Select the correct answer from each drop-down menu. The graph represents the piecewise function.
Answers
The functions will be defined as y = x² if 0 ≤ x < 3, y = -x + 10 if 3 < x ≤ 6, and y = x + 2 if 6 ≤ x ≤ 10.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The graph is given below.
The function can be defined as
The parabolic equation will be
f(x) = x²
The equation of the absolute function will be
f(x) = |x - 6| + 4
Then we have
[tex]f(x) = \left\{\begin{matrix}y=x^2 & 0\leq x < 3 \\\\y=-x+10 & 3 < x\leq 6 \\\\y=x+2 & 6\leq x \leq 10 \\\end{matrix}\right.[/tex]
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Related Questions
Is this right if not please tell me explanation
Answers
Answer:
No, right answer is = 1017.36
Answer:
1017.36
Step-by-step explanation:
All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:
[tex]\pi * 6^{2}*9 = 1017.88[/tex]
instead of
[tex]3.14*6^{2}*9 = 1017.36[/tex]
like you had written above. So the final is actually supposed to be 1017.36
Will Give 50 POINTS If CORRECT
Arrange the steps in order that would be used to algebraically solve a system of linear and quadratic equations.
1) Solve each equation for y.
2) Solve for x.
3) Set the 2 equations equal.
4) Insert x back into an equation to find the y value.
Answers
Answer:
3, 2, 4, 1
Step-by-step explanation:
Could someone explain and show how to solve these
Answers
The answers to the given question are as follows:-
1. Cos(∠mA) = [tex]\dfrac{3}{5}[/tex]
2. Sin(∠mA) = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex]
3. Tan(∠mB) = [tex]\dfrac{b}{a}[/tex]
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The angles will be calculated by using trigonometric identities.
1. For the first triangle:-
Cos∠mA = [tex]\rm \dfrac{Base}{Hypotenuse}[/tex]
We can see in the first triangle base is 3 and the hypotenuse is 5.
Cos∠mA = [tex]\dfrac{3}{5}[/tex]
2. For the second triangle:-
Sin∠mA = [tex]\rm \dfrac{Perpendicualr }{Hypotenuse}[/tex]
We can see in the first triangle Perpendicular is √20 and the hypotenuse is √35.
Sin∠mA = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex]
3. For the third triangle:-
Tan∠mB = [tex]\rm \dfrac{Perpendicualr }{Base}[/tex]
We can see in the first triangle Perpendicular is b and the Base is a.
Tan∠mA = [tex]\dfrac{b}{a}[/tex]
Therefore answers to the given question are as follows:-1. Cos(∠mA) = [tex]\dfrac{3}{5}[/tex]2. Sin(∠mA) = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex] and 3. Tan(∠mB) = [tex]\dfrac{b}{a}[/tex]
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Find the number of rectangles an and Squares in chess 8 by 8 board respectively.
Answers
Answer:
squares: 204
rectangle: 1,296
Step-by-step explanation:
Board Size: 8 x 8
The total number of squares is thus:
[tex]1^{2} + 2^{2} + ... + n^{2}[/tex]
sum = [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]
For a chess board, with n = 8,
sum = [tex]\frac{(8)((8) + 1)(2(8) + 1)}{6}[/tex]
sum = 204
the number of rectangles on a chess board,
to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.
Aleena cuts 3/8 part of ribbon for her project.then again she cuts 4/5 part of the remaining ribbon the next day.find the total length of the Ribbon ,if 6.5 m of ribbon still remain
Answers
The total length of the ribbon is 52 m.
Let x = the original length of the ribbonAleena initially cuts 3/8 of the ribbon, i.e. a length of (3/8)x.
How much is left?1 - (3/8)x = (5/8)x.
On the next day, she cuts 4/5 of the remaining ribbon.i.e. (4/5) * (5/8)x = (20/40)x = (1/2)x
How much of the ribbon has she now cut away?(3/8)x + (1/2)x = (3/8)x + (4/8)x = (7/8)x
That means 1 - (7/8)x = (1/8)x remains, and that is a length of 6.5 m.
We now need to determine the following:1/8 of what number is 6.5?
Let y = the unknown number.
