Final answer:
We use reverse operations to solve Joseph's equation and find that the original number could have been either 8 or -8.
Explanation:
The question asks us to determine Joseph's original number based on a series of mathematical operations. We can set up an equation to represent the problem statement: let x be the original number. The sequence of operations given is:
Square x and subtract 8.
Divide this result by 7.
Add 12 to the result from step 2.
The final result is 20.
Representing this mathematically: ((x2 - 8) / 7) + 12 = 20. To find x, we need to work backward through these operations:
Subtract 12 from both sides: ((x2 - 8) / 7) = 8.
Multiply both sides by 7: x2 - 8 = 56.
Add 8 to both sides: x2 = 64.
Take the square root of both sides: x = 8 or x = -8 (considering both positive and negative square roots).
Therefore, Joseph's original number could have been either 8 or -8.
Which ordered pairs are solutions to the inequality x+3y≥−8?
Select each correct answer.
a. (−6, 0)
b. (0, −3)
c. (−5, −1)
d. (−16, 2)
e. (−1, −2)
The cost of attendance at State College is $19,500 for the first year. Devise a periodic savings plan that will allow you to make small deposits for 5 years at a simple interest rate of 1.5% and save enough to pay for the first year at the college. 15 points!@!!
Which law would you use to simply the expression 3^10/3^4
PLEASE HELP
Describe the graph of y=1/2x-10 -3 compared to the graph of y=1/x
Answer: The graphs are attached.
Step-by-step explanation: We are to describe the graph of the function [tex]y=\dfrac{1}{2x-10}-3[/tex] compared to the graph of the function [tex]y=\dfrac{1}{x}.[/tex]
The graphs of both the functions are shown in the attached figure.
We can see that the graph of the function [tex]y=\dfrac{1}{2x-10}-3[/tex] is stretched by a factor of 0.5, shifted 5 units to the right and 3 units downwards as compared to the graph of the function [tex]y=\dfrac{1}{x}.[/tex]
Answer:
The graph of [tex]y=\frac{1}{2x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
Step-by-step explanation:
Given : The graph of [tex]y=\frac{1}{2x-10}-3[/tex] compared to the graph of [tex]y=\frac{1}{x}[/tex]
To find : Describe the comparison of the graphs.
Solution :
Let the parent function be[tex]y_1=\frac{1}{x}[/tex]
Transformed function [tex]y_2=\frac{1}{2x-10}-3[/tex]
Vertically Stretch:
If y =f(x) , then y= a f(x) gives a vertical stretch if a> 1.
Multiplying the parent function by 2 means you are stretching it vertically,
i,e [tex]y_1=\frac{1}{x} \rightarrow \text{Vertically stretch by 2} \rightarrow \frac{1}{2x} [/tex]
Shifting right :
f(x)→f(x-b), graph is transformed by b unit
Subtracting 10 means you are moving it right by 10 units
[tex]y_1=\frac{1}{2x} \rightarrow \text{Shifted right by 10 units} \rightarrow y_1=\frac{1}{2x-10}[/tex]
Shifting down :
f(x)→f(x)-b , graph is transformed by b unit
Subtracting 3 means you are moving it down by 3 units
[tex]y_1=\frac{1}{2x-10} \rightarrow \text{Shifted down by 3 units} \rightarrow y_1=\frac{1}{2x-10}-3=y_2[/tex]
Refer the attached figure below.
The graph of [tex]y=\frac{1}{2x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
a ladder leans against a wall and reaches a point 35 feet up the wall.The base of the ladder is 7 feet from the wall.To the nearest tenth of a foot, what is the length of the ladder
Place the indicated product in the proper location on the grid. -4x 3 y 2 (7xy 4 )
Answer:
-28x^4y^6
Step-by-step explanation:
Given are two terms as
[tex]-4x^3y^2[/tex] and
[tex]7xy^4[/tex]
To find the product
we group like terms and find their product
Here we have -4 and 7 for coefficients : Product =-28
x terms are x^3 and x hence product = x^(1+3) =x^4
y terms are y^2 and y^4 hence product = y^(2+4) = y^6
Hence product is
[tex]-28x^4y^6[/tex]
A circle is inscribed inside a square as shown. If graphed on the coordinate plane, the coordinates of the center of the circle would be (2, 5) and the coordinates of one other point on the circle would be (5,2). Find the area of the square. A) 12 2 B) 18 C) 24 2 D) 72
A tire at the top of a hill starts rolling down the hill. If the diameter of the tire is 36 inches, how many inches has the tire rolled if it has rotated exactly 10 times down the hill?
