For the linear function, y increases by a of 3 each time x increases by 1. For the exponential function, y increases by a(n) of 3.
Answers
For the exponential function, y increases by a factor of 3.
To determine this we take:
The linear equation is y = 3*x
when x = 1
y = 3*1 = 3
when x = 2
y = 3*2 = 6
Then as x increases by one unit, y increases by 3 units.
Then the correct statement would be something like:
"For the linear function, y increases by a sum of 3 each time x increases 1"
The exponential function is:
[tex]y = 3^x[/tex]
When x = 1
[tex]y = 3^1 = 3[/tex]
When x = 2
[tex]y = 3^2 = 3*3[/tex]
when x = 3
[tex]y = 3^3 = 3*3*3[/tex]
So when x increases by 1, we multiply the previous value of y by 3.
Then the correct sentence is something like:
"For the exponential function, y increases by a factor of 3".
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"For the linear function, y increases by a sum of 3 each time x increases 1"
"For the exponential function, y increases by a factor of 3".
Now, According to the question:
Let's Know:
What is Exponential Function?
An exponential function is a Mathematical function in the form f (x) = [tex]a^x[/tex], where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Now, For the linear function:
y = 3x
when x = 1
y = 3×1 = 3
when x = 2
y = 3×2 = 6
Then as x increases one unit, y increases 3 units.
"For the linear function, y increases by a sum of 3 each time x increases 1"
Now, For the exponential function:
[tex]y = 3^x[/tex]
When x = 1
[tex]y = 3^1[/tex] = 3
When x = 2
[tex]y = 3^2[/tex] = 3×3
when x = 3
[tex]y = 3^3[/tex] = 3×3×3
So when x increases by 1, we multiply the previous value of y by 3.
"For the exponential function, y increases by a factor of 3".
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Related Questions
HELP GEOMETRY PLS FIND LENGTH
Answers
Answer:
Below
Step-by-step explanation:
Right triangle....use pyhtagorean theorem
c^2 = a^2 + b^2
(2 sqrt5)^2 = 2 ^2 + ?^2
16 = ?^2 ? = 4 units
let r be the region bounded by the graphs of y=sin(pi x) and y=x^3-4x as shown in the figure above
Answers
Area shaded represents the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.
What is the area bounded by two curves?An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.
Given is the region {r} bounded by the graphs of y = sin(πx) and y = x³ - 4x.
Refer to the graph attached. The shaded region is the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.
Therefore, area shaded represents the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.
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steve has 1 4/5 cups of flour. tyler has 1 2/3 cups of flour. do they have enough flour to bake a cake that needs 3 cups of flour. its fractions btw please help me its one of the last questions i asked about the other one as well so if you can please answer that it would be amazing
Answers
Answer:
Yes, they have enough flour to bake a cake that needs 3 cups of flour.
Step-by-step explanation:
1 4/5 = 9/5
1 2/3 = 7/3
We add both numbers
9/5 + 7/3 = 27/15 + 35/15 = 62/15 = 4.1 cup of floor
4.1 > 3
So,they have enough flour to bake a cake that needs 3 cups of flour,
How do you draw a line segment in math?
Answers
The first step in constructing a segment congruent to a given segment is to draw a vertex and a ray.
Step 1: draw a vertex and a ray.
Step 2: Draw a line segment that is longer than the specified line segment if we are not given the line segment on which we are to create the congruent section. The portion we just sketched will be known as the second line segment.
Step 3: Place the needle of the compass at an endpoint of the second line segment.
Step 4: Draw an arc of the circle so that it intersects the line segment.
Step 5: Label the point where we placed the needle and the point of intersection using two letters. The congruent line segment we want is the line segment formed by these two endpoints.
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pattern of association
Answers
In mathematics, the pattern of association refers to the type of correlation that is found between two variables which includes positive, negative, or no correlation.
What is the pattern of association ?The connection between two or more variables is referred to as a pattern of association. There are various variations of this relationship, including a positive correlation, a negative correlation, and no correlation. When both variables rise or fall at the same time, there is a positive correlation. In other words, as one variable rises, the other one rises as well, and vice versa.
When two variables move in the opposing directions, there is a negative correlation. The other variable reduces as one grows, and vice versa. When there is no correlation between the variables, a no correlation exists. This indicates that there is no pattern in the data and that the variables do not change simultaneously.
