Answer:The combined functions W(x) and G(x) represent the amount of wood and glass required to produce a picture frame. Based on the information provided,
W(x)= 2[(f+g)(x)] and G(x) = (f-g)(x)
By looking at the values of the given table, it can be observed that the rate of change in the amount of glass required (G(x)) is not constant, it increases as x increases.
On the other hand, the rate of change in the amount of wood required (W(x)) is not constant as well, it increases as x increases too.
It's not mentioned any information about constant rate of change for f and g.
Therefore, the correct statement that describes the combined functions W(x) and G(x) is: "Neither the amount of wood required nor the amount of glass required has a constant rate of change."
It's important to mention that the problem provided does not have a unique solution, because the values for f and g are not defined so it's not possible to infer their behaviour over time.
It is only possible to infer the behaviour of the functions W(x) and G(x) given the information provided, and it is clear that the rate of change for both functions does not remain constant, but it increases as x increases.
Step-by-step explanation:
7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.
Answer: To replace the three steps with a ramp, the height of the ramp must be equal to the total height of the steps. Since each step is 10 cm high, the total height of the three steps is 3 * 10 = 30 cm.
The length of the ramp must be equal to the length of the steps, since the ramp is replacing them. Since each step is 35 cm long, the total length of the three steps is 3 * 35 = 105 cm.
So the length of the ramp to replace the three steps leading to the front door is 105 cm, correct to one decimal place.
Step-by-step explanation:
"-12<-3x-15" less than or equal to 36
Answer:
-17 ≤ x < 1
Step-by-step explanation:
-12 < -3x - 15 ≤ 36
Add 15 to all 3 "sides."
-12 + 15 < -3x - 15 + 15 ≤ 36 + 15
3 < -3x ≤ 51
Divide all 3 "sides" by -3. Remember that when you multiply or divide an inequality by a negative number, you much change the direction of the inequality sign.
3/(-3) > -3x/(-3) ≥ 51/(-3)
-1 > x ≥ -17
Rewrite in standard order.
-17 ≤ x < 1
4 is the slope of a line y - 4x = 0 true or false
it is false but 4 is not y-4x=0
the point (3, 1) is located on a line with slope of 1/3. which point could also be located on the line?
The point (5,5/3) also lies on the line.
A point (x, y) is located on a line with slope m if and only if it satisfies the equation:
y = mx + b
where b is the y-intercept of the line. In this case, we know that the point (3, 1) is located on the line, so we can use the information to find the value of b and then write the equation of the line in slope-intercept form.
The y-coordinate of the point (3, 1) is 1, so we can substitute this into the equation and solve for b:
1 = (1/3) * 3 + b
This simplifies to:
1 = 1 + b
so, b = 0
So, the equation of the line is
y = 1/3 * x +0
Now we can use this equation to find the coordinates of any point that lies on the line. So any point (x, y) that satisfies this equation could also be located on the line.
For example, we can pick any x, calculate corresponding y.
x=5, y=5/3
So point (5,5/3) also lies on the line.
Read more about intercepts here:
https://brainly.com/question/24363347
https://brainly.com/question/25722412
Help me I'm stuck with this one, HELP!!!!!
Answer:
b= 106 or b= -58
Step-by-step explanation:
word sentence
82= b-24
solution b equals 106
or
word sentence 82= 24-b
solution b equals -58
Need Help Solving This.
On solving the provided question, we can say that 50 will therefore be the missing number in the odd numbers 2 5 10 x 2637.
What are odd numbers?A number that is odd is one that can't be partitioned flawlessly into matches. One remains after dividing an odd number by two. The numbers 1, 3, 5, 7, 9, 11, 13, and 15 are consecutively odd. While odd numbers cannot be divided in half, even numbers can. 3, 5, 7, 9, 11, 13, and 15 are unusual cases. Even numbers include 2, 4, 6, 8, 10, 12, and 14.
According to the given question:
Following the numbers 3, 5, 7, 9, 11, and 13, which are all odd numbers, the provided series moves on to 13.