A) 180
B) 360
C) 36π
D) 360π
Answer:
Therefore ,(D) 360π inches.
Step-by-step explanation:
Given: A tire at the top of a hill starts rolling down the hill. If the diameter of the tire is 36 inches.
To find: How many inches has the tire rolled if it has rotated exactly 10 times down the hill.
Solution : We have given that diameter of tire = 36 inches.
Radius = [tex]\frac{Diameter}{2}[/tex]
Radius = [tex]\frac{36}{2}[/tex]
Radius = 18 inches.
Circumference of tire = 2 * π radius
Circumference of tire = 2 * π 18
= 36π
We need to rolled the tire 10 times down the hill
then, 10 * 36π = 360π inches.
Therefore ,(D) 360π inches.
Which graph represents the function?
The resulting graph of the rational function is the Graph at the top right graph 2.
To depict the rational function f(x) = 2/(x - 1) + 3, we must consider its characteristics. The function has a vertical asymptote at x = 1 because the function is undefined at that point, and it has a horizontal asymptote at y = 3 due to the behavior of the function as x approaches infinity. The graph will approach these asymptotes but never cross them.
For values of x greater than 1, the function will decrease towards the horizontal asymptote because the (x - 1) in the denominator increases, which causes the value of f(x) to decrease.
However, because of the '+3' term in the function, the curve will approach y = 3 as x goes to infinity.
To graph this function, plot several points where x is not equal to 1, then draw the curve that passes through these points while approaching the respective asymptotes.
The portions of the graph should fall above the horizontal line y = 3 for x < 1 and approach y = 3 from below for x > 1.
Therefore, the resulting graph of the rational function is the Graph at the top right graph 2.
The probable question may be:
Which graph represent the rational function f(x)=2/x-1+3
Given a collection of paired sample data, the ____________ algebraically describes the relationship between the two variables, x and y.
Final answer:
The linear equation describes the algebraic relationship between two variables in a paired sample data set, with the slope and y-intercept being key components of this equation.
Explanation:
Given a collection of paired sample data, the linear equation algebraically describes the relationship between the two variables, x and y. The most fundamental representation of a linear association is through a linear equation, which graphically manifests as a straight line in a scatter plot. Two commonly used forms of linear equations are y = mx + b and y = a + bx. The latter is frequently used in statistical contexts to differentiate from the algebraic context.
In these equations, m or b (when used as a coefficient) is known as the slope, indicating the rate of change or how much y changes as x changes. The y-intercept represented by a is the point at which the line crosses the y-axis, typically where x equals zero. A linear relationship between two variables is confirmed when a scatter plot of the pair shows points that approximate a straight line.
Help!!!!! Please!!!
Using the given xy-graph, find the equation of the given line E in slope-intercept form.
The equation of line E will be x = 8.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the diagram, line E is perpendicular to the x-axis and parallel to the y-axis.
The slope of the line which is parallel to the y-axis will be ∞. Then the equation of line E will be
y = ∞x + c
y = (1/0)x + c
0y = x + c
x + c = 0
From the graph, the value of the variable c will be negative 8.
Then the equation of line E will be x = 8.
More about the linear equation link is given below.
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[4 - (3c - 1)][6 - ( 3c - 1)]
Could use some help!
Dakota and Christine went shopping. Dakota bought two scarves and one hat for $13 Christine bought one scarves and two hats for $14 what is the price of one hat and one scarf
What is the solution of the square root of 3x+28-8=x (-8=x is not in the square root) any explanation and answer is appreciated!
You work at an ice-cream shop. One of your jobs is to order new ice-cream cones. You pick the cone that is 5 inches high and has a diameter of 3.5 inches. What is the volume of each cone? Use 3.14 to approximate pi. Round your answer to the nearest whole number.
Answer:
the correct answer is 16 cubic inches
Step-by-step explanation:
The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, with mean of 6.1 hours and standard deviation of 1.0 hour. Let x represents a random medical resedent selected at the hospital. Find P(x < 5.3).
