Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each equation of the piecewise function represented in the graph to its corresponding piece of the domain.
Answers
The definition of the piecewise function for this problem is given as follows:
f(x) = 1, 0 < x < 1.f(x) = x, 1 < x < 2.f(x) = 3, 2 < x < 3.f(x) = 4, 3 < x < 4.What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
For 1 < x < 2, the function is a increasing line with slope of 1, while for the other intervals the function is constant, hence the definition is given as follows:
f(x) = 1, 0 < x < 1.f(x) = x, 1 < x < 2.f(x) = 3, 2 < x < 3.f(x) = 4, 3 < x < 4.More can be learned about piece-wise functions at brainly.com/question/19358926
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Related Questions
Question 7 of 25
f(x)=√x-4. Find the inverse of f(x) and its domain.
O A. f¹(x) = x² + 4; x≥0
OB. f¹(x) = (x+4)²; x≥-4
O c. f¹(x) = x² + 4; x ≥-4
O D. f¹(x) = (x+4)²; x≥0
Answers
Answer:
Domain of inverse = Range of f = x>-4
Hence B
The length of a planet's orbit around a star is approximately 22,200,000 km. It takes the planet about 1230 Earth days to complete a full orbit. What is the planet's average speed in kmh-1 to 3sf?
Answers
Answer:
Approximately \(12.9\; \rm km \cdot h^{-1}\), assuming that this orbit is circular.
Step-by-step explanation:
The question is asking for a tangential velocity with the unit \(\rm km \cdot h^{-1}\). The unit of the given distance is already in \(\rm km\) as required. Convert the unit of the orbital period to hours:
\(\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}\).
Calculate the angular velocity \(\omega\) of this planet from its orbital period:
\(\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}\).
Given the radius \(r\) of the orbit of this planet, the tangential velocity \(v_{\perp}\) of this planet would be:
\(\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}\).
If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: \(4.73\times 10^{3}\; \rm km \cdot h^{-1}\).
Which graph represents the function f(x) = |x| - 4?
Answers
Answer: The top graph.
Step-by-step explanation: The inflection is at x = 0, since the absolute value of x starts becoming greater as x decreases. E.g., at x = -2,
f(x) = |x| - 4
f(x) = |-2| - 4
f(x) = 2 - 4
f(x) = - 2
At x = -4
f(x) = |x| - 4
f(x) = |-4| - 4
f(x) = 4 - 4
f(x) = 0
3. Juanita has been offered a job that pays $497.35 for a 35-hour work week. A second
company offers her a job at $16.75/h, but will only guarantee 30 hours per
week.
Which job would you advise Juanita to take?
Answers
Answer:
The second job because, it pays more and it has less hours.
Step-by-step explanation:
A Moving to another question will save this response. ≪ Question 16 4 points Jean purchases a house for $750,000 and is able to secure an interest only, 5 year fixed rate mortgage for $600,000 at 5% interest. After five year, the house appreciates to $792078.31. What is Jean's equity as a percent of the house value? Write your answer as a percent rounded to two decimal points without the % sign (e.g. if you get 5.6499%, write 5.65 ). Nastya takes our a 10-year, fixed rate, fully amortizing loan for $622422 with 5.2% interest and annual payments. What will be her annual payments? Round your answer to the nearest cent (e.g. if your answer is $1,000.567, enter 1000.57).
Answers
Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).
To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.
Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.
To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.
Therefore, Jean's equity as a percent of the house value is 24.26%.
Now, let's move on to Nastya's question.
To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:
P = r * PV / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments
Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years
First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.
Next, we substitute the values into the formula and solve for P:
P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))
Using a calculator, we get P ≈ $7,350.68.
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Beth wants to build a thin wire frame for a photo that is $$15 cm long and $$6 cm wide. What length of wire will she need to go around the entire photo?
