The simplified expression for f(x+h) - f(x) / 6 is h.
We need to find and simplify the expression f(x+h) - f(x) / 6 for the function f(x) = 6x - 1.
Step 1: Find f(x+h)
To find f(x+h), replace 'x' with '(x+h)' in the original function f(x) = 6x - 1.
f(x+h) = 6(x+h) - 1
Step 2: Simplify f(x+h)
f(x+h) = 6x + 6h - 1
Step 3: Subtract f(x) from f(x+h)
Now, subtract f(x) from f(x+h) to get:
(f(x+h) - f(x)) = (6x + 6h - 1) - (6x - 1)
Step 4: Simplify the expression
(6x + 6h - 1) - (6x - 1) = 6h
Step 5: Divide by 6
Now, divide the expression by 6:
(f(x+h) - f(x)) / 6 = 6h / 6
Step 6: Simplify the final expression
6h / 6 = h
So, the simplified expression for f(x+h) - f(x) / 6 is h.
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I also need help on this one please help
Answer: blue
Step-by-step explanation:
or b
Santiago can text 74 words in 4 minutes. At this rate, how many minutes would it take him to text 37 words?
Fill out the table of equivalent ratios until you have found the value of x.
Answer:
To find the value of x in this situation, you can set up a proportion using equivalent ratios. The equivalent ratios will show the relationship between the number of words Santiago can text and the time it takes him to text them.
74 words : 4 minutes :: 37 words : x minutes
To solve for x, you can cross-multiply and divide:
74 * x = 37 * 4
x = (37 * 4) / 74
This simplifies to:
x = 2 minutes.
Step-by-step explanation:
Three children bought a ball. 1/2 of the money the first child took out is equal to 1/4 of the money taken out by the second child, but the third child took out $500 more than the first child. How much $ did each child make?
Using equations to solve the word problem, the first child withdrew $700, second child withdrew $1500, and third child withdrew $1250.
What is Word ProblemA word problem is a mathematical exercise that requires the student to read and understand a narrative description of a problem, identify the mathematical quantities involved, and then formulate and solve an equation to find the solution. Word problems often involve real-world scenarios such as shopping, money, and time.
Let's define our variables;
x = first childy = second childz = third childWe can proceed to write linear equations with our variables
1/2x = 1/4y ...eq(i)
z = 500 + x ...eq(ii)
From equation (i)
x = 1/2y
z = 500 + 1/2 y
x = 750
x = 1/2(y)
750 = 0.5y
y = 750 * 2
y = 1500
z = 500 + x
z = 500 + 750
z = 1250
The first child took out $750, the second child took out $1500, and the third child took out $1250.
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Find four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term. Show your work.
Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448
Four numbers forming a geometric sequence can be calculate as follows
these terms: a₁, a₂, a₃, a₄
a₁ = a₂ + 35
a₃ = a₄ + 560
Use the formula for the n-term:
a₂ = a₁r
a₃ = a₁r²
a₄ = a₁r³
replace
a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35
a₁r² = a₁r³ + 560 ⇒ a₁(1 - r)r² = 560
Subtracting from the first equation to the second:
r² = 560/35
r² = 16
r = √16
r = ± 4
Use the first equation to find the first term:
a₁( 1 ± 4) = 35
1. a₁ = 35/-3 = -35/3
2. a₁ = 35/5 = 7
We have two sequences:
r = 4
-35/3, -140/3, - 560/3, -2240/3
r = -4
7, -28, 112, - 448
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534 is what percent of 600?
show work
Answer:
89%
Step-by-step explanation:
534/600*100
= (534*100)/600
= 53400/600
= 89
Basics of percentage you can use this for also other unknown percentages just replace the “ 534 “ and the “ 600 “
Answer:
89‰
Step-by-step explanation:
[tex]\frac{534}{600} X100 = 89[/tex]‰
Now consider just a small mass element of the string. What is the vertical velocity of the string at the origin at time, t
The vertical velocity of the string at the origin at time t would be zero, as the origin is a fixed point.