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Use the data that shows the ages of the U.S. population to create a histogram. Tell whether the data is positively skewed, negatively, or if it has a normal distribution.
Answers
The histogram Illustrated shows that the data is negatively skewed.
How to explain the histogram?Negatively skewed distribution means that the distribution type where more values plot on the graph's right side, the tail of the distribution is longer on the left side.
When a distribution is negatively skewed in statistics, more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
From the histogram we can easily say that most of the population of US are lying on the left of histogram therefore the given data is negatively skewed
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Write the equation for the parent linear value function, f(x)=x, that has been transformed by:
1. reflecting across the x-axis, vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left
2. vertical shrink by a scale factor of 1/4 and a horizontal shift 10 units right.
3. reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left
Answers
The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that, the equation for the parent linear value function, f(x)=x, that has been transformed by,
a) Reflecting across the -axis, vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left :-
Rule for reflection across x-axis = y = f(x) → y = -f(x)
After reflection,
f(x) = -x
And there is a vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left
f(x) = -4(x+4)+5
Therefore, the function will be f(x) = -4(x+4)+5
b) Vertical shrink by a scale factor of 14 and a horizontal shift O units right.
For vertical shrink = f(x)/14 = x/14
For horizontal shift = (x-o)/14
Therefore, the function will be f(x) = (x-o)/14
c) Reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left.
Rule for reflection across x-axis = y = f(x) → y = -f(x)
f(x) = -x
For a vertical shift of 4 units up and a horizontal shift 7 units left =
f(x) = (-x-7)+4
Hence, The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4
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In the given figure,the bisector of <ACU meets Au at O.Prove that <COT=1/2(<CAT+<CUT)
Answers
In the given figure, the bisector of <ACU meets Au at O therefore <COT=1/2(<CAT+<CUT)
What is congruent angles?You should be aware that the word congruent means similar or the same. congruent angles are angles that are similar in size.
The question is to prove that <COT = <A + <OCA
= <CAT + 1/2 <OCA
= <CAT + 1/2(<TUC - <CAT)
Simplify further to have
=1/2<CAT +1/2<TUC
=1/2C<CAT+<CUT
Conclusively the two angles are congruent to each other
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A restaurant buys baked goods from a local bakery. The table below gives the number of loaves of bread, bags of cookies, and cupcakes the restaurant bought
over the course of three weeks. The restaurant buys no other baked goods from the bakery.
Number bought
Week 1 Week 2 Week
7
4
8
Loaves of bread
6
6 3
Bags of cookies
Cupcakes
3
5 4
If the restaurant spent $89 on baked goods in week 1, $82 in week 2, and $77 In week 3, what is the cost for each item?
Cost for a loaf of bread: s
Cost for a bag of cookies: $
Cost for a cupcake: $
X
5
acer
a
E
E
Submit Assignmen
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Answers
The cost for a loaf of bread is $5, the cost for a bag of cookies is $13, and the cost for a cupcake is $2.50.
What is cost?Cost is the amount of money or resources required to purchase, produce, or maintain something. It can refer to the price of goods or services, the amount of money spent on labor and materials, or the amount of time used to complete a task. Cost is often associated with the decision-making process, as it helps an individual or organization determine the value of a product or service and evaluate if it is worth the investment.
Therefore, the restaurant spent $35 on loaves of bread, $52 on bags of cookies, and $2 on cupcakes in week 1; $24 on loaves of bread, $39 on bags of cookies, and $3 on cupcakes in week 2;
and $40 on loaves of bread, $21 on bags of cookies, and $4 on cupcakes in week 3.
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I need help bad on this one don’t know what to do
Answers
The correct option is " count 2 units below x=2 line."
What is reflection?In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyper plane as a set of fixed.
Here, given that,
We have to find the reflection of point B(4,5) on the line x=2
Hence, from the given option the correct option is,
" count 2 units below x=2 line."
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Write least to greastest plssssssssssssssssssss
Answers
Answer:
-3.5/-3/-2.5/-21/2/ -2
what is the difference between the maximum and minimum values of f ?
f(x) = cos (2x) + cos x
how do i find the max and min of such?
