The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is
dy/dx = 12x³ - 6x² - 7.
We have,
The power rule states that if we have a term of form a[tex]x^n[/tex], the derivative with respect to x is given by [tex]d/dx(ax^n) = nax^{n-1}.[/tex]
Applying the power rule, we differentiate each term as follows:
[tex]d/dx(3x^4) = 3 \times 4x^{4-1} = 12x^3\\d/dx(-2x^3) = -2 \times 3x^{3-1} = -6x^2\\d/dx(-7x) = -7 \times 1x^{1-1} = -7[/tex]
d/dx (5) = 0 (since 5 is a constant)
Combining these derivatives, we get:
dy/dx = 12x³ - 6x² - 7
Therefore,
The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is
dy/dx = 12x³ - 6x² - 7.
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Find the indicated real nth root(s) of a. n=3, a=729
Answer:
9
Step-by-step explanation:
n=3, a=729
For any odd integer, n ; a will have only one real nth root which will be a positive integer.
Similarly, for any integer, n, that is > 1 ; related by the expression ;
p^n = a ; the nth root of a = p
Therefore,
If n = 3 ; a = 729
p^3 = 729
To obtain the value of p ; take the cube of both sides
(p^3)*1/3 = 729^1/3
p = 9
Hence, the real nth root of 729 is +9 when n = 3
PLZ HELP!!!!
If a vertical parabola opens downward, has its vertex in the fourth quadrant,
and y =ax +bx +c is the equation of this parabola, which of the following
can be true?
a 0, b >0, and c >0
a >0, b 0
a 0, and c >0
a 0, and c 0, b 0
a >0, b >0, and c <0
Answer:
False
Step-by-step explanation:
A nonlinear function that can be written on the standard form
ax2+bx+c,wherea≠0
is called a quadratic function.
All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is
y=x2
picture51
The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate
x=−b2a
The y-coordinate of the vertex is the maximum or minimum value of the function.
a > 0 parabola opens up minimum value
picture52
a < 0 parabola opens down maximum value
picture53
A rule of thumb reminds us that when we have a positive symbol before x2 we get a happy expression on the graph and a negative symbol renders a sad expression.
The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation
x=−b2a
The y-intercept of the equation is c.
picture54
When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.
Example
Graph
x=x2+2x+1
Make a table of value for some values of x. Use both positive and negative values!
x y = x2 + 2x + 1
-3 4
-2 1
-1 0
0 1
1 4
2 9
3 16
Graph the points and draw a smooth line through the points and extend it in both directions
picture55
Notice that we have a minimum point which was indicated by a positive a value (a = 1). The vertex has the coordinates (-1, 0) which is what you will get if you use the formula for the x-coordinate of the vertex
x=−b2a=−22⋅1=−1
and that the line has an y-intercept of (0, 1) which could have been determined from the c-value which is 1.
If you have an absolute value of a that is greater than 1 the parabola will be narrower than the parental quadratic function. And the opposite that if you have a absolute value of a that is less than 1 then the parabola will be wider than the parental quadratic function.
The vertical parabola opens downward, has its vertex in the fourth quadrant, and y = ax + bx +c is the equation of this parabola given conditions none of them is true.
A nonlinear function that can be written on the standard form
[tex]ax^{2} + bx +c = 0 where (a\neq 0)[/tex]
This called a quadratic function.
All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is'
[tex]y = x^{2}[/tex]
The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate .
x = −b2a
The y coordinate of the vertex is the value maximum or minimum of the function.
a > 0 parabola opens up minimum value
a < 0 parabola opens down maximum value
A rule of thumb reminds us that when we have a positive symbol before we get a happy expression on the graph and a negative symbol renders a sad expression.
The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation
x = −b2a
The y-intercept of the equation is c.
[tex]XY = x^{2} +2X +1[/tex]
When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.
[tex]x = x^{2} +2x+1[/tex]
Make a table of value for some values of x. Use both positive and negative values!
This is the points lies on parabola
-3 4-2 1
2 9
3 16
Graph the points and draw a smooth line through the points and extend it in both directions.
Notice that we have a minimum point which was indicated by a positive a value (a = 1). The vertex has the coordinates (-1, 0) which is what you will get if you use the formula for the x-coordinate of the vertex
x =−b2a =−22⋅1 =−1
And that the line has an y-intercept of (0, 1) which could have been determined from the c-value which is 1.
If you have an absolute value of a that is greater than 1 the parabola will be narrower than the parental quadratic function. And the opposite that if you have a absolute value of a that is less than 1 then the parabola will be wider than the parental quadratic function.
For more information about basics of parabola click the link given below .
https://brainly.com/question/13053904.
Which of the following ordered pairs are solutions to the system of equations below?
(-3, 7)
(3, 7)
(-3, -7)
(3, -7)
Answer:(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
(-3, -7)
Step-by-step explanation:
8. Oscar charges $25 for the first hour of tutoring and $15 for each additional hour or fraction of an hour. The rates that Latoya charges for x hours of tutoring are modeled with the function shown. 30x, 06. Who will charge more to tutor for 5.5 hours, Oscar or Latoya? How much more?
Answer:
a. Oscar charges more to tutor for 5.5 hours than Latoya.
b. Oscar charges more by a difference of $1.00 for tutoring 5.5 hours.
Step-by-step explanation:
Charges by Oscar:
1st hour of tutoring = $25
Additional hour or fraction = $15
For tutoring for 5.5 hours, Oscar charges:
1st hour of tutoring = $25
4.5 hours of additional tutoring = $75 ($15 * 5)
Total charges = $100
Charges by Latoya:
= 30x, 0.6, where x = hours of tutoring
Total charges = 30 * 5.5 * 0.6 = $99
Therefore, Oscar charges more for tutoring 5.5 hours than Latoya by $1 ($100 - $99).
A line intersects the point (0, -11)
and has a slope of 0. What is the
slope-intercept equation for this line?
y = [?]
Answer:
The slope-intercept equation having slope is '0' and intercept c= -11
y = 0 x - 11
Step-by-step explanation:
Explanation:-
Given a point ( 0,-11) and has a slope m= 0
The equation of the straight line
y - y₁ = m ( x-x₁ )
y - (-11) = 0 (x -0)
y +11 = 0
y = -11
If i dont get this done ima get grounded for like a bazziin years so plaese HALP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
HELPPPPPP WHAT ARE THESES QUESTIONS PLSSS DUEEEE SOON
Answer:
yes and no
Step-by-step explanation:
Answer:
down below
Step-by-step explanation:
yes and no, answered in different post
A bookshelf is 16.5 inch long. If each book is 2.5 in wide, how many books can fit on the shelf?
Answer:
6.
Step-by-step explanation:
6 books make 15 inches therefore another one wont fit so 6.
HELP PLEASE ANSWER 7
Answer:
f(x) = 7
Step-by-step explanation:
we use the bottom equation (4x+3) because
1 > 0
so
4(1) +3 = 7
is -5 +(-2) negative or postive
Answer:
-7
Step-by-step explanation:
-5 + (-2) is the same thing as
-5 - 2.
(X^3-2x^2+5x+6)÷(X-3)
How do I solve this with long division?
Answer: X^2+3X+9+- 2x^2+33/X-3
Step-by-step explanation:
Factorise
x2 — 73 — 44
Answer:
Step-by-step explanation:
here you go mate
step 1
x^2-73-44 equation
step 2
x^2-73-44 (CLT)
step 3
(x^2)+(-73+-44) simplify
answer
x^2-117
Does the point (-9, 18) satisfy the equation y = -2x?
yes
no
Answer:
Yes
Step-by-step explanation:
If you plug the numbers into the equation and solve it
18 = -2(-9)
18 = 18
Question 1
Jessie has been training for a half-marathon. Jesse trains on a track where each lap is of a mile. If
esseran 2 miles, how many laps did she run?
Answer:
Jessie runs 2 lap
Step-by-step explanation:
Given:
1 lap = 1 miles
Jessie runs = 2 miles
Find:
Number of lap Jessie runs
Computation:
Given that; 1 lap = 1 miles
So,
1 miles = 1 lap
And
2 miles = 2 lap
So,
Jessie runs 2 lap
why is -3>1-1 not correct
Answer:
It is incorrect because -3 is less than 0
Step-by-step explanation:
Say we have a number line that is- uhm
-5 to five so he numbers would look somewhat like
-5 -4 -3 -2 -1 0 1 2 3 4 5
(lesser to greater)
if you take -3>1-1 and simplify 1-1
you would now have -3>0
this statement says -3 is greater than 0
if you look on our number line which goes from lesser to greater then you see that -3 is less than 0 therefore -3>1-1 is incorrect.
plz answer this :) 10 pionts
Answer: Well... this is a long question.
1. All are moving 7 units to the left.
2. A = 0, B = 1 east, C = 1 east and 8 south, D = 8 south.
3. A = 0, B = 26 east, C = 26 east and 8 south, 8 east and 8 south.
write the following phrase as a mathematical expression the product of the rate, r, and 9
Multiply:
7.11
х
10.2
Answer:
I think that The answer is 72.522
Pls help I’m confused
Answer:
C or D but im pretty sure its C
Step-by-step explanation:
4(3m+10)>-3m-51+8m help pls
Answer:
m > -13
Step-by-step explanation:
4 (3m + 10) > -3m - 51 + 8m
12m + 40 > 5m - 51
12m - 5m > -51 - 40
7m > -91
m > -91/7
m > -13
Please mark me the Brainliest!?!
Richard gets his hair cut every 3 weeks. His hair dresser charges him $25.00 each time. A reasonable tip is 10%. Richard pays him $28.00 each time. What percent, to the nearest whole does Richard tip his hairdresser?
Answer:
5
Step-by-step explanation:
Answer:
12%
Step-by-step explanation:
28 - 25 = 3
3/25 = 0.12
0.12 x 100 = 12%
twelve is what percent of 42
Answer:
28.57 percent
hope that helped
Answer:3.5 percent of 42 gives you 12
Step-by-step explanation:
5/9(F-32)= -62.1 what is F?
Answer:
a
Step-by-step explanation:
Simplify (2^3)^-2
A. -1/64
B. 1/64
C. 2
D. 64
Answer:
B, 1/64
Step-by-step explanation:
[tex]2^{3}[/tex] = 8
[tex]8^{-2}[/tex] = [tex]\frac{1}{8^2}[/tex] = [tex]\frac{1}{64}[/tex]
Answer:
B. 1/64
Step-by-step explanation:
Got it right on the assignment
How many terms are in the expression below?
5x+18
i think the answer is 2
i dont know for sure
Chase thought that only 23 people Would come to the banquet but 48 people endd up coming what was his percent error
Answer:
the percent of people that end up coming as error is 12%
Chase made a miscalculation of 52.08% percent.
What is Percentage Error?
The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.
Given that, Chase anticipated that just 23 people would attend the event; however, 48 individuals showed up.
The general formula for percentage error:
Percentage Error(%e) = ((Estimated Number – Actual Number)/ Actual number) x 100.
Hence,
Percentage error done by chase = (23 - 48) * 100/48
Percentage error done by chase = -52.08%
Therefore, the Percentage error done by chase is 52.08%
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Will mark Brainlest, if you answer fast!!!
Answer:
-2x
Step-by-step explanation:
Mario's Pizza just received two big orders from customers throwing parties. The first customer, Amelia, bought 10 regular pizzas and 1 deluxe pizza and paid $133. The second customer, Jaden, ordered 7 regular pizzas and 9 deluxe pizzas, paying a total of $284. What is the price of each pizza?
Answer:
The regular costs 11 dollars each while the deluxe cost 23 each.
Step-by-step explanation:
You need to setup two equations.I used two variable for the prices of the types of pizzas because they are unknown.I used x for the cost of regular and y for the cost of deluxe.The equation I did are 10x+y=133 and 7x+9y=284.You need to solve one equation only.I solved the first one.
Yan ate 1/4 of a pizza. What friction of the pizza is left?
Answer:
3/4
Step-by-step explanation:
If he/she ate 1/4 then there would still be 3/4
Describe fully the single
transformation that maps
triangle A onto triangle B
Total marks: 2
pls don’t answer if you don’t know
Answer:
The single transformation that maps triangle A onto triangle B is a reduction by a scale factor of 1/2 with the center of reduction at (1, 2)
Step-by-step explanation:
In order to locate the center of reduction from triangle A to triangle B, straight lines are drawn from the corner of triangle A to the corresponding corner of triangle B. The lines drawn will intersect at the center of reduction as shown in the attached drawing created with Microsoft Word