Therefore,
After 37, there will be a break before 50.
50 will therefore be the missing number.
To know more about odd numbers visit:
https://brainly.com/question/2057828
#SPJ1
On solving the provided question, we can say that in this function f(x) = /16/1224 x^2 + 7x/5 + 1.5 = > f(2) = 2234.2454
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
in this function
f(x) = /16/1224 x^2 + 7x/5 + 1.5
f(2) = 2234.2454
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
The derivative of the function f is given by f′(x)=x^2−2−3xcosx. On which of the following intervals in [−4,3] is f decreasing?
The function f'(x) = x² - 2 - 3xcosx is decreasing on (- 4, - 3) and (- 1, 1).
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f'(x) = x² - 2 - 3xcosx.
We know a function f(x) is decreasing if f'(x) is < 0.
Therefore,
x² - 2 - 3xcosx < 0.
x² - 3xcosx < 2.
x(x - 3cosx) < 2.
Now, 3cosx can be [- 3, 3].
x(x - 3) < 2 and x(x + 3) < 2.
x < 2 Or x - 3 < 2 and x < 2 or x + 3 < 2.
x < 2 Or x < 5 and x < 2 or x < - 1.
But x should be in [- 4, 1], Therefore it is decreasing at (- 4, - 3) and (- 1, 1).
learn more about functions here :
https://brainly.com/question/12431044
#SPJ1
What does (AM) represent to segment [BC]? Justify.
AM is a perpendicular bisector of BC.
What is a bisector example?A ray that divides an angle into two equal parts is known as an angle bisector or the bisector of an angle. For instance, each measurement will be equal to 30 degrees if ray AX divides an angle of 60 degrees into two equal parts. There is an angle bisector for each angle.
A line's bisector is defined.To divide a segment or an angle into two congruent parts is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.
To know more about bisector visit:-
brainly.com/question/28663444
#SPJ1
What is the following difference?
2ab(√/192ab²)-5[√/81a¹b³
O-3ab √3ab²
O 18ab² (2/3a)-45a2b² (2√3b)
0-7ab(2√3ab²)
O
8ab(√3ab²-15ab² (2√3ab)
Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)
what are expressions ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.
given
Rewrite the above expression as:
[tex]2ab\sqrt[3]{3*4^{3} *ab^{2} } - 5\sqrt[3]{3*3^{3} * a^{4}b^{5} }[/tex]
Evaluate the cube roots
[tex]2ab {4\sqrt[3]{3ab^{2} } } - 5 {3ab\sqrt[3]{3ab^{2} }[/tex]
Evaluate the differences
-7ab(2√3ab²)
Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
What are four consecutive even integers if the first integer is −4? Responses
A) -4,-3,-2,-1
b) -4,-2,0,2
c) -4,-6,-8,-10
D)-4,-5,-6,-7
The asked consecutive even integers are -4,-2,0,2
What are consecutive integers?Consecutive integers are whole numbers that follow each other without gaps. For example, 15, 16, 17 are consecutive integers.
Given that, what are four consecutive even integers if the first integer is −4
We know that, Consecutive even integers are even integers that follow each other, and they differ by 2. If x is an even integer, then x + 2, x + 4 and x + 6 are consecutive even integers.
Therefore, here x = -4,
-4+2 = -2
-4+4 = 0
-4+6 = 2
Hence, the asked consecutive even integers are -4,-2,0,2
Learn more about Consecutive integers, click;
https://brainly.com/question/1767889
#SPJ1
Find the 8th term of the geometric sequence whose common ratio is 3/2 and whose first term is 6.
Answer:
A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. This ratio is called the common ratio of the sequence.
In this case, the common ratio is 3/2 and the first term is 6. The nth term of a geometric sequence can be found using the formula:
a_n = a_1 * r^(n-1)
where a_n is the nth term, a_1 is the first term, and r is the common ratio.
Substituting the given values, we have:
a_8 = 6 * (3/2)^(8-1) = 6 * (3/2)^7
Calculating, we find that the 8th term is:
a_8 = 6 * (3/2)^7 = 6 * (9/2) = 27
Therefore, the 8th term is 27.
Step-by-step explanation:
Match each compound inequality on the left to the graph that represents its solution on the right.
Note that equation 1 matches the Line Graph in option (B), equation 2 matches option (C), and equation 3 matches option (A).
How would you define a Line Graph?It is a graph that depicts a line connecting many points or a line indicating the relationship between the points. The graph depicts quantitative data between two changing variables by connecting a sequence of succeeding data points with a line or curve.
With regard to the above-given graphs,
The inequalities are given as
1. 4x + 3 > 15 or —6x ≥ 12
2. —8x > —24 and —10 ≤ 2x -6
3. -29 ≤ 9x -2 < 16
Note that the way to identify the plots on the line graphs is by solving the above equations.
1) 4x + 3 > 15 or —6x ≥ 12
4x + 3 > 15 can be solved by subtracting 3 from both sides, resulting in 4x > 12. Dividing both sides by 4 gives x > 3.-6x ≥ 12, can be solved by dividing both sides by -6, resulting in x ≤ -2.2) —8x > —24 and —10 ≤ 2x -6
To solve for x in —8x > —24, divide both sides by -8
x > 3;
So solve for —10 ≤ 2x -6; add 6 from both sides and divide by 2
-4/2 ≤ x
-2 ≤ x or x ≥ -2
3) -29 ≤ 9x -2 < 16
To solve this inequality, you can start by isolating the variable on one side of the inequality. To do this, you can add 2 to both sides to get:
-29 + 2 ≤ 9x < 16 + 2
-27 ≤ 9x < 18
Now divide both sides by 9 to get:
-3 ≤ x < 2
This means that x can be any number that is greater than or equal to -3 and less than 2.
Given the above results, it is correct to state that equation 1 matches option (B), equation 2 matches option (C), and equation 3 matches option (A).
Learn more about Line Graphs:
https://brainly.com/question/19040584
#SPJ1
Full Question:
See the attached.
Please i have a question you can help me for answer.
The question is
Follow the construction program to build below the figure
° Draw a segment {ST} of length 9 cm.
°Draw the circle with center T and radius 4 cm
.
° Draw the circle with diameter {ST}
° The two circles intersect at A and B. Without measuring, give the length of the segments {TA} and {TB}:
The length of segments TA and TB are both 4 cm.
How to determine the diagram and the lengthsTo solve this problem, we can use the properties of circles and the relationship between the radius and the diameter.
Since the radius of the circle with center T is 4 cm, the diameter of this circle is 2 * 4 = 8 cm.
Since the length of segment ST is 9 cm, the diameter of the second circle is also 9 cm.
Since the radius of the circle with center T is 4 cm, the radius of the second circle is also 4 cm.
Since the two circles intersect at points A and B, the segments TA and TB are equal in length.The length of segment TA and TB is the radius of the second circle, which is 4 cm.
Therefore, the length of segments TA and TB are both 4 cm.
The figure is attached
Learn more about Properties of circles in
brainly.com/question/30066312
#SPJ1
convert 84min into fraction
Answer:
[tex]\frac{7}{5}[/tex]
Step-by-step explanation:
I am thinking that you mean 84 minutes compared to an hour?
[tex]\frac{84}{60}[/tex] ÷ [tex]\frac{12}{12}[/tex] = [tex]\frac{7}{5}[/tex]
Hot dogs and corndogs were sold at last night's football game. A total of 81 were sold which allowed the concession stand to bring in $201. How many of each were sold?
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
What is total cost?Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.
According to question:-
step1
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
step2
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
To know more about total cost visit:
brainly.com/question/12717815
#SPJ1
Barrett is comparing the membership fees for two museums. The art museum charges a one-time fee of $8.25 plus $2.25 per month. The science museum charges a one-time fee of $10.75 plus $3.50 per month. How much does Barrett save by joining the art museum instead of the science museum? Enter your answers in the boxes.
(blank) $ + (blank) $ m put answers in blanks
Barrett saves by joining the art museum instead of science museum is $2.50 plus $1.25 per month.
What is concept of savings?Saving money is one of the essential aspects of building wealth and having a secure financial future. Saving money gives you a way out of the uncertainties of life and provides you with an opportunity to enjoy a quality life.Savings represents an individual's unspent earnings. It is the amount that remains after meeting the household expenses.
What are benefits of membership?Member benefits are the perks, services, and access that members receive as part of their membership. In other words they are what members get in exchange for joining the organization and if applicable, paying member dues.
Now we have
Fee charged by science museum= $10.75
Fee charged by art museum =$8.25
Now by subtracting he saves =$2.50
Again
he saves =amount charged by science - amount charged by arts
= $3.50 -$2.25
= $1.25
In the results he saves $2.50 +$1.25 per month.
To learn more about saving visit;
https://brainly.com/question/30004719
#SPJ1
What is the greatest common factor of 3x
Answer:
It is not possible to find the greatest common factor of 3x.
Step-by-step explanation:
The greatest common factor (GCF) of a set of numbers is the largest number that divides into all of the numbers in the set.
In this case, you have provided a variable, 3x, and not a set of numbers. Therefore, it is not possible to find the greatest common factor of 3x.
If you have a set of numbers that you would like to find the greatest common factor of, please let me know and I will be happy to help.
How would I complete these answers?
so, we can say that therefore, the sample of 20 cheerleaders used for the study provides the solution to the issue.
Describe sample.A sample is a controlled, abridged version of a bigger group. It is a demographic subset containing characteristics from a larger population. Samples are used in statistical testing when population sizes are too large to accommodate all prospective participants or observers in the experiment.
The 20 cheerleaders that are used as a sample for this study are.
Explanation: Because only 20 cheerleaders were chosen from high schools in California for the research of the banana influence on speed and endurance, the sample available was limited to those 20 cheerleaders. As a result, the sample's results were based on those 20 cheerleaders.
To know more about sample visit
brainly.com/question/27860316
#SPJ1
If s is directly proportional to t, and s = 30 when t = 15, find t when s = 64.
Step-by-step explanation:
please refer to sketch for detail
Ashanti cashed her paycheck at Cash-n-Go. The fee at Cash-n-Go is 7.5% of the amount of the check. Her paycheck was $670. How much was the fee for Ashanti to cash her paycheck?
Answer:
$50.25
Step-by-step explanation:
7.5% as a decimal is 0.075.
So, the fee is [tex](0.075)(670)=\$50.25[/tex].
Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
X
6
-
X
The equation has Select an option
0
attempt 1 out of 2
The equation has one solution.
A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.
A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.
How to evaluate the equation?From the information provided, we have the following equation:
x - 6 = 6 - x
Rearranging the equation by collecting like terms, we have the following solution:
x + x = 6 + 6
2x = 12
x = 12/2
x = 6
Substituting the value "6" into the equation, we have the following solution;
x - 6 = 6 - 6
x - 6 = 0
Assuming x = 8, we have the following solution;
x - 6 = 8 - 6
x - 6 = 2
Read more on equation here: https://brainly.com/question/24882531
#SPJ1
Complete Question:
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x - 6 = 6 - x
The equation has _____.
A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.
A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.
Flying against the wind, an airplane travels 4720 kilometers in 8 hours. Flying with the wind, the same plane travels 4040 kilometers in 4 hours. What is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 800 km/h while the rate of the wind is 210 km/h
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let x represent the speed of the airplane in still air and y represent the speed of the wind.
Flying against the wind, an airplane travels 4720 kilometers in 8 hours. Hence:
x - y = 4720 km / 8 hr
x - y = 590 (1)
Flying with the wind, the same plane travels 4040 kilometers in 4 hours. Hence:
x + y = 4040 km / 4 hr
x + y = 1010 (2)
From both equations:
x = 800, y = 210
The speed of the airplane is 800 km/h
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Find the slope of the line through each pair of points.
