Rachel made an error in simplifying the given rational expression. Let's go through the steps to identify her mistake and find the correct simplified expression.
Given rational expression:
[tex](x^2 + 3x) / (32 + 6x)[/tex]
Rachel's work:
[tex](x^3 + 3x^2) / (22 + 6x)[/tex]
Step 1: Rachel incorrectly wrote [tex]x^3[/tex] instead of [tex]x^2[/tex] in the numerator. This is where the mistake occurred.
The correct work should be as follows:
Step 1: The numerator remains the same as [tex]x^2 + 3x.[/tex]
Step 2: The denominator should be simplified, which is [tex]32 + 6x.[/tex]
Therefore, the correct simplified expression would be:
[tex](x^2 + 3x) / (32 + 6x)[/tex]
It is important to note that no further simplification can be done without more information about the values of x or any other constraints. So, the final answer would be [tex](x^2 + 3x) / (32 + 6x)[/tex]. Rachel mistakenly wrote x^3 instead of x^2 in her work. The correct simplified expression is [tex](x^2 + 3x) / (32 + 6x).[/tex]
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An ice cream factory makes 140 quarts of ice cream in 2 hours. How many quarts could be made in 12 hours? What was that rate per day?
Answer:
840 quarts could be made in 12 hours. The rate per day is 1680 quarts could be made per day.
Step-by-step explanation:
140/2=x/12
reduce/simplify 140/2 to 70
so 70/1=x/12.
cross product
70*12=1*x
840=x
One day has 24 hours,
so we multiply 2 by 12 to get 24,
thus 840*2=1680.
Two roads, A and B, run parallel to each other. A third road, C, passes through both A and B. Road C creates an exterior angle of 77 with road A.
What is the measure of the alternate exterior angle made by the intersection of road B and road C?
The measure of the alternate exterior angle made by the intersection of road B and road C is 77 degrees.
How to calculate the angle?The pair of angles known as alternate exterior angles are those that are formed on the opposite side of the transversal from the parallel lines' outer side.
According to the alternate exterior angle theorem, alternate exterior angles are regarded as congruent angles or angles of equal measure when two parallel lines are intersected by a transversal.
In this case, two roads, A and B, run parallel to each other. A third road, C, passes through both A and B. Road C creates an exterior angle of 77 with road A. Therefore, the angle will also be equal to 77°.
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A= (a, b}
B = {1,2,3}
Select the expression that is an element of AxBxB.
a. (1,2,3)
b. (a, a,1)
c. (b,2^2)
d. (2.1.1)
The expression that is an element of AxBxB is (1,2,3)
The given data is A= (a, b}, B = {1,2,3}
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.
[tex]& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\[/tex]
[tex]& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\[/tex]
[tex]& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}[/tex]
The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.
The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.
Therefore, the expression that is an element of AxBxB is (1,2,3).
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The graph of g(x) = (One-half)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
Graph of g(x) = (1/2)ˣ i.e. Graph of f(x) = 2x reflected over the y-axis is drawn below.
What is function?
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.
f = {(a, b)| for all a ∈ A, b ∈ B}.
Given, the function
f(x) = (2)ˣ
g(x) = (1/2)ˣ
g(x) is the graph of f(x) reflected over y- axis.
The rule of reflection over y-axis:
(x, y) → (-x, y)
Thus, when a graph gets reflected over y-axis it means that horizontal components are additive inverse of the original horizontal components.
Therefore the graph of g(x) = (1/2)ˣ is as follows.
Hence, below is the graph of g(x) = (1/2)ˣ that is graph of f(x) reflected over y- axis.
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A cyclist rode for 3.5 hours and completed a distance of 60.9 miles. If she kept the same average speed for each hour, how far did she ride in 1 hour?
Part A
Estimate the quotient. Include an equation to show your work. Explain your thinking.
Part B
Find the exact distance she rode in 1 hour by completing the division. Enter the answer in the box.
