Answer:
f(x) = x^3 - 7x + 1
Step-by-step explanation:
ƒ”(x)=6x ==> ƒ”(x)=6 * (x^1)
f'(x)=6/(1+1) * x^(1+1) + C ==> C is a constant that doesn't affect the derivative
f'(x)=6/2 * x^2 + C ==> simplify the first derivative
f'(x)=3 * x^2 + C ==> f'(x)=3(x^2) + C
f'(-3)=3((-3)^2) + C ==> plug in -3 into the derivative equation
f'(-3)=3(9) + C ==> simplify
20=3(9) + C ==> plug in 20 for f'(-3)
20=27+C
20-27=27-27+C ==> solve for C
C=-7
f'(x)=3(x^2) + (-7) ==> plug in -7 for C
f'(x)=3(x^2) - 7 ==> simplify
f(x) = 3/(2+1) * x^(2+1) - 7x + C
f(x) = 3/3 * x^3 - 7x + C
f(x) = x^3 - 7x + C
f(-3) = (-3)^3 - 7(-3) + C ==> plug in -3 into f(x)
f(-3) = -27 - (-21) + C
f(-3) = -27 + 21 + C ==> simplify
f(-3) = -6 + C
-5 = -6 + C ==> plug in -5 for f(-3)
-5 + 6 = -6 + 6 + C ==> solve for C
C = 1 ==> simplify
f(x) = x^3 - 7x + 1
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Identify the correct base case for a proof by induction for the following statement.
1+3+5+. +(2n-1)=n^2
we prove the following step using proof by induction
What is proof by induction?
For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.
We are given a statement 1+3+5+. +(2n-1)=n^2
Now first let us prove the statement for n=1 where n is the number of terms
On the left hand side = 1
And on the right hand side = 1^2 = 1
Hence the statement is proved for n =1
Now let us prove the statement for n= k
Therefore we have 1+3+5+....+k=k^2
Now let us prove the statement for n= k+1
Hence we have
1+3+5+....+k+(k+1)=
k^1+k+1
= (k+1)^2
Hence proved
Therefore we prove the following step using proof by induction
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It costs chevy $20,000,000 to develop and market a new model of cars. The company sells each car for $25,000. If chevy wants to make a profit of more than $5,000,000, write an inequalty that represents this.(Inequality is this question i need help on)
The inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.
Given that, it costs chevy $20,000,000 to develop and market a new model of cars.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Let the number of cars sold be x.
So, selling price of cars is $25,000x
Profit =Selling price-Cost price
⇒ 25,000x-20,000,000≤5,000,000
Solve the inequality
Add 20,000,000 on both the sides of an inequality, we get
25,000x≤25,000,000
⇒ x≤25,000,000/25,000
⇒ x≤1000
Therefore, the inequality for the given situation is 25,000x-20,000,000≤5,000,000 and the solution for the obtained inequality is x≤1000.
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Find the value of x.
The value of x is 5.
What is a polygon?A polygon is a flat object whose sides are made up of lines. It is a two-dimensional form called a polygon. The sides of regular polygons are all the same length.
Given the polygon and its exterior angle measures.
The sum of the measures of the exterior angles of a polygon is 360°, therefore, it follows:
(10x + 43)° + 66° + (12x + 39)° + (7x + 15)° + 52° = 360°
29x + 215° = 360°
29x = 360° - 215°
29x = 145°
x = 5
Hence, the value of x is 5.
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Explain how you can tell if a table of values represen a proportional relationship.
A table of values that represents a proportional relationship must have a constant rate and must pass through the origin
How to identify a table of values of proportional relationshipFrom the question, we have the following parameters that can be used in our computation:
A table that is has proportional relation
A table of values can be represented as
x y
a b
c d
......
.....
For the table of values to be proportional, the following must be true
x y
0 0
a b
c d
......
.....
Also, it must have a constant ratio
i.e. b/a = d/c
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.........i need help past due
Answer:
The 3rd box and 4th box will be checked
Step-by-step explanation:
The ratio 9:7 for apples to oranges means for every 9 apples there will be 7 oranges. So, the 3rd box and 4th box will be checked.
2. The table shows the snacks in Melissa's
pantry.
SNACK
Granola Bar
Chips
Fruit Snack
AMOUNT
4
3
5
What is the probability that she chooses a fruit
snack, puts it back, and then chooses a granola
bar?
The probability of choosing a fruit snack replaced and then choosing a granola bar is 5/36.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, Mellisa has options to choose from 3 different snacks,
N(GB) = 4, N(C) = 3, and N(FS) = 5.
So, The sample space N(S) = N(GB) + N(C) + N(FS).
N(S) = 12.
The probability of choosing a fruit snack is,
P(FS)
= N(FS)/N(S).
= 5/12.
Given, She puts it back so replaced and hence the events are independent.
So, The probability of choosing a granola P(GB) = N(GB)/N(S).
= 4/12.
= 1/3.
Therefore The combined probability is (5/12)×(1/3).
= 5/36.
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(
2
5
+
2
2
i)
2
in simplest a+bia+bi form.
The complex number (25 + 22i)² in simplest form a + ib is 141 + 1100i
What is a complex number?A complex number is a number in the form z = x + iy where
x and y are real numbers and i = √(-1)How to find the complex number (25 + 22i)² in the simplest form?To find the complex number (25 + 22i)² in the form a + ib, we proceed as follws.
(25 + 22i)² = (25 + 22i)((25 + 22i)
Expanding the brackets, we have that
(25 + 22i)² = (25 + 22i)((25 + 22i)
(25 + 22i)² = [25 × 25 + 25 × 22i + 25 × 21 + (22i)²]
(25 + 22i)² = [625 + 550i + 550i + 484i²]
(25 + 22i)² = [625 + 550i + 550i + 484 × (-1)] Since i² = -1
(25 + 22i)² = [625 + 550i + 550i - 484]
Collecting like terms, we have that
(25 + 22i)² = [625 - 484 + 550i + 550i]
(25 + 22i)² = 141 + 1100i
So, (25 + 22i)² = 141 + 1100i
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When you multiply a three digit number by a two digit number what i the greatet number of digit the product can have
On multiplying a three digit number by a two digit number the greatest number of digit the product can have is 5 digits.
Let , the two numbers be 788 and 12
on multiplying,
788 * 12
=9456
Again,
let the numbers be 999 and 99
999 * 99
=98901
Therefore, it is clear that the maximum number of digits in the product will have is 5 digits.
Repeated addition is the process of multiplication. The calculation of the product of two numbers can be done in a number of ways. Here, you can see what is meant when a number is multiplied by a two-digit number .
Find out how to multiply a number by a two-digit number in the sections below. The three different approaches used to determine the multiplication are shown in detail.
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There are only blue weet, green weet and red weet in a box. The ratio of the number of blue weet to the number of green weet i 2:7. The ratio of the number of green weet to the number of red weet i 3:1. There are le than 140 weet in the box. What i the greatet poible number red weet in the box?
The greatest possible number of red sweets in the box is 28.
If the ratio between blue and red sweets is x, then the number of blue sweets equals 2x and the number of green sweets equals 7x. If the ratio between green and red sweets is y, then the number of green sweets equals 3y and the number of red sweets equals y. In this case, the number of green sweets must be the same.
7x = 3y
Additionally, 140 is the sum of all of them,
thus,
2x + 3y + y < 140
2x + 4y < 140
x + 2y < 70
x + 2 × 7x/3 < 70
3x + 14x < 210
17x < 210
x < 12.36
and x ought to be a whole number, therefore x = 12
, and the total number of sweets will equal 136.
y = 7 × 12/3 = 28
thus, The greatest possible number of red sweets in the box is 28.
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(complete question)
There are only blue sweets, green sweets, and red sweets in the box. The ratio of the number of blue sweets to the number of green sweets is 2:7 The ratio of the number of green sweets to the number of red sweets is 3:1 there are less than 140 sweets in the box. What is the greatest possible number of red sweets in the box? Your final answer must include, 'red sweets'.
In GHI, h = 820 inches, G=102° ahd H=10°. Find the length of g, to the nearest
inch.
Answer:
4619 inches
Step-by-step explanation:
You want the length of side g in ∆GHI where G=102°, H=10°, and h=820 inches.
Law of sinesThe law of sines tells us ...
g/sin(G) = h/sin(H)
g = h·sin(G)/sin(H) = (820 in)sin(102°)/sin(10°)
g ≈ 4619 in
The length of side g is 4619 inches.
<95141404393>
Two numbers have a sum
of 12. The same two numbers have difference of 4. What are the two numbers?
Answer:
8 and 4
Step-by-step explanation:
Answer: 8 and 4
Step-by-step explanation:
A spring is attached at one end to support B and at the other end to collar A represented in the figure. Collar A slides along the vertical bar between points C and D. In the figure, the angle is the angle created as the collar moves between points Cand D. When the spring is stretched and the distance from point A to point Bis 5.3 feet, what is the value of e to the nearest tenth of a degree? 3 ft B 00000 А
The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°
Given,
A spring is attached at one end to support B and at the other end to collar A.
Part A: Reference angle (θ) = 28°
We have to find out the distance of point A to point B.
Adjacent = 3 ft (given)
Apply the trigonometry function to find AB
cos θ = adj / hypotenuse
Substituting all the values ,
cos 28°= 3/AB
AB = 3/cos 28°
AB = 3.4 ft (nearest tenth of a foot)
Part B:
It is given that Distance from point A to point B is 5.2 feet
We have to calculate the Value of θ
adjacent = 3 ft
hypotenuse = AB = 5.3 ft
To find θ , We will again apply the trigonometry function
cos θ = adjacent/hypotenuse
Substituting all the given values
cos θ = 3/5.3
θ = cos⁻¹ ( 3 / 5.3)
θ = 54.8°
That is,
The length of point A to point B is 3.4 feet
The value of θ is 54.8°
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What percent is 24 out of 36
Answer:
66.67
Step-by-step explanation:
(24*100)/36
It takes 3 days for Sonia to prepare the walls and paint her room. her friend Jennifer wants to help her on the job. If Jennifer does the same job entirely her own, she needs 5 days to complete it. How many days does it take if both Sonia and Jennifer work together on the job
The number of days it would take if both Sonia and Jennifer work together on the job is 1 7/8 or 1.875 days.
How long would it take them working together?Let the amount of time (in days) that it would take both Sonia and Jennifer working together to paint Sonia's room be t. Additionally, the amount of work done by both Sonia and Jennifer to paint her room in 1 day is given by:
The amount of work done by Sonia in 1 day is 1/x or 1/3.
The amount of work done by Jennifer in 1 day is 1/y or 1/5.
Therefore, the amount of work done by both Sonia and Jennifer working together to paint Sonia's room in 1 day is given by this mathematical expression:
Combined work done = 1/x + 1/y
Combined work done = 1/3 + 1/5
Combined work done = 8/15
Next, we would calculate the combined time as follows:
8/15 × t = 1
Combined time, t = 15/8
Combined time, t = 1 7/8 or 1.875 days.
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PLS ANSWERRRRRSSSSSSS. I GIVE BRAINLIESTTT
Answer:
x = 5.4
Step-by-step explanation:
[tex]\frac{7.2}{4}[/tex] = [tex]\frac{x}{3}[/tex] Cross multiple and solve for x
4x = (7.2 x3)
4x = 21.6 Divide both sides by 4
x = 5.4
Answer:
x = 5.4
Step-by-step explanation:
[tex]\frac{x}{7.2} =\frac{3}{4}[/tex]
[tex]x=\frac{(7.2)(3)}{4} =\frac{21.6}{4} =5.4[/tex]
Hope this helps
helppppp pleaseeeeeeeeeeer
By using the property of congruency of triangles,
[tex]\angle[/tex]PSR = [tex]\angle[/tex]PSQ has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
PS bisects [tex]\angle[/tex]QPR [Given]
PQ [tex]\cong[/tex] PR [Given]
[tex]\angle[/tex]QPS [tex]\cong \angle[/tex]RPS [PS bisects [tex]\angle[/tex]QPR]
PS [tex]\cong[/tex] PS [Reflexive property of congruence]
[tex]\Delta[/tex] PQS [tex]\cong \Delta[/tex] PRS [SAS axiom]
[tex]\angle[/tex]PSR = [tex]\angle[/tex]PSQ [Corrosponding parts of congruent triangles are congruent]
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What is an equation of the line that passes through the point (6,1)(6,1) and is parallel to the line x+3y=15x+3y=15?
The equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15 is 3y+x=9.
What is an equation of a line?The general equation of a straight line is given by the expression
y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.
Given,
The line is parallel to the line x + 3y = 15 and passes through the point (6,1).
The procedures listed below can be used to find the equation of the line that runs parallel to the line x + 3y = 15 and passes through the point (6,1).
Step 1 - Keep in mind that two parallel lines have equal slopes.
Step 2: As a result, the line's slope across point (6,1) is -1/3.
Step 3: Accordingly, the equation of a line passing through the point (6,1) and being parallel to the line (x + 3y = 15) may be found using the one-point slope form of a line.
The one-point slope form is shown below in Step 4:
y-y₁=m(x-x₁)
Step 5: In the equation above, substitute the values of the known terms.
y-1=-(1/3)(x-6)
3y - 3 = -x + 6
3y +x = 9
Therefore, the equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15 is 3y+x=9.
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The sports store bought a baseball bat for $60 and sold it for $84. What percentage is the markup? 15 POINTS!!! WILL VOTE BRAINLIEST
Answer: 28.57% mark up.
Step-by-step explanation:
If you subtract 25.57% from 84.00 you get 60.00
Find f + g if f(x) = 3x-2 and g(x) = 5x + 2.
f(x) +g(x)= (3x-2)+(5x+2)
=3x-2+5x+2 (-2or +2 become cancelled )
=3x+5x
8x
HELP ASAP!! I will give Brainiest!
Angles X and Y are supplementary. Angle X measures 132.54°, and angle Y measures (m - 15)°. Find mzY
47.46°
62.46
85.08
117.54°
Answer:
47.46
Step-by-step explanation:
Answer: The answer is A. 47.46°.
Step-by-step explanation: Hope this helps.
Which option below is a different way of writing -5-(-7)?
Answer: I mean- can you found it out yourself by studying. There's your answer.
Step-by-step explanation:
just study not cheat.
We often use functions to model or represent situations and relationships. These
representations can be as equations, graphs, tables, or even verbal descriptions.
What does it mean to "represent" something? In what other situations have you heard
that term used, and how was its meaning in those situations similar to its usage in
algebra? please help
Answer:
Step-by-step explanation:
If a fair die is rolled 4 times, what is the probability, rounded to the nearest
Question
Which ordered pairs cause this relation NOT to be a function? Why?
{(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)}
Responses
A (0.5, 1), (3, 1); The same y-value has different x-values.(0.5, 1), (3, 1); The same y-value has different x-values.
B (3, 1) and (3, 2); The same x-value has different y-values.(3, 1) and (3, 2); The same x-value has different y-values.
C (3, 1) and (3, 2); The x-value in a function cannot be greater than the y-value.(3, 1) and (3, 2); The x-value in a function cannot be greater than the y-value.
D (0.5, 1) and (0, 0.5); A function cannot contain decimals.
Ordered pair (3, 1) and (3, 2) causes the relation to not be a function; The same x-value has different y-values.
How do you find out if a set of ordered pairs is a function or not?
For a set of ordered pairs to be a function, there must not be any two points that have the same first elements. This means that, the
x-coordinates must not repeat for any two given points.
According to the given question:
Given ordered pairs of a relation are
(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)
Domain set of the relation= {0, 0.5, 1, 3}
Co-Domain set of the relation = {0.5, 1, 2, 6}
Clearly the image of the x-coordinate 3 is not unique.
Hence, (3, 1) and (3, 2); The same x-value has different y-values.
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41°
x=
(7x)°
5.) solve!!!
Answer: x = 7
Step-by-step explanation:
Sum of the interior angles of a triangle must equal 180.
41 + (7x) + 90 = 180
7x = 180 - 90 - 41
7x = 49
x = 49/7 = 7
theres 4 questions that i need help with asap. #geometry
please help.
After solving the equation we know ABCD is a parallelogram.
What is parallelogram?
A parallelogram is a two-dimensional shape with four straight sides. All of the sides are equal in length and the opposite sides are parallel. Additionally, opposite angles are also equal. The shape is called a parallelogram because parallel lines are present on either side. Parallelograms can come in many different forms, such as rectangles and rhombuses. The properties of a parallelogram include the fact that the diagonal line that divides the parallelogram into two halves bisects the angles. Additionally, the cross product of the two diagonals is equal to the area of the parallelogram. Parallelograms are used in a variety of areas, including architecture, engineering, and mathematics. Depending on the application, parallelograms can be used to construct a variety of shapes, such as circles and ellipses.
Given: A (2,5), B (7,6), C (6,2), D (1,1)
AB ⇒ A (2,5), B (7,6) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(-5+1)^{2}+(-6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(-4)^2+(-8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
CD ⇒ C (6,2), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7-3)^{2}+(6+2)^{2} }[/tex]
⇒ [tex]\sqrt{(4)^2+(8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
BC = B (7,6), C (6,2) ⇒ [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(3+5)^{2}+(-2+6)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
AD ⇒ A (2,5), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7+1)^{2}+(6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
As, AB = CD = BC = AD all sides are equal.
Hence proved, ABCD is a parallelogram.
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the hour property of the datetime structure stores the hour as an integer between 1 and 24. question 47 options: true false
False. The hour property of the datetime structure stores the hour as an integer between 0 and 23.
To support varied needs, three different property types are available:
1. Date — A day of the Gregorian calendar, without reference to a time zone or locale. The unit is a whole day, such as July 23, 2006.
2. Time of Day — A time of day, without reference to a time zone or locale. The unit is seconds, such as 15 seconds after 1:25 P.M.
3. Date Time — A date and time, stored internally to the millisecond if available, in a known time zone. For example 15.452 seconds after midnight on July 23, 2006 in London, U. K.
When presented with a DateTime value, a corresponding date and a time-of-day (in a specified time zone) can be determined.
However, the converse is not usually true: when starting with a Date and a TimeofDay value, multiple differing but "correct" DateTime values can be constructed, depending on assumptions about time zone, Daylight Savings Time, and other considerations. For example, when the date is January 1 in London, it can be December 31 in New York.
Thus, the given statement is false.
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The following loop is intended to print the numbers
2 4 6 8 10
Fill in the blank:
for i in ________:
print (i)
range(2,11,2) because range is a tool for defining a range between two numbers and adding a step value.
How would you describe the range?Range is the difference between the highest and lowest values in a range of numbers. To calculate the range, subtract the smallest number from the largest number in the set.
How do you find range?The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.
range(2,11,2) because range is used to create a range between number and add step value
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Which of the following statements is INCORRECT?
A. FE = 58
B. DE = 58
C. x = 8
D. DF = 40
Answer: B
Step-by-step explanation:
It says DE is 40 so B is incorrect.
A shopper wants to ensure he has enough cash to purchase a $390 grandfather clock, so he
asks a clerk what the total will be with the sales tax included. The clerk tells him the total will
be $429. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answer: The sales tax percentage is 10%
Step-by-step explanation:
we find the price by take 429 - 390 = $39
Then we take 39 divided by 390 then timed a 100 = 10%
from a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. in how many ways can this be done?
Total ways of required selection is 686, obtained from the sum of the cases of 3, 4 and 5 women in the committee.
What is defined as combination?Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in combinations.
Given that 5 persons are to be selected with a condition of minimum 3 women. Therefore the different possibilities are:
1) 3 women and 2 men
2) 4 women and 1 man
3) 5 women
Final answer will be the sum of the above results.
Total ways to select 3 women from 6 women and 2 men from 8 men,
Total ways = ⁶C₃ * ⁸C₂
Similarly total ways for 4 women and 1 man = ⁶C₄ * ⁸C₁
Total ways for 5 women = ⁶C₅ * ⁸C₀
Add the three results to get the final answer,
Total number of ways = (⁶C₃ * ⁸C₂) + (⁶C₄ * ⁸C₁ ) + (⁶C₅ * ⁸C₀)
Total number of ways = 560 + 120 + 6 = 686
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