The origin is a fixed point, so it does not move. This means that the vertical velocity of the string at the origin at time t would be zero.
The origin of the string is a fixed point, meaning that it does not move. This implies that the vertical velocity of the string at the origin at time t would be zero, as the origin does not move or change its position. Since the origin is a fixed point, the vertical velocity of the string at the origin at time t would remain constant, and would be equal to zero. Thus, the vertical velocity of the string at the origin at time t would be zero.
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Can somebody please help me with this ASAP? I need to show work too btw
Answer:
1) 92,22,66
2) 106,13,61
3) 87,34, 59
4)20,74,86
Step-by-step explanation:
1) Let the unknown angle be x
92 + 22 + x= 180( Sum of angles in a triangle )
114+ x = 180
x= 180-114
=66
2) 106+ 13 + x =180
119 +x = 180
x= 180-119
x= 61
3) 59+34 +x = 180
93+x = 180
x= 180-93
=87
4) 86+74 +x=180
160 +x =180
x= 180-160
=20
Answer:
the correct answer has to be c
8 less than 3 times a number is at most 30
8 less than 3 times a number is at most 30 can be written as 8 < 3N ≤ 30
How to write and solve a word problem?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Since 8 less than 3 times a number is at most 30
Let the number be N
Thus, 8 less than 3 times a number is at most 30 can be written as:
8 < 3×N ≤ 30
8 < 3N ≤ 30
Note: at most means less than or equal (≤)
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a₁
27. You invest an amount of money in mutual fund. After four years, the balance of your account is $1669.34
and after ten years, it is $2,576.29. If the amount of money that is in your account is said to be growing
exponentially, write a function that describes the amount of money in your mutual fund for time t. Then find
the value of the mutual fund after 15 years. (Hint: think y = ab*).
Answer:
417.335=x
Step-by-step explanation:
What are the factors that allow exponential growth to occur?
Exponential growth occurs when an entity experiences a rapid increase in size or output. This type of growth can be seen in companies, economies, and populations, and it requires certain conditions to be in place in order to be successful.
Factors that allow exponential growth to occurAbundant Resources: Access to abundant resources is a key factor for exponential growth to occur. This could be in the form of capital, resources, labor, and other inputs.Increasing Returns: Exponential growth requires increasing returns, which is when the output of a given input increases. This could be seen in the form of economies of scale, network effects, and other similar effects.Innovation: Innovation is another key factor for exponential growth. New products and processes can lead to a rapid increase in growth.Adaptability: The ability to quickly adapt to changing conditions is essential for exponential growth. Companies must be able to quickly adjust their strategies to capitalize on new opportunities.Risk Taking: Successful companies must be willing to take risks in order to achieve exponential growth. There are often no guarantees of success, but the potential rewards can be great.Learn more about exponential function: brainly.com/question/2456547
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Which of the following statements best describes the value of the expression 12x + 12, when x = 8? A. The result is not a whole number. B. The result is a prime number. C. The result is a composite number. D. The result is a whole number that is neither prime nor composite.
Answer: The result is a composite number
Hope this helps :)
Step-by-step explanation:
C
12x + 12, x=8
12*8 + 12
96 + 12
108
The number 108 is a composite number, but not prime and it is a whole number.
Sheila either walks or cycles to school
the probability she walks to school is 0.65
if she walks to school, the probability she is late is 0.4
If she cycles, the probability she is late is 0.1
Work out the probability that on any one day Sheila is late
The probability that Sheila is late on any one day is 0.295 or 29.5%.
We can use the law of total probability to find the probability that Sheila is late on any one day.
The law of total probability states that for any event B, the probability of event B occurring can be calculated by summing the probability of event B occurring given that event A has occurred, multiplied by the probability of event A occurring. Symbolically, this can be represented as:
P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2) + ... + P(B|An) * P(An)
In this case, event B is Sheila being late, and events A1 and A2 are Sheila walking or cycling to school, respectively. The probabilities of these events occurring are:
P(A1) = 0.65 (the probability that Sheila walks to school)
P(A2) = 0.35 (the probability that Sheila cycles to school, since 1- 0.65)
P(B|A1) = 0.4 (the probability that Sheila is late given that she walks to school)
P(B|A2) = 0.1 (the probability that Sheila is late given that she cycles to school)
Plugging these values into the equation gives:
P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2) = 0.4 * 0.65 + 0.1 * 0.35 = 0.26 + 0.035 = 0.295
So the probability that Sheila is late on any one day is 0.295 or 29.5%.
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if the first angle is 34 more than the 2nd and the 3rd is 5 less than twice the first what are the angles of the triangle?
The angles of the triangle are 20.75, 54.75, 104.5
What is the angle sum property of a triangle?The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°
Given here: if the first angle is 34 more than the 2nd and the 3rd is 5 less than twice the first. Let the second angle be x then first angle is x+34 and the 3rd angle is 2x+63
Using the triangle sum property we get
x+x+34+2x+63= 180
4x=83
x=20.75
Hence, the angles of the triangle are 20.75, 54.75, 104.5
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Marco is making blueberry muffins. The ratio between flour and blueberries for the recipe being used is shown in the table below.
Cups of Cups of
Flour Blueberries
14
21
22
How many cups of blueberries will Marco need if he has 2 cups of flour to use?
Acup
BO cup
2
6 cups
2
4
1
C014 cups
Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.
What is a ratio?An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3. 1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.
Here,
Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.
The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.
With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.
The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.
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6.
In George's classroom, there are 6 girls for every 2 boys. What is the ratio of boys to the total number of students
A. 1:3
B. 3:1
C. 1:4
D. 4:1
In the diagram of the right triangle shown, find the value of c.A.112 B.20 C.16 D.784
Answer:c
Step-by-step explanation:
Is circumcenter acute or obtuse?
An acute triangle's circumcenter may be found inside, on, or outside the triangle. Exactly midway down the hypotenuse is where a right triangle's circumcenter is located (longest side). Every time an obtuse triangle is formed, its circumcenter lies outside the triangle.
What is a triangle's circumcenter?The circumcenter of a triangle is the point where three perpendicular bisectors of its sides meet. A triangle's circumcenter is defined as the point at which the perpendicular bisectors of its own sides cross. In all other senses, the circumcenter is the point at which a triangle's sides intersect to form a bisector.
Thus, circumcenter is acute or obtuse is depend on the triangle's circumcenter.
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An acute triangle's circumcenter may be found inside, on, or outside the triangle. Exactly midway down the hypotenuse is where a right triangle's circumcenter is located (longest side). Every time an obtuse triangle is formed, its circumcenter lies outside the triangle.
What is a triangle's circumcenter?
The circumcenter of a triangle is the point where three perpendicular bisectors of its sides meet. A triangle's circumcenter is defined as the point at which the perpendicular bisectors of its own sides cross. In all other senses, the circumcenter is the point at which a triangle's sides intersect to form a bisector.
Thus, the circumcenter is acute or obtuse is depend on the triangle's circumcenter.
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The following sample space could represent which repeated experiment?
S: {WW, WL, LW, LL}
Rolling a number cube twice
Rolling a number cube once
Playing a video game twice
Playing a video game once
The sample space, S: {WW, WL, LW, LL} represent the experiment Playing a video game twice.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
1. Rolling a number cube twice
Drawing a possibility space allows us to see all the 36 outcomes of throwing a cube twice.
So, this is not the required case.
2. Rolling a number cube once
Drawing a possibility space allows us to see all the 6 outcomes of throwing a cube once.
So, this is not the required case.
3. Playing a video game twice
This case can be considered because it gives 4 outcome of Winning(W) and Losing(L).
4. Playing a video game twice
This case cannot be considered because it gives 2 outcome of Winning(W) and Losing(L).
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Answer:
yep its C :)
Step-by-step explanation:
I got it right on my quiz.
what are the values of x and y in the diagram below
Answer:
b. x = 62 degree, y = 118 degree
Step-by-step explanation:
x is the vertical angle to the 62-degree angle, so x = 62 degree
We see that the angle x add with the angle y equal to 180 degrees, so to find y, we take
180 - 62 = 118 degree.
So, the answer is b. x = 62 degree, y = 118 degree
Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
y = 4x² +3
If rotating a graph around a point leaves the graph intact, the graph is said to be symmetric with respect to that point.
How to find graph is symmetric?Since anything that is mirrored around a horizontal line will fail the Vertical Line Test, no function can by definition be symmetric about the x-axis (or any other horizontal line).
If rotating a graph around a point leaves the graph intact, the graph is said to be symmetric with respect to that point. When two points are always present on a graph, the graph is symmetric with respect to the origin.
If there is a point (a, b) on the graph for every (a, b) on the graph, then the graph is said to be symmetric with respect to the x axis, and f(x, y) = f(x, y).
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Find the lateral surface area and the total surface area of the following cylinder i.Radius =21cm and height= 45cm
ii.Radius =28cm and height=28
Answer:
Radius =21, height = 45
Lateral Surface Area = [tex]5937.61[/tex] cm²
Total Surface Area = [tex]8708.49[/tex] cm²
Radius = 28, height =28
Lateral Surface Area = [tex]4926.01[/tex] cm²
Total Surface Area = [tex]9852.03[/tex] cm²
Step-by-step explanation:
If r is the radius of a cylinder with height h
Lateral surface area
[tex]L = 2\pi rh[/tex]
Top and bottom surface area for each which is a circle is [tex]\pi r^2[/tex]
So total bottom and top surface area = [tex]2 \pi r^2[/tex]
Total surface area =
[tex]2\pi rh + 2\pi r^2 = 2\pi r(h + r)[/tex]
For r = 21, h = 45
[tex]L = 2 \pi \cdot 21 \cdot 45 = 1890 \pi = 5937.61 \;cm^2[/tex]
[tex]T = 2\pi \cdot 21 (21 + 45) = 2772 \pi = 8708.4948\;cm^2[/tex]
For r = 28, h = 28
[tex]L = 1568\pi = 4926.01 cm^2[/tex]
[tex]T = 3136\pi = 9852.03 \;cm^2[/tex]
What do you understand by combination and substitution reaction give one example each class 10?
The substitution reaction is defined as a reaction in which a small or functional part of one chemical compound is replaced by another group of chemical compound, or it is a reaction in which one atom or molecule of a substance gets replaced by another atom or molecule.
There are certain conditions which are to be followed while a substitution reaction,
The temperatures should be kept low, just like the room temperatureA strong base, such as NaOH, must be diluted for the reaction. If the base concentration is higher, there is a risk of dehydrohalogenation occurring.The solution must be aqueous in nature, example water.The hydrolysis of alkyl bromide (R-Br) under basic circumstances is an example of a substitution process. Example, R-Br + OH R -> OH + Br.
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What does it mean aspect ratio 1 to 3?
Aspect ratio refers to the proportion of the width to the height of a rectangular image or screen. It is commonly represented as two numbers separated by a colon, such as 4:3 or 16:9.
An aspect ratio of 1:3 means that the width of the image or screen is one-third of its height. This aspect ratio is not commonly used for standard images or screen sizes but it can be used for special cases such as vertical videos.
In general, for images and videos, the aspect ratio of 4:3 was used in the past, but now the aspect ratio of 16:9 is more common, and it's the standard aspect ratio used in most modern televisions, computer monitors, and digital cameras.
Also, it's worth noting that the aspect ratio of 1:3 represents a very elongated shape, and it's not suitable for most practical uses, as it would not be able to display most standard content without black bars on the top and bottom of the screen.
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y divided by 6.85=1.2
what dose y=
The value of y for the given conditions is 82.2.
What is division?Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
Given a phrase, y divided by 6.85=1.2
y ÷ 6.85 = 12
y/6.85 = 12
multiply both sides by 6.85
y/6.85(6.85) = 12 x 6.85
y = 82.2
Hence the value of y is 82.2.
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.4
Similar triangles JKL and NOP, with dimensions in centimeters (cm), are shown.
+
4 cm
K 4 cm
2 cm
J 4 cm
N
What is the length, in centimeters, of side OP?
PLEASE HURRY JDJDJDJNDND
The length in centimeters of side OP is 8.
Properties of similar triangles.A triangle is a plane figure which is bounded by three straight sides, and has a sum of its internal angle to be 180^o.
Two or more triangles can be referred to as similar if the corresponding sides and measure of corresponding internal angles have some common properties on comparison.
Thus on comparing the corresponding sides of the two given similar triangles, we have;
JK/ ON = KL/ OP
2/ 4 = 4/ OP
2OP = 4*4
= 16
OP = 16/ 2
= 8
OP = 8 cm
Therefore, the length of side OP is 8 cm.
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Which of the following graphs does NOT describe y as a function of x?
HELP ASAP!
Answer:
The second graph is not a function of x
Step-by-step explanation:
Note : -
1st graph : f(x) = secant inverse x
3rd graph : f(x) = c (constant function)
4th graph : It is a function which is +ve
HELP ME QUICK
In Shawn's class, all the students have pets. Of those pets,1/5 are cats. Of those cats, 2/3 are alley cats. What fraction of the pets are alley cats?
Answer:
2/15
Step-by-step explanation:
You want to know the fraction that is 2/3 of 1/5.
TimesIn this context, "of" means "times."
2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15
2/15 of the pets are alley cats.
PLEASE I NEED HELP WITH THESE (Tuesday & Thursday)
On solving the question we can say that the , plot the equation by points in the graph to get the line in the graph.
What are equation?Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.
The equation are
y = 1/2x - 2
for y = 0 , x= 4
and for x = 0 , y = -2
y = -3/4 x +
for y = 0 , x= 4
and for x = 0 , y = 3
Plot the points in the graph to get the line in the graph.
Again for
y = -2x + 1
for y = 0 , x = -1/2
for x= 0 , y = 1
and y = 3x -4
for y = 0 , x = 4/3
and for, x =0 , y = -4
again plotting the points in the graph.
similarly for
y + 2x = 3
for y = 0 , x = 3/2
and x = 0 , y = 3
plotitng the point in the graph we get the solution.
and 2y - 3x = 1
for y = 0 , x = -1/3
and x = 0 , y = 1/2
Plotting the points in the graph we can get the solution.
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Choose all of the correct statements.
Group of answer choices
The graph does not show a proportional relationship.
The graph is proportional because it is a straight line going through the origin.
The constant of proportionality is 10 calories per minute.
There is no constant of proportionality.
The correct statements on the graph of time and calories is:
The graph is proportional because it is a straight line going through the origin.The constant of proportionality is 10 calories per minute.When is a graph proportional ?When two numbers are multiplied or divided, there is a proportionate relationship. Although a linear equation frequently includes a proportional component in addition to some constant number, a linear relationship can also be proportional.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
As shown in the graph, the straight line passed through the origin which means that it is a proportional relationship.
The constant of proportionality in this case is therefore:
= Calories at a minute / Minute
= 20 / 2 minutes
= 10 calories per minute
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helo everyone i need help
if fourth and sixth terms of a Fibonacci sequence are 105 and 225 respectively what are the first seven terms of the sequence?
The first seven terms of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 105, 225.
What is sequence?Sequence is an ordered arrangement of elements, usually numbers or objects, which follows a specific pattern. It is a mathematical concept that is used in a variety of areas, such as computer science, data analysis, and number theory. A sequence can be finite, like the first 10 numbers in the counting sequence, or it can be infinite, such as the set of natural numbers. It is important to understand the concept of a sequence in order to be able to use it in various areas.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers, starting from 0 and 1.
The Fibonacci sequence is named after mathematician Leonardo Fibonacci, who introduced the sequence in his book Liber Abaci in 1202.
The sequence is also known as the Golden ratio, because the ratio of successive numbers in the sequence converges on the Golden ratio of 1.618. The first seven terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, and the fourth and sixth terms of the sequence are 105 and 225 respectively.
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