Answers
Answer:
42
Step-by-step explanation:
1. PerimeterPerimeter is \(2l+2w\)
2. Solving\(2(15)+2(6)=30+12=42\)Answer: 42
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y= - 2x + 4
2x + y = 4
Answers
Answer:
Infinite amount of solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -2x + 4
2x + y = 4
Step 2: Solve for x
Substitution
Substitute in y: 2x + (-2x + 4) = 4Combine like terms: 4 = 4Here we see that 4 does indeed equal 4.
∴ the systems of equations has an infinite amount of solutions.
Answer:
Infinite amount of solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
Equality Properties
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Algebra I
Terms/Coefficients
Coordinates (x, y)
Solving systems of equations using substitution/elimination
Step-by-step explanation:
Step 1: Define Systems
y = -2x + 4
2x + y = 4
Step 2: Solve for x
Substitution
Substitute in y: 2x + (-2x + 4) = 4
Combine like terms: 4 = 4
Here we see that 4 does indeed equal 4.
∴ the systems of equations has an infinite amount of solutions.
The sun of D and 5 is greater than or equal to -1 and the sun of D and 5 is less than or equal to 4. List 3 integers that satisfy the inequality
Answers
Answer:
-5, -2, -1
Step-by-step explanation:
Inequalities
The question provides us with two conditions:
D+5≥-1
D+5≤4
Solve the first inequality. Subtract 5 to both terms:
D≥-1-5
D≥-6
Solve the second inequality. Subtract 5 to both terms:
D≤4-5
D≤-1
We must find three numbers that comply with both conditions, i.e. it must be greater or equal -6 and less or equal than -1. Any integer number in the interval [-6,-1] solves the problem. We select the following list:
-5, -2, -1
What is a simpler form of the expression? -3(-4y+3)+7y please explain, i don’t understand it.
Answers
Answer:
19y - 9
Step-by-step explanation:
We can use the acronym PEMDAS. First, we need to calculate -3(-4y+3) by distributing. This is -3 * (-4y) + (-3) * 3 = 12y - 9 so the expression becomes 12y - 9 + 7y. Next, we need to combine like terms. 12y and +7y are like terms since they both have y so combining them gives us 12y + 7y = 19y. -9 stays by itself since there are no other constants so the final answer is 19y - 9.
Hey, it's really very easy to simplify .
I will write step by step.
Given:= -3 (-4y + 3) +7y
Now, let's Distribute:= (-3) (-4y) + (-3) (3) + 7y
= 12y + -9 + 7y
Now, Combine Like Terms:= 12y + -9 + 7y
= (12y + 7y) + (-9)
= 19y + -9Therefore, 19y + -9 is the answer.
help please
with number 4
Answers
7/15 multiplied by 5/6
Answers
Answer:
The answer will be 35/36
Answer:
\(\frac{7}{18}\)
Step-by-step explanation:
\(\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\)
a trucker driver can expect to make $us55,065 per year in the us. assuming that this driver works 70 hours per week and 52 weeks per year, what is the equivalent salary in canadian dollars per hour?
Answers
The equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
To convert the annual salary of a truck driver in the US from US dollars to Canadian dollars, you can use the current exchange rate between the two currencies. The exchange rate fluctuates constantly, so you will need to use the most current rate.
Assuming the current exchange rate is 1 US dollar to 1.26 Canadian dollars, the annual salary of a truck driver in the US, $55,065, is equivalent to 71,040.90 Canadian dollars. If the truck driver works 70 hours per week and 52 weeks per year, their hourly wage in Canadian dollars would be $28.13.
Here's the calculation:
Annual salary in Canadian dollars = $55,065 * 1.26 = $71,040.90
Hourly wage in Canadian dollars = $71,040.90 / (70 hours/week * 52 weeks/year) = $28.13/hour
Keep in mind that this is just a rough estimate, as the exchange rate can change over time, and the actual wage may vary depending on the driver's experience, location, and other factors.
So, the equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
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Answer number 2 please.
Answers
Answer:
Obtuse scalene triangle
Step-by-step explanation:
1. Angles:
-> Acute triangle: all angles less than 60° -> Right triangle: one angle is 90° -> Obtuse triangle: one angle is greater than 90°- Given the information above, we can see that the triangle has one angle that's greater than 90° (129°), so this triangle is obtuse.
