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.
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
Complete the tasks to subtract the polynomials vertically. (1.3t3 + 0.4t2 – 24t) – (0.6t2 + 8 – 18t) What is the additive inverse of the polynomial being subtracted? –0.6t2 + (–8) + (–18t) –0.6t2 + (–8) + 18t –0.6t2 + 8 – 18t 0.6t2 + (–8) + 18t
Final answer:
The additive inverse of the polynomial [tex](0.6t^2 + 8 - 18t)[/tex]being subtracted is [tex]-0.6t^2 - 8 + 18t.[/tex] This involves changing the sign of each term in the polynomial.
Explanation:
The additive inverse of a polynomial is obtained by changing the sign of each term in the polynomial. Given the polynomial to be subtracted ( [tex]0.6t^2 + 8 - 18t)[/tex], its additive inverse is found by changing the sign of each term, resulting in [tex]-0.6t^2 - 8 + 18t.[/tex] This operation flips the signs, preparing the polynomial for the subtraction process without altering its magnitude but reversing its direction on the number line.
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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What is the order of 5 x 10^4, 7 x 10^-5, 3 x 10^-9, 8 x 10^4 from least to greatest?
The numbers 5 x 10⁴, 7 x 10⁻⁵, 3 x 10⁻⁹, and 8 x 10⁴ ordered from least to greatest are 3 x 10⁻⁹, 7 x 10⁻⁵, 5 x 10⁴, and 8 x 10⁴.
The order of the numbers 5 x 10⁴, 7 x 10⁻⁵, 3 x 10⁻⁹, and 8 x 10⁴ from least to greatest is as follows:
3 x 10⁻⁹7 x 10⁻⁵5 x 10⁴8 x 10⁴Here, the least number is 3 x 10⁻⁹ because it has the smallest exponent indicating the smallest value.
The greatest number is 8 x 10⁴, which has the highest exponent denoting the largest value.
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!@!!
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!
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]
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.
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.
If your car gets 33 miles per gallon, how much does it cost to drive 370 miles when gasoline costs $2.80 per gallon?
[4 - (3c - 1)][6 - ( 3c - 1)]
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.
The system of equations below has no solution 2/3x+5/2y=15 4x+15y=12 which equation could represent a linear combination of the system
Answer:
B.)0=26
Step-by-step explanation: Keep it simple
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
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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A line Segment is part of a line that is bounded by two distinct end points. True or False?
The part of a line that connects two points.
It has definite end points.
Adding the word "segment" is important, because a line normally extends in both directions without end.
A diagram of line segment is attached with the solution .
Evaluate the expression for y = -7.
2y = __
Answer:
2y=-14
Step-by-step explanation:
If y=-7 and you multiply y by 2, you do the same thing to both sides and get -7 × 2 = -14
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)
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 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
Which law would you use to simply the expression 3^10/3^4
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
can someone answer this ?
A circle has a circumference of 1pi
what is the diameter if the circle
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
What is the area of this figure?
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:
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