(4, 18), (4, -11)
Answer:
undefined
Step-by-step explanation:
slope formula:
m =y2-y1 / x2-x1
m= -11-18 / 4-4= -29/0
you cannot divide by zero so the slope is undefined
From the set {28, 56, 112}, use substitution to determine which value of x makes the equation true.
x ÷ 2 = 56
The number in the replacement set that will make the equation true is (c) 112
How to determine the solution to the expressione/equation?From the question, we have the following parameters that can be used in our computation:
x ÷ 2 = 56
Rewrite the expression properly
so, we have the following representation
x/2 = 56
Also, we have the replacement set to be
{28, 56, 112}
In the given equation, we have the variable to be
The variable is x
Multiply 2 to both sides of the expression
So, we have the following representation
2 * x/2 = 56 * 2
Evaluate the products on both sides of the equation
x = 112
Hence, the solution is x = 112
Read more about equation at
brainly.com/question/2972832
#SPJ1
What are the domain and range of f(x) = x - 3| +6?
O Domain: {x|x is all real numbers}
Range: {yly ≥ 6}
O Domain: {x|x≥ 3}
Range: {y ly ≥ 6}
O Domain: {x|x is all real numbers}
Range: {yly 2-6}
O Domain: {x|x≥ 3}
Range: {yly 2-6}
The domain and range of the absolute value function are the ones in the first option.
Domain: {x|x is all real numbers}Range: {yly ≥ 6}What are the domain an range of the absolute value function?Here we have the absolute value function:
f(x) = |x - 3| + 6
The domain for all absolute value functions is the set of all real numbers, as there are no input that generates a problem with the function.
And the range, the set of the inputs, has a minimum at the vertex.
Remember that if the vertex is (h, k), then we can write the function as:
f(x) = |x - h| + k
Then in this case:
f(x) = |x - 3| + 6
The vertex is at (3, 6)
Then the range is the set of all real values equal to or larger than 6, or:
y ≥ 6
Then the correct option is the first one:
Domain: {x|x is all real numbers}
Range: {yly ≥ 6}
Learn more about absolute value functions:
https://brainly.com/question/3381225
#SPJ1
15 points help please solve each equation for both variables
Answer:
I hope this helps. Let me know if you have any doubts. Have a nice day!!
Combine the like terms to create an equivalent expression.
4r + 14 - r - 6 =
[tex]4r + 14 - r - 6[/tex]
Combine Like Terms:
[tex](4r-r)+(14-6)[/tex]
[tex]=\fbox{3r + 8}[/tex]
What is the radius of a globe that has a volume of 268.08 in³?
Answer:
4 inches is the radius
Step-by-step explanation:
You are going to run at a constant speed of 6.5 miles per hour for 30 minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S = dt.]
Answer:
Below
Step-by-step explanation:
S = dt S = distance d = rate = 6.5 m/ hr t = time = 30 min = 1/2 hr
S = (6.5 m/hr) *(1/2 hr) = 3.25 miles
The value of distance you will run will be;
⇒ Distance = 3.25 miles
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
You are going to run at a constant speed of 6.5 miles per hour for 30 minutes.
Here,
Speed = 6.5 miles per hour
Time = 30 minutes
= 30/60 hour
= 1/2 hour
We know that;
⇒ Speed = Distance / Time
Substitute all the values we get;
⇒ 6.5 = Distance / (1/2)
⇒ 6.5 × 1/2 = Distance
⇒ Distance = 3.25 miles
Thus, We get;
⇒ Distance = 3.25 miles
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ1
Draw a diagram of x + 2 and a separate diagram of 3x when x is 2.
The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.
The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.
What is diagram in mathematics?In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.
For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).
A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.
Learn more about diagram in brainly.com/question/11729094
#SPJ1