The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 seconds. Use the graph of the function to complete Parts 1-3. After traveling for 16 seconds, the automobile begins to slow its speed at a steady rate. Use the coordinates on the graph to determine the rate at which the car is slowing down, in miles per hour per second. During which interval of time does the automobile experience the greatest change in its speed? What is the change in the automobile’s speed during this interval? For a time period of approximately 10 seconds, the automobile experiences no change in its speed. During which interval of time does the automobile’s speed remain constant? At what speed is the automobile traveling during this interval?
Answer:
1. The car is slowing down at a rate of 2.5mph/s
2. The greatest acceleration is 10 mph/s.
3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.
Step-by-step explanation:
1. The deceleration of the car is from 16 seconds to 24 seconds is the slope [tex]m[/tex] of the graph from 16 to 24:
[tex]m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s[/tex]
the negative sign indicates that it is deceleration.
2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.
From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope [tex]m[/tex]:
[tex]m= \dfrac{45-5}{28-24}= 10mph/s[/tex]
3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.
The speed of the automobile in that interval, as we see from the graph, is 25 mph.
A line segment has endpoints of (-3, 2) and (5, -2). Find the distance between the endpoints.
Round your answer to the nearest tenth (one number past the decimal). If the second number past the decimal is 5 or greater, round up.
Answer:
[tex]d=8.9\ units[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
(-3, 2) and (5, -2)
substitute the values in the formula
[tex]d=\sqrt{(-2-2)^{2}+(5+3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{80}\ units[/tex]
[tex]d=8.94\ units[/tex]
Round to the nearest tenth
[tex]d=8.9\ units[/tex]
If h(x) = 5 + x and k(x)= 1/x, which expression is equivalent to (kxh)(X)?
Answer:
It can be solve this in two ways,
1) as if the h(x) = 5x and 2) as if h(x) = 5 + x
1) If h(x) = 5x and k(x) = 1/x
Then (k o h) (x) = k ( h(x) ) = k(5x) = 1/(5x)
2) If h(x) = 5 + x and k (x) = 1/x
Then (k x h)(x) =k ( h(x) ) = k (5+x) = 1 / [5 + x]
1/(5+x) is the correct answer
Step-by-step explanation:
Which of the following is not a composition of isometries:
A. Reflection over x=2 then rotation 90 degrees clockwise about the origin
B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin
C. Translation (x,y)->(x-2,y+1) then reflection over the y-axis
D. Reflection over the x-axis then reflection over the y-axis
Answer:
B
Step-by-step explanation:
When you dilate a shape you change the size, changing the composition of isometries.
Option B is not a composition of isometries.
Explanation:The composition of isometries refers to combining multiple isometries (transformations that preserve distance) to create a new transformation. To determine which of the options is not a composition of isometries, we need to verify if each option preserves distance. If any option does not preserve distance, it is not a composition of isometries. Let's analyze each option:
A. Reflection over x=2 then rotation 90 degrees clockwise about the origin: Both reflection and rotation are isometries, as they preserve distance. Therefore, this option is a composition of isometries.
B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin: Dilation, when the scale factor is not 1, does not preserve distance. Therefore, this option is not a composition of isometries.
C. Translation (x,y)-> (x-2, y+1) then reflection over the y-axis: Both translation and reflection are isometries, as they preserve distance. Therefore, this option is a composition of isometries.
D. Reflection over the x-axis then reflection over the y-axis: Both reflections are isometries, as they preserve distance. Therefore, this option is a composition of isometries.
In summary, option B is the only one that is not a composition of isometries.
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For the following exercises, write the interval in set-builder notation
10. (-infinity, 6)
11. (4, infinity)
12. [-3,5)
13. [-4,1]U[9, infinity)
14. (-infinity, infinity)
Final answer:
Set-builder notation is a method to define intervals through a property shared by all members. The notation for the given intervals includes conditions that represent the endpoints or infinity, expressing the range of the variable in each set.