Answers
The maximum value of the function f ( x ) = 2
The minimum value of function f ( x ) = - ( 9/8 )
The difference between the maximum and minimum values of f ( x ) = 25/8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as f ( x )
The value of f ( x ) = cos (2x) + cos x be equation (1)
On simplifying the equation , we get
To maximize f ( x ) = cos ( 2x ) + cos x , differentiate it with respect to x
So ,
f' ( x ) = -2 sins ( 2x ) - sinx
And , For the function to achieve a minimum value , f′(x) should be 0
So , Substituting the values in the equation , we get
-2 sins ( 2x ) - sinx = 0
Adding sinx on both sides of the equation , we get
-2 sins ( 2x ) = sin x
-2 ( 2 sin x cos x ) = sin x
Divide by -4 on both sides of the equation , we get
sin x cos x = sin x / 4
Divide by sin x on both sides of the equation , we get
cos x = ( -1/4 )
Hence minimum value is f ( x ) = 2 x ( 1/16 ) - ( 1/4 ) - 1
The minimum value of f ( x )= - 9/8
And , the function is maximum at cosx = 1
So , f ( x ) = 2 x 1 - 1 + 1 = 2
The maximum value of f ( x )= 2
So , the difference between the maximum and minimum values of f ( x ) =
Maximum value - Minimum value = ( 2 - ( -9 / 8 ) )
Maximum value - Minimum value = ( 16 + 9 ) / 8
Maximum value - Minimum value = 25/8
Hence , the difference between the maximum and minimum values of function f ( x ) is = 25/8
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\01.02 stay safe warning there is a checkbox at the bottom of the exam form that you must check prior to submitting this exam. failure to do so may cause your work to be lost. question 1(multiple choice worth 5 points) (01.02 lc) which is a cause of shin splints?
Answers
Shin splints are a common cause of lower leg pain and can be caused by a variety of factors, such as poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot.
Shin splints is a term used to describe pain that occurs along the shin bone (tibia), which runs down the front of the lower leg. Common causes of shin splints include poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot. Poorly fitting shoes can put excessive pressure on the back of the heel and the front of the foot, leading to inflammation and pain in the shin area. Weak calf muscles can cause the foot to overpronate or roll inward, which can put extra strain on the shin bone and its muscles. Running on uneven terrain can also cause the shin bone to suffer from too much pressure, leading to shin splints. Finally, overpronation of the foot is when the foot rolls inward excessively and puts extra strain on the shin bone and its muscles. Shin splints can cause pain and discomfort and should be treated as soon as possible by rest, stretching, icing, and wearing properly fitting shoes.
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name two numbers that are 5 units from 3 on the number line are represented by equation | n - 3| = 5. What are these two numbers?
Answers
Note that the two numbers given the equation |n-3| = 5 which are 5 units from 3 on the number line are: -2 and 8.
What is the rationale for the above answer?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in elementary mathematics. Every number line point is assumed to correspond to a real number and every real number to a number line point.
One more quality of number lines that is worth noting is that it stretched to the positive infinity and to the negative infinity with zero as the center point.
Given that we have been given the reference point of 3, this means that both numbers must extend one to the positive infinity constrainted by 5 units and one to the negative infinity constrained by 5 units.
Hence,
To find the two numbers that are 5 units away from 3, we can set up two equations:
n - 3 = 5 and n - 3 = -5
Solving for n in the first equation: n = 8
Solving for n in the second equation: n = -2
Therefore, the two numbers that are 5 units away from 3 on the number line are -2 and 8.
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Solve the following system:
4x+3y=-2 and 6y=-4-8x
Answers
To solve this system, first multiply the first equation by 2 to get 8x+6y=-4.
What is equation?An equation is a mathematical statement that expresses two values or ideas as equal. It consists of two parts: an expression and an equals sign. The expression on the left side of the equals sign is compared to the expression on the right side of the equals sign. An equation may be used to describe relationships between physical, chemical, and mathematical quantities.
Then add the two equations to get 14x=-8. Therefore,
x=-8/14 and substituting x=-8/14
into the first equation yields y=3/2.
Thus, the solution to the system is x=-8/14 and y=3/2.
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A chemical company is testing a new environmentally safe weed killer. The graph below shows the results of testing on two different gardens.
How many weeds did garden A start with?
After how many days were there no weeds observed in Garden A?
After how many days were there no weeds observed in Garden B?
What is the rate of weeds dying per day in garden B?
After how many days did Garden A and B have the same amount of weeds?
Answers
Answer:
can i get brainliest?
Step-by-step explanation:
Garden A started with: 25 weeds
Days after no weeds garden A: 2 days after
Days after no weeds garden B: 6 days after
Rate of weeds dying garden B: -2.5 per day i think
Garden a and b same weeds: Day 1
graph y = x + 9 y = -1/3 + 5
Answers
Answer:
-3,6
Step-by-step explanation:
To convert feet to yards, you multiply the number of feet by 13. Name the two quantities in this situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable that depends on it? Write an equation that represents the function. Draw the graph of the function. Label at least two points with input-output pairs.
Answers
Answer:
Step-by-step explanation:
divide 13 by how many feets u have then what ever you get is the answer
THANK YOU
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges 1503 to rent trucks plus an additional fee of 125.25 for each ton of sugar. The second company does not charge to rent trucks but charges 250.50 for each ton of sugar.
Answers
By solving an inequality, we will see that for more than 12 tons of sugar, the first company will be the cheaper option.
For how many tons of sugar is the first company a better option?
We know that the first company charges a fixed amount of $1503, plus $125.25 for each ton of sugar, then the total cost for x tons of sugar is:
f(x) = $1503 + $125.2*x
While the second company only charges $250.50 for each ton of sugar, then the cost for x tons of sugar is:
g(x) = $250.50*x
The first company will be a better option for all the values of x such that the following inequality is true:
f(x) < g(x)
Replacing the functions we will get:
$1503 + $125.2*x < $250.50*x
Now we can solve that inequality for x.
$1503 < $250.50*x - $125.25*x
$1503 < $125.25*x
$1503/$125.25 < x
12 < x
So for more than 12 tons of sugar, company one is the best option.
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A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75.
Which packaging should the company use to minimize cost? Explain.
The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.
The cylindrical containers should be used because they will cost the company $2.50 less than using the rectangular boxes.
The rectangular prism boxes should be used because they will cost the company $5.00 less than using the cylindrical containers.
The cylindrical containers should be used because they will cost the company $5.00 less than using the rectangular boxes.
Answers
The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers. (option A).
Which box should be used?The first step is to determine the number of each type of box shape that would be needed for the pencils.
Number of rectangular prism boxes that would be needed = total number of pencils / capacity of the box
Number of rectangular prism boxes that would be needed = 2400 / 60 = 40 boxes
Number of cylindrical boxes that would be needed = total number of pencils / capacity of the box
Number of cylindrical boxes that would be needed = 2400 / 80 = 30
Now determine the total cost of using each type of box shape.
Total cost of using the cylindrical boxes = 30 x 0.75 = $22.50
Total cost of using the rectangular prism boxes = 40 x 0.50 = $20
Difference in cost = $22.50 - $20 = $2.50
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Answer:
^^ A on edge
Step-by-step explanation:
What is the area of the following circle?
Either enter an exact answer in terms of \piπpi or use 3. 143. 143, point, 14 for \piπpi and enter your answer as a decimal.
Answers
As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.
what is circle ?A circle is formed when every point in the plane that is a specific distance apart from another point does so (center). Thus, it is a curve made up of points that are separated from one another by a set distance while moving in the plane. It is also rotationally symmetric about the center at all angles. A circle is a closed, two-dimensional object where each pair of points in the plane is equally separated from the "center." A specular symmetry line is made by drawing a line through the circle. It is also rotationally symmetric about the center at all angles.
given
Radius of the circle
Radius, = d / 2 = 7
Area of the circle = pi * r * r = pi *49 = 49pi
Substituting the value of π = 3.14,
Area of the circle = 49 * 3.14 = 153.86 unit²
As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.
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-6x +3 factorisatoin
Answers
Answer:
3(-2x+1)
Step-by-step explanation:
If you flip a coin 8 times, what is the best prediction possible for the number of times it will land on heads?
Answers
Answer: 4 times
Step-by-step explanation:
35/128 is your chances of getting heads, 8 divided by 2 = 4
list the angles of MNO in order from smallest to largest if MN=9 NO=7.5 and OM=12
f N O M
g O M N
h O N M
j M O N
Answers
The list of angles M, N and O as required to be ordered from smallest to largest in the task content is; O < M < N.
What is the order of the angles M, N and O from smallest to largest?As evident in the task content;
MN = 9 NO = 7.5 and OM = 12
By simply creating a triangle and labelling the triangle according to the dimensions above; it follows that;
angle O is opposite side MN;
angle M is opposite side NO;
angle N is opposite side OM;
Also, recalling that the smaller an angle measure, the smaller is the side length opposite the angle. This is evident in the ratio as portrayed in the sine rule of triangles.
Therefore, the correct order of the angles from smallest to largest is; O < M < N.
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Find the value of the variables
Answers
Answer:
x = 121 degrees
y = 59 degrees
w = 59 degrees
z = 53 degrees
v = 121 degrees
Step-by-step explanation:
31 + 90 + w = 180 ==> these three angles are in the top left triangle.
Triangles add up to 180 degrees
121 + w = 180 ==> solve for w
w = 59 degrees
y = w ==> these angles are opposite adjacent angles; they are congruent
y = 59 degrees ==> Both angles are equal. So both angles are 59 degrees
68 + y + z = 180 ==> triangles add up to 180 degrees
68 + 59 + z = 180 ==> plugin 59 for y
127 + z = 180 ==> solve for z
z = 53 degrees ==> subtract 137 on both sides
w + x = 180 ==> w and x are on a straight line.
Straight lines add up to 180 degrees.
59 + x = 180 ==> plugin 59 for w
x = 121 degrees ==> subtract 59 on both sides
v + y = 180 ==> v and y are also on a straight line.
v + 59 = 180 ==> plugin 59 for y
v = 121 degrees ==> subtract 59 on both sides
x = 121 degrees
y = 59 degrees
w = 59 degrees
z = 53 degrees
v = 121 degrees
Write the quadratic function in vertex form y=x^2–4x-1
Answers
On solving the provided question, we can say that - the give quadratic equation [tex]y = x^2 - 4x - 1[/tex], there are no like terms so it doesn't factor.
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
here,
y = [tex]x^2 - 4x - 1[/tex]
so, the above quadratic equation, there no like terms, so it does not give any factor.
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Simon traveled 250 miles in 5 hours what is his average speed
Answers
Important Formulas:
[tex]s=\dfrac{d}{t}[/tex]
__________________________________________________________
Given:
[tex]d=250mi[/tex] (distance)
[tex]t=5h[/tex] (time)
[tex]s=?[/tex] (speed)
__________________________________________________________
Finding speed:
[tex]s=\dfrac{d}{t}[/tex]
[tex]s=\dfrac{250}{5}[/tex]
__________________________________________________________
[tex]\fbox{s = 50 mi/hr}[/tex]
Answer:
50 miles per hour (mph).
Step-by-step explanation:
250 / 5 = 50 miles per hour (mph).
The data below shows the ratio of brown to green crayons in four kindergarten classrooms.
13 to 19
15 to 28
18 to 32
30 to 68
Which table below correctly shows these ratios in a three-column table?
Brown 13 15 18 30
Green 19 28 32 68
Total 32 43 50 98
Brown 19 28 32 68
Green 13 15 18 30
Total 32 43 50 98
Brown 13 28 18 30
Green 19 15 32 68
Total 32 43 50 98
Brown 32 43 32 30
Green 19 28 18 68
Total 13 15 50 98
Answers
Jack and Cameron are riding their bikes. Jack bikes 1/6 mile. Cameron bikes 12 times as far as Jack. How far did Cameron bike?
Answers
Answer:
2 miles
Step-by-step explanation:
1/6 × 12 = 2
You can work it as fractions to understand better
1 over 6 × 12 over 1. It's the same as 12÷6
rewrite the expression as a single logarithm and simplify the result. ln|sin x| + ln|cot x|
Answers
The expression can be rewritten as a single logarithm as:
ln|sin x| + ln|cot x| = ln(|sin x||cot x|) = ln|cos x|
This is possible because logarithm function is a monotonically increasing function, meaning that if a > b then log(a) > log(b) and log(a*b) = log(a) + log(b) that's why we can add the two logarithms.
The result is simplified by combining the absolute values of the sin and cot functions into a single term. The absolute value is removed since the product of two positive numbers is always positive. The final result is ln|cos x|, which is the natural logarithm of the product of the sine and cotangent of x.
It is important to note that the cotangent function is defined as 1/tan(x) so that cot(x) = 1/tan(x) and cot(x) is only defined for x where sin(x) is not equal to 0.
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