(1/8)y = 6.5
Multiply both sides of the equation by 8 to clear the fraction.
y = 52 m
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N(t) = 100,000e−(t − 10)2/8
The secant line can be used to approximate the derivative at a particular point on the graph by placing either the right or the left side of the secant line on that point. (Round your answer to the nearest integer.)
(a) Consider the point on the graph at t = 10 days and set one end of the secant line at this point. Set the other end of the secant line at the point that is 1 day earlier. What is the approximation of the slope of the graph at t = 10 days using this secant line?
(b) Consider again the point on the graph at t = 10 days. Set one end of the secant line at t = 10 days and the other end at the point that is 1 day later. What is the approximation of the slope of the graph at t = 10 days using this secant line?
Answers
The approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.
How to determine the slope of the secant lines?(a) t = 10 days and a day earlier
This means that:
t = 10 and t = 9
The function is given as:
[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]
Calculate N(10)
[tex]N(10) = 100000e^{\frac{-(10 - 10)^2}{8}}[/tex]
Evaluate
N(10) = 100000
Next, calculate N(9)
[tex]N(9) = 100000e^{\frac{-(9 - 10)^2}{8}}[/tex]
Evaluate
N(9) = 88249.6902585
The slope is then calculated using"
[tex]m = \frac{N(10) - N(9)}{10 - 9}[/tex]
This gives
[tex]m = \frac{100000 - 88249.6902585}{10 - 9}[/tex]
Evaluate
m = 11750.3097415
Approximate
m = 11750
(b) t = 10 days and a day later
This means that:
t = 10 and t = 100
The function is given as:
[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]
In (a), we have:
N(10) = 100000
Next, calculate N(11)
[tex]N(9) = 100000e^{\frac{-(11 - 10)^2}{8}}[/tex]
Evaluate
N(11) = 88249.6902585
The slope is then calculated using:
[tex]m = \frac{N(11) - N(10)}{11 - 10}[/tex]
This gives
[tex]m = \frac{88249.6902585 - 100000}{11 - 10}[/tex]
Evaluate
m = -11750.3097415
Approximate
m = -11750
Hence, the approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.
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The table represents a bicycle rental cost in dollars as a
unction of time in hours.
Bicycle Rental
Time
Cost
(hours)
($)
0
0
2
10
4
20
6
30
8
40
Which explains whether or not the function represents a
direct variation?
O This function represents a direct variation because it
passes through the origin and has a constant rate of
change of $5 per hour.
O This function represents a direct variation because it
has a positive, constant rate of change of $10 per
hour.
O This function does not represent a direct variation
because it does not represent the cost for 1 hour.
This function does not represent a direct variation
because the function rule for the cost is to add $10,
not multiply by a constant.
Answers
Answer:
(a) This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Step-by-step explanation:
The equation of direct variation is ...
y = kx
for some constant k. Here, we have x in hours and y in dollars. We can see if k is constant for the values given in the table.
__
constant of variationSolving the direct variation formula for k, we have ...
k = y/x
Using the table values, we can see if this is constant:
k = dollars/hour = 10/2 = 20/4 = 30/6 = 40/8 = 5
The "rate of change" is constant at $5 per hour.
The function represents direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Which expression is equivalent to [tex]8/x^6[/tex]? Assume x> 0
Answers
An equivalent expression is given by (2 / x ^ 3) * sqrt (2)
We have the following expression
8 / x ^ 6
Rewriting we have
sqrt (8 / x ^ 6)
What is the expression?
The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.
sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))
(2 / (x * x * x)) sqrt (2)
(2 / x ^ 3) * sqrt (2)
An equivalent expression is given by
(2 / x ^ 3) * sqrt (2)
Therefore an equivalent expression is given by (2 / x ^ 3) * sqrt (2).