2. Sides:
-> Scalene triangle: all sides have different lengths-> Isosceles triangle: two sides have same length-> Equilateral triangle: all sides are the same- Given the information above, we can see that all the sides in the triangle are different, so this triangle is scalene.
Therefore, the answer is an obtuse scalene triangle.
if you have five friends who tell you they all have had a great experience with their purchase of a chevrolet, and if you use this fact to decide to buy a chevrolet, the form of logic evident here is a(an): a. median. b. statistic. c. inference. d. hypothesis.
Answers
The correct option is b. The form of logic evident in this scenario is a statistic.
In this scenario, the logic being used is based on a statistic. A statistic is a numerical value or measure that represents a specific characteristic or trend within a population. In this case, the statistic is derived from the experiences of the five friends who have had a great experience with their Chevrolet purchases. By observing their positive experiences, you are using this statistic to make an inference about the overall quality or satisfaction associated with Chevrolet vehicles.
It's important to note that the logic being used here is based on a sample size of five friends, which may not necessarily represent the entire population of Chevrolet buyers. The experiences of these friends can be seen as a form of anecdotal evidence. While their positive experiences are valuable and can provide some insight, it is always advisable to consider a larger sample size or gather additional information before making a purchasing decision. So, while the form of logic evident here is a statistic, it is essential to exercise caution and gather more data to make a well-informed decision.
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A six sided die is rolled three times. Find the probability that the result is an even number for every roll.
A. 1/9
B. 3/8
C. 1/3
D. 1/8
Answers
\(|\Omega|=6^3\\|A|=3^3\\\\P(A)=\dfrac{3^3}{6^3}=\left(\dfrac{3}{6}\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}=12.5\%\)
explain how to use multiplication to evaluate 9/5 ÷ 2/5
Answers
To find the value of the expression we have to used crossed multiplication, then:
The length of a side of a square is 5x + 2 units. If the perimeter is 48, what would the equation be to represent this information?
Answers
Answer:
9.2
Step-by-step explanation:
5x-2=48
5x+2-2=48-2
5x/5=46/5
=9.2
Hi :)
The formula for finding the perimeter of a square is \(P=4a\), where P=perimeter, a=side length.
We know \(a\), so we plug that into the equation
\(P=4(5x+2)\)
Now we also know the perimeter, so we plug that into the formula
\(48=4(5x+2)\)
Or
\(4(5x+2)=48\)
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Find the total surface area of this cuboid
Answers
Answer:
Total Surface Area =
148cm²
Explanation:
in the picture
The total surface area of cuboid is 158 cm².
What is the total surface area of cuboid?
The surface area of a cuboid is the total area of all of the faces of a cuboid.
If, the length (l), width (w), and height (h) of the cuboid
then, use the formula: surface area (SA)=2lw+2lh+2hw.
Here, given that,
l = 6cm
w = 4cm
h = 5cm
So, required total SA = 2( 24+30+20)
=158 cm²
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someone please help i will mark you brainliest
Answers
f (x) = (x-1) (x+3)..........................................less the periods
Find the circumference of each circle. Use 3.14 or 22/7 for π. Round to the nearest tenth if necessary.
I'm going to keep asking because I have no clue how to solve these
Answers
Answer:
219.8 yd
Step-by-step explanation:
Circumference Formula= πd or 2πr
Plug in the values. The diameter of this circle is 70 yds.
70(3.14) (replace 3.14 for π)
70*3.14=219.8 yds
Hope this helps ^^
Find the least common denominator.
12 - y2
The least common denominator of the rational numbers (82 – 81 + 15) and 15(52 - 6x + 9) is
32
Reset
Next
Answers
Answer:
52/82
Step-by-step explanation:
6-9+15-52
15-81+82
52/82
En una clase de matemáticas hay 3 niñas y 3 niños del séptimo grado y 7 niñas y 5 niños del octavo grado. La maestra elige al azar un estudiante del
séptimo grado y un estudiante del octavo grado en la clase para una competencia. Cuál es la probabilidad de que los estudiantes que ella seleccione sean
Escribir la respuesta como una fracción en forma reducida.
ninas?
Answers
Answer:
No comprendo espanol. Yo se un muy poco.
Step-by-step explanation:
The group wants to travel from its current location on the map to the South Pole, and then directly back to the base camp. How many miles will they have to travel? Explain your answer.
Answers
Using the Pythagorean Theorem, it is found that the group will have to travel 90 miles.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:
\(h^2 = l_1^2 + l_2^2\)
In this problem:
First, the group travels 5 x 5 = 25 miles to the south pole.Then, the distance to the camp is the hypotenuse of a right triangle with sides of 25 miles and of 12 x 5 = 60 miles, hence:\(d^2 = 25^2 + 60^2\)
\(d = \sqrt{25^2 + 60^2}\)
d = 65.
The total distance is given by:
Td = 25 + 65 = 90 miles.
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Can someone help me pls it’s due tomorrow
Answers
Answer:
1. 63.08 Rs
2. 5.03 Rs
3. 25.2 Rs
Explanation: answer to Q1 is already given.
Q2.=petrol price December2013 - December2011
=78.56-73.53
=5.03 Rs.
Q3.=Diesel price Aug '14 - Jan '11
=67.26-42.08
=25.2 Rs.
sorry idk the answer of Q4.
A sequence can be generated by using an=an−1+9, where a1=−5 and n is a whole number greater than 1. What are the first four terms in the sequence?
A.−5, 4, 13, 22
B.9, 4, −1, −6
C.−5, −45, −405, −3645
D. 9, −45, 225, −1125
Answers
Answer:
A
Step-by-step explanation:
For the sequence, the defining formula is given as;
an = Previous term + 9
So a2 will be -5 + 9 = 4
a3 will be 4 + 9 = 13
a4 will be 13 + 9 = 22
a5 will be 22 + 9 = 31
So the sequence of numbers will be;
-5, 4 , 13 , 22 , 31
Find vectors that span the kernel of A. -1 0 A= [\begin{array}{ccc}1&-1&-1&1&1\\-1&1&0&-2&2\\1&-1&-2&0&3\\2&-2&-1&3&4\end{array}\right]. There are infinitely vectors that work, enter the ones with a l in the following locations. ker(A) = span [a 1 b c d] [e f g 1 h] ker(A) = span ____
Answers
The solutions to this equation are of the form x = s[v1] + t[v2] + u[v3] + v[v4], where v1, v2, v3, and v4 are the vectors that span the kernel of A. For the given matrix A, the kernel is spanned by the vectors [1 1 0 0 0], [1 0 -1 0 0], [0 1 0 -1 0], and [-1 2 1 0 1].
To find the vectors that span the kernel of A, we need to solve the equation Ax = 0, where 0 is the zero vector.
We can do this by row reducing the augmented matrix [A|0].
RREF([A|0]) = [\begin{array}{ccc|c}1&-1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&0\end{array}\right]
The solutions to this equation are of the form:
x = s[\begin{array}{c}1\\1\\0\\0\\0\end{array}\right] + t[\begin{array}{c}1\\0\\-1\\0\\0\end{array}\right] + u[\begin{array}{c}0\\1\\0\\-1\\0\end{array}\right] + v[\begin{array}{c}-1\\2\\1\\0\\1\end{array}\right]
where s, t, u, and v are constants.
Therefore, the vectors that span the kernel of A are:
[\begin{array}{c}1\\1\\0\\0\\0\end{array}\right], [\begin{array}{c}1\\0\\-1\\0\\0\end{array}\right], [\begin{array}{c}0\\1\\0\\-1\\0\end{array}\right], and [\begin{array}{c}-1\\2\\1\\0\\1\end{array}\right].
To enter them in the given format, we can use:
ker(A) = span [\begin{array}{c}a\\1\\b\\c\\d\end{array}\right] [\begin{array}{c}e\\f\\g\\1\\h\end{array}\right]
where a, b, c, d, e, f, g, and h are the constants corresponding to the vectors above.
So, ker(A) = span [\begin{array}{c}1\\1\\0\\0\\0\end{array}\right] [\begin{array}{c}0\\1\\-1\\0\\0\end{array}\right] [\begin{array}{c}0\\0\\0\\1\\0\end{array}\right] [\begin{array}{c}-1\\0\\1\\0\\1\end{array}\right]
To find the vectors that span the kernel of A, we first need to row reduce A to its row echelon form (REF) or reduced row echelon form (RREF). The matrix A is given as:
A = \[\begin{array}{ccccc}1&-1&-1&1&1\\-1&1&0&-2&2\\1&-1&-2&0&3\\2&-2&-1&3&4\end{array}\right]
After row reducing the matrix A, we get the RREF:
RREF(A) = \[\begin{array}{ccccc}1&-1&0&0&-1\\0&0&1&0&-2\\0&0&0&1&1\\0&0&0&0&0\end{array}\right]
Now, we can find the kernel of A by solving the homogeneous system Ax = 0, where x is a vector [a b c d e]^T. Using the RREF(A), we get the following system of equations:
1. a - b - e = 0
2. c - 2e = 0
3. d + e = 0
From equation 1, we get b = a - e.
From equation 2, we get c = 2e.
From equation 3, we get d = -e.
Now, we can write the vector x as a linear combination of two vectors, one with a 1 in the first position and the other with a 1 in the fourth position:
x = a[1 1 0 0 1] + e[0 0 2 1 -1]
So, the kernel of A (ker(A)) is spanned by the vectors:
ker(A) = span \[\begin{array}{c}[1, 1, 0, 0, 1], [0, 0, 2, 1, -1]\end{array}\right]
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a + b + c= What when a=8,b=11,c=-13
Answers
Answer:
6
Step-by-step explanation:
brainlyiest
Answer:
six
Step-by-step explanation:
8 plus 11 subyract 13
Find a Doctor, is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc) During a "slow time for them, they have 9 staff members taking calls from customers. On average, one call arrives every 5 minutes (standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes) Round your answer to 2 decimal places) How long does a customer spend on average waiting on hold before they can start speaking to a representative? Minutes
Answers
On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.
To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.
Given:
9 staff members taking calls.
On average, one call arrives every 5 minutes (standard deviation of 5 minutes).
Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).
To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:
"M" stands for Markovian or memoryless arrival and service times.
"c" represents the number of servers.
In our case, we have an M/M/9 queuing model since we have 9 staff members.
The average waiting time for a customer on hold is given by the following formula:
Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))
Where:
c = number of servers (staff members) = 9
μ = average service rate (1 / average service time)
λ = average arrival rate (1 / average interarrival time)
ρ = λ / (c * μ)
First, let's calculate the average arrival rate (λ):
λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute
Next, calculate the average service rate (μ):
μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute
Now, calculate ρ:
ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407
Finally, calculate the waiting time:
Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))
= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))
≈ 1.16 minutes
Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.
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F(x)=-2x^2+3x+7 find f(3)
Answers
Answer:
f(3) = -2
Step-by-step explanation:
Given the f(x) = -2x² + 3x + 7, to find f(3):
We can substitute 3 as the value of x in the given function:
f(x) = -2x² + 3x + 7
f(3) = -2(3)² + 3(3) + 7
f(3) = -2(9) + 9 + 7
f(3) = -18 + 9 + 7
f(3) = -9 + 7
f(3) = -2
Therefore, f(3) = - 2.
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A tower that is 120 feet tall casts a shadow 131 feet long. Find the angle of elevation of the sun to the nearest degree.
Answers
Using a trigonometric relation we can see that the angle is 42.49°
How to find the angle of elevation?We can think of this as a right triangle, sich that we know the two catheti and we want to find one of the angles wich is the angle of elevation of the sun.
With respect to that angle, we have:
Adjacent cathetus = 131 ft
Opposite cathetus = 120ft
Using the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing the values that we know:
tan(a) = 120/131
a = Atan(120/131)
a = 42.49°
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