Answer:
See the attachment for the graph of the piecewise function.
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
\(f(x)=\begin{cases}2-x^2,\;\;\;1\leq x < 3\\2-3x,\;\;\;3\leq x \leq5\end{cases}\;[1,5]\)
Therefore, the function has two definitions:
f(x) = 2 - x² when x is greater than or equal to 1 and less than 3.f(x) = 2 - 3x when x is greater than or equal to 3 and less than or equal to 5.When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely in that direction.First piece of the functionSubstitute the endpoints of the first function's domain -1 ≤ x < 3 into the first function:
\(x=1\implies f(1)=2-1^2=1 \implies (1,1)\)
\(x=3\implies f(3)=2-3^2=-7 \implies (3,-7)\)
Therefore, place a closed circle at (1, 1) and an open circle at (3, -7).
As the function is quadratic (a parabola that opens downwards), join the points with a curve.
Second piece of the functionSubstitute the endpoints of the second function's domain 3 ≤ x ≤ 5 into the second function:
\(x=3\implies f(3)=2-3(3)=-7 \implies (3,-7)\)
\(x=5\implies f(5)=2-3(5)=-13 \implies (5,-13)\)
Therefore, place a closed circle at (3, -7) and a closed circle at (5, -13).
As this function is linear, join the two points with a straight line.
You will notice that both pieces of the function share the endpoint (3, -7).
As (3, -7) is included in the second piece of the function, the function is continuous at (3, -7) and the closed circle is optional at that point.
A net and four figures are shown: Which figure can be formed from the net? (Input the number only.)
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
It’s 2 because
2 has 6 sides and the net has 6 squares
picture folding up the net. You’ll h]get number 2
simplify (6k +5)(5k +5)
Answer:
30k^2+55k+25
Step-by-step explanation:
30k^2+30k+25k+25
=30k^2+55k+25
\(30k { }^{2} + 30k + 25k + 25\)
\(30k ^{2} + 55k + 25\)
Item 18
A florist has 1,276 flowers to divide into bunches of 9 flowers. The florist makes as many bunches as possible.
How many bunches of flowers does the florist make, and how many flowers are left over?
Enter your answers in the boxes.
The florist can make
bunches with
flowers left over.
Answer:
141 bunches, 7 flowers left
Step-by-step explanation:
Number of bunches of flowers that can the florist make is 23 flowers
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, we have,
If 60% of the flowers in a bunch are lilies,
then there are 40 x 0.6 = 24 lilies in each bunch.
That means there are 40 - 24 = 16 roses and carnations in each bunch.
The ratio of carnations to roses = 3 : 5
Let's call the number of carnations in each bunch "3x" and the number of roses in each bunch "5x". That means
3x + 5x = 16 (the total number of carnations and roses)
8x = 16
x = 2
So there are 3 x 2 = 6 carnations in each bunch.
If the florist has only 140 carnations, they can make 140 / 6 = 23.333... bunches of flowers. However, since they can't make a fraction of a bunch, the florist can only make 23 bunches of flowers.
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complete question:
A florist is making some bunches of flowers for a wedding. Each bunch contains some carnations, roses, and lilies. Each bunch is the same. - A bunch contains 40 flowers -60% of the flowers are lilies The ratio of carnations to roses is 3:5 The florist only has 140 carnations. How many bunches of flowers can the florist make?
hint: 180 *
1. Find the missing angle.
29
R
61
T
Answer:
∠ R = 90°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , that is
∠ R + ∠ S + ∠ T = 180° , substitute values
∠ R + 29° + 61° = 180°
∠ R + 90° = 180° ( subtract 90° from both sides )
∠ R = 90°
Natalie and phil are running for 6th grade class president. Natalie receives 16 votes, and phil receives 12 votes.
Answer:
Natalie win as the 6th grade class president
Step-by-step explanation:she win by 4 points after Phil and Natalie has 16 votes and Phil has 12 votes
X=-2.
ㄱ
f(x) = 2x-2+5
Step-by-step explanation:
from,
f (x) = 2x-2+5
BUT x=-2
f (x) = 2 (-2)-2+5
= -4-2+5
= -6+5
= -1
so,
f (x) = -1
10. Leo runs the 100-meter dash in 19.305
seconds. Explain and show how you can
write an expression in expanded form
for the decimal that shows more than 0
hundredths.
