Answers
Answer
[tex]f^{\prime}(x)=6(x+1)(x^{2}+2x+7)^{2}[/tex][tex]f^{\prime}(1)=1200[/tex]Explanation
Given
[tex]f\mleft(x\mright)=(x^2+2x+7)^3[/tex]To find the derivative, we have to apply the chain rule:
[tex][u(x)^n]^{\prime}=n\cdot u(x)^{n-1}\cdot u^{\prime}(x)[/tex]Considering that in our case,
[tex]u(x)=x^2+2x+7[/tex][tex]u^{\prime}(x)=2x+2+0[/tex]and n = 3, then:
[tex]=3\cdot(x^2+2x+7)^{3-1}\cdot(2x+2)[/tex]Simplifying:
[tex]f^{\prime}(x)=3\cdot2(x+1)(x^2+2x+7)^2[/tex][tex]f^{\prime}(x)=6(x+1)(x^2+2x+7)^2[/tex]Finally, we have to replace 1 in each x in f'(x) to find f'(1):
[tex]f^{\prime}(1)=6((1)+1)((1)^2+2(1)+7)^2[/tex][tex]f^{\prime}(1)=6(1+1)(1+2+7)^2[/tex][tex]f^{\prime}(1)=6(2)(10)^2[/tex][tex]f^{\prime}(1)=6(2)(100)[/tex][tex]f^{\prime}(1)=12(100)[/tex][tex]f^{\prime}(1)=1200[/tex]Related Questions
A graph has age (weeks) on the x-axis, and height (inches) on the y-axis. Points are grouped closely together. One point is outside of the cluster. Which statement is true? There is no relationship between the height of the plant and its age. Although the outlier is an extreme value, it should be included in the interpretation. By excluding the outlier, a better description can be given for the data set
Answers
Answer:
Step-by-step explanation:
The answer is C
Answer:All three 1. to compare groups, not individuals2. to lessen the influence of outliers3. to clearly see trends
Explanation:edge 2022
The heights, in feet, of 12 trees in a park are shown below.8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47Use the drop-down menus to explain the interquartile range of the data.
Answers
Given:
The heights, in feet, of 12 trees in a park are:
8,11,14,16,17,21,21,24,27,31,43,47.
Required:
To find the interquartile range of the given data.
Explanation:
We have given the heights of 12 trees in feet.
Therefore, the total number of quantitties (elements) in given data is even.
Thus, the median (M) of the data is,
[tex]\begin{gathered} M=\frac{21+21}{2} \\ \Rightarrow M=\frac{42}{2} \\ \Rightarrow M=21 \end{gathered}[/tex]The median (Q) of the first half of the data 8,11,14,16,17 is given by,
[tex]Q=14[/tex]since the number of quantities are odd.
The median (Q') of the second half of the data 24,27,31,43,47 is given by,
[tex]Q^{\prime}=31[/tex]since the number of quantities are odd.
Hence, the interqurtile range (R) is,
[tex]\begin{gathered} R=Q^{\prime}-Q \\ \Rightarrow R=31-14 \\ \Rightarrow R=17 \end{gathered}[/tex]Final Answer:
The interquartile range is,
[tex]R=17[/tex]The first option is spread.
The second option is range.
The third option is 17.
The fourth option is middle 50%.
which point lies on the wall with point slope equation y+5=2(x+8)
Answers
The slope intercept form of equation is given as
(y - y1) = m(x - x1)
Where m = slope
From the equation: y + 5 = 2(x + 8)
Equate y + 5 = 0 and x + 8 = 0
y + 5 = 0
y = 0- 5
y = -5
For x + 8 = 0
x + 8 = 0
x = 0 - 8
x = -8
Hence, the point is (-8, -5)
The answer is (-8, -5)
in the diagram the figures are simular, what is x?triangle with 30cm and 13cmtriangle with 24cm and x
Answers
If the figures are similar, the proportion between the corresponding sides is the same.
The side of 30 cm corresponds to the side of 24 cm, and the side of 13 cm corresponds to the side of x cm.
