[tex]f(x) = x^2 +x (2a+2b) +4ab-x\\\\f'(x) = 2x+x \cdot 0 + 2a+2b + 0 -1\\\\~~~~~~~~=2x+0+2a+2b-1\\\\~~~~~~~~=2x+2a+2b-1[/tex]
From the definition of the derivative,
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]
We have
[tex]f(x) = x^2 + x(2a+2b) + 4ab - x = x^2 + (2a+2b-1)x + 4ab[/tex]
and so
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{\left((x+h)^2 + (2a+2b-1)(x+h) + 4ab\right) - \left(x^2 + (2a+2b-1)x + 4ab\right)}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{x^2 + 2xh + h^2 + (2a+2b-1)x + (2a+2b-1)h + 4ab - x^2 - (2a+2b-1)x - 4ab}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{2xh + h^2 + (2a+2b-1)h}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} (2x + h + 2a+2b-1)[/tex]
[tex]\displaystyle f'(x) = \boxed{2x + 2a + 2b - 1}[/tex]
Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches.He cuts out another rectangle that is the same length and twice as wide. What is the perimeter of the new rectangle.
Answer:
66 inches
Step-by-step explanation:
perimeter = 2(l+b)
here, perimeter is 50 and length is 17
let the width be x,
=> 50 = 2(17+x)
=> 50 = (2*17)+(2*x)
=> 50 = 34 + 2x
=> 50 - 34 = 2x [transposing method]
=> 16 = 2x
=> 16/2 = x
=> 8 = x
8 inches = width of the first triangle
we know, the other rectangle's length is 17
and it is said that the width is twice the width of the first triangle
so the length = 17, width = 2*8 = 16
for the perimeter
p = 2(l+b),
=> p = 2(17+16)
=> p = (2*17)+(2*16)
=> p = 34+32
=> p = 66
so the perimeter of the other rectangle is 66
Answer:
66
Step-by-step explanation:
that answer was incorrect. change your answer and try again!
Select the correct answer.
Consider the piecewise function shown on the graph.
Over which interval of the domain does the graph represent an exponential function?
A. x ≥ 6
B. -3 ≤ x ≤6
C. x ≥ 1
D. -4 < x ≤ 1
Answer:
The answer is D I hope this helps
The required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.
Given that,
A graph of a function is shown that has 3 distinct functions for its domain, we have to determine which of these 3 functions shows an exponential function.
The function which is in format f(x) = where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Since, as we can see throughout the graph the graph constantly decreases to -4 and then shows a parabolic function from -4 to 0.9 afterward it starts increasing exponentially.
Thus, the required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.
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What is the Area of the circle in pi units if the diameter is 6 cm?
Answer:
9π cm
Step-by-step explanation:
Given diameter of circle (d) = 6cm
radius (r) = d/2 = 6/2 = 3cm
Area of circle = πr²
= π × 3²
= π × 9
= 9π
The area of the circle in pi units when the diameter of this circle is 6 centimeters is 9π centimeters.
What is the area of the circle?
The area of the circle is the space occupied by it. It is the product of pi and square of its diameter divided by 4. The area of the circle can be given as,
[tex]A=\pi\dfrac{d^2}{4}[/tex]
Here (d) is the diameter of the circle. The diameter of the circle is 6 cm.
[tex]d=6[/tex]
Put this value in the above formula to find the area of the circle as,
[tex]A=\pi\dfrac{6^2}{4}\\A=\pi\dfrac{36}{4}\\A=\pi\times9\\A=9\pi\rm\; cm[/tex]
Thus, the area of the circle in pi units when the diameter of this circle is 6 centimeters is 9π centimeters.
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5. A pyramid with a triangular base has a volume of 80 cubic meters and a base
area of 20 square meters. Find the height of the pyramid.
The height of the triangular pyramid will be equal to H=12 feet.
What is a triangular pyramid?A triangular pyramid is a pyramid having triangular faces the other sides of the pyramid are simliar triangles.
It is given that:-
The Volume of the pyramid=80 cubic meters
The Base area of the pyramid=20 square meters
The height of the pyramid=?
We know that the volume of a pyramid is given as:-
V=(1÷3)x Base area x height
V=(1÷3)x20 x H
H=(80x30)÷20
H=12 feet
Hence the height of the triangular pyramid will be equal to H=12 feet.
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[tex]\log _ { 5 } ( 2 m + 5 ) = 3log5(2m+5)=3[/tex]
solution needed
with briefly explained
Answer:
m = 60
Step-by-step explanation:
log is another way to write an exponent.
Example:
exponent form:
7^2 = 49
log form:
log_7 (49) = 2
In your question, we need to change to exponent form, from log form.
log_5 (2m+5)=3
5 is the base. 3 is the exponent.
Now it can be solved.
5^3 = 2m+5
125 = 2m + 5
120 = 2m
60 = m
What is the area of the composite figure?
500
490.62
245.31
745.31
Answer:
745.31
Step-by-step explanation:
20x25=500
(2(12.5)pie)/2=245.435
245.435+500=745.31
6. The circular floor carpet has an area of 484π in? What is the radius of the floor carpet?
Which is a graph of =3−1 y = 3 x - 1 ?
Answer:
The one on the top right
Step-by-step explanation:
first, look at the y-intercept:
two of the graphs (top-right and bottom-left) have the correct y-intercept of (0, -1).
(The y-intercept is 0 and then the last term of the equation in this form)
next, look at the slope:
slope is in the form of rise/run
the slope for this equation is 3, or 3/1
so look at the graphs, find the y-intercept point and go up three cells and over one.
Only one of the graph's lines goes through this point, and that is the top-left one
Quickly Help will make you brainliest These figures are congruent. What series of transformations moves
quadrilateral ABCD onto quadrilateral A'B'C'D'?
y
-8 4
8
B
A
-8
Note: Rotations are clockwise. Reflections are over the x- or y-axis.
G
8
4
+
D
B
A
4
C
D'
X
The series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is C. reflection, translation.
What is transformation?It should be noted that transformation simply means the movement of object in a coordinate plane.
The common type of transformation in mathematics include translation, rotation, reflection, and dilation.
Here, the series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is reflection, and translation. Reflection is flipping the pre image and producing the mirror image while translation is movement of the pre image
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Answer:
A
Step-by-step explanation:
Tony walks 1/3 of a mile to school each day. He also walks home from school. How many miles will he have walked in one five-day school week?
Answer:
3 1/3 miles per five day weekAeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison.
How many unique random numbers need to be selected from the table of random digits?
3
400
800
1,200
The number of unique random numbers that need to be selected from the table of random digits will be A. 3.
What is a random number?It should be noted that a random number simply means a number that occurs when it is impossible to predict it.
From the information given, there are 1200 subjects and there are three treatments. In order to get treatment number, there must be three unique random numbers.
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What is the answer to the problem 20.754 - 14.526
Answer:
6.228
Step-by-step explanation:
There are 6 swimmers in a race. In how many ways can they finish in first and second place?
-12
-30
-120
-360
Answer:
step 1. 6x2=12 first place way
step 2. 12×2=24
step 3. 24+6=30 second place way
Jillian and Dawn are playing a game of miniature golf. In this game, the score on a hole is the number of putts it takes to get the ball into the hole. The winner is the player with the lowest score. After playing 18 holes, Jillian’s mean is 2.4 and Dawn’s mean is 3.3. Which explains who won the game?
Jillian won the game because her score varied less than Dawn’s score.
Jillian won the game because the person with the lower mean took fewer putts on average for each hole.
Dawn won the game because the person with the greater mean played better.
Dawn won the game because her mean absolute deviation was less than Jillian’s.
Answer:
Step-by-step explanation:
Discussion
This should be answered with the mean. The lower the mean, the lower the score it took to get the mean. So B is the answer.
IT IS B OK LETS GO YES
Suppose that two lines, AB and CD, are intersected by a transversal.
Which of the following reasons alone could be used to show that the lines are parallel?
Answer: A, B
Step-by-step explanation:
A and B are unique to parallel lines, C and D are not.
Consider the following geometric sequence 2,6,18,54
Answer:
Multiply the number by 3 to get the next number.
Step-by-step explanation:
Kristy incorrectly says
that the volume of the sphere below is
144T cubic units. What mistake might Kristy
have made?
The mistake that Kristy made in calculating the volume is that she treated it as a hemisphere instead of a Sphere.
How to find the Area of a Sphere?We are given the volume of the sphere as 144π cubic units.
From the attached file, we see that the radius of the sphere is 6.
Formula for Volume of a Sphere is;
V = ⁴/₃πr³
Thus;
V = ⁴/₃π * 6³
V = 288π cubic units
Thus, the mistake that Kristy made in calculating the volume is that she treated it as a hemisphere instead of a Sphere.
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the ohitcome of a single trial of a random experiment. Compute the probability of each of the following events. 00 Event A: The sum is greater than 9. Event B: The sum is not divisible by 6. Write your answers as fractions.
Answers:
P(A) = 1/6
P(B) = 5/6
=========================================================
Explanation:
Let's calculate P(A).
Refer to the dice chart below.
We have
3 copies of "10"2 copies of "11"1 copy of "12"There are 3+2+1 = 6 sums that are greater than 9.