Explanation:
Writing intervals in set-builder notation involves describing a set through a property that its members share. Here is the set-builder notation for each interval provided:
10. (-infinity, 6) in set-builder notation is: [tex]\{x | x < 6\}[/tex]11. (4, infinity) in set-builder notation is:[tex]\{x | x > 4\}[/tex]12. [-3,5) in set-builder notation is: [tex]\{x | -3 \leq x < 5\}[/tex]13. [-4,1]U[9, infinity) in set-builder notation is: [tex]\{x | -4 \leq x \leq 1\} \cup \{x | x \geq 9\}[/tex]14. (-infinity, infinity) in set-builder notation is simply the set of all real numbers, which can be written as: [tex]\{x | x \text{ is a real number}\}[/tex]To express these sets, we use 'x' as our variable and conditions such as x < 6 that define the range of values 'x' can take. The 'U' symbol represents the union of two sets, indicating that the set includes all elements from both intervals.
What is the area of the rectangle
A) 50 units
B) 54 units
C) 60 units
D) 65 units
Answer:
I'd say C.60but because of the half units its possibly B. but definitely not A or D.
Step-by-step explanation:
Because the short sides are approximately 6 units long and the long sides are 10 units long. You multiply it to find the area and you get 60.
hope this helps
The area of the graph rectangle is 60 sq. units.
The correct option is D) 60 sq. units.
What is the area of the rectangle on the graph?The area of a rectangle is expressed as:
Area = length × width
First, we use the distance formula to find the length and width of the rectangle.
[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
From the graph, the length is between the points (-1,1) and (8,-2):
Hence;
[tex]Length = \sqrt{(8-(-1))^2 + (-2 - 1)^2}\\\\Length = \sqrt{(8+1)^2 + (-2 - 1)^2}\\\\Length = \sqrt{(9)^2 + (-3)^2}\\\\Length = \sqrt{81 + 9}\\\\Length = \sqrt{90}\\\\Length = 3\sqrt{10}[/tex]
Next, we find the width which is between the points (-1,1) and (-3,-5):
[tex]Width = \sqrt{(-3 - (-1))^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-3 + 1)^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-2)^2 + (-6)^2}\\\\Width = \sqrt{4 + 36}\\\\Width = \sqrt{40}\\\\Width = 2\sqrt{10}[/tex]
Now, plug the values for the length and width into the above formula and solve for the area:
Area = length × width
Area = 3√10 × 2√10
Area = 3 × 2 × 10
Area = 60 sq. units
Therefore, the area measures 60 sq. units.
Option D) 60 sq. units is the correct answer.
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Elijah and Jonathan play on the same soccer team. They have played 3 of their 15,
games. They each create a model to represent x, the number of games their team has left
to play. Their models are shown below. Explain whether each model is correct.
Who is correct
Answer:
Only Elijah's model is correct
Step-by-step explanation:
The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.
Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play
This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play
Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.
Elijah's model is correct .
Elijah and Jonathan play on the same soccer team. They have played 3 of their 15 games.
x is the number of games that are left to be played.
Elijah and Jonathan have 12 games left on their soccer team.
Elijah and Jonathan both try to simulate the situation which are shown in figure.
Creating some model which look like a balance between quantities.
Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance.
On the other side Elijah placed 15 cubes.
The value of each cube = 1
so 15 [tex]\times 1 = 15[/tex] which are equal to total number of games.
Since 3 games are already played so on the left hand side
3 boxes of magnitude 1 each are placed.
[tex]x[/tex] is the number of games that are left.
Jonathan uses a table with three x values in a row and a 15 is the total number of games to be played are represented in the second row trying to model the same situation.
This table doesn't show the number of games left to play.
Which are 12 in number
According to Jonathan's model
[tex]3x = 15 \\x =5[/tex]
This does not model the number of games left which are 12 in number and hence
Jonathan's model does not explains the situation
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The sum of three consecutive integers is 105. What are the three integers?