So if the proportion is the same, we have that:
[tex]\begin{gathered} \frac{30}{24}=\frac{13}{x} \\ 30\cdot x=24\cdot13 \\ x=\frac{24\cdot13}{30}=\frac{4\cdot13}{5}=\frac{52}{5}=10.4 \end{gathered}[/tex]So the value of x is 10.4 cm, therefore the answer is b.
A string that is 10 1/2 feet long is cut into 3 equal pieces. How long is each piece?
Answers
Answer:
3½
Step-by-step explanation:
10½=21/2
since it is cut into 3 pieces we can as well said it is divided into 3
21/2 divide 3
21/2 / 3/1
21/2 ×1/3
=7/2
=3½
please rate as brainliest
Answer:
The answer is 3.5
Step-by-step explanation:
Why?
Because since we know we have to divide the measurement of the string with the amount of pieces which will be
= 10 1/2 divided by 3
How long is each piece= 3.5
So that means each piece is 3.5
Hope this answers your question!
4) Math Club members want to advertise their fundraiser each week in the school paper. They knowthat a front-page ad is more effective than an ad inside the paper. They have a $30 advertisingbudget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertiseat least 20 times. a) Write and graph a system of inequalities to model the number of advertisements the club canpurchase to stay under budget. Be sure to label all parts of your graph.b) State one solution that would work. How much money will remain in the club's budget?
Answers
Problem:
Math Club members want to advertise their fundraiser each week in the school paper. They know that a front-page ad is more effective than an ad inside the paper. They have a $30 advertising budget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertise at least 20 times.
a) Write and graph a system of inequalities to model the number of advertisements the club can purchase to stay under budget. Be sure to label all parts of your graph.
Solution:
Let us denote the number of front-page ads by x, and the number of inside ads by y:
x = number front-page ads
y= number of inside ads
Now, because they have a $30 advertising budget and It cost $2 for each front-page ad and $1 for each inside page ad, the first inequality that we have is:
[tex]2x+\text{ y }\leq30[/tex]If we represent the graph of the equality (line) 2x+y = 30, we have:
On the other hand, because the club wants to advertise at least 20 times, the second inequality that we have is:
[tex]x+y\ge20[/tex]If we represent the graph of the equality (line) x+y = 20, we have:
Now, the intersection point of the above lines, that is 2x+y = 30 and x+y = 20 is found as follows:
we have
y = 30 - 2x
and
y = 20-x
then
30-2x = 20-x
and
30-20 = 2x-x
that is
10 = x
when x = 10 then y = 20-x = 20-10 = 10
what is the answer help pls
Answers
Answer:
1 ½ feet
Step-by-step explanation:
The shortest lizard is ½ a feet
The longest lizard is 2 feet
To find the difference in length:
2-½ = 1½ feet
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year. When will the sharks be equal in length? Let x = time in years Let y = length of the sea creatures
Answers
In 20 years the length of shark will be equal.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year.
. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year.
Let x = time in years Let y = length of the sea creatures
So, the equation can be written as
For Green land shark: y= 37+ 0.75x
For Spiny Dogfish: y= 22 + 1.5x
When both equation are equal
37+ 0. 75x = 22 + 1.5x
37- 22 = 1.5x - 0.75x
15 = 0.75x
x= 15/0.75
x= 20
and, y= 22 + 1.5(20)= 52
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6 eggs weigh 3/4 of a pound. How much does each egg weigh? 1/4 pounds1/6 pounds1/8 pounds2/3 pounds
Answers
Which describes a line passing through (3,3) that is perpendicular to the line described by y=3/5x+2 ?
Answers
Given:
Point (3,3)
The equation of the line,
[tex]y=\frac{3}{5}x+2[/tex]To find the equation of the line that passes through (3,3) and is perpendicular to the line:
The perpendicular slope is,
[tex]m=-\frac{5}{3}[/tex]Using the point-slope formula,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{5}{3}(x-3) \\ y=-\frac{5}{3}x+5+3 \\ y=-\frac{5}{3}x+8 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y=-\frac{5}{3}x+8[/tex]Let us find the intercepts.
When x=0, we get y=8
So, the y-intercept is (0,8).
When y=0, we get
[tex]\begin{gathered} -\frac{5}{3}x+8=0 \\ \frac{5}{3}x=8 \\ x=\frac{24}{5} \\ x=4.8 \end{gathered}[/tex]So, the x-intercept is (4.8,0).