What is the area of this figure?
The average rate of change from x = 0 to x = 15 is about −4.667. How does the average rate of change from x = 0 to x = 20 compare to this number? The average rate of change from x = 0 to x = 20 is decreasing the average rate of change from x = 0 to x = 15.
Answer: The average rate of change from x = 0 to x = 20 is decreasing
✔ slower than
the average rate of change from x = 0 to x = 15.
Suppose that the height of the slide is 2 feet, when x = 20. What is the average rate of change over the entire slide?
-3.9
Step-by-step explanation:
So, the two answers are: Slower than, and -3.9
Find the values of x for which f(x) = g(x). (Enter your answers as a comma-separated list.) f(x) = x2, g(x) = x + 20
Order the set of numbers from least to greatest.
A book is in the shape of a right rectangular prism. It measures 8 1/2 inches tall, 7 inches wide, and 2 1/2 inches thick. What is the volume of the book? 47 1/2 in³ 80 1/2 in³ 148 3/4 in³ 179 1/2 in³
140% of a number is 364. Find the number
The number whose 140% is 364 is 260.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number = M
140% of M = 364.
140/100 x M = 364
Solve for M.
M = 364 x 100 / 140
M = 260
Thus,
140% of 260 is 509.6.
Learn more about percentages here:
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Find an equation of the line perpendicular to the graph of 14x-7y=4 that passes through the point at (2,-9)
Answer:
The correct answer is D) y= -1/2x-8.
Step-by-step explanation:
Edge 2021.
can someone answer this ?
A circle has a circumference of 1pi
what is the diameter if the circle
Question 1(Multiple Choice Worth 1 points)
(05.02 LC)
Which equation does the graph below represent?
A coordinate grid is shown. The x-axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y-axis values are from negative 20 to positive 20 in increments of 4 for each grid line. A line is shown passing through the ordered pairs negative 4, 16 and 0, 0 and 4, negative 16.
y = fraction 1 over 4x
y = 4x
y = fraction negative 1 over 4x
y = −4x
Solve
8x^2+5=35
Round to the nearest hundredth.
The solutions are
___ and ___
Thanks! I need help with this one.
Answer:
The solutions are [tex]1.94[/tex] and [tex]-1.94[/tex]
Step-by-step explanation:
we have
[tex]8x^{2} +5=35[/tex]
Solve for x
Subtract [tex]5[/tex] both sides
[tex]8x^{2} +5-5=35-5[/tex]
[tex]8x^{2}=30[/tex]
Divide by [tex]8[/tex] both sides
[tex]8x^{2}/8=30/8[/tex]
[tex]x^{2}=15/4[/tex]
Take square root both sides
[tex]x=(+/-)\sqrt{\frac{15}{4}} \\ \\x1=\frac{\sqrt{15}}{2}=1.94\\ \\x2=-\frac{\sqrt{15}}{2}=-1.94[/tex]
The solutions are [tex]1.94[/tex] and [tex]-1.94[/tex]
Which of the binomials below is a factor of this trinomial?
x2 - 3x - 10
A. x + 2
B. x - 2
C. x - 1
D. x + 1
The binomials below are a factor of this trinomial that will be x + 2. Option A is correct.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that, the expression is, x² - 3x - 10
Binomials in algebra are two-term expressions joined by a plus or minus sign, such as ax+b. While the second term might or might not, the first term always contains a variable.
A binomial can be solved or simplified for further work by factoring, which is the process of looking for simpler terms that, when multiplied together, produce the original binomial expression.
Thus, the binomials below are a factor of this trinomial that will be x + 2. Option A is correct.
Learn more about Polynomial here:
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Will bought 3 college textbooks. One cost $32, one cost $46, and one cost $39. What is the average price of his books? What statement correctly calculates the average
The average price of the textbooks Will bought is $39, calculated by adding the individual prices and dividing by the number of books.
To calculate the average price of the textbooks Will bought, we simply sum up the costs of the three textbooks and divide by the number of textbooks. Let's do the math:
Add the cost of the textbooks: $32 + $46 + $39 = $117.Divide the total cost by the number of books: $117 / 3 = $39.The average price of the textbooks is $39.
If your car gets 33 miles per gallon, how much does it cost to drive 370 miles when gasoline costs $2.80 per gallon?