Answer:
[tex]\displaystyle f'(-3) = \frac{7}{9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightCalculus
Derivatives
Derivative Notation
Derivative of a constant is a 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle f(x) = \frac{-7}{x}[/tex]
[tex]\displaystyle x = -3[/tex]
Step 2: Differentiate
Quotient Rule: [tex]\displaystyle f'(x) = \frac{\frac{d}{dx}[7]x - \frac{d}{dx}[x](-7)}{x^2}[/tex]Basic Power Rule: [tex]\displaystyle f'(x) = \frac{(0)x - x^{1 - 1}(-7)}{x^2}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{(0)x - x^0(-7)}{x^2}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{(0)x - 1(-7)}{x^2}[/tex]Multiply: [tex]\displaystyle f'(x) = \frac{0 + 7}{x^2}[/tex]Add: [tex]\displaystyle f'(x) = \frac{7}{x^2}[/tex]Step 3: Solve
Substitute in x [Derivative]: [tex]\displaystyle f'(-3) = \frac{7}{(-3)^2}[/tex]Evaluate exponents: [tex]\displaystyle f'(-3) = \frac{7}{9}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Solve 9x + 18 = 6y - 3x for y
Answer:
y = 2x + 3
Step-by-step explanation:
The length of rectangle PQRS is expressed as 2x+7. The width of rectangle PQRS is expressed as 3x−4. Which expression describes the area of rectangle PQRS?
A.6x^2
B.6x^2-29x-28
C.6x^2-15
D.6x^2+13x-28
Answer:
[tex]area = length \times width \\ = (2x + 7)(3x - 4) \\ = (6 {x}^{2} - 8x + 21x - 28) \\ = (6 {x}^{2} + 13x - 28) \: sq \: units[/tex]
The area of the rectangle PQRS is given by the formula D) 6x²+13x-28.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
The area of a rectangle is given by the formula:
A = l × w, where l is the length and w is the width.
In this case,
The length is 2x + 7 and the width is 3x - 4.
Therefore, the area of the rectangle is:
[tex]A = (2x + 7)(3x - 4)\\A = 6x^2 - 8x + 21x - 28\\A = 6x^2 + 13x - 28[/tex]
Therefore, the expression that describes the area of rectangle PQRS is D) 6x²+13x-28.
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(x+1)^2 = -4
What are the solutions?
Answer:
x = 4i - 1 or
x = 4i + 1
Step-by-step explanation:
(x+1)^2 = -4
x+1 = (+-)4i
x = +-4i - 1
==>
x = 4i - 1 or
x = 4i + 1
PLEASE HELPP :(
Does the relationship shown in the table represent a direct or inverse variation relationship?
A: Direct, as x increases, y also increases
B: Direct, as x increases, y decreases
C: Inverse, as x increases, y also increases
D: Inverse, as x increases, y decreases
Step-by-step explanation:
i think
C: Inverse, as x increases, y also increases
Step-by-step explanation:
C: Inverse, as x increases, y also increases
hope it is helpful to you
Help PLEASE ILL MARK BRAINLIEST!!!
Mario ran backwards 5 spaces then jumped up 3 spaces. How can we show this as an ordered pair?
Please help!! Thanks in advance!! NO links!!
Kallan will spin each spinner one time. What is the probability that the first spinner will land on a number greater than 7 and the second spinner will land on blue?
Answer:
probability for numbers greater than seven would be: 5/12
probability for landing on blue would be: 2/8
Step-by-step explanation
first, I counted all of the spaces, then I counted only the blue , or only the numbers over 7.
Can somebody please help? It don't get it
Answer: 4
14 is shown... then you have 10 that is shown how much more would it take to make 14..... 4 more
10+x=14
x=4
Answer:
Equation: 14 - j = 10
j = 4
Step-by-step explanation:
You are road tripping down the California coast and you notice you need to fill up your gas tank. In CA, sales tax is 2.25%. You spend $56.00 to fill up your tank. How much are you paying in sales tax?
Answer:
$1.26
Step-by-step explanation:
So you just have to find 2.25% of 56.
To find a certain percentage of something, you multiply it. Let's write out a sentence explaining what you need to do. You have to find:
2.25% of 56
Whenever you've got a sentence like this, all you've got to do is change the word "of" to a multiplication symbol. And now you've got an expression:
2.25% × 56
Let's convert the percentage to a decimal. To do this, you simply remove the percent symbol, then move the decimal point 2 places to the left.
2.25% = 0.0225
And now you have:
0.0225 × 56
Then you just do the math! I am assuming you already know how to do decimal multiplication so I'm not going to explain the process here.
But once you multiply 0.0225 × 56, you get an answer: 1.26
Hope this was helpful to you, and don't forget to choose the Brainliest answer!
how do i do tangent lines?
Answer:
x = 154°
Step-by-step explanation:
The 4 interior angles of the quadrilateral sum to 360°
The angles between the tangents and the radii = 90°
Then
x = 360° - (90 + 90 + 26)° = 360° - 206° = 154°
how much paper is needed to cover a rectangular bulliten board that is 29 in. wide and 37 in. high?
Answer:
1073 inches squared.
Step-by-step explanation:
To find how much paper is needed to cover the board, you have to find the area. The formula of area for rectangles is length times width or as you said in the question width times height.
To find the answer:
Area = length * width
Area = 29 * 37
Area = 1073 inches squared.
Don't forget to add the units!
6(2x-3) - 2(2x+1)
can someone get an answer for that ASAP pls
no links :)
Answer: 8x−20
Step-by-step explanation:
Distribute:
=(6)(2x)+(6)(−3)+(−2)(2x)+(−2)(1)
=12x+−18+−4x+−2
Combine Like Terms:
=12x+−18+−4x+−2
=(12x+−4x)+(−18+−2)
=8x+−20
Answer:
[tex]6 \times 2x = 12x\\ 6 \times - 3 = - 18 \\ - 2 \times 2x = 4x \\ - 2 \times 1 = - 2 \\ now \: add \: like \: terms \\ 12x - 4x = 8x \\ - 18 - 2 = 20 \\ \frac{ - 8x}{8} = \frac{20}{8} \\ x = 2.5 \: or \: \frac{5}{2} [/tex]
Step-by-step explanation:
brainiest please
The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job: Have Cell Phone Do Not Have Cell Phone Total Have Part time Job 40 10 50 Do Not Have Part time Job 10 40 50 Total 50 50 100 Based on the table, how many students have both a cell phone and a part-time job? (5 points) Question 14 options: 1) 10 2) 40 3) 50 4) 100
Answer:
I think it is B, so the correct answer is 40
Step-by-step explanation:
Answer:
The other guy is correct, the correct answer is B. 40.
Step-by-step explanation:
Under Students that have a cell phone and under students that have a part-time job the total amount of people is 40
Find the total area round to the nearest 10th if necessary use the pi symbol on calculator
Answer:
[tex] Total \:area\approx 290.5\: ft^2 [/tex]
Step-by-step explanation:
Total area [tex] =\frac {1}{2} \pi r_1^2 +\frac {1}{2} \pi r_2^2 [/tex]
(where [tex] r_1 = 22/2 = 11 \: ft, \: \:\:r_2 = (30-22)/2 = 4 \: ft[/tex])
[tex]\therefore Total \:area=\frac {1}{2} \pi( r_1^2 + r_2^2) [/tex]
[tex]\therefore Total \:area=\frac {1}{2} \times 3.14(11^2 + 8^2) [/tex]
[tex]\therefore Total \:area=1.57(121 + 64) [/tex]
[tex]\therefore Total \:area=1.57(185) [/tex]
[tex]\therefore Total \:area=290.45\: ft^2 [/tex]
[tex]\therefore Total \:area\approx 290.5\: ft^2 [/tex]
When graphing a sine curve model using the equation Y = sin bx, the period (or wavelength) will be represented by
3
27
So be
period
Determine the equation for the sine curve that models the G# wave if the
wavelength of G# = 0.828 meters.
a.
y = sin(6.03x)
b. y = sin(0.828x)
C. y = sin(5.68x)
d. y = sin(7.59x)
Please select the best answer from the choices provided
use pic to answer
Answer:
its D, y= sin(7.59x)
Step-by-step explanation:
just took the quiz on edge
how to tell the transformation of graphs?
Answer:
:D
Step-by-step explanation:
if the parent function, y=f(x) has a number added (y=f(x)+4) the graph will be translated up. If the parent function has a number subtracted, y=f(x)-4, the graph will be translated down. The image explains more simply, and there are more possible translations (shown in image)
A triangle has interior angles of 101 degrees, 65 degrees, what is the other degree?
Answer:
180 degrees - 101 degrees - 65 degrees = 14 degrees
Michelle drives her car around a square track each side of the track is 30 feet long. How many times does the car need to go around the track to go a total distance of1,200 feet/
Answer:
10 times
Step-by-step explanation:
distance covered once is equal to the perimeter of the square
perimeter of the square = 4 x length
4 x 30 = 120 ft
number of times = 1200 / 120 = 1-
Select the correct answer.
What is the value of x in the triangle?
Answer:
D. 2√2
Step-by-step explanation:
sin 45° = 1/√2
P/H = 1/√2
x/4 = 1/√2
= 1/√2 × 4
= 4/√2
x = 4×√2/√2×√2
= 4√2 /2
= 2√2
Option D. 2√2
A boat leaves the dock and travels 7 miles due south, then 24 miles due west.
How far is the boat from the dock?
A. 625 mi
B. 31 mi
C. 17 mi
D. 25 mi
Answer:
D
Step-by-step explanation:
The boat is a distance of 25 miles far away from the dock. which is the correct would be an option (D).
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
A boat leaves the dock and travels 7 miles due south, then 24 miles due west which is given in the question.
According to Pythagoras's theorem,
In a right-angled triangle, "the square of the hypotenuse is equal to the sum of the squares of the other two sides."
perpendicular²+base²=hypotenuse²
The hypotenuse = c
Here , perpendicular = 7 and base = 24
⇒ 24² + 7² = c²
⇒ 576 + 49 = c²
⇒ 625 = c²
⇒ c² = 625
⇒ c = 25
Therefore, the boat is a distance of 25 miles far away from the dock.
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could you help me with this maths problem please
10 - ____ = 9 1/8
i need to find the fraction taken away from 10 to get 9 1/8
Answer:
12
Step-by-step explanation:
I forgot Sorry
Answer:
The answer is 7/8.
You can simply bring 9⅛ to the left hand side
You'll have your answer .
To verify
10-7/8 = 73/8
which further simplifies to 9⅛.
Thanks
5 of 10
A fair dice is rolled.
Work out the probability of getting a number more than 4.
Give your answer in its simplest form.
Answer: 1/3
Step-by-step explanation:
numbers more than 4 are: 5, and 6
so 2/6 chance of rolling a number greater than 4
in simplest form this is 1/3
Answer:
number 4 are t is greater
If P( 9,r ) = 3,024, what is r ?
plz plz plz... help mè
I mark it... :(
Answer:
[tex] \frac{9i}{(9 - r)i} = 3024 \\ (9 - r)i = 9i \div 3024 = 362880 \div 3024 = 120 = \\ = 1 \times 2 \times 3 \times 4 \times 5 = 5i \\ r = 4[/tex]
Help! Will give out brainliest
Answer:
75
Step-by-step explanation:
don't know how to explain hope this helps
it would be 75
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Please help I need to get this done
Answer:
48
Step-by-step explanation:
So you take 7x-92+6x+12=180
And then you get x=20
Plug in 20 for x for <LOM
And you get and you get 48
Hope this helped!!
Tell whether the statement is always, sometimes, or never true. Explain.
1. If x and y are supplementary angles, then y is acute.
2. If x and y are complementary angles, then x is obtuse.
Answer:
1. If x and y are supplementary angles, then y is sometimes acute because supplementary angles are angles that add up to 180 degrees. So, y can be acute while x can be obtuse, y can be obtuse while x can be acute, or both can be right angles.
2. If x and y are complementary angles, then x is never obtuse. Complementary angles are angles that add up to 90 degrees, and obtuse angles are angles over 90 degrees, so it's impossible to have an obtuse angle as a complementary angle.
Step-by-step explanation:
Answer:
1) Sometimes
2) Never
Step-by-step explanation:
1) you could have two angles add up to 180 degrees and one of them could be less than 90
example, x = 140° and y = 40°
2) if two angles are complementary then their sum is 90° so neither angle must be less than 90°, thereby making them both acute angles
PLEASE HELP!!!! I NEED THE ANSWERS URGENTLY!
Find each missing length. Give all answers in simplest radical form.
Step-by-step explanation:
here's your solution
==> by using Pythagoras theorem
==> base^2 = hypotenuse^2 - perpendicular^2
==> hypotenuse = 18 , perpendicular = 16
==> base^2 = 18^2 - 16^2
==> base^2 = 324 - 256
==> base^2 = 68
==> base = √68
==> base = 8.24
[tex]hope \: it \: helps[/tex]
Is the ratio 15:12 equivalent to these? Explain your reasoning.
Let's simplify the ratio
[tex]\\ \sf\longmapsto 15:12[/tex]
[tex]\\ \sf\longmapsto \dfrac{15}{12}[/tex]
Cancel by 3[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]
[tex]\\ \sf\longmapsto 5:4[/tex]
Find the distance between the points
Answer:
12 hope this help
Step-by-step explanation:
HELP PLEASEEEE I WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
we need to make two rectangles.
one that is 13.1 Km X (9.3-4.2) Km
13.1 * 5.1 = 66.81
the next box is 4.2 X (13.1-8.1)
4.2*5 = 21
area total = 21 + 66.81 = 87.81[tex]Km^{2}[/tex]
Help help help help help help dont troll
Answer:the correct answer is C
Step-by-step explanation: