Answer:
f'(x) = [tex]\frac{1}{x+2}[/tex]
Step-by-step explanation:
using the chain rule to differentiate
f(x) = g(h(x)) , then
f'(x) = g'(x) × h'(x)
f(x) = ln(2x + 4) , then
f'(x) = [tex]\frac{1}{2x+4}[/tex] × [tex]\frac{d}{dx}[/tex] (2x + 4)
= [tex]\frac{1}{2x+4}[/tex] × 2
= [tex]\frac{2}{2x+4}[/tex]
= [tex]\frac{1}{x+2}[/tex]
Simplify the expression using the Distributive Property and explain each step.
70[2.50+(−0.60)]+25[3.75+(−0.70)]
The new expression by using distributive property is: 209.25
What is distributive property?
In mathematics, the distributive property tell the solution method for the expression who are in the form of a(b + c). In this, first add the expression which are in the parenthesis and later multiply it.
According to the question, the given expression is as follows:
70[2.50+(−0.60)]+25[3.75+(−0.70)]
Using distributive property, whose list contains parenthesis, exponents, multiplication/division, addition/subtraction. This is the list in which the given expression need to simplify.
First parenthesis calculation,
2.5 + - 0.6 = 1.9 and 3.75 + - 0.7 = 3.05
Now, substitute the values:
70(1.9) + 25(3.05)
Multiply it: 133 + 76.25;
Add it: 209.25
Hence, the new expression by using distributive property is: 209.25
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what is the slope of a line that runs through the points (10,10) and (5,10)
The slope of the line that passes through the points (10,10) and (5,10) is 0
How to determine slope of a line?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1 ( 10,10 )
x₁ = 10y₁ = 10Point 2 ( 5,10 )
x₂ = 5y₂ = 10To determine the slope, plug these coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 10 - 10 )/( 5 - 10 )
Slope m = ( 0 )/( 5 - 10 )
Slope m = ( 0 )/( -5 )
Slope m = 0
Therefore, the slope of the line is 0.
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One week, Claire earned $395.00 at her job when she worked for 25 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $126.40?
hurry, please<3
Answer:
8?
Step-by-step explanation:
so if 25 hours gets her to 395 dollars that you divide 395 by 25 to get how much money she makes per hour.
you get 15.8 then you have to see how many hours she has to work to make 126.40 which is 8 cuz 15.8 * 8 = 126.4
I THINK??
Rashon has a dimes and y nickels. He has no less than 12 coins worth at most $0.95
combined. Solve this system of inequalities graphically and determine one possible
solution.
A possible solution of the system of inequalities is 5 dimes and, 8 nickels
How to determine a possible solution?From the question, the given parameters are:
Number of coins = Not less than 12
Worth = At most $0.95
Represent dime with x and nickels with y
So, we have the following inequalities
x + y >= 12
0.1x +0.05y <= 0.95
Next, we plot the graph of the inequalities (see attachment)
From the graph, we have a possible solution to be (5, 8)
This is so because this point is in the shaded region
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Find the value of the variable.
Answer:
x = 22
Step-by-step explanation:
(88 - x)° = 3x°
-x - 3x = -88
-4x = -88
[tex]x = \frac{-88}{-4} \\\\ x = 22[/tex]
what is eighty nine divided by six
Answer:
about 14, (its not a whole number but its the closest i could get)
Step-by-step explanation:
Answer:
14.833333333
Step-by-step explanation:
I'm assuming you want a rounded answer (14.83), but if you didn't it's 14.83 into perpetuity (meaning that the 3's don't end!)
Hopefully, I helped!
Kayla's mom left a 20% tip for a restaurant bill that was $35. She used the expression 1.20 (35) to find the total cost. Which equivalent expression could she also use to find the total cost?
O 35 +0.2
O (1+0.2)35
O 1+0.2(35)
O 1.02(35)
The equivalent expression which could be used to find the total cost is; ( 1 + 0.2 ) 35.
What is the equivalent expression to the given expression 1.20 (35)?It follows from the task content that the expression which is equivalent to 1.20(35) as given in the task content is to be determined.
Since the given expression whose equivalent is to be determined is; 1.20 (35).
Since a 20% tip indicates a 0.2 fraction of the whole, the resulting equation is therefore;
( 1 + 0.2 ) 35.
And ultimately, the required equivalent expression is; (1 + 0.2) 35.
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Question number 4, how do I do the equation for question 4?
100 ml of the first solution and 200 ml of the second are required.
I need this answer in detail as soon as possible.
This is grade 6 maths
It will be better if you write in in a paper step by step answer and attach the picture.
The answer is 14metres 4m long 3m wide 2 x (4+3) = 14
I know it's easy but, I'm thinking of different ways of doing it.
Answer:
9 students
Explanation:
Every 8th person that entered the cinema received a free ticket.
The number of students who entered in the first hour = 76.
The first person given a ticket was the 8th person.
To calculate the number of persons who received a free ticket, we can view this problem as an arithmetic sequence in which:
• The first term = 8
,• The last term = 76.
,• The common difference (every 8th person) = 8.
Using the formula for the last term of an arithmetic sequence, we have:
[tex]\begin{gathered} l=a+(n-1)d_{} \\ 76=8+8(n-1) \end{gathered}[/tex]Our goal is to find n, the number of students.
[tex]\begin{gathered} 76=8+8n-8 \\ 76=8n \\ n=\frac{76}{8} \\ n=9.5 \end{gathered}[/tex]Since the number of students that entered in the first hour is not more than 76, we have that:
[tex]\begin{gathered} n\le9.5 \\ \implies n=9 \end{gathered}[/tex]9 students received a free ticket.
Geometry lvl 1 stuff but im dum
Answer:
A
Step-by-step explanation:
Point A
:] its ok we all dum sometimes lol
The ratio of mystery books to fantasy books in the library is 7:9.
Fill in the missing values to show the possible number of
mystery and fantasy books.
Mystery Books Fantasy Books
21
Select Answer -
63
Select Answer -
27
54
Select Answer
117
Answer:
42
81
91
Step-by-step explanation:
m = mystery
f = fantasy
[tex]\frac{m}{f}[/tex] = [tex]\frac{m}{f}[/tex]
Compare the ratio with the actual numbers. Solve for the missing number
[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{54}[/tex] you need to multiply 9 by 6 to get 54 so multiply 7 x 6 to get 42.
[tex]\frac{7}{9}[/tex] = [tex]\frac{63}{f}[/tex] Multiply 7 x 9 to get 63,so multiply 9 by 9 to get 81.
[tex]\frac{7}{9}[/tex] = [tex]\frac{m}{117}[/tex] 9 x 13 is 117, so multiply 7 by 13 to get 91.
Pls help me with this due tomorrow!
Answer: y = 3x +1
Step-by-step explanation:
y =mx +b
m(slope) = 3
b(y-int) = ?
y = 3x+b
substitute in values
4 = 3(1) +b
4 = 3+b
b = 1
y= 3x+1
Kareem went for a drive in his new car. He drove at a speed of 63 miles per hour for 157.5 miles. For how many hours did he drive?
Answer: He drove for 2 hours and 30 minutes. Hope you do great! :)
Answer:2.5 hours
Step-by-step explanation:
HELP! I have a paper due and I have no idea how to do this problem! I attached a screenshot of the problem any help is appreciated.
Answer:
7.5
Step-by-step explanation:
750 is the volume, so divided by then is 75, then divided by 10 again is 7.5
Hope this helps!
Answer:
7.5
Step-by-step explanation:
10x10x7.5=750
Jenna had a collection of 206 quarters, nickels, and dimes. She has twice as many nickels as
she does dimes. All of her coins together are worth $31.70. How many of each coin does she
have?
With equational proof
In linear equation, $56.65are the value of the coins in dollars .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.We need to find how many of the 206 coins are nickels, dimes, or quarters.
We know the quantities of each coin in relation to one another.
From that relationship we can set up a ratio.
Let Q = number of quarters
Let D = number of dimes
Let N = number of nickels
Then Q:D:N = 1:1:2
this tells us if the girl had 4 coins, she would have 1 quarter, 1 dime, and 2 nickels.
We want to keep this same ratio but we want the total number of coins to be 206.
If we divide 206 by 4, we get the number that we use to multiply our ratio.
206/4 = 51.5
So she has 51.5 quarters, 51.5 dimes, and 103 nickels.
the value of the coins in dollars = 51.5(0.10) + 51.5(0.05) + 103(.25) = $56.65
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What is a line that passes through (3,1) and (0,-3)
Graph slope
Answer:
y=4/3x-3
Step-by-step explanation:
(y2-y1)/ (x2-x1)
Factor each quadratic expressionx^2-2x-15
When we are factoring a quadratic function, we are trying to reverse the following equation
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now, comparing the right-hand side of the above equation and the one given in the problem we see that
[tex]\begin{gathered} a+b=-2 \\ ab=-15 \end{gathered}[/tex]This means the question simplifies to "what are the two numbers that if I add them I get -2 and if I multiply them I get -15? "
Well, If we set a = -5 and b = 3, then
[tex]\begin{gathered} -5+3=-2 \\ -5\cdot3=-15 \end{gathered}[/tex]Hence, our expression factors to
[tex](x-5)(x+3)[/tex]francesco obtains a loan of $18,965.00. the loan has a simple interest rate of 3%. how much interest will francesco owe at the end o the first year
The interest owned by Francesco at the end of one year would be $19023.69.
What is the formula to calculate the simple interest on a given principle amount?
The simple interest on a given principle amount [P] at rate [r%] for [t] years is given by -
I = (P x r x t)/100
Given is Francesco who obtains a loan of $18,965.00 at an interest rate of 3% for 1 year.
From the data given, we can write -
Principle amount = [P] = $18,965.00
Rate = [R] = 3%
Time = [T] = 1 year
Now, using the formula for calculating the simple interest, we get -
I = PRT/100
Substituting the values -
I = (18965 x 0.3 x 1)/100
I = (18965 x 0.3)/100
I = 189.65 x 0.3
I = 58.69
Amount = P + 58.69 = 18965 + 58.69 = 19023.69
Therefore, the interest owned by Francesco at the end of one year would be $19023.69
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Which inequality represents the situation: "Macy has at least $75 to spend on her homecoming
dress including a 8.1% tax?"
a. 0.081d > 75
b. d + 0.081d ≥ 75
c. d + 0.081d < 75
d. d + 0.081d ≤ 75
Write a word to match the equation. 3+( 4 x 12 )
Answer:
The sum of 3 and the product of 4 times 12.
Step-by-step explanation:
The equal sign would mean the words "the sum", which also corresponds with "3+". The 4 x 12 would be referred to by "the product" and "times".
A piece of pipe that is 8 feet long is cut into 1/4 ft pieces. How many pieces can be cut from the pipe?
Responses
A 30 pieces
B 28 pieces
C 8 pieces
D 32 pieces
Answer:it is 32 peices d
Step-by-step explanation:
Determine the domain of the function f(x) = 1/√x-1 + 1/√2-x
The domain of the function is 1 ≤ x < 2.
What is domain ?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).
We have f : [tex]\frac{1}{\sqrt{x-1} } + \frac{1}{\sqrt{2-x} }[/tex]
[tex]\sqrt{x-1}[/tex] ≥ 0
x- 1 ≥ 0
x ≥ 1
Similarly , [tex]\sqrt{2-x}[/tex] > 0
2 - x > 0
2 > x
So our domain is 1 ≤ x < 2.
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A circular swimming pool has a radius of 4
metres and a depth all over of 3 metres. Find the
volume of water in cubic metres, to the nearest
cubic metre. __m³.
Help please
Answer: The volume of the circular swimming pool to the nearest cubic meter is 151 [tex]m^{3}[/tex].
Step-by-step explanation: According to the question the swimming pool is in the shape of a cylinder, and the top is circular having a radius and depth.
To calculate the volume of a cylinder(pool) we will use the formula for the volume of a cylinder:
The radius of the cylinder = 4 m
height h=3
The volume of the cylinder (V) = [tex]\pi r^{2} h[/tex]
=[tex]\pi (4)^{2} *3[/tex]
Plugging π =3.142
= 3.14*16*3
=150.72 [tex]m^{3}[/tex]
rounding off to the nearest cubic meter
=151 [tex]m^{3}[/tex]
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Can you please help me , last one like this
Answer:
-5
Step-by-step explanation:
m = (11 - 6) / (13 - 14) = 5/(-1) = -5
Answer:
-5
Step-by-step explanation:
1-6/15-14=-5/1=-5
QUICKLYYY
Which situation below has the lowest constant of proportionality?
A) 40 ounces of fabric softener cost $20.00.
B) 20 ounces of powder laundry detergent costs $4.00.
C) 30 ounces of laundry scent boosters cost $12.12.
D) 90 ounces of liquid laundry detergent cost $36.00.
Answer: D
Step-by-step explanation:
Because I can math
Fill in the missing number.
80% of 95 =
Answer: The answer is 76
Step-by-step explanation:
I need help with this question
Answer:
x = 7
Step-by-step explanation:
For line q and line r to be parallel lines,
the angle with a measure of 108 and the angle represented with measure 15x + 3 must be alternate interior angles which means two angles have equal measures so we can write the following equation:
15x + 3 = 108 subtract 3 from both sides
15x = 105 divide both sides by 15
x = 7
PLEASE QUICK HELP MEE
Answer: 130 degrees
Step-by-step explanation:
The interior angle where line c intersects line b is equal to 50 (given). therefore, its supplementary angle is 130 degrees. the opposite angle is therefore equal to 130 degrees, which makes angel x equal to 130 degrees.
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Use the given graph to complete the table. Then write an equation representing the relationship.
The equation of the relation is y = 3/2x.
x | y
0 0
2 3
4 6
How to Write the Equation that Represents a Proportional Relationship?To write the equation for the proportional relationship between two variables, x and y, find the unit rate, k, which is k = y/x.
Substitute the value of k into y = kx to write the equation of the relationship.
Using a point on the line, (2, 3):
k = y/x = 3/2
Substitute k = 3/2 into y = kx:
y = 3/2x
Using the equation, substitute each of the values of x in the table to get the corresponding value of y:
For 0:
y = 3/2(0)
y = o
For 2:
y = 3/2(2)
y = 3
For 4:
y = 3/2(4)
y = 6
The table is:
x | y
0 0
2 3
4 6
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