[tex]\huge\boxed{x-2y=-6}[/tex]
Hey there! We can solve this problem by setting up the equation in slope-intercept form and changing it into standard form.
(I'm assuming that the problem meant the slope is [tex]\frac{1}{2}[/tex].)
[tex]\begin{aligned}y&=mx+b&&\smash{\Big|}&&\text{Start with slope-intercept form.}\\y&=\frac{1}{2}x+3&&\smash{\Big|}&&\text{Substitute in the known values.}\\-\frac{1}{2}x+y&=3&&\smash{\Big|}&&\text{Move the variables to the left.}\\x-2y&=-6&&\smash{\Big|}&&\text{Multiply everything by $-2$.}\end{aligned}[/tex]
differentiate the given function:
Answer:
[tex]\displaystyle h'(x) = \frac{1 + x - arcsin(x)\sqrt{1 - x^2}}{\sqrt{1 - x^2}(1 + x)^2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationAlgebra II
SimplifyingCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative 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]
Special Trig Derivatives:
Arcsine: [tex]\displaystyle \frac{d}{dx}[arcsin(x)] = \frac{1}{\sqrt{1 - x^2}}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle h(x) = \frac{arcsin(x)}{1 + x}[/tex]
Step 2: Differentiate
Quotient Rule: [tex]\displaystyle h'(x) = \frac{(1 + x)\frac{d}{dx}[arcsin(x)] - \frac{d}{dx}[1 + x][arcsin(x)]}{(1 + x)^2}[/tex]Special Trig Derivative [Arcsine]: [tex]\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - \frac{d}{dx}[1 + x][arcsin(x)]}{(1 + x)^2}[/tex]Derivative Property [Addition/Subtraction]: [tex]\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - (\frac{d}{dx}[1] + \frac{d}{dx}[x])[arcsin(x)]}{(1 + x)^2}[/tex]Basic Power Rule: [tex]\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - 1[arcsin(x)]}{(1 + x)^2}[/tex]Multiply: [tex]\displaystyle h'(x) = \frac{\frac{1 + x}{\sqrt{1 - x^2}} - arcsin(x)}{(1 + x)^2}[/tex]Rewrite [Multiply]: [tex]\displaystyle h'(x) = \frac{\frac{1 + x}{\sqrt{1 - x^2}} - arcsin(x)}{(1 + x)^2} \cdot \frac{\sqrt{1 - x^2}}{\sqrt{1 - x^2}}[/tex]Simplify [Multiply]: [tex]\displaystyle h'(x) = \frac{1 + x - arcsin(x)\sqrt{1 - x^2}}{\sqrt{1 - x^2}(1 + x)^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Anybody Know This. ?
Answer: (Option 1) They are similar triangles.
Step-by-step explanation: Just because there are different letters doesn’t mean that they aren’t similar triangles. The measurements are also alike, so you can call them congruent and similar.
Is this rational or irrational I really need help ASAP! Will mark brainlist.
Answer:
Irrational
Step-by-step explanation:
Since 7 is a prime number, it has no square factors and its square root cannot be simplified. It is an irrational number, so cannot be exactly represented by pq for any integers p,q .
Answer: irrational
Step-by-step explanation: 7 is a prime number and its square root can not be simplified.
Hope this helps!
Need help asap! Complete the table below.
Answer:
Step-by-step explanation:
if the speed is 6 bracelets per hour then the table will go like this
2 12
5 30
7 42
11 66
16 and 2/3 hours is 100 bracelets
What is the product of -5/8 and -6/7
Answer:
-1 27/56
Step-by-step explanation:
Using the given fractions,
−58+−67
Applying the fractions formula for addition,
=(−5×7)+(−6×8)8×7
=−35+−4856
=−8356
Simplifying -83/56, the answer is
=−12756
Evaluate the expression
b(a + c)
when a= = -3, b= -4, and c= 2
Step-by-step explanation:
b(a + c)
=-4(-3+2)
=12-8
=4
Answer:4
Step-by-step explanation:
Steps a (-3) add c (2) is -1
Then you have to times -1 by -4 which is 4 :D
Find the distance between the two points
I just need help with this please.
Answer:
-5/2 is located on the left of -1
Step-by-step explanation:
50 POINTS!!!
Please I need fast and correct answer. I will award best answer with brainliest!!!
Answer:
[tex]measure angle 1 = 62 ------> given\\measure angle 4 = 62 --------> vertical angle theorem[/tex]
Step-by-step explanation:
vertical angle theorem states that the angle vertical from another angle has to be congruent
p.s. i found it
There are 8 roses in a vase of 13 flowers. The rest are daisies.
(a) What is the ratio of daisies to roses?
0
X х
(b) What is the ratio of all flowers in the vase to daisies?
?what is it
Answer:
a.) 8/5
b.) 5/13
Which inequality is represented by this graph?
Answer:
x>0
Step-by-step explanation:
What is the equation of a line that passes through the point (3, 11) and is parallel to the line y=2x-4
Answer:
The answer should be y=2x+5
What fraction of an hour is 28 minutes?
Give your answer in its simplest form.
Answer:
3.57
Step-by-step explanation:
A local charity is making fruit baskets for elderly citizensbin the neighborhood. Each badket have 15:pieces of fruit. They brought 1,620 pieces of fruit total. Without completing the division, choose Yes or No for each statements
Answer
They can make at least 1,000 baskets
They can make at least 10 baskets
Answer:
Yes, no, no
Step-by-step explanation:
Answer:10 baskets yes
100 baskets yes
1000 baskets no
Step-by-step explanation:
How can you find the slope of the line that passes through the points (0, 0) and (2, 4)? Explain.
The slope of the line that passes through the points (0, 0) and (2, 4) is m = 2
The slope(m) of the line passing through the points (x₁, y₁) and (x₂, y₂) is given by the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
For the line that passes through the points (0, 0) and (2, 4)
x₁ = 0, y₁ = 0, x₂ = 2, y₂ = 4
Substitute x₁ = 0, y₁ = 0, x₂ = 2, y₂ = 4 into the equation [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{4-0}{2-0} \\\\m = \frac{4}{2} \\\\m = 2[/tex]
The slope of the line that passes through the points (0, 0) and (2, 4) is m = 2
Learn more here: https://brainly.com/question/23935638
if Jazzy sells her old bike for $104 and some toys for 68 she uses the money for four month karate lessons the cost of lessons is the same each month which strip diagram shows how to find Jazzy's cost for one month of karate lessons.lend a hand please also this is 4th grade
Answer:
C
Step-by-step explanation:
She sells her bike for 104 dollars
She sells toys for 68 dollars
Total 172
The question is a bit ambiguous. There are 4 divisions. So I would assume that you need to divide 172 by 4. If you do that you get 43
I think that what they are getting at is the answer is C. There are 4 months shown. And 1 month would be 43 dollars. She has enough for 3 more months.
Do people who sit for at least 8 hours per day have more health problems than
those who sit for fewer than 8 hours per day?
Is statistical or non-statistical?
Answer:
Its statistical
Step-by-step explanation:
7 Given: -8(w + 1) = -5(w + 10); Prove: w = 14
Statements
Answer:
w=14
Step-by-step explanation:
-8(w + 1) = -5(w + 10)
Remove the parentheses
-8w-8+-5w-50
Move terms
-8w+5w=-50+8
Collect like terms and calculate
-3w=-42
Then divide on both sides
Given: a mod 7 = 5 and b mod 7 = 6 Find (a + b)mod 7. Do not use specific numbers for a and b. Consider a, b as generic particulars. Show steps but you do not need to provide reasons.(7 points)
Answer:
wouldn't it be 77
Step-by-step explanation:
If 7 = 5 is a and 7 = 6 is b and you add them you will get 11 then multiply it by 7 which would give you 77
or If you add 7 + 7 = 14 multiply 11
Or the answer is 154
How many parts 3 percent milk and 40 percent cream would be needed to make 500 pounds of 5 percent milk
Answer:
ok i have this same question so what you are going to take the 3 and just maove it to the side and then you fail
Step-by-step explanation:
Multiply. Enter your answer as a simplified mixed number.
-4(7/10)
The product is:
Answer:
−2.8 or - 2 8/10
Step-by-step explanation:
hope that helps
A construction company can remove 3/4 tons of dirt from a construction site each hour. how long will it take them to remove 36 tons of dirt from the site? (Answer needs to be in simplest form)
Answer:
48hours
Step-by-step explanation:
36÷(3/4)
36*(4/3)
144/3
48
Whats the rate and unit rate for 7 pencils for 9 dollars
Answer:
7 to 9
Step-by-step explanation:
The sum of two numbers is 32. The larger is 3 less than 6 times the smaller. What is the larger number?
Answer:
23
Step-by-step explanation:
32=3x-4+x
32=4x-4
+4 +4
36=4x
/4 /4
9=x
Larger #= 3x-4
Larger #= 3(9)-4
Larger #= 27-4
larger #= 23
Help me
Solve 5n = 35.
Answer:
n=7
Step-by-step explanation:
7 times 5 equals 35.
Answer:
n=7
Step-by-step explanation:
Give:5n = 35
To solve the n. we need to divide both side by 5.
5n/5=35/5
n=7
how many solutions are there 14x + 6 = 2(5 + 7x) - 4
Answer:
infinitely many solutions
Step-by-step explanation:
14x + 6 = 2(5+7x)-4
14x + 6 = 10 + 14x - 4
14x + 6 = 14x + 6
infinitely many solutions because both sides of the equation are equal
Dillon is packing equal quantities of pretzels and crackers for snacks. Dillon bags the pretzels in groups of 5 and the crackers in groups of 11. What is the smallest number of crackers that he can pack?
someone plz help me please
Answer:
16. c)
12. b)
10. c)
2. a) <- you were right
4. a)
Step-by-step explanation:
16. 10x - 2y = -6
-2y/-2 = (-10x - 6)/-2
y = 5x + 3
12. x + y = -3
y = -x - 3
Answer:
one is C. Two is A. Not sure about third but the 4 one is correctly A. Last one is C. i'm so sorry if this sucked. I really hoped this helped! Sorry if it's wrong :)
Write an equation to match this graph
Answer:
its y=x+7
Step-by-step explanation:
The length of a rectangle is
4
inches more than
4
times the width. If the area of the rectangle is
168
square inches, find the length and the width.
Answer:42
Step-by-step explanation: