If the pool is rectangular, she can measure the length and width and add up the lengths of all four sides to find the total distance around the pool. If the pool is a different shape, Brianna would need to measure the lengths of each side and add them up to find the total distance around the pool. This information can then be used to calculate the amount of stone needed for the edging around the pool. By knowing the total distance around the pool, Brianna's parents would have a good estimate of how much stone they need to buy for the edging, which is typically sold by the linear foot.
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The complete question is:
In the backyard, Brianna's parents constructed a swimming pool. The pool's circumference, according to Brianna, is 120 feet.
40 Ft
20 Ft
1. Is she correct? Explain why or why not. (You must mention the following in your explanation: If she is right, demonstrate the steps she took to determine the pool's circumference. Determine the right distance and demonstrate all effort if she is mistaken.)
2. So that her parents will know how many feet of stone to purchase for the pool's edging, describe (using words this time) how Brianna would calculate the distance around the pool.
Andy and dale solved 35 puzzles together. 1/3 of the puzzles that Andy solved are twice the number of puzzles Dave solved. How many puzzles did each boy solve?
Answer:
Andy: 30Dale: 5Step-by-step explanation:
You want to find the number of puzzles solved by each boy if they solved 35 puzzles together, and 1/3 of the number Andy solved is twice the number Dale solved.
EquationsLet 'a' and 'd' represent the numbers of puzzles solved by Andy and Dale, respectively. Then ...
a + d = 35
1/3a = 2d
SolutionMultiplying the second equation by 3, we get an expression for 'a' that can be used in the first equation:
a = 6d
6d +d = 35
d = 35/7 = 5
a = 6(5) = 30
Andy solved 30 puzzles; Dale solved 5.
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Find y in equilateral AABC. (A) 90° (B) 70° (C) 60° (D) 45°
Variable y in equilateral 60°, Thus correct option is C) 60°.
What does an equilateral triangle mean?An equilateral triangle is one with equal-sized sides on all three sides and angles that can all reach a maximum of 60 degrees. An equilateral triangle is a triangle with three equal sides, also referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a special case of an isosceles triangle. Three equal angles of 60 degrees also make up an equilateral triangle.
The sum of all the angles in a triangle is 180.
It is given that the triangle ABC is an equilateral triangle.
So ∠A+∠B+∠C =180°
∠A=B=∠C
3∠A=180°
∠A=60°
Therefore y in ΔABC is C) 60°
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Indicate the method you would use to prove the two 's . If no method applies, enter none.
HA
None
LA
LL
HL
Option A is correct. Use HL to prove two triangles are congruent.
Given:
In triangle ABC and triangle DEF as shown in figure below.
AB≅DE [leg] [Given]
AC≅DF [Hypotenuse side] [Given]
∠B = ∠D = 90°
HL(Hypotenuse -Leg) postulates states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Then, by HL postulates;
ΔABC ≅ ΔDEF.
Therefore, the method you use to prove the two triangle congruent is, HL.
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What is the Lower Quartile for the following set of data:
1, 8, 1, -4, 12, -2, 15, 6
The lower quartile for the given data is -2, since it is the 25th percentile and is the value that lies at the 25th position when the data is sorted in ascending order.
1. Sort the data in ascending order: -4, -2, 1, 1, 6, 8, 12, 15
2. Calculate the 25th percentile: 25th percentile = (n + 1) * 0.25 = (8 + 1) * 0.25 = 2.25
3. The 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively.
4. The lower quartile is -2.
The lower quartile (also known as the 25th percentile) is the value that lies at the 25th position when the data is sorted in ascending order. To find the lower quartile of the given set of data (1, 8, 1, -4, 12, -2, 15, 6), the data needs to be sorted in ascending order. This gives us the following data: -4, -2, 1, 1, 6, 8, 12, 15. Now, to calculate the 25th percentile, we use the formula (n + 1) * 0.25, where n is the number of data points. In this case, n = 8, so the 25th percentile = (8 + 1) * 0.25 = 2.25. This means the 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively. Therefore, the lower quartile for the given data is -2.
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g even rolls suppose you roll a fair six-sided die until you get a 6. what is the expected number of rolls given that all the numbers you see are even?
The expected number of rolls is 12.The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2.
The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2. Therefore, the expected number of rolls can be calculated by multiplying the probability of rolling an even number (1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 12.
The expected number of rolls to get a specific result on a fair die can be calculated by multiplying the probability of achieving that result by the number of sides on the die. For example, if you wanted to know the expected number of rolls to get an odd number on a fair, 6-sided die, you would multiply the probability of rolling an odd number (3/6, or 1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 3. The same calculation could be applied to determine the expected number of rolls to get a specific number (e.g. a 4) on a fair, 6-sided die. The probability of rolling a 4 would be 1/6, and the expected number of rolls to get a 4 would be 1/6 x 6 = 6.
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Find the missing side length using trig please!
Answer: 25 inches
Step-by-step explanation:
cos60 = adjacent over hypotenuse
cos60 = a/50
50cos60 = 25
Let f(x)=p(x)/q(x) where p(x) and p(x) are polynomials with no common factors other than 1. Describe how to find the x-intercepts and the vertical asymptotes of the function
To find the x-intercepts of a rational function of the form f(x) = p(x)/q(x), we set p(x) = 0 and solve for x. To find the vertical asymptotes, we set q(x) = 0 and solve for x.
Vertical asymptotes are vertical lines that a function approaches but never touches or crosses as the independent variable (usually denoted as x) approaches a certain value.
To find the x-intercepts of the function, we need to set the numerator of the rational function equal to zero and solve for x. This is because x-intercepts occur when the function value is equal to zero. Therefore, we can write:
p(x) = 0
Solving this equation will give us the values of x where the function intersects the x-axis. It is important to note that if p(x) has a degree greater than or equal to q(x), then the function will have a slant asymptote instead of a vertical asymptote.
To find the vertical asymptotes of the function, we need to look at the denominator of the rational function. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In the case of a rational function, this happens when the denominator is equal to zero. Therefore, we can write:
q(x) = 0
Solving this equation will give us the values of x where the function has a vertical asymptote. It is important to note that if the degree of q(x) is greater than the degree of p(x), then the function will have a horizontal asymptote instead of a vertical asymptote.
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The difference of a number and
its reciprocal is 15/13. What is the
number.
Solving the equation: x - 1/x = 15/13
We will see that the value of x is 28/13
How to find the number?For a number x, we define the reciprocal number as 1/x.
We know that the difference between theses two is 15/13, then we can write:
x - 1/x = 15/13
(x² - x)/x = 15/13
(x² - x) = (15/13)*x
x² - x - (15/13)*x = 0
x² - (1 + 15/13)*x = 0
x² - (28/13)*x = 0
x*(x - 28/13) = 0
x = 0 is not a solution, because 1/x exists, then the solution is x = 28/13.
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i need this fast Question 7(Multiple Choice Worth 1 points) (05.02 MC) At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000 for 500 tickets, how many students attended the play? 100 200 300 400
The number of students attended the play are 400 in number.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000
5x+10y=3000
The total number of tickets are 500
x+y=500
y=500-x
Now plug this in above equation
5x+10(500-x)=3000
5x+5000-10x=3000
5000-5x=3000
Add 5x on both sides
5000-3000=5x
2000=5x
Divide both sides by 5
400=x
Hence, the number of students attended the play are 400 in number.
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Mr. Rankin purchased a box of
copy paper for his office. The
box is 18 inches long, 12 inches
wide, and 10 inches tall. The box
is completely filled with
packages of tightly packed
paper. Each package measures
12 inches by 9 inches by 2
inches. How many packages are
in the box?
Answer:
10 packages
Step-by-step explanation:
When Mr. Rankin opens the box and looks straight down on it, he could see two packages. The 12x9 paper package can fit two, side by side in the 18X12 box.
Then there also can fit a stack 5 packages tall. Each bundle is 2 inches tall and the box is 10 inches tall.
Two stacks, 5 deep is 10 packages. see image.
the letter grades (a, b, c, d, f) of business analysis students are recorded by a professor. this variable's classification . a. is time series data b. is categorical data c. is quantitative data d. cannot be determined
The letter grades (A, B, C, D, F) for business analysis students are categories that represent different levels of achievement, so the variable's classification is (b) Categorical Data.
The Categorical data are defined as the variables that represent characteristics or attributes, and they are often expressed as labels or categories.
The Quantitative data, on the other hand, are the numerical values which represent measurements or quantities.
Since the letter grades are not numerical values and do not represent a measurement or quantity, they cannot be classified as quantitative data.
Therefore , the letter grades represents a Categorical Variables .
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The given question is incomplete , the complete question is
The letter grades (A, B, C, D, F) of business analysis students are recorded by a professor. this variable's classification .
(a) is time series data
(b) is categorical data
(c) is quantitative data
(d) cannot be determined
Terri wants to know the height of the big Christmas tree on the town square. She stands 20 feet from the base of the tree. Elliot places a mirror on the ground between Terri and the tree so that she can see the top of the tree in the mirror. The mirror is located 16 feet from the base of the tree. If Terri's eye level is 5.5 feet from the ground, how tall is the tree?
Answer:
22ft
Step-by-step explanation:
Always good to try and draw out the scenario, it can make it more easily understandable.
Have a look at the pic.
Hope its clear.
how does one do this equasion 6234653928+294292342-424624642x16515615615165161x1156+6466456
The given Expression simplifies to -8.1069556e+27
What is BODMAS rule?BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. A mathematical expression's order of execution is explained using the BODMAS.
Given an equation to solve,
6234653928 + 294292342 - 424624642 x 16515615615165161 x 1156 + 6466456
Let us consider this Expression as A + B - C * D * E + F, with the corresponding terms being equal
By, the BODMAS rule,
First step: Multiply C, D, E. Let this be G
Now, the equation will look like this: A + B - G + F
Second step: We can add and subtract according to the signs now
On solving, the expression simplifies to -8.1069556e+27
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If a1 =7 and a n =4a n−1 then find the value of a 4 .
The value of a₄ is 19.
What is arithmetic progression?
A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor. The common difference in that mathematical progression is the constant difference.
Here, we have
Given: a₁ =7 and aₙ = aₙ₋₁ + 4
We have to find the value of a₄.
a₁ =7
aₙ = aₙ₋₁ + 4
aₙ - aₙ₋₁ = 4
The common difference is 4.
In order to solve, replace the value of the previous answer with the equation for the next answer.
a₁ = 7
a₂ = 7 + 4 = 11
a₃ = 11 + 4 = 15
a₄ = 15 + 4 = 19
Hence, the value of a₄ is 19.
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The time taken to cook Wkg is given by the expression (48w + 23) minutes. Calculate the time it would take to cook 3kg of meat giving in hours and minutes
Work Shown:
48w+23
48*3+23
144+23
167
It takes 167 minutes to cook 3 kg of meat.
Convert this to hours+minutes format.
167 min = 120 min + 47 min
167 min = 120/60 hr + 47 min
167 min = 2 hr + 47 min
The population of the Switzerland in 2022 is about 26 million. The estimated population of Switzerland is given by the function P(t)=26(1.03)^t, where t represents the time in years since 2022.
i need help with this problem
Answer: Yes. for each input there is exactly
ONE output
Step-by-step explanation:
I did the test and it was true.
What is the area of this compound figure?
Answer: 2707
Step-by-step explanation: just multipli
Answer:
186m^2
Step-by-step explanation:
This compound figure will be divided to three rectangular.
1) 18x9=162
2) (18-12)x2=12
3) 2x6=12
so, total is 161+12+12=186^2
(c) What is the shortest possible distance between the building and the end of the ramp if the architect redesigns the building so that the doorway is 1.3 feet above the parking lot?
The required shortest distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.
What is the slope?The slope is defined as the ratio measure of rise to measure of the run.
Here,
The shortest possible distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.
This is because, if the doorway is 1.3 feet above the parking lot, the ramp will need to rise 1.3 feet in order for a person or vehicle to be able to enter the building. The length of the ramp will be equal to the rise, so in this case, the shortest possible distance between the building and the end of the ramp would be 1.3 feet.
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the perimeter of the shaded part of a square is 28 inches. find the area of the square
Answer:
Step-by-step explanation:
A square has 4 equal sides therefore to find the side of one we would divide the perimeter by 4. Doing that we get 7 inches.
Now seeing as it has four equal sides in order for us to find the area we would do:
Area = side x side = 7x7 = 49 squared inches
Which choice is the explicit formula for the following geometric sequence?
0.3,-0.06, 0.012, -0.0024, 0.00048, ...
A. an=0.3(0.2)"
B. an=-0.2(0.3)(n-1)
C. an= -0.3(-0.2)(n-1)
D. an= -0.3(0.2)(n-1)
E. an = 0.3(-0.2)(n-1)
The formula for given sequence is aₙ = 0.3(-0.2)ⁿ⁻¹ i.e. E.
What exactly is a sequence?
A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. Can you figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.
Now,
Given sequence is 0.3,-0.06, 0.012, -0.0024, 0.00048, ...
Of all given options only E satisfies the given sequence because
for E
a₁=0.3*-0.2¹⁻¹
=0.3*1
=0.3
a₂=0.3*-0.2²⁻¹
=-0.3*0.2
=-0.006
a₃=0.3*-0.2³⁻¹
=0.3*0.04
=0.012
hence,
The formula for given sequence is aₙ = 0.3(-0.2)ⁿ⁻¹.
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Rewrite the expression in terms of ln 5 and ln 6.
ln(27000)
We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.
Why are logarithm qualities significant?Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.
We can use the logarithmic property that says:
log_a(xⁿ) = n×log_a(x)
to break down 27000 into factors that involve 5 and 6.
First, we can write:
27000 = 5³× 6³
When we take the natural logarithm of both sides, we obtain:
ln(27000) = ln(5³ × 6³)
Using the property above, we can simplify this expression as:
ln(27000) = ln(5³) + ln(6³)
Using another logarithmic property that says:
log_a(bⁿ) = c×log_a(b)
we can further simplify the expression:
ln(27000) = 3ln(5) + 3ln(6)
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HOW DO I DO THIS??????????
Keith and his friends are heading to the Thunder Beach water park. They plan to purchase the group package, which costs $78 for 6 people. That's $3 less per person than the normal cost for an individual. What is the normal cost for an individual?
a special domino set contains all number pairs from double-0 to double-8, with each number pair occurring only once. for example, the following domino counts as 1-4 and 4-1. how many dominos are in the set?
There are 40 dominos in the set which contains all number pairs from double-0 to double-8.
The domino set contains all number pairs from double-0 to double-8, which means that there are nine possible values for each half of the domino and they are - 0, 1, 2, 3, 4, 5, 6, 7, and 8.
Since each number pair occurs only once, we can count the total number of dominos in the set by counting the number of distinct pairs of values that can be formed by combining the numbers on the two halves of the domino.
There are 9 possible values for the first half of the domino and 9 possible values for the second half, so there are 9 x 9 = 81 possible pairs of values.
However, we need to divide this by 2 to avoid counting each pair twice, since a domino with the values A-B is the same as a domino with the values B-A.
Therefore, the total number of distinct dominos in the set is 81/2 = 40.5, but since dominos cannot be counted in halves, the closest integer number of dominos is 40.
So there are 40 dominos in the set.
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Jake will run at a constant rate of 8 minutes per mile. Ethan will longboard at rate of 5 minutes per mile for the first two miles then will slow down and longboard at a rate of 10 minutes per mile. Make two tables finding the times for each boys results for 1,2,3,4,5 and 6 miles
The time and distance of both the boys Jake and Ethan when they meet with each other is equal to 40 minutes after covering 5 miles.
Constant rate by which Jake run is equal to 8 minutes per mile.
Rate of Ethan longboard for first two miles = 5 minutes per mile
Rate of Ethan longboard for rest of the miles = 10 minutes per mile
Time taken by each of them is :
Miles Time taken by Jake (minutes) Time taken by Ethan(minutes)
1 8 min 5 min
2 16 min 10 min
3 24 min 20 min
4 32 min 30 min
5 40 min 40 min
6 48 min 50 min
Therefore , time and distance at which Jake and Ethan meet is equal to 40 minutes that is at 5 miles.
The above question is incomplete , the complete question is:
Jake will run at a constant rate of 8 minutes per mile. Ethan will longboard at rate of 5 minutes per mile for the first two miles then will slow down and longboard at a rate of 10 minutes per mile. Make two tables finding the times for each boys results for 1,2,3,4,5 and 6 miles.
Find out the time and distance at which both meet.
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