The expanded form of the expression is 10 + 9 + 0.3 + 0.00 + 0.005
How to write in expanded form ?He runs the 100 meters dash in 19.305 seconds.
Therefore, the seconds he runs the race can be represented in expanded form as follows:
Expanded form is a way to write a number by adding the value of its digits.
We can use a place value chart to think of the value of a number's digits.
Therefore,
19.305 in expanded form is as follows:
19.305 = 10 + 9 + 0.3 + 0.00 + 0.005
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What is the equation of this line?
a.y = 2x
b.y=−12x
c.y=12x
d.y=−2x
Answer:
Im thinking its y=-2x but Im not 100% sorry if its wrong
Find the median of the following set of numbers. 98, 67, 98, 102, 74, 95, 99
Answer:
98
Step-by-step explanation:
to find median you put the numbers in order from least to greatest then you see what number is in the middle
Answer:
98Step-by-step explanation:
The median of an information set is found by putting the information set in ascending numerical order and identifying the center number. If there are an odd number of data values within the data set, the median could be a single number. If there are an excellent number of data values within the data set, the median is that the average of the 2 middle numbers. Sorting the information set for the values entered above we have:
98, 67, 98, 102, 74, 95, 99
Since there's an odd number of data values during this data set, there's just one middle number. With 7 data values, the center number is that the data value at position 4. Therefore, the median is 98.
Quadrilateral ABCD is a rhombus.
AD = 13 cm & BD = 24 cm,
find AC
Answer:
64
Step-by-step explanation:
what function is g(x)
The transformed function of f(x) = |x| is, B. g(x) = |(1/6)x|.
What are some rules for function transformation?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over the x-axis, (x, -y).
Given, A modulus function f(x) = |x| the parent function.
Now, We know,
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0.
(bx , y).
Therefore, The function stretched horizontally by 6 units would be,
g(x) = |(1/6)x|.
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Consider the function \(y=\sqrt{5x-5}+1\)
Which inequality is used to find the domain?
The inequality is used to find the domain of the given function is
5x-5 ≥ 0
What is a function?A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.
Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.
Since, the function is a square root function.
We know that,
The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.
The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :
5x-5 ≥ 0
Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0
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Enter the coordinates of the point
on the unit circle at the given angle.
240°
EXPLANATION:
To convert degrees to radians, multiply by π / 180 °
since a full circle is 360° or 2π radians.
240°⋅π / 180° radians
Cancel the common factor of 60
4 × π / 3 radians
Combine 4 and π / 3.
4π / 3 radians
HOPE ITS HELPS !!!!!
The coordinates of the points on unit circle at the given angle 240 degrees is\((\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )\)
The formula for calculating Radians is:
\(radians= (degrees)\)×\(\frac{\pi }{180}\)
Formula for calculating coordinates of point (x, y) on circle:x=rcosθ
y=rsinθ (where r is the radius of circle for unit circle r=1)
According to the question
we have
θ = 240 degrees and, r =1
so, 240 degrees = 240×\(\frac{\pi }{180}\)
⇒240 degrees = \(\frac{4\pi }{3}\) (in radians)
Therefore, the coordinates of the points on unit circle at angle \(\frac{4\pi }{3}\) is calculated as
\(x=(1)cos\frac{4\pi }{3}\) (for unit circle r=1)
\(x=\frac{-1}{2}\)
And,
\(y=(1)sin\frac{4\pi }{3}\) (for unit circle r=1)
\(y=\frac{-\sqrt{3} }{2}\)
Hence, the coordinates of the point on unit circle at angle 240 degrees is \((\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )\)
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PLEASE HELP I NEED THE GRAPH NOTHING ELSE PLZZ
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the linear inequality shown below on the provided graph.
y > -3x + 8
plssssss helppppppppppp
Answer:
Step-by-step explanation:
You can write an equation based upon where the curve has "zeroes" or when the curve touches/goes through the x axis.
Take opposite sign
Bounces off at -2 , this means there is a multiplicity
(x+2)²
Goes through at +1
(x-1)
Put it together:
y = (x+2)²(x-1)
guidance counselor compiles data relating a student's English grade to the number of languages studied. The results are shown in the frequency table below.
A 4-column table with 3 rows titled English grade versus number of languages studied. The first column has no label with entries English only, English and another language, total. The second column is labeled 90 or above with entries 15, 110, 125. The third column is labeled lower than 90 with entries 105, 270, 375. The fourth column is labeled total with entries 120, 380, 500.
The counselor converts the frequency table to a conditional relative frequency table by column.
A 4-column table with 3 rows titled English grade versus number of languages studied. The first column has no label with entries English only, English and another language, total. The second column is labeled 90 or above with entries 0.12, 0.88, 1.0. The third column is labeled lower than 90 with entries 0.28, 0.72, 1.0. The fourth column is labeled total with entries X, Y, 1.0.
What is the value of X?
0.16
0.20
0.24
0.40
Answer:
C:0.24
Step-by-step explanation:
If a=6 and b = 2 then 4a+ b/2
Answer:
25
Step-by-step explanation:
(* ̄3 ̄)╭
Can someone please explain this to me and help me
Answer:
ok
Step-by-step explanation:
Which term can be added to the list so that the greatest common factor of the three terms is 12h3?
36h3, 12h6, __________
The term that can be added to the list so that the greatest common factor of the three terms 12h3 36h3, 12h6, is 48h5
How can the term be known?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.
The term that can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12 without any fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.
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In 1995 there were 501 computer viruses reported. Since then, the viruses have been replicating at a
rate of 57% per year. How many viruses are projected for the year 2021?
Therefore, there are projected to be approximately 1541 computer viruses in the year 2021.
What is exponential growth?Exponential growth is a pattern of growth where a quantity grows at a constant percentage rate per unit of time. In other words, the rate of growth is proportional to the current value of the quantity. This type of growth is often seen in natural phenomena such as population growth, the spread of diseases, and the growth of financial investments. Exponential growth can be described mathematically by an exponential function of the form y = abˣ, where a is the initial value, b is the growth factor, and x is the time variable.
Here,
To solve this problem, we can use exponential growth formula:
A = P(1 + r)ˣ
where:
A = final amount
P = initial amount
r = growth rate
t = time (in years)
Let's first calculate the number of years from 1995 to 2021:
2021 - 1995 = 26 years
Using the given information, we can plug in the values into the formula:
A = 501(1 + 0.57)²⁶
A = 501(3.08)
A = 1540.68
Rounding to the nearest whole number, we get:
A ≈ 1541
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Ram, Shyam and Moha purchased biscuits of different brands P, Q and R. Ram purchased 10 packets of P, 7 of Q and 3 packets of R. Shyam purchased 4 packets of P, 8 packets of Q and 10 packets of R. Mohan purchased 4 packets of P, 7 packets of Q and 8 packets of R. If brand P costs € 4, Q costs € 5 and R costs € 6 each, then using matrix operation, find the amount of money spent by these persons individually.
The amount of money spent by these persons individually will be $ 93, $116, and $ 99.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.
Ram, Shyam, and Mohan purchased biscuits from different brands P, Q, and R.
Ram purchased 10 packets of P, 7 packets of Q, and 3 packets of R.
Shyam purchased 4 packets of P, 8 packets of Q, and 10 packets of R.
Mohan purchased 4 packets of P, 7 packets of Q, and 8 packets of R.
If brand P costs € 4, Q costs € 5, and R costs € 6 each.
Then the amount of money spent by these persons individually will be
Then these are shown in the form of a matrix. Then we have
\(\begin{bmatrix}10 & 7 & 3 \\4 & 8 & 10 \\4 & 7 & 8 \\\end{bmatrix} \begin{bmatrix}4 \\ 5 \\ 6 \\\end{bmatrix}\)
Then the amount of money spent by these persons individually will be
\(\begin{bmatrix}10 & 7 & 3 \\4 & 8 & 10 \\4 & 7 & 8 \\\end{bmatrix} \begin{bmatrix}4 \\ 5 \\ 6 \\\end{bmatrix} = \begin{bmatrix} 93\\ 116 \\99 \end{bmatrix}\)
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a snail is 20 inches about the ground. It slips down 6 inches and the creeps up 12 inches. what is the snails height now?
Answer:
26 inches
Step-by-step explanation:
The snail starts 20 inches above the ground: +20
The snail slips (goes down) 6 inches: 20 - 6 = 14
The snail goes up 12 inches: 14 + 12 = 28
The snail is 28 inches above the ground.
Hope this helps!
A population numbers 18,000 organisms initially and grows by 16% each year.
Answer:
The answer is 20,880
Step-by-step explanation:
This won't be a very long explanation. What I did was add 18,000 plus 16% and I got 20,880.
Hope this helps!
Have a nice day/night/afternoon.
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What are three numbers that are divisible by both two and five
Answer:
10, 20, 30
Step-by-step explanation:
You want three numbers divisible by both 2 and 5.
Common multiplesIn order for a number to be divisible by 2, it must have 2 as a factor. If it is to be divisible by 5, it must have 5 as a factor. You want numbers divisible by both 2 and 5, so both 2 and 5 must be factors of the numbers. The values 2 and 5 have no factors in common, so their least common multiple is 2×5 = 10.
Any integer multiple of this value will be divisible by both 2 and 5. A multiple of 10 will end in 0. That is, any integer with a units digit of 0 is divisible by both 2 and 5. Examples are ...
10, 20, 30
The total mass of a trolley and some watermelons is 27 kg.
The total mass of the same trolley and some mangoes is 11 kg.
The mass of the watermelons was thrice the mass of the mangoes.
Answer:
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
Step-by-step explanation:
Let's assign variables to the masses involved to solve the problem systematically.
Let's say:
Mass of the trolley = T kg
Mass of the mangoes = M kg
Mass of the watermelons = W kg
According to the given information:
The total mass of the trolley and mangoes is 11 kg:
T + M = 11 -- Equation (1)
The mass of the watermelons is three times the mass of the mangoes:
W = 3M -- Equation (2)
Now, we can use these equations to find the values of T, M, and W.
From Equation (2), we can express M in terms of W:
M = W / 3
Substitute this value of M into Equation (1):
T + W / 3 = 11
Multiply through by 3 to eliminate the fraction:
3T + W = 33 -- Equation (3)
Now, we have a system of two equations (Equation 2 and Equation 3) with two unknowns (T and W). We can solve this system to find the values.
Since we don't have a specific value for any variable, we can express the solution in terms of the variables.
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
Explain the difference between an indefinite integral and a definite integral.
A) An indefinite integral, after evaluating it at the limits of integration, results in a particular number. A definite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
B) A definite integral, after evaluating it at the limits of integration, results in a particular number. An indefinite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
C) An indefinte integral cannot always be integrated analytically and may require numeric integration, while it is always possible to integrate a definite integral. Definite integrals always return a real number after evaluation at its limits of integration.
D) A definite integral is defined and continuous over the interval of integration and has finite limits of integration. An indefinite integral is also defined and continuous over the interval of integration, but may have as a limit of integration.
The answer is A.
An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).
A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫
a
b
f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.
In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.
Raul has a circular koi pond in a 30-foot square patio. Find the area of the patio that is not part of the pond to the nearest hundredth. Show your work.
Answer:
193.14 ft^2
Step-by-step explanation:
Please help !!!!!! 20 points
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
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What does an equal sign mean mathematically?
Answer:
It means that the both sides of the expression in the given equation must be/are congruent.
Hope this helps!
PLEASE HELP!!! - There are 12 green cubes,9 blue cubes, and 4 white cubes in a bag. Write the probability of pulling out each color as a percentage.
A green cube ____
A blue cube _____
A white cube ____
Answer: green cube=48% chance, blue=36% chance, white =16% chance.
Step-by-step explanation: 1. You want to add up all the cubes. There are 25 cubes in total (9+4+12=25)
2. For the green cube, we know there are 12 cubes, so there would be a 12/25 chance which is a 48% chance
3. The same thing applies to the blue cube. There are 9 of them so it would be a 9/25 chance (36%)
4. There are 4 white cubes. 4/25 is a 16% chance.