This is out of 6*6 = 36 sums total
P(A) = 6/36 = (1*6)/(6*6) = 1/6
----------------------
Now to calculate P(B).
The multiples of 6 in the table are: 6, 12
There are 5 copies of "6"There is 1 copy of "12"There are 1+5 = 6 items that are a multiple of 6. This means we have 36-6 = 30 sums that aren't a multiple of 6
P(B) = 30/36 = (5*6)/(6*6) = 5/6
Side note: it's probably coincidence that P(A)+P(B) = 1 in this case.
Examine the following PSA How is the creator of this PSA sharing a viewpoint about the importance of reading? by providing a strategy for encouraging kids to read more often by showing what will happen if people do not read frequently by highlighting one of the benefits that comes from reading by featuring a specific fact about the importance of reading
The statement third “by highlighting one of the benefits that comes from reading” is correct.
What is reading?Reading is a thinking process that entails interpreting words in deriving information.
We have statements about the importance of reading:
by providing a strategy for encouraging kids to read more often.by showing what will happen if people do not read frequently.by highlighting one of the benefits that comes from reading.by featuring a specific fact about the importance of reading.According to the PSA, the correct statement about the importance of reading is by highlighting one of the benefits that comes from reading.
Thus, the statement third “by highlighting one of the benefits that comes from reading” is correct.
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Answer:
C
Step-by-step explanation:
Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
To choose the three players fairly, Coach Bennet decides to set up a free throw contest. The three players who make the most consecutive free throws will get to go to the summer basketball clinic.
How many different orders of top-three finishers are possible?
Drag the tiles to the correct locations on the equation. Not all tiles will be used.
Answer:
nCr = 14!/3!11! =364
Step-by-step explanation
line pass through the line (-3, -7.5)tahila determined that the equation of line n is y=0.5x explain the error tahila made while dterming her equation and include the correct equation in your answer
The equation of the line will be (assuming the y-intercept equal to zero):
y = 2.5*x
What is Tahila's mistake?
We know that we have a linear equation of the form:
y = a*x + b
Such that we know that the line passes through (-3, -7.5), notice that the proposed equation is:
y = 0.5*x
If you evaluate that in -3, you get:
y = 0.5*-3 = -1.5
So this line does not pass through (-3, -7.5).
If we assume that b = 0 in the linear equation, then we can find the value of a as:
-7.5 = a*-3
a = 7.5/3 = 2.5
Then the linear equation is:
y = 2.5*x
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a drawing of a room has a scale of 1 inch = 4 feet. if the actual dimensions of the room are 14 feet by 16 feet. what are the dimesnsions of the room o on the drawing
Answer:
3.5 inches by 4 inches
Step-by-step explanation:
please help awnser this question correctly
laura cuts a square out of scrap paper. what is the angle measure of the piece left over?
HURRY UP I NEED THIS ANSWER BEFORE 12:30!!!
Answer:
I would be a right angle or 90°
Explanation:
If a square is cut out of the paper, every corner of a square is a right angle, so there's your answer.
hope i helped :)
In 2012, the population of all of the people on Earth was approximately seven billion. Write the population in scientific notation.
Answer:
7 × 10^9 (that 9 is a exponent)
Step-by-step explanation:
hELP ME PLSSSSSSSSSSSSSSSS!!!
Someone please help me!?
Answer:
rise is 11 and run is 2
Step-by-step explanation:
i believe but not fully sure
Answer:
5.5
Step-by-step explanation:
Line is passing through the points (1, 0) and (3, 11)Slope of line [tex]=\frac{11 -0}{3-1}[/tex]Slope of line [tex]=\frac{11}{2}[/tex]Slope of line [tex]=5.5[/tex]please solve quickly
If a student is selected randomly, the probability that the student is a junior given that the student is male is 14%.
What is the probability?Probability determines the odds that an event would happen. The odds of the event happening lie between 0 and 1.
p (Junior | Males) = number of males that are junior / total number of males
2 / (4 + 6 + 2 + 2 ) = 2/14 x 100 = 14%
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Find the quotient 16)4.88
Answer:
if this is 4.88/16 then the answer is 0.305.
Sadie earns $11.25 per hour. Do her earnings vary inversely or directly with
her number of hours worked? Determine how many hours she worked in a
week if her earnings were $146.25.
Division is one of the four fundamental arithmetic operations. The number of hours Sadie worked to earn $146.25 is 13 hours.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given Sadie earns $11.25 per hour. Therefore, it can be concluded that her earnings vary varies directly with the number of hours she worked.
The number of hours she worked to earn $146.25 is,
The Number of hours = ($146.25)/($11.25) = 13 hours
Hence, the number of hours Sadie worked to earn $146.25 is 13 hours.
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