Miles:
A. The quotient is given as follows: 60.9 miles / 3.5 hours.
B. The exact distance that she rode in one hour is of: 17.4 miles.
How to obtain the distance?The measures in this problem are obtained considering the relation between velocity, distance and time.
The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.The parameters for this problem are obtained as follows:
Distance of 60.9 miles.Time of 3.5 hours.Hence the average velocity is obtained as follows:
v = d/t
v = 60.9/3.5
v = 17.4 miles per hour.
This means that the exact distance that she rode in one hour is obtained as follows:
17.4 = d/1
d = 17.4 miles.
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PLEASE SOLVE ALL I BEGGIING YOU!!!
Which graph represents the function
f (x) = |x+2| +1?
Answer: The first graph
Step-by-step explanation:
Graph the absolute value using the vertex and a few selected points.
Hope this helps !
Which statements are true about rhombus MNPQ?
The statements that are true about rhombus MNPQ include A. and B.
How to explain the rhombus?A quadrilateral with a diamond shape is a rhombus. It has four equal sides with the opposite sides running parallel to one another. It resembles a square that is skewed.
A rhombus is a quadrilateral with four equal-length sides in plane Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Based on the diagram, it should be noted that NR equals QR as they are the same.
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What is the domain of the function answer?
The domain of a function is the set of all possible input values for which the function produces a valid output.
The domain of a function is the set of all possible input values for which the function produces a valid output. To find the domain of a specific function, you will need to look at the equation and determine what values are acceptable for the inputs. For example, if the equation is y = x2 + 5, then the domain of the function would be all real numbers, since any real number can be plugged in for x and the equation will produce a valid output.
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A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
(4 points)
30.625 cm2
61.25 cm2
19.25 cm2
49.625 cm2
The surface area of the square pyramid is B)61.25[tex]cm^2[/tex]
What is surface area of square pyramid?
The term "square pyramid" also refers to a polyhedron having a square base and four triangular faces. Where the four faces come together is known as the apex. The pyramid's faces connect the base and the tip. The calculation for the square pyramid's surface area adds the areas of the four triangular faces and the base.
Here the given measures are base = 3.5 cm and height = 7cm.
Now using surface area formula then
Surface area of the square pyramid = Base area + 2bl square unit.
Base area = 3.5 × 3.5 = 12.25[tex]cm^2[/tex]
=> Surface area = 12.25+ 2×3.5×7
=> Surface area = 12.25+49
=> Surface area = 61.25[tex]cm^2[/tex]
Hence the surface area of the square pyramid is B)61.25[tex]cm^2[/tex]
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Which equation can be used to find what percent 18 is of 125
Answer: 22.5
Step-by-step explanation: To get a percentage of a number you multiply the number you want the percentage of (125), and multiply it by your percent in decimal form. So basically the equation went like this: 125 x 0.18 = 22.5. Another example of this would be if you wanted to find 60 percent of 20. You would just take 60 and put it in decimal form and multiply. 20 x 0.60 = 12. Hope this helps!
Which could be the measures of the three angles of an acute triangle.A. 40, 90, 50B. 45, 45, 90C. 25, 25, 130D. 70, 80, 30
Answer:
Option D
Step-by-step explanation:
Remember that the sum of all angles in ANY triangle is 180 degrees. Also, remember that an acute triangle has angles that are all less than 90 degrees. So not only do our options have to add up to 180 degrees, but they also have to be less than 90 degrees in order for the triangle to be acute.
We can immediately exclude options A, B, and C because all three options have angles greater than 90 degrees, which means the triangle isn't acute.
Your answer is option D or "70, 80, 30." Since...
70 + 80 + 30 = 180
70 < 90
80 < 90
30 < 90
Hope this helps.
Samuel pays $59.99 plus $0.25 for each minute over 450 minutes for his cell phone plan. Monica pays $64.99 plus $0.10 for each minute over 450 minutes for her cell phone plan. Which system of equations represents this situation? Let x represent the number of minutes over 450.
Using the slope and y - intercept, the linear function that models this problem is y = -33.333x + 68.32
What is System of Linear EquationsA system of linear equation is a set of at least two linear equations containing the same set of variables. Linear equations use only polynomial coefficients and the operations of addition, subtraction, multiplication and division. The solutions to a linear equation system are the values of the variables which make all the equations true.
To solve this problem, we have to define our variables and set our system of linear equations.
Let;
x = number of minutesy = total costUsing the data given, we can find the slope and y - intercept of a linear function that represents this.
slope (m) = y₂ - y₁ / x₂ - x₁
m = 64.99 - 59.99 / 0.10 - 0.25
m = -33.333
Using the slope in the slope-intercept form of a linear equation
y = mx + c
Taking one point;
59.99 = -33.333(0.25) + c
c = 68.32
The linear equation can be written as;
y = -33.33x + 68.32
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Can the sides of a triangle have lengths 4 7 and 8?
It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.
Now, According to the question:
We know that:
What is triangle inequality rule?
The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the third side. The Triangle is a polygon with three line segments as its boundaries.
Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.
We have the sides:
4 , 7 and 8
4 + 7 > 8
It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side.
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Segment BD bisects segment AC. Solve for x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
Given that segment BD bisects segment AC, the value of x is 5.8 units.
Properties of similar triangles.If the corresponding sides and/ or internal angles of two shapes have some common properties, then it can be said that the shapes are similar. Though similarity does not mean congruency.
Given that segment BD bisects segment AC, the value of x can be determined by comparing the sides of triangles ABD and BCD.
Thus, we have;
x/ 7 = 14/ 17
17x = 7 * 14
= 98
17x = 98
x = 98/ 17
= 5.76
x = 5.8 units
Thus to the nearest tenth, the value of x is 5.8 units.
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What is 7t + 2 = -12
Bob has 22 missing assignments in his history class. He completes 19 of them What percent of missing assignments does Bob still need to complete?
Answer:
he has 86.36% percent out of 100
Rashid travels 240km from Abu Dhabi to Sharjah driving 120km/h for 2 hours. His parents strongly suggest he slow down by v km/h, even though it will take him t hours longer to make the trip, or he will lose his driving privilege. Which relation shows time, t, it will now take Rashid to make the trip relative to the speed, v with which he slows down?
Answer: The relation between the time it will take Rashid to make the trip, t, and the speed at which he slows down, v, can be determined by using the formula:
distance = speed * time
We know that Rashid travels 240 km from Abu Dhabi to Sharjah and that he originally drove at 120 km/h for 2 hours. So, we can write the equation:
240 = 120 * 2
Now, if Rashid slows down by v km/h, then the new speed is (120 - v) km/h and the new time, t, can be determined by substituting the new speed and distance into the equation:
240 = (120 - v) * t
So the relation shows that t = (240 / (120 - v))
This relation shows that the time, t, it will now take Rashid to make the trip is directly proportional to the speed, v, at which he slows down. As Rashid slows down, the time taken to make the trip will increase, and as he speeds up, the time will decrease.
Step-by-step explanation:
One solution, no solutions, or infinitely many solutions? Write another system of equations with the same number of solutions that uses the first equation only.
12x+51y=156
-8x-34y=-104
The system of equations 12x + 51y = 156 and -8x - 34y = -104 has infinitely many solutions
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Given the equation:
12x + 51y = 156
Dividing by 3:
4x + 17y = 52 (1)
Also:
-8x - 34y = -104
Dividing by 2:
-4x - 17y = -52 (2)
To solve both equation by elimination, add equation 1 and 2:
0 = 0
The equation has infinitely many solutions
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What is the median age of the presidents at their death? a. 69 c. 68 b. 67. 5 d. 70.
The median age of the presidents at their death is 69.
What is median?The median is the value that is exactly in the middle of a dataset when it is arranged in order. It is a measure of central tendency which separates the lowest 50% from the highest 50% of values.
The median formula is {(n + 1) / 2}th, where “n” is the number of items in the set and “th” means the (n)th number. To find the median, first arrange the data points from smallest to largest.
The steps for finding the median differ depending on whether we have an odd or an even number of data points. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.
In this case, the number of data points is even, that is 38. So, the median is:
= {(n + 1) / 2}th
= {(38 + 1) / 2}th
= 19,5th
Thus, it means the median is the average of the 19th and 20th in the data points. So, it will be:
Median = (68 + 70) / 2
Median = 138 / 2
Median = 69
Hence, the median age of the presidents at their death is 69.
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Although part of your question is missing, you might be referring to this full question: This list shows the age at which 38 U.S. Presidents died.
46 58 64 68 73 80 90
49 60 65 70 74 81 93
53 60 66 71 77 83
56 63 67 71 78 85
56 63 67 71 78 88
57 64 67 72 79 90
What is the median age of the presidents at their death?
A. 69
C. 68
b. 67.5
d. 70
the admision to a local fair is $10 each for adult and $6 for each child. Each ride costs $1.50 for an adult and $1 for a child.
An adult and child will each go on 7 ride. How much more did the adult spend?
The cost of admission for an adult is $10 and for a child is $6
The cost of each ride for an adult is $1.50 and for a child is $1
The adult will spend $10 for admission + $1.5 x 7 rides = $17.5
The child will spend $6 for admission + $1 x 7 rides = $13
The adult spent $17.5 - $13 = $4.5 more than the child.
Solve the following system of equations graphically on the set of axes below.
Y = -1/6x+7
Y = 2x-6
The solution for the given system of equations would be (6, 6).
What is the system of equations?
A system of equations is a set of two or more equations that are solved simultaneously. Each equation in the system contains one or more variables, and the goal is to find the values of the variables that satisfy all the equations in the system.
y = -1/6x + 7
y = 2x - 6
To graph the equations y = -1/6x + 7 and y = 2x - 6, we can follow these steps:
Plot the y-intercepts of the equations: The y-intercept is the point where the line crosses the y-axis. For the equation y = -1/6x + 7, the y-intercept is (0,7), and for the equation y = 2x - 6, the y-intercept is (0,-6).
Draw the lines: Starting from the y-intercepts, use the slope of the lines to draw the lines. The slope of the first equation is -1/6 and the slope of the second equation is 2.
Find the x-intercept: The x-intercept is the point where the line crosses the x-axis. For the equation y = -1/6x + 7, the x-intercept is (-42,0) and for the equation y = 2x - 6, the x-intercept is (-3,0)
Locate the point of intersection: The point of intersection of the two lines is the solution of the system of equations. The point of intersection for the given equation is (3,1).
Label the axes and the lines: Label the x- and y-axes, and give the lines descriptive names or equations.
Now draw the graph, we get
Hence, the solution for the given system of equations would be (6, 6).
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What are the 3 problem solving steps?
The three various steps of problem-solving methods are.
Clarifying.Ideating.Developing.What does it mean, exactly, to "solve problems"?A problem must be defined, its root cause must be found, then there must be a search for, ranking, and selection of potential solutions, followed by their implementation. the actions taken to fix issues.
Clarifying:
The first step in resolving any problem is to clarify the current circumstance.You can handle it more easily and move forward as a result.Salespeople should probe as much as they can during conversations with clarifyers to learn more.Ideating:
Any problem must first be understood in order to be resolved.It makes it easier for you to control and gives you the freedom to move forward.Salespeople must ask as many questions about clarifications as they can when working with clarifyers.Developing:
Developers take great care when choosing the best course of action.These people have an obsession with accuracy.To find out what sets a customer's choice apart from the alternatives, salespeople should present them with a few options.To know more about the problem-solving, here
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Determine the y-intercept of -5x+7y=8
Answer:
The y-intercept of -5x+7y=8 is (0,8/7)
Step-by-step explanation:
The y-intercept of a linear equation is the point where the graph of the equation crosses the y-axis. In this equation, when x = 0, the equation becomes 7y = 8, so the y-intercept is (0, 8/7).
Answer:I hope this helps
Step-by-step explanation:
-5x+7y=8
To find the -intercept, substitute x=0 something like this
-5 times 0+7y=8
Solve the equation for Y which is something like
y=8/7 this your answer for the y intercept.
Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2,−9) and (−6,7)
Answer: y = 1/4x +1
Step-by-step explanation:
First, we can find the midpoint of the line segment using the average of x and y coordinates of the endpoints:
M(x,y) = ((-2 + (-6))/2 , (-9 + 7)/2)
M(x,y) = (-4, -1)
To find the slope of the perpendicular bisector, we have to take the negative reciprocal of the slope of the line segment which is (y2-y1)/(x2-x1) = (7-(-9))/(-6-(-2)) = -16/4 = -4
Slope of the perpendicular bisector = -1/slope of the line segment = -1/(-4) = 1/4
Now we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
y - (-1) = 1/4(x + 4)
y = 1/4x +1
so the equation of the perpendicular bisector of the line segment whose endpoints are (-2,-9) and (-6,7) is y = 1/4x +1
(a) Find the intercept(s)
▪️If there are more then one, separate them with commas
▪️If there are none select “none”
(b) Find the axis of symmetry
(c) Find the coordinates of the vertex
Please help tomorrow is the last day of the semester and I need to pass.
The conventional equation y = ax2 + bx + c yields the vertex (h, k) as h(x-coordinate of the vertex) = -b/2a.
what is coordinates ?When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.
given
a) the intercepts are (4,0) , (1,9) and (-2 , 0 ) of the given figure
b) The equation for the parabola's axis of symmetry can be found in the vertex's x-coordinate.
(1,9) is the axis of symmetry
c) The conventional equation y = ax2 + bx + c yields the vertex (h, k) as h(x-coordinate of the vertex) = -b/2a.
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In the past year, Christine watched 44 movies that she thought were very good. She watched 55 movies over the whole year. Of the movies she watched, what percentage did she think were very good?
Answer:
80 %
Step-by-step explanation:
Christine enjoyed 44 out of the 55 movies she watched.
This can be represented as
44/55 movies. This fraction simplified is 4/5 or 80 %
What is sum of angles of a triangle class 7?
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
The smallest polygon with three sides and three interior angles is a triangle.
A triangle is a three-sided polygon that consists of three vertices, three sides, and three angles. Three types of triangles—scalene, isosceles, and equilateral—can be distinguished based on the length of their sides.
It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the size of its angles. A triangle's internal angles add up to 180 degrees. Two more terms—altitude and triangle median—are introduced to you in this essay.
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Which relation has an inverse function?
An inverse function or anti function is defined as a function, in which the graph can be reverse into another function. hence commonly , if any type of function “f” takes x to y then, the inverse of “f” function will take y to x. hence the function is represented as ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1} and F^{-1}[/tex].
let us assume that f and g are inverse functions, then the condition for f(x) = y if and only if g(y) = x
when the graph is represented in an original function which has to be one-to-one function in order to assure that its inverse is an function. A function is said to be a one to one function only if function of every second element corresponds to the first value .
The graph of function is the inverse of a function which reflects two things, that is , one represents the function and second represents the inverse of the function, over the line y = x. This line in the graph passes through the origin and which has slope value equal to 1 and represented as;
y = f-1(x) which is equal to x = f(y)
This relation is basically similar to y = f(x), which tells that graph of f but the part of x and y are reversed here. So if we have to draw the graph of f-1, then we have to manipulate the positions of x and y in coordinate axes.
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What is 4/3 as an exponent?
Answer:
4/3 as an exponent is 4 to the 3rd power ( so four with a three right above it a little)
Step-by-step explanation: