Answer:
[tex]\displaystyle \frac{d}{dx} = 6(2x + 9)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (2x + 9)^3[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{dy}{dx} = 3(2x + 9)^2 \cdot \frac{d}{dx}[2x + 9][/tex]Basic Power Rule [Addition/Subtraction, Multiplied Constant]: [tex]\displaystyle \frac{dy}{dx} = 6(2x + 9)^2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
what is the difference in length of the honeybee that is 1/2inch and an 7/8 inch mosquito?
1/2 7/8
1/2x4=4/8
4/8 7/8
3/8 is the difference
if EF=4, FG=6x and EG=8x what is EG?
∵EG=8X FG= 6X
∴EF= EG- FG=2X=4
∴X=2
so,EG=8X=16
Drag the correct steps into order to solve the equation -3x – 6 = 18 for x.
The solution to the linear equation -3x - 6 = 18 is x = - 8
What is the solution of the equation?The solution of the linear equation is calculated as follows;
The given linear equation;
-3x - 6 = 18
Move the constant term to the other side of the equation.
-3x - 6 + 6 = 18 + 6
-3x = 24
Divide both sides of the equation by the coefficient of x (-3) to isolate x.
(-3x) / (-3) = 24 / (-3)
x = -8
Thus, the solution to the linear equation -3x - 6 = 18 is x = - 8
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shen baked b cookies. his family ate 11 of them. using b, write an expression for the number of cookies that remained.
Step-by-step explanation:
So, lets write out the equation you have right now.
B - 11 = ?
You can have B be whatever you want. It must be higher than 11 (unless your teacher or whoever your guardian is allows negative numbers). In this case, I will use 15.
B = 15
15 - 11 = ?
Solve the equation and you get 4. Simple!
What is the value of x?
The angles are vertical angles so they are equal
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60
6x - 3x = 60 - 3
3x = 57
x = 19
Answer
x = 19
sand sells 81/2 cent per pound how much save by buying 100 pounds at $8.25
Answer:
The amount of money saved will be $0.25
Step-by-step explanation:
Sand sells [tex]8\frac{1}{2}[/tex] cents per pound.
So, the cost of 100 pounds will be: [tex]8\frac{1}{2}*100=\frac{17}{2}*100 = 850[/tex] cents.
We know that, 1 dollar = 100 cents.
So, 850 cents [tex]=\frac{850}{100} dollar = \$8.50[/tex]
Thus, the amount of money saved by buying 100 pounds at $8.25 will be: [tex](\$8.50-\$8.25)= \$0.25[/tex]
The amount saved by buying 100 pounds at $8.25 is the change in price per pound and the discounted price, which is 0.25 cents
Price per pound = 8.50 cent
Calculating the cost per pound of of Sand at $100 for $8.25 :
100 = 8.25
1 = p
Cross multiply :
100p = 8.25
p = 8.25 / 100
p = $0.0825 = 0.0825 × 100 = 8.25 cent
The amount saved = 8.50 - 8.25 = 0.25 cent
Therefore, the amount saved by buying 100 pounds at $8.25 is 0.25 cent.
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which equation best represents the graph
If Joelle multiplied $792$ by a positive integer and came up with a perfect square as her answer, then what is the smallest integer she could have multiplied $792$ by
Joelle should multiply 792 by 22 to get a perfect square
To figure out the smallest integer that Joelle could have multiplied by 792 to get a perfect square, we need to factorize 792 and ensure all prime factors appear in even powers.
First, we find the prime factorization of 792:
[tex]792 =2^3 \times 3^2 \times 11[/tex]
For a number to be a perfect square, all the exponents in its prime factorization must be even. The exponents of 2 and 11 are not even in this factorization, so we must multiply 792 by the smallest factors that will make these exponents even. So, we need an additional factor of 2 (to make [tex]2^4[/tex]) and an additional factor of 11 (to make [tex]11^2[/tex]). Therefore, we multiply as follows:
[tex]2 \times 11 = 22[/tex]
So, the smallest integer Joelle could have multiplied 792 by to get a perfect square is 22.
Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y-2x. What error did Marcus make?
(3x²-2y²+5x)+(4x²+12y²-7x)
This is all about combining like terms.
(7x²+10y²-2x) is what I got.
(7x-10y-2x) is what Marcus got.
Marcus didn't add the squared symbol for 10y and he added a negative sign for 10y. He did -10y but it is +10y² because -2y²+12y²=10y². So, his problem is that Marcus didn't add right.
Hope this helps.
If it does, I would appreciate a brainliest rank.
<3
Answer:
He combined the terms –2y2 and 12y2 incorrectly.
Method B: Take the absolute value of the difference of the two numbers.
When taking the absolute value, show the larger number first, then show the lesser number first when finding the difference.
Method B: Take the absolute value of the difference of the two numbers. (2 pts)
|larger number – smaller number| |smaller number – larger number|
Answer-
The absolute value of the difference of the two numbers was found to be 7.
Solution-
The given two numbers are, 2 and -5.
Between these two number,
larger number = 2
smaller number = -5
(∵ As 2 is right of -5 on the number line)
[tex]\left |larger\ number-smaller\ number \right|[/tex]
[tex]=\left |2-(-5)\right |[/tex]
[tex]=\left |2+5 \right|= 7[/tex]
[tex]\left | smaller\ number -larger\ number \right|[/tex]
[tex]=\left |(-5)-2 \right|[/tex]
[tex]=\left |-5-2 \right|=\left |-7 \right|=7[/tex]
Therefore, it can be proved the order doesn't matter if we take the difference in absolute value.
In the graph what are the and y coordinates of the center.
A. (0,2)
B. (2,-1)
C. (1,0)
D. (-1,-2)
Answer:
The center of this ellipse is (-1, 2).
None of those choices are correct.
how many different ways can 4 tickets be selected from 50 tickets if each ticket wins a different prize
What is the width of a rectangle with length 25 in. and area 375 in.^2?
Answer:
15 inches
Step-by-step explanation:
Area of a rectangle = width × length
We know the area and length so we can put them into the equasion.
375 in.^2 = width × 25 in.
We know that something times 25 is equal to 375. Therefore, we have to divide 375 by 25, which equals 15.
So, 375 in.^2 = 15 in. × 25 in.
The width of the rectangle is 15 inches.
To find the width of a rectangle, given its length and area, we can use the formula for the area of a rectangle:
Area = Length × Width
We are given that the length of the rectangle is 25 inches and the area is 375 square inches.
Let's substitute these values into the formula:
375 in² = 25 in × Width
To find the width, we need to isolate it on one side of the equation. We can divide both sides of the equation by 25 inches:
375 in² / 25 in = Width
Simplifying the expression:
15 in = Width
Therefore, the width of the rectangle is 15 inches.
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What is the Recipical of 8/19?
The question states that we are looking for the reciprocal of 8/19.
Recall what a reciprocal is. A reciprocal, when looking at a number, is what is multiplied with it for it to equal 0. It is commonly regarded as just the fraction flipped. (For example, the reciprocal of 1/2 would be 2, or 2/1. 2 * 1/2 = 1)
But why does flipping a fraction work?This goes back to the simplifying, when multiplying two fractions together.
If you were to multiply two fractions, say [tex]\frac{5}{4}[/tex] and [tex] \frac{4}{5}[/tex], you could look at the numerator of one and the denominator of another, and cancel them out. In this case, the numerator of one is 5, and the other is also 5. Cancelling those out makes both one. If you cancel out 4 and 4 too, you get 1/1 * 1/1, or just 1.
We could go on asking why these methods work forever. Why does cancelling out a numerator and a denominator of separate fractions work? (A simple explanation is when the separate fractions are multiplied together, you could divide both sides by the factor which was originally used to cancel out with, which is what was stated above but simpler.)
Now, we can figure out the answer.Since we know the reciprocal is just the flipped form of the fraction, we can simply flip 8/19 to get our answer.
8/19 flipped is 19/8, which is our answer.
Hope this helped!After it is purchased, the value of a new car decreases $4000 each year. After 3 years, the car is worth $18,000. What was the original value of the car?
THE QUESTION:After it is purchased, the value of a new car decreases $4000 each year. After 3 years, the car is worth $18,000. What was the original value of the car?
THE WORK: $4000x$3 = $12000_$18000-$12000 = $6000
MY ANSWER: based on my work, the answer is $24000
Final answer:
To find the original value of a car that depreciates by $4,000 each year, we add the total depreciation over 3 years ($12,000) to the car's value after 3 years ($18,000), resulting in an original price of $30,000.
Explanation:
The student is asking about the calculation of the original price of a car given its depreciation rate and its value after a certain period. Since the new car decreases by $4000 each year and after 3 years the value of the car is $18,000, we can calculate the original value by reversing the depreciation.
Depreciation calculation:
Value of the car after 3 years: $18,000Annual depreciation: $4,000/yearTotal depreciation over 3 years: 3 years * $4,000/year = $12,000Original price = Current price + Total depreciationOriginal price = $18,000 + $12,000Original price = $30,000
Evaluate m^2-3m+5 where m= -4
Answer:
33 is your answer
Step-by-step explanation:
Plug in -4 for m in the expression
(-4)^2 - 3(-4) + 5
Simplify. Remember to follow PEMDAS. First, solve the number connected to the power sign.
(-4)^2 = (-4)(-4) = 16
Next, solve -3(-4). Multiply
-3(-4) = 12
Finally, combine like terms.
16 + 12 + 5 = 33
33 is answer
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~Senpai
it cost $12 to attend a golf clinic with a local pro. buckets of balls for practice during the clinic cost $3 each how many buckets can you buy at the clinic if you have $30 to spend
the answer would be 6 buckets
15t+17=13t+14
solce the equation
[tex]15t+17=13t+14\\\\2t=-3\\\\t=-\dfrac{3}{2}[/tex]
a swimming center builds a new pool that has the dimensions 3a^6 by a^2 by b4 . what is the volume of the pool
Answer:
Volume = length * width * depth
= 3a^6 * a^2 * b^4
= 3a^(6+2)b^4
= 3a^8b^4 cubic units Answer.
Step-by-step explanation:
The exponents 6 and 2 are added when the terms are multiplied
Swimming pool is generally build as a cuboid.
Volume of cuboid refers to the measurement of the space in the cuboid. It is the product of length, breadth and height of the cuboid.
Therefore the formula to calculate volume of cuboid will be:
[tex]\rm Volume\:of\:cuboid = \rm length\times breadth \times height[/tex]
The volume of the pool will be [tex]\rm 3a^8 b^4[/tex].
To reach the above answer, following calculations are required:
Given:
Dimensions of the pool:
[tex]\begin{aligned} \rm Length &= 3a^6\\\rm Breadth &= a^2\\\rm Height &= b^4\end[/tex]
Therefore, volume of pool will be as follows:
[tex]\begin{aligned} \rm Volume\:of\:cuboid &= \rm length\times breadth \times height\\&= 3a^6 \times a^2 \times b^4 \\&= 3a^{6+2}b^4\\&= 3a^8b^4 \end[/tex]
Volume of pool = [tex]\rm 3a^8b^4[/tex]
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find the least common multiple of 4 and 7
28 is the least common multiple. To find the least common multiple, you look through the numbers both 4 and 7 go into. The smallest of those number is the least common multiple, or LCD.
Answer: The least common multiple of 4 and 7 is 28.
Step-by-step explanation:
↓↓↓↓↓↓↓↓
First, find the prime factorization of 4.
2×2=4
Next, find the prime factorization of 7.
7×1=7
Then, multiply each factor the greater number of times it occurs.
7×2×2=28
Hope this helps!
Thank you for posting your question.
-Charlie
Jakes batting average for softball season is 0.368 what is Jake’s batting average written in expanded form
write the fact family. for 6, 4, 24
6 times 4 is 24
4 times 6 is 24
24 divided by 6 is 4
24 divided by 4 is 6
A figure in the first quadrant is rotated 180° counterclockwise about the origin. In which quadrant will the rotated figure appear?
A. first quadrant
B. second quadrant
C. third quadrant
D. fourth quadrant
Question
A figure in the first quadrant is rotated 180° counterclockwise about the origin. In which quadrant will the rotated figure appear?
A. first quadrant
B. second quadrant
C. third quadrant
D. fourth quadrant
Answer:
A. first quadrant.
Hope this helps!
C the third quadrant
under a counterclockwise rotation about the origin of 180°
a point (x, y ) in the first quadrant maps to ( - x, - y ) a point in the third quadrant.
-3|15-s|+2s^3 when s =-3?
Answer:
-3|15 - (-3)| + 2(-3)³ = -3|18| + 2(-27)
= -3(18) + 2(-27)
= -54 + (-54) = -108
what is the y intercept of -3x-5y=60
Answer: y-intercept = -12
Step-by-step explanation:
[tex]-3x = 60+5y[/tex] Add [tex]5y[/tex] on both side
[tex]-3x-60 = 5y[/tex] Subtract [tex]60[/tex] on both sides
[tex]-\frac{3}{5}x-12=y[/tex] Divide 5 on both sides
The y-intercept of the line -3x - 5y = 60 is equal to -12.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, a linear equation in standard form that models it is given by;
-3x - 5y = 60
By making y the subject of formula, we have the following:
5y = -3x - 60
y = -3x/5 - 12
By comparison, we have the following:
y-intercept, b = -12.
slope, m = -3/5.
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the sum of three consecutive even integers is 258. write an equation ad solve to find the integers
The consecutive integers are 85,86,87
Explanation:
n
:
the first number
n
+
1
:
the second number
n
+
2
:
the third number
n
+
(
n
+
1
)
+
(
n
+
2
)
=
258
3
n
+
3
=
258
3
n
=
258
−
3
3
n
=
255
n
=
255
3
n
=
85
n
+
1
=
85
+
1
=
86
n
+
2
=
85
+
2
=
87
which property is illustrated by the following statement? 50pts
2(-3/9)=(-3/9)2
Associative Property of Addition
Commutative Property of Multiplication*
Inverse Property of Multiplication
Commutative Property of Addition
* is the one i think it is. Am I Right?
When multiplying numbers, it doesn't matter which number is first or second.
The correct answer is: Commutative Property of Multiplication
Hi!
2(-3/9)=(-3/9)2
Answer - Communative Property of Multiplication
The reason thats the answer is because the fact that is dosent matter what number goes first or last, it will still be the same result.
Help please i dont know what to do?
plug the numbers into the formula: V = (4*6)/3
simplify parentheses: V = 24/3
divide: V = 8
(5x^4-2x^3-7x^2-39)÷(x^2+2x-4)
Using the Polynomial Division: Divide 5[tex]x^{4}[/tex]−2[tex]x^{3} -7x^{2} -39 by x^{2}[/tex] +2x−4 using long polynomial division.
Answer to the Polynomial Division: [tex]5x^{2} -12x+37+\frac{-122x+109}{x^{2}+2x-4}[/tex]
The question deals with the division of two polynomial expressions in mathematics. The process involves division of highest degree terms in the polynomials and subtraction of the result from the numerator polynomial, similar to the technique of long division.
Explanation:The question involves the division of two polynomial expressions, which is a topic in Mathematics, specifically Algebra. The division of polynomials is performed similarly to the long division we use for numbers. In this case, the polynomial (5x^4-2x^3-7x^2-39) is divided by the polynomial (x^2+2x-4).
To perform the division, we divide the highest degree terms in the polynomials. So, we divide 5x^4 (from the numerator polynomial) by x^2 (from the denominator polynomial) to get 5x^2. Multiply this by the entire denominator polynomial and subtract the result from the numerator polynomial. The process is continued until we cannot continue dividing any further.
The result is your answer, which might be another polynomial or a number. Similar to long division with numbers, there might be a remainder after the division.
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Which numbers below belong to the solution set of the equation 16x=224
x would equal 14 hope this helps