Answer:
34, 35, 36
Step-by-step explanation:
34 + 35 + 36 = 105
Answer:
34
35
36
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 105.
We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 105. Therefore, you can write the equation as follows:
X + X + 1 + X + 2 = 105
To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 105
3X + 3 = 105
3X + 3 - 3 = 105 - 3
3X = 102
3X/3 = 102/3
X = 34
Which means that the first number is 34, the second number is 34+1 and third number is 34+2. Therefore, three consecutive integers that add up to 105 are:
34
35
36
2. What elevation is Point E on Map 1? *
10 feet
30 feet
50 feet
70 feet
3. What elevation is Point F on Map 1? *
10 feet
30 feet
50 feet
70 feet
Answer:
c then b
Step-by-step explanation:
2 - The elevation at Point E is 50 feet, marked by a contour line, 3 - Point F is at 70 feet elevation, illustrating the informative nature of topographic maps.
On Map 1, Point E is situated at an elevation of 50 feet, as it lies directly on the contour line representing this specific elevation. Contour lines on a topographic map connect points of equal elevation, allowing us to visualize the three-dimensional terrain on a two-dimensional surface.
In this context, every point on the contour line labeled "50 feet" shares the same elevation—50 feet above a reference point, typically sea level. Moving to Point F on Map 1, it is positioned on the contour line corresponding to an elevation of 70 feet.
This indicates that Point F is situated 70 feet above the same reference point. Topographic maps are invaluable tools for understanding the landscape's elevation variations, aiding hikers, geologists, and cartographers in navigating and representing the Earth's surface features accurately.
The contour lines on such maps provide a detailed depiction of the elevation changes, and by closely following them, one can trace the undulations of the terrain.
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the first four terms of a geometric sequence is a1 = 3
a2=12
a3=48
a4=192
What formula can be used to find an
HURRY PLEASE
Answer:
not 100% sure of this but I think its a4=192
HELP ME YOU MUST EXPLAIN THE ANSWER
Answer: 4) 7c ^2d - 7c + 4d - 10
Explanation:
First write equastion as seen:
5c^2d - 4c + 3d - 3 + 2c^d - 3c+ d - 7
Next add the c^2d’s together:
7c^2d - 4c + 3d - 3 + 3c + d - 7
Add the c’s together:
7c^2d - 7c + 3d - 3 + d - 7
Add the d’s:
7c^2d - 7c + 4d - 3 - 7
Lastly add the normal numbers:
7c^2d - 7c + 4d - 10
Thus, that is your answer!
Hope this helps! :)
When Angela turned 10, her parents deposited $5,000 in a college fund for her. When Angela enrolled in college at 18, her account had $6,800 to help pay her expenses. If the account paid simple interest, what was the annual interest rate?
Answer:
The annual interest rate was 4.5% in Angela's college fund.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Investment when Angela was 10= US$ 5,000
Duration of the investment = 8 years
Balance of the account when Angela turned 18 = US$ 6,800
2. Let's find the annual interest rate of this investment after 8 years or 20 quarters, using the following formula:
FV = PV * (1 + r) ⁿ
PV = Investment when Angela turned 10 = US$ 5,000
FV = Balance of the account when Angela turned 18 = US$ 6,800
number of periods (n) = 8
Replacing with the real values, we have:
6,800 = 5,000 * (1 + r) ⁸
6,800/5,000 = (1 + r) ⁸ (Dividing by 5,000 at both sides)
34/25 = 1⁸ + r⁸
34/25 - 1 = r⁸ (1⁸ = 1)
34/25 - 25/25 =r⁸ (1 = 25/25)
9/25 = r⁸
0.36 = r⁸ (9/25 = 0.36)
⁸√0.36 = ⁸√r⁸
0.045 = r
r = 4.5%
The annual interest rate was 4.5% in Angela's college fund.
Answer:
The answer is 4.5
Step-by-step explanation:.
To determine the interest rate, substitute the numbers for the values in the I equals Prt formula. I equals one thousand eight hundred, P equals five thousand and t equals eight because the money was in the bank for eight years.