Hence, the correct option which satisfies the equation of the line is D (last option).
Which of the following is equivalent to the expression below? (2+31) + (8-21) O A. 6+1 O B. 6+5; O C. 10+57 O D. 10 + 1
Answers
Given the expression:
[tex](2+3i)+(8-2i)[/tex]Let's find the equivalent expression from the choices given.
To find the equivalent expression, let simplify.
To simplify the expression, take the following steps:
• Remove the parentheses:
[tex]2+3i+8-2i[/tex]• Combine like terms:
[tex]\begin{gathered} 2+8+3i-2i \\ \\ 10+i \end{gathered}[/tex]Therefore, the equivalent expression is:
[tex]10+i[/tex]ANSWER: D
D. 10 + i
If the scale factor is 4, what is the measurement of x?24 m4 m20 m16 m
Answers
Let:
[tex]\begin{gathered} 6k=x \\ \end{gathered}[/tex]where:
k = scale factor
If the scale factor is 4, then:
[tex]\begin{gathered} 6(4)=x \\ 24=x \\ x=24 \end{gathered}[/tex]writing to explain in your own words tell what it meant by the absolute value of an integer
Answers
An absolute value of an integer is defined as a positive value/ digit of an integer regardless of the sign.
The symbol used is as shown below;
[tex]\parallel\text{ -3 }\parallel[/tex]or single lines as;
This means in absolute value of an integer , negative 2 is equal to positive 2.
Answer
In summary, an absolute value of an integer is a non-negative value , and the sign will only indicate direction, if well stated.
Pyramid with the square base. Is this correct? Base=64in^2LA= 112in^2TA=176in^2
Answers
The given figures is of square pryamid with the square base
Area of square = side x side
In the given figure, the length of the base of the square = 8in
Area of base of square = 8 x 8
Area of base of square = 64 in²
The lateral area of a right pyramid can be calculated by
multiplying half of the perimeter of the base by the slant
height.
Lateral surface area = 1/2 x Perimeter of the base x slant height
Since, the base of the pryamid is square so, the perimeter for the base pf pryamid = 4side
Perimeter = 4 x side
Perimeter = 4 x 8
Perimeter of the base of pryamid is 32 in
Slant height is given as 7in
Lateral surface area = 1/2 x 7 x 32
LAteral surface area = 7 x 16
Lateral surface area = 112 in²
The total surface area can be calculated by adding base are to the lateral surface area
Total surface area = Lateral surface area + Base area
Total surface area = 112 + 64
Total surface area = 176 in²
Answer:
Area of base of square = 64 in²
A cone has a height of 17 centimeters and a radius of 7 centimeters. What is its volume? Use = 3.14 and round your answer to the nearest hundredth. cubic centimeters
Answers
To find the volume of the cone, we will use the formula below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height
From the question,
π = 3.14
r =7
h=17
substitute the values into the formula
[tex]V=\frac{1}{3}\times3.14\times7^2\times17[/tex][tex]V\approx871.87\text{ cubic centimeters}[/tex]
If the function rule is to add 6, and an output value is 6, what is the input value?options:01-612
Answers
Given,
If the function rule is to add 6, and an output value is 6.
To find: What is the input value?
Solution:
When we add 0 to any number, we got the same number.
So adding 0 with 6 we get the same number 6.
[tex]6+0=6[/tex]Thus, the answer 0 is the correct option.
The table shows the volume of water released by a dam over a certain period of time. Graph a line representing the data in the table, and find the slope and y-intercept of the line from the graph. Then enter the equation for the graph in slope-intercept form.
Answers
Okay, here we have this:
Considering the provided information. we are going to calculate the slope, and y-intercept of the line, so we obtain the following:
First we will calculate the slope using the following formula:
m=(y2-y1)/(x2-x1)
m=(80000-40000)/(10-5)
m=40000/5
m=8000
y-intercept:
y=mx+b
40000=(8000)5+b
40000=40000+b
b=0
Finally we obtain that the equation of the line is: y=8000x.
Let's graph the equation:
In a certain fraction, the denominator is 3 less than the numerator. If 1 is added to both the numerator and denominator, the resulting fraction is equal to 10/7 Find the original fraction.
Answers
The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).
If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.
Then, we can write:
[tex]\begin{gathered} \frac{x+1}{(x-3)+1}=\frac{10}{7} \\ \frac{x+1}{x-2}=\frac{10}{7} \\ 7(x+1)=10(x-2) \\ 7x+7=10x-20 \\ 7x-10x=-20-7 \\ -3x=-27 \\ x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]With the value of x, we can replace it in the fraction and know the value of it:
[tex]\frac{x}{x-3}=\frac{9}{9-3}=\frac{9}{6}=\frac{3}{2}[/tex]Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.
Meg owes the bank more than $15. Use , or = to make the statement true. Meg's account value ? -$15 2 What is the value of point A? ? How far is point A from 0 (absolute value)? || HAR
Answers
Answer; Meg's account is < - $15
Meg is owing the bank more than -$15
This implies that, the amount she is owing is more that -$15
The amount she is owing the bank could be -$16, -$17
Therefore, her current back account is less than -$15
Meg's account value is < -$15
consider the polynomial function p given by p(x)=7x³-2x²+3x+10. Evaluate the function at x = -3.
Answers
Answer: -206
Step-by-step explanation:
[tex]p(-3)=7(-3)^3 -2(-3)^2 +3(-3)+10=-206[/tex]
Bella competed in the 5,000 m race at the Olympics she finished in the race 14.2 minutes after the race Bella wrote the equation c equals 18.1 m to model the relationship between the number of calories she burned c and the number of minutes she ran m.how many calories did Bella burn in the first 10 minutes of the 5,000 meter race.
Answers
Answer
She burnt 181 calories in that first 10 minutes of the 5,000 meter race.
Explanation
Bella wrote the equation that relates her calories burnt (c) to number of minutes (m) she has run as
c = 18.1m
The question then asks us to find how much calories she burnt in the first 10 minutes of the 5,000 meter race.
That is, find c when m = 10 minutes
Recall,
c = 18.1m
c = 18.1 (10)
c = 181 calories.
Hope this Helps!!!
Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Answers
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
A witch's brew calls for I 1/4 cups of
pond water. Wendy the witch has
access to a small frog pond
with 7 1/2 cups of water in it.
How many times can she
make her special brew?
Answers
The witch can make her special brew 6 times with the amount of water present in the small frog pond.
Given that:-
Total amount of water present in the small frog pond = 7 and 1/2 cups = 15/2 cups
Amount of water the witch needs to make her special brew = 1 and 1/4 cups = 5/4 cups
We have to find the number of times Wendy the witch can make her special brew with the amount of water present in the small frog pond.
We know that,
Number of times the witch can make the brew = Total amount of water/Water needed for brew
Hence, by simple division, we can write,
Number of times the witch can make the brew = (15/2) ÷ (5/4) = (15/2)*(4/5) = 6 times.
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This question has two parts. First, answer Part A. Then, answer Part B. Part A Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram. Which of the following shows the marked diagram of the situation?restate the conjecture as a specific statement using the diagram you chose from part AIn quadrilateral ABCD, AB is congruent to___ and ____ is parallel to CD. show that ABCD is a ____
Answers
We have the following:
We can know when they are congruent, since being congruent they are equal sides.
By notation we know that " ' " means that they are the same, therefore
[tex]AB=DC[/tex]And the parallel lines are:
[tex]BA\parallel CD[/tex]Therefore, the answer is B.
In quadrilateral ABCD, AB is congruent to CD and AB is parallel to CD. show that ABCD is a parallelogram
the variables x and y are related proportionaly. when x=4,y=10 find y when x =18when x=18,y=_____
Answers
For variables to be related proportionally, the relationship must have a constant of proportionality. In our case we will represent the constant of proportionality as k. Therefore,
[tex]\begin{gathered} y=kx \\ \text{where} \\ k=\text{constant of proportionality} \\ 10=4k \\ k=\frac{10}{4} \\ k=\frac{5}{2} \end{gathered}[/tex]Now lets find y when x = 18
[tex]\begin{gathered} y=kx \\ y=\frac{5}{2}\times18 \\ y=\frac{90}{2} \\ y=45 \end{gathered}[/tex]In order for the parallelogram to be a rhombus, x equals?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
parallelogram diagram
Step 02:
geometry:
solve for x:
(5x + 25)° = (12x + 11)°
5x + 25 = 12x + 11
25 - 11 = 12x - 5x
14 = 7x
14 / 7 = x
2 = x
The answer is:
x = 2
Downhill RacerA snowboardertravels 105 metersin 7 seconds.A skier travels for4 seconds andcovers 72 metersHow far will a skier travel in 2minutes? Explain how you figured it out.
Answers
To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).
A skier travels for 4 seconds and covers 72 meters.
Constant Rate (Speed):
[tex]\text{ }\frac{\text{ Distance Traveled}}{\text{ Time}}\text{ = }\frac{\text{ 72 meters}}{\text{ 4 seconds}}\text{ = }18\text{ meters/second}[/tex]Determining the distance covered in 2 minutes:
Step 1: Convert the time in minutes into seconds.
[tex]\text{ 2 (minutes) x }\frac{\text{ 60 seconds}}{\text{ 1 (minute)}}\text{ = 2 x 60 seconds = 120 seconds}[/tex]Step 2: Multiply the time by the constant rate (speed) of the skier.
[tex]\text{ Distance Traveled = 120 (seconds) x }18\text{ }\frac{\text{ meters}}{\text{ (second)}}[/tex][tex]\text{ = 120 x 18 meters}[/tex][tex]\text{ Distance Traveled = 2,160 meters}[/tex]Therefore, in 2 minutes, the skier travels 2,160 meters.
Use the “complete the square” method to solve the following problemx^2 + 3x + 11 = 0
Answers
[tex]x^2+3x+11=0[/tex][tex](\frac{1}{2}\times3)^2=(+\frac{3}{2})^2[/tex][tex]\begin{gathered} x^2+3x=-11 \\ x^2+3x+(+\frac{3}{2})^2=-11+\frac{9}{4} \\ \\ (x+\frac{3}{2})^2=-\frac{35}{4} \\ \\ x+\frac{3}{2}=\sqrt{\frac{-35}{4}} \\ \\ x+\frac{3}{2}=\pm\frac{\sqrt{35}}{2}i \\ \\ x=\frac{-3}{2}\pm\frac{\sqrt{35}}{2}i \end{gathered}[/tex]
The answers are
[tex]x=\frac{-3}{2}+\frac{i\sqrt{35}}{2},\text{ }x=\frac{-3}{2}-\frac{i\sqrt{35}}{2}[/tex]Solve using elimination.–2x − 7y = 9x − 7y = –15
Answers
The question wants us to solve the following system of equations by elimination:
[tex]\begin{gathered} -2x-7=9 \\ x-7y=-15 \end{gathered}[/tex]Solution
[tex]\begin{gathered} -2x-7y=9\text{ (Equation 1)} \\ x-7y=-15\text{ (Equation 2)} \\ \\ \text{Subtract both equations} \\ -2x-7y-(x-7y)=9-(-15) \\ -2x-7y-x+7y=9+15 \\ -2x-x-7y+7y=24 \\ -3x=24 \\ \text{Divide both sides by -3} \\ -\frac{3x}{-3}=\frac{24}{-3} \\ \\ \therefore x=-8 \\ \\ \text{Substitute the value for x into Equation 1}.\text{ This will help us find y.} \\ -2x-7y=9 \\ -2(-8)-7y=9 \\ 16-7y=9 \\ \text{Subtract 16 from both sides} \\ -7y=9-16 \\ -7y=-7 \\ \text{Divide both sides by -7} \\ -\frac{7y}{-7}=-\frac{7}{-7} \\ \\ \therefore y=1 \end{gathered}[/tex]Answer
The answer to the system of equations is:
x = -8
y = 1
Help in solving for y. Need to know the slope and y-intercept in the equation
Answers
Given the following equation:
8x - 5y = 10
then, we can solve it for y as follows:
5y = 8x -10
y = (8/5)x - (10/5)
y = (8/5)x - 2
So, the slope is m = 8/5 and the y-intercept is yo = -2.