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A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sen
Answers
Answer:
Both plans cost the same when 50 texts are sent
Step-by-step explanation:
Both the plans cost the same amount $22.5 when 50 texts are sent:
[tex]20+0.05*50 = 10+0.25*50[/tex]✔️
Have a nice day! :)
help I will gave u brilliant answer please help
Answers
Answer:
a) 15/8 b) 25/18
Step-by-step explanation:
a) First bring all the fractions to a common denominator (I'm going to use 8th's). 5/8 is already simplified, 1/2=4/8, and 3/4=6/8. Then, simply add the numerators and leave the denominator: [tex]\frac{5+4+6}{8} =\frac{15}{8}[/tex]
Since this can not be simplified any further, your final answer is 15/8.
b) Start by bringing all the fractions to a common denominator (for this problem, we'll use 18th's). 2/3=12/18, 1/6=3/18, and 5/9=10/18. Then just add all the numerators and leave the denominator the same: [tex]\frac{12+3+10}{18} = \frac{25}{18}[/tex]
Since this cannot be simplified further either, your final answer is 25/18.
Hope this helps! :)
Answer:
so to add we need to find lcm
Step-by-step explanation:
a) 5/8 + 1/2+3/4 lcm of 2,4 and 8 = 8
5/8 = 5/8
1x4
2x4 = = 4/8
3x2
4x2 = 6/8
5/8 + 4/8 + 6/8 = 15/8
b) 2/3 + 1/6 + 5/9 lcm of 3 , 6 and 9 = 18
2x6
3x6 = 12/18
1x3
6x3 = 3/18
5x2
9x2 = 10/18
12/18 + 3/18 + 10/18 = 25/18
what function is increasing at the highest rate
Answers
5. Sabrina put $3,000 into a Money Market (high-yield savings)
account with an interest rate of 2.6% compounded quarterly.
a. Write an equation to model the amount in the account over
time.
b. Assuming no deposits or withdrawals are made, how much
money would be in the account after 15 years? Show your
calculation.
c. How would this problem be different if it was compounded
"continuously" instead? Calculate the amount after 15 years.
d. Name 2 or more other situations (other than a savings
account) where you might encounter compound interest later in
your life.
Answers
let me answer the last one first
compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.
hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.
hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.
now let's do the others
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]
Please help on this two questions!!
Answers
2.) This is letter D. Tyler did not make a mistake.
A rectangular prism has length of 5 feet and a width of 9 feet. If the surface area of the prism is 174 square feet,
what is its height?
5ft
4ft
6 ft
3 ft
Answers
kung 5ft and a width of 9ft and the area of prism is 174 the answer is 5ft
Which expression would be easier to simplify if you used the associative
property to change the grouping?
Answers
Answer:
B
Step-by-step explanation:
Seeley takes home $4800 per month. What is the maximum amount he can
spend each month on loan and credit card payments without being in danger
of credit overload?
OA. $1600
OB. $1200
OC. $960
OD. $480
Answers
Answer:
1200
Step-by-step explanation:
I'm not 100% sure but that seems like the most reasonable answer
HELP (WORTH 20 POINTS)
Answers
Answer:
1 matter
2 atoms
3 molecules
4 matter and energy
5 solid liquid and gas
6 mass
i dont know the rest to be honest
Step-by-step explanation:
Juniper measured his bed twice: once in meters and once in
millimeters. Which is true?
A) The number of meters will be greater.
B) The number of millimeters will be greater.
C) They will both be the same.
Answers
Answer:
B
Step-by-step explanation:
millimeter means one-thousandth of a meter meaning the number of millimeters will be larger by a factor of 1000.
Answer:
B
Step-by-step explanation:
Millimetres is A LOT smaller than meters, meaning the individual number of millimetres is larger than the individual number of meters.
Which region represents the solution to the given system of inequalities? y<-1/2x and y>_2x+3
Answers
The region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The question is incomplete:
The complete question is:
Which region represents the solution to the given system of inequalities?
ABCDy < -1/2x and y ≥ 2x+3 and the missing figure is shown in the picture please refer to the picture.
We have two inequalities:
y < -1/2x
y ≥ 2x+3
After drawing the inequalities on the coordinate plane we see that the intersection region is on the region C.
Thus, the region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.
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What is the explicit formula for this geometric sequence?
64, 16, 4, 1,
Answers
Answer: [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]
Step-by-step explanation:
The common ratio is 16/64 = 1/4, so substituting into the formula, we get that [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]
Diana put $8000 in a 10-year CD
paying 5% interest compounded
monthly. After 2 years, she
withdrew all her money, and as an
early withdrawal penalty, she paid
back all the interest she made
during the first year. How much
money was Diana left with?
Answers
Th amount of money that Diana is left with is $8,430.23.
How much is Diana left with?The first step is to determine the interest earned in the first year and the total amount that was made in the 2 years.
The formula used to determine the future value with monthly compounding is:
P(1 + r)^( n x m)
Where:
P = present value r = periodic interest rate n = number of years m = frequency of compoundingTotal amount made in 2 years = $8000 x ( 1 + 5% / 12)^(12 x 2) = 8839.53
Interest earned in the first year = [ $8000 x ( 1 + 5% / 12)^(12) ] - 8000 = $409.29
Amount she is left with = 8839.53 - $409.29 = $8430.23
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What are the zeros of the function f(x) = x4 − 4x2 − 5?
Answers
Answer:
A graph shows zeros to be ±3. Factoring those out leaves the quadratic
(x-2)² +1
which has complex roots 2±i.
The function has roots -3, 3, 2-i, 2+i.
Step-by-step explanation:
Answer:
See below ~
Step-by-step explanation:
The function is :
f(x) = x⁴ - 4x² - 5
=============================================================
Plotting on a graph :
⇒ Once plotted on graph, check where the line of the function intersects the x-axis
⇒ Those will be the zeros of the function
===========================================================
Solution :
⇒ x = -2.236
⇒ x = 2.236
Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 5 vertices and 8 edges have?
Answers
Answer:
5 faces
Step-by-step explanation:
V – E + F = 2
We know that V = 5 and E = 8
Substitute these into the equation
5 -8+F = 2
-3+F =2
Add 3 to each side
-3+F+3 = 2+3
F=5
Find the surface area of the square pyramid. Enter your answer in the box.
A square pyramid. The side length of the base is 11 centimeters. The height of each of the 4 triangular faces is 10 centimeters.
(answer)_cm²
pls answer A.S.A.P
Answers
372.0796686
Simplify is needed
How many cups are there in 3/8 gallon?
Answers
Answer:
6 cups
Step-by-step explanation:
Answer:
That would be 6 cups I believe
Chelsea collected 12 containers each with 3 grams of sand and Pierre collected 8 containers each with sand. They collected the same amount of sand every day for 4 days. How many grams of sand did Chelsea and Pierre have altogether?
Answers
Answer:
288 grams
Step-by-step explanation:
Chelsea
12 × 3 = 36
48 × 4 = 192
Pierre
8 × 3 = 24
24 × 4 = 96
together
192 + 96 = 288 grams
Samples of size n = 60 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the mean is taken for each sample. What is the distribution of the sample means?
Answers
The distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).
How is the sample explained?Calculating the sample mean is as simple as adding up the number of items in a sample set and then dividing that sum by the number of items in the sample set.
Here, the distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).
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Question 5 of 5
Drag each tile to the correct box. Not all tiles will be used. Consider the recursively defined function below. f(1) = 0.75 f(n) = f(n-1) + 0.35, for n = 2, 3, 4, ...
Create the first five terms of the sequence defined by the given function.
1.8
0.75
2.15
1.0
1.35
1.7
1.1
1.45
Answers
Based on the calculations, the sequence defined by the given function are 0.75, 1.1, 1.45, 1.80 and 2.15.
How to create the terms of the sequence?In this exercise, you're required to create the first five (5) terms of the sequence defined by the given function as follows:
For the first term, we have:
f(1) = 0.75
For the second term, we have:
f(2) = f(2-1) + 0.35
f(2) = 0.75 + 0.35
f(2) = 1.1.
For the third term, we have:
f(3) = f(3-1) + 0.35
f(3) = 1.1 + 0.35
f(3) = 1.45.
For the fourth term, we have:
f(4) = f(3-1) + 0.35
f(4) = 1.45 + 0.35
f(4) = 1.80.
For the fifth term, we have:
f(5) = f(3-1) + 0.35
f(5) = 1.80 + 0.35
f(5) = 2.15.
Therefore, the sequence defined by the given function are 0.75, 1.1, 1.45, 1.80 and 2.15.
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I need help with question 20
Answers
An altitude connects the vertex of a triangle with the opposite side creating a right angle
Question 3 of 10
Select the expression that is equivalent to (x-3)².
Answers
=> x^2 -3x -3x +9
=> x^2 -6x +9