Answer:
4x +68x -66x -5Step-by-step explanation:
You want the derivatives of the three quadratic functions given.
f(x) = 2x² +6x -3f(x) = 4x² -6x +2f(x) = 3x² -5x +3DerivativeThe derivative of the terms of a polynomial can be found using the power rule:
\(\dfrac{d}{dx}x^n=n\cdot x^{n-1}\)
When this rule is applied to a quadratic, it looks like this:
f(x) = ax² +bx +c
f'(x) = 2ax +b
1. f(x) = 2x² +6x -3f'(x) = 2·2x +6
f'(x) = 4x +6
2. f(x) = 4x² -6x +2f'(x) = 2·4x -6
f'(x) = 8x -6
3. f(x) = 3x² -5x +3f'(x) = 2·3x -5
f'(x) = 6x -5
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3. it normally takes julius 4 hours to mow the lawn, but because he is in a hurry he asks his son, marcos, to help him. if marcos mows the lawn by himself, it would take him 6 hours. a. marcos thinks it will take them 5 hours to mow the lawn when working together. but his dad said that was not true, and it would take less time. without doing any calculations, who is correct? why?
Julius is correct that it will take less time for them to mow the lawn when working together.
Both Julius and Marcos have different predictions on how long it will take them to mow the lawn when working together. Marcos believes it will take them 5 hours, while Julius thinks it will take less time. Without any calculations, we can determine who is correct based on the concept of work rates.
When working alone, Julius takes 4 hours to mow the lawn. This means his work rate is 1 lawn per 4 hours. Similarly, Marcos takes 6 hours to mow the lawn alone, so his work rate is 1 lawn per 6 hours.
When working together, their work rates are combined. To find the total work rate, we add their individual work rates: 1/4 + 1/6 = 5/12.
This means that together, Julius and Marcos can mow 5/12 of the lawn in one hour. To mow the entire lawn, they need to complete 1 whole unit of work.
Since their combined work rate is 5/12, it will take them less than 5 hours to finish mowing the lawn. Therefore, Julius is correct in saying that it will take them less time than what Marcos predicted.
In conclusion, Julius is correct that it will take less time for them to mow the lawn when working together.
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2x + 3 = 23 steps for x?
Answer:
x=10
Step-by-step explanation:
work in the photo
Answer:
x=10
Step-by-step explanation:
Subtract 3 from both sides
2x=23-3
Simplify 23-3 to 20
2x=20
Divide both sides by 2
x= 2 0/2
Simplify 20/2 to 10
x=10
Page 2. Consider the shaded region R which lies between y=0, y = 3r, and r=3. 1 Using either method, set up the integral that represents the volume of the solid formed by revolving the region R about
To set up the integral that represents the volume of the solid formed by revolving the shaded region R about an axis, we can use the method of cylindrical shells.
First, let's visualize the region R. It lies between the lines y = 0 and y = 3r, and the line r = 3. Since r = 3 is a vertical line, it represents a cylindrical boundary for the region.
Next, we need to determine the limits of integration for both the height and the radius of the cylindrical shells.
For the height, we can see that the region R extends from y = 0 to y = 3r. Since r = 3 is the upper boundary, the height of the shells will vary from 0 to 3(3) = 9.
For the radius, we need to find the distance from the y-axis to the line r = 3 at each y-value. We can do this by rearranging the equation r = 3 to solve for y: y = r/3. Thus, the radius at any y-value is given by r = y/3.
Now, we can set up the integral for the volume using the formula for the volume of a cylindrical shell:
V = ∫[a,b] 2πrh(y) dy,
where r is the radius and h(y) is the height of the cylindrical shell.
Plugging in the values we determined earlier, the integral becomes:
V = ∫[0,9] 2π(y/3)(9 - 0) dy
= 2π/3 ∫[0,9] y dy
Evaluating this integral gives us the volume of the solid formed by revolving the region R about the specified axis.
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Please help this is due tomorrow help
Answer: $4.50
Step-by-step explanation:
6+6+3.5= 15.5 paid with a 20 so 4 dollars and 50 cents change
Answer:
Step-by-step explanation:
Since Aiden paid only the admission price not the skate rental price soo..
3.50 for himself and 6*2 =12 for his friends
3.50+12=15.50
20-15.50 = 4.50 in change :)
Your family is driving to the mountains for the weekend You travel 200 kilometers in the first two hours during the next hour you stop for lunch and only travel 25 kilometers. What is your average speed. Can you please use (D=st)
Answer: (D= 87.5 kilometers per hour)
Step-by-step explanation: First, divide 200 by 2, which equals to 100. Next, divide 25 by 2, which is 12.5. Lastly, subtract 100 minus 12.5, which equals 87.5. You should end up with a result of (D= 87.5 kilometers per hour).
Mark invests $500 on a saving plan.The bank pays 5% interest each year on his investment. How much interest will he have after 2 years? (40 points NEED HELP WITH WORK PLS)
Answer:
551
Step-by-step explanation:
5% of 500 25
5 of 525 26.25
525+26.25
551.25
Sine interest formula: total = start amount x 1 + interest rate x time)
Total = 500 x (1+ 0.05 x 2)
Total = $550
Interest = 550 - 500 = $50
What is the measure of
∠1 if
∠1 is (8x)
∘ and
∠2 is (2x - 3)
∘?
∠1 + ∠2 = 180
Substituting the given expressions for ∠1 and ∠2:
8x + (2x - 3) = 180
Simplifying and solving for x:
10x - 3 = 180
10x = 183
x = 18.3
Now we can substitute x back into the expression for ∠1 to find its measure:
∠1 = 8x = 8(18.3) = 146.4 degrees.
Therefore, if ∠1 and ∠2 add up to 180 degrees and ∠1 is given as 8x° and ∠2 is given as (2x - 3)°, then ∠1 measures 146.4 degrees
Answer:
<1=146.4
<2=34.6
Step-by-step explanation:
<1+<2=180 degrees
So,
8x+(2x-3)=180
10x-3=180
10x=183
X=18.3
subsitute:
<1=8x
<1=8(18.3)
<1=146.4
<2=2x-3
<2=2(18.3)-3
<2=34.6
The Watkins family is trying to decide which kind of in-ground pool to install. They are determining whether to put in a saltwater pool or a basic chlorine pool. The graphs below model the average annual cost of owning each type of pool after t years.
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do you know?
The chlorine pool is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
The saltwater pool is more cost effective because the y-value at 10 years is less on graph A than it is on graph B.
They would be equally cost effective because the vertical asymptotes for each graph are the same.
They would be equally cost effective because the horizontal asymptotes for each graph are the same.
Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.
As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.
When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.
Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
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Answer:
a
Step-by-step explanation:edge
For every 1000 hits a You Tube channel gets it makes £40 from ad revenue. How many hits will the You Tube channel need to make £1?
Answer:
25 hits
Step-by-step explanation:
you would divide 1000 by 40 and get 25
find : a 1/2 of i 2 3/4 ii 4 2/9
1) 2 3÷4 = 11÷4
hence, 11÷8 = 1.37 .
2) 4 2÷9 =38÷9 .
hence, 38÷18 = 2.11 .
simplify 2 3÷4 = 11÷4
and
4 2÷9 = 38÷9.
now 1/2 of 11/4 = 11/8 = 1.37.
1/2 of 38/9 = 38/18 = 2.11 .
PLS HELP! DUE TODAY WILL MARK BRAINLIEST
3. Find the measure of arc JK
Hint - arc LK is a semi-circle!
Find arc JK.
A) 90
B) 116
C) 128
D) 130
Answer:
KJ = 128°
Step-by-step explanation:
JL = 2×26 = 52°
KL= KJ + JL
KJ = KL-JL
KJ = 180° - 52°
KJ = 128°
A theater has 1,464 seats. The seats are arranged into 62 equal-sized "regular" sections plus one "premium" front-row section. How many seats are in a regular section? How many seats are in the premium front-row section? Explain.
In the theater, that have 1,464 seats.
1426 seats are in "regular" sections
38 seats are "premium" front-row section
How to find the number of seats in the "regular" sectionsThe seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient
The division is as follows
1464 / 62
= 23 19/31
The number of seats in the regular section is 23 * 62 = 1426
The remainder will be arranged in premium front row
using equivalent fractions
19 / 31 = 38 / 62
the remainder is 38 and this is the seat for the premium front row section
OR 1464 - 1426 = 38 seats
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The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $356 to drive 380 mi and in June it cost her $404 to drive 620 mi. The function is C(d)=0.2+280 (b) Use part (a) to predict the cost of driving 1800 miles per month. (c) Draw a graph (d) What does the slope represent? What does the C-intercept represent? Why does a linear function give a suitable model in this situation?
(b) $640 (c) y-int of 280, positive slope (d) It represents the cost (in dollars) per mile. It represents the fixed cost (amount she pays even if she does not drive). A linear function is suitable because the monthly cost increases as the number of miles driven increases.
To predict the cost of driving 1800 miles per month, substitute 1800 in the given function C(d) = 0.2d + 280C(1800) = 0.2 (1800) + 280= $640 per month. Therefore, the cost of driving 1800 miles per month is $640.
(b) Graph is shown below:(c)The slope of the graph represents the rate of change of the cost of driving a car per mile. The slope is given by 0.2, which means that for every mile Lynn drives, the cost increases by $0.2.The y-intercept of the graph represents the fixed cost (amount she pays even if she does not drive).
The y-intercept is given by 280, which means that even if Lynn does not drive the car, she has to pay $280 per month.The linear function gives a suitable model in this situation because the monthly cost increases as the number of miles driven increases.
This is shown by the positive slope of the graph. The fixed cost is also included in the function, which is represented by the y-intercept. Therefore, a linear function is a suitable model in this situation.
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did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle?
∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.
We are given that:
AB = BC
Now, draw a angle bisector from point B to the line AC in a way that it intersects AC at D.
Now, we get that:
∠ABD = ∠CBD ( BD is the angle bisector)
BD = BD ( common line)
So, ΔABD ≅ Δ CBD ( SAS property)
So,
∠A = ∠ C ( CPCT rule)
Also, it will be true for every isosceles triangle.
Therefore, we get that, ∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.
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Your question was incomplete. Please refer the content below:
There is an isosceles triangle with AB = BC. Prove that ∠A = ∠C.
Did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle.
PLEASE HELP!!!!
When using the Desmos graphing calculator to find the least-squares regression line for the data below, what do you type in as the expression to generate the parameters and statistics?
x subscript 2 baseline y subscript 2 baseline
1 2
2 9
3 7
4 12
y subscript 2 baseline tilde m x subscript 2 baseline plus b
y subscript 2 baseline equals m x subscript 2 baseline plus b
y tilde m x plus b
y = mx + b
Given: The Table of Values
To Find: The least-squares regression line for the data set in the table by using the desmos graphing calculator.
SolutionThe general form of least-squares regression line is: y = mx + b Where, m is the slope and b is the y-intercept.
Where, m is the slope and b is the y-intercept.By using the desmos graphing calculator, we get
m 2.55 b -6.435 Substitute these Values
y = (2.55)x + (-6.435)
y = 2.55x - 6.435
Answer: A
The expression to generate the parameters and statistics is y tilde m x plus b, the correct option is C.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
x subscript 2 baseline y subscript 2 baseline;
1 2
2 9
3 7
4 12
Now,
To find the least-squares regression line for a data set using Desmos, you need to follow these steps:
Enter the data as a table in Desmos. For example, type {1, 2, 3, 4} in the x column and {2, 9, 7, 12} in the y column.
Type y tilde m x plus b in the expression box. This tells Desmos to find the values of m and b that minimize the sum of squared errors between y and y tilde (the predicted values).
Click on the wrench icon next to the expression to see the parameters and statistics. You should see something like this:
m = 2.8 b = -1.6 r² = 0.84
This means that the equation of the least-squares regression line is:
y tilde = 2.8 x - 1.6
And that the coefficient of determination (r²) is 0.84.
Therefore, by expression the answer will be y tilde m x plus b.
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Please help I am being timed!
Solve
7k – 8 = 28 + 24k
A. -2 2/17
B. -2
C. -1 5/31
D. 1 3/17
Sorry if this is easy I'm bad at math
(02.01 LC) Each person in a simple random sample of 1,200 received a survey, and 325 people returned their survey. How could nonresponse cause the results of the survey to be biased?
The volume of a fish tank is 30 cubic feet. if the density is 0.3fish over feet cubed, how many fish are in the tank? 100 10 9 3
Number of fishes in the tank are 9.
Given
Density (d)= 0.3 fish/ft³
Volume of a fish tank (V) = 30 ft³
number of units(n)= ?
Density, mass of a unit volume of a material substance. The formula for density is d = n/V, where d is density, n is quantity(number of units), and V is volume. Density is commonly expressed in units of grams per cubic centimetre.
d = n/V
d = n/V
n = d * V
n = 0.3 fish/ft³ * 30 ft³
number of units(n) = 9
Hence,
Number of fishes in the tank are 9.
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Answer: The correct answer is (c) 9.
Step-by-step explanation:
0.3 x 30 = 9
The ratio of men to women working for a company is 3 to 5. If there are 152 employees total, how many women work for the company?
Answer:
38
Step-by-step explanation:
mhmm
. Classify the relationship between the pair of angles. ∠10 and ∠12.
Answer: consecutive interior angles
Step-by-step explanation:
f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).
Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
Step-by-step explanation:
To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:
-x² + 5 = -2x + 2
Expanding the right-hand side:
-x² + 5 = -2x + 2
-x² + 2x + 3 = 0
Solving for x using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 2, and c = 3
x = (-2 ± √(2² - 4(1)(3))) / 2(1)
x = (-2 ± √(4 - 12)) / 2
x = (-2 ± √(-8)) / 2
Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
3 Consider the line y= 3/4x+3. Find the equation of the line that is perpendicular to this line and passes through the point (-8, 6).
ANSWER
\(y\text{ = -}\frac{4}{6}x\text{ - }\frac{14}{3}\)EXPLANATION
We have to find the equation of the line perpendicular to the given line:
\(y\text{ = }\frac{3}{4}x\text{ + 3}\)and passes through the point (-8, 6)
A line perpendicular to another line has a slope that is the negative inverse of the line.
The slope of the given line is 3/4, so the slope of the line we are looking for is -4/3
Now, we use the point slope method to find the equation:
y - y1 = m(x - x1)
where m = slope
(x1, y1) = point the line passes through
So, we have:
\(\begin{gathered} y\text{ - 6 = -}\frac{4}{3}(x\text{ - (-8))} \\ y\text{ - 6 = -}\frac{4}{3}(x\text{ + 8)} \\ y\text{ - 6 = -}\frac{4}{3}x\text{ + (-}\frac{4}{3}\cdot8) \\ y\text{ - 6 = -}\frac{4}{3}x\text{ - }\frac{32}{3} \\ \Rightarrow\text{ y = -}\frac{4}{3}x\text{ - }\frac{32}{3}\text{ + 6} \\ y\text{ = -}\frac{4}{6}x\text{ - }\frac{14}{3} \end{gathered}\)That is the equation of the line.
i’m lost on this help would be nice
Answer:
3x - 4 = 14
+4. +4
3x = 18
÷3. ÷3
x = 6
21 and 22 are complementary
angles. The measure of Z1 is (2x + 7)º.
The measure of Z2 is (3x + 58)°. What
is the value of x?
What are the two requirements that make a Polygon?
Answer: Radeon R9 390 graphics card with a Core i5-2300 2.8GHz or FX-6350 processor
Step-by-step explanation:
Answer:
Equiangular and Equilateral
Step-by-step explanation:
I tried
The gcf of 18,36 and me is 2.
I am a multiple of 5
I am greater than 18 and less than 30
Based on the information provided, the only possible number that satisfies all the conditions is 20.
What is GCF?
GCF stands for "Greatest Common Factor". It is also sometimes referred to as the "Greatest Common Divisor" (GCD). The GCF of two or more numbers is the largest positive integer that divides evenly into each of the numbers. In other words, it is the largest factor that the numbers have in common.
The GCF (Greatest Common Factor) of 18, 36, and a number N is 2. Since 18 and 36 are both even numbers with a common factor of 2, any number that satisfies this condition must also be even and have a factor of 2.
The number N is a multiple of 5. Since the number is even and has a factor of 2, the only even multiple of 5 between 18 and 30 is 20.
Finally, we are given that N is greater than 18 and less than 30. The only number that satisfies all the given conditions is therefore 20.
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A bakery asked its customers to name their favorite bread. Wholewheat crunch was
the favorite of 3/5 of the customers. What percent of the customers said whole-wheat crunch was their favorite bread?
Answer: use a cucumber
Step-by-step explanation:
Dr. Tyler’s team is in charge of marking the hooved animals. The table shows the data collected on all the marked hooved animals. In terms of the number of moose, what is the relative frequency of male moose, female moose, adult moose, and baby moose? Write your answers as simplified fractions.Elk Mountain Goat Deer Moose Male 105 71 42 52 Female 120 93 63 34 Adult 173 103 72 58 Baby 52 61 33 28
Answer:
Male elk:
7/30
Female elk:
4/15
Adult elk:
173/450
Baby elk:
26/225
The relative frequency of male elk is 7/30, female elk is 4/15, adult elk is 173/450, and baby elk is 26/225.
What is Relative Frequency?Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.
Dr. Tyler’s team is in charge of marking the hooved animals.
The table shows the data collected on all the marked hooved animals.
Male 105 71 42 52
Female 120 93 63 34
Adult 173 103 72 58
Baby 52 61 33 28
The relative frequency of male elk, female elk, adult elk, and baby elk is given by;
\(\rm Male \ Elk =\dfrac{105}{105+120+173+52} =\dfrac{105}{450}=\dfrac{7}{30}\\\\Female \ Elk =\dfrac{120}{105+120+173+52} =\dfrac{120}{450}=\dfrac{4}{15}\\\\Adult\ Elk =\dfrac{173}{105+120+173+52} =\dfrac{173}{450}\\\\Baby \ Elk=\dfrac{52}{450}=\dfrac{26}{225}\)
Hence, the relative frequency of male elk is 7/30, female elk is 4/15, adult elk is 173/450, and baby elk is 26/225.
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Hurry please!!!!
Which type of transformation is described by (x, y) + (x+2, y+3)?
(А)
a translation 2 units to the right and 3 units down
(В
a translation 2 units to the left and 3 units down
a translation 2 units to the right and 3 units up
D
a translation 2 units to the left and 3 units up
(x, y) → (x+2, y+3) means a translation 2 units to the right and 3 units up.
What is transformation?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
here, we have,
Given the rule of transformation:
(x, y) → (x+2, y+3)
If we move horizontally 2 units to the right, 2 is added to the x-coordinate of any given point, and then 3 units up.
In other words,
(x, y) → (x+2, y+3) means Translation 2 units right and 3 units up.
For example,
Let say if we have the point A(4, 5)
Using the translation rule:
(x, y) → (x+2, y+3)
A(4, 5) → A'(4 + 2, 5 + 3) → A'(6, 8)
Therefore, the new position of A(4, 5) after translating 3 units right and 2 units up would be: A'(6,8).
Hence, (x, y) → (x+2, y+3) means a translation 2 units to the right and 3 units up.
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QUESTION 8 We will define a checkerboard matrix to be a square matrix A = (aj), where if i + j is even dij = if i + j is odd 8.1 Write out the 4x4 checkerboard matrix. 8.2 Find the basis for the nullspace of A, and the nullity and rank of A. 8.3 What will be the rank and nullity of the 17x17 checkerboard matrix?
The 4x4 checkerboard matrix is constructed with alternating 1s and 0s based on the position of the elements. The basis for the nullspace of the checkerboard matrix is found, and its nullity and rank are determined. Additionally, the rank and nullity of a 17x17 checkerboard matrix are determined.
8.1 To construct the 4x4 checkerboard matrix, we assign values based on the parity of the row and column indices. If the sum of the row index (i) and column index (j) is even, the element (aij) is 1. Otherwise, if the sum is odd, the element is 0. The resulting 4x4 checkerboard matrix is:
A = |1 0 1 0|
|0 1 0 1|
|1 0 1 0|
|0 1 0 1|
8.2 to find the basis for the nullspace of A, we need to solve the equation Ax = 0, where x is a vector. By performing row operations on the matrix, we can bring it into row-echelon form:
|1 0 1 0|
|0 1 0 1|
|1 0 1 0|
|0 1 0 1|
Row 3 - Row 1:
|1 0 1 0|
|0 1 0 1|
|0 0 0 0|
|0 1 0 1|
Row 4 - Row 2:
|1 0 1 0|
|0 1 0 1|
|0 0 0 0|
|0 0 0 0|
The reduced row-echelon form shows that the last two rows are dependent on the first two rows. Therefore, the basis for the nullspace is the vector {(-1, 1, -1, 1)}. The nullity of A, which is the dimension of the nullspace, is 1.
The rank of A is the number of linearly independent rows, which in this case is 2.
8.3 The rank and nullity of the 17x17 checkerboard matrix can be determined using the same approach. Since the matrix is larger, it is not feasible to write it out here. However, we can observe a pattern based on the size of the matrix. For an n x n checkerboard matrix, if n is even, the rank will be n/2 and the nullity will also be n/2. If n is odd, the rank will be (n + 1)/2 and the nullity will be (n - 1)/2.
Therefore, for the 17x17 checkerboard matrix, the rank will be (17 + 1)/2 = 9, and the nullity will be (17 - 1)/2 = 8.
In summary, the basis for the nullspace of the 4x4 checkerboard matrix is {-1, 1, -1, 1}, resulting in a nullity of 1 and a rank of 2. For the 17x17 checkerboard matrix, the rank is 9, and the nullity is 8.
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