Multiply five thousand by eight.
Divide both sides by forty thousand and evaluate.
Finally, convert the decimal zero point zero four five to four point five percent.
please help!!!
Select the correct locations on the image
Select function f and function g such that the sum of f and g is function h
The functions f and g that adds up to h(x) are:
f(x) = -2x+3 and g(x) = 7x-9
Step-by-step explanation:
Required output is:
h(x) = 5x-6
In order to find the required f and g functions we will see that which of the two functions add up to h(x)
In order to make our work easier we can see the functions f and g whose coefficients of add up to 5x
Then we can select from the functions that produce h(x)
So,
Pair 1 whose coefficients of x add up to 5 is:
f(x) = -2x+6 and g(x) = 7x-9
Adding both functions
[tex](f+g)(x) = -2x+6+7x-9\\= 5x-3[/tex]
Pair 2 that adds up to 5x
f(x) = 8x+9 and g(x) = -3x-3
Adding both functions:
[tex](f+g)(x) = 8x+9-3x-3\\= 8x-3x+9-3\\=5x+6[/tex]
Pair 3 is:
f(x) = -2x+3 and g(x) = 7x-9
Adding both functions
[tex](f+g)(x) = -2x+3+7x-9\\= -2x+7x+3-9\\=5x-6[/tex]
Hence,
The functions f and g that adds up to h(x) are:
f(x) = -2x+3 and g(x) = 7x-9
Keywords: Functions, Sum of functions
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Which graph represents 7 x − 2 y ≤ 5 7x−2y≤5
Answer:
7x-2y≤5
7x-2y≤5
Step-by-step explanation: Graph is down below!!
Hope this helps you out!☺
Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.
We need to find the graph which represents the inequality 7x−2y≤5.
What is inequality?In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Now,
Write in y=mx+b form.
y≥7/2x-5/2
Use the slope-intercept form to find the slope and y-intercept.
Slope: 7/2
y-intercept:(0, -5/2)
Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.
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Which functions are decreasing?
Select ALL answers that are correct.
Answer:
1st and 2nd graph are decreasing functions
Step-by-step explanation:
Increasing function means, as we go from left to right, the function goes "ABOVE" and thus, increases.
Decreasing function means, as we go from left to right, the function goes "DOWN" and thus, decreases.
We will look at all the 4 graphs given. We look from "LEFT-TO-RIGHT".
The first one goes "DOWN", so its decreasing.
The second one also goes "DOWN, so this is decreasing as well.
The third one goes "UP", so it is increasing.
The fourth function stays the same, so it is neither increasing nor decreasing. It is constant.
Thus,
1st and 2nd graph are decreasing functions, only
Katelynn earned $1240 in two weeks at the recreation
center during a trap shooting tournament. She earned
$480 the first week and the rest the second week.
Write an algebraic equation to model the situation.
Answer:
The money earn in second week is $ 760 and
The algebraic equation to model the situation is $ x = $ 1240 - $ 480
Step-by-step explanation:
Given as :
The total money earn by Katelynn in tow weeks = $ 1240
The money earn by Katelynn in first week = $ 480
Let The money earn by Katelynn in second week = $x
Now,
From equation
The total money earn by Katelynn in tow weeks = The money earn by Katelynn in first week + The money earn by Katelynn in second week
Or, $ 1240 = $ 480 + $ x
Or, $ x = $ 1240 - $ 480
So, x = $ 760
So, The money earn in second week is $ 760
∴ The algebraic equation to model the situation is $ x = $ 1240 - $ 480
Hence , The money earn in second week is $ 760 and
The algebraic equation to model the situation is $ x = $ 1240 - $ 480 Answer
the radius of the aluminum atom is 143pm. the radius of the aluminum atom is 54pm. by what percentage did the radius change as the ion formed?
Answer:
There was 62.23% change in radius as the ion formed.
Step-by-step explanation:
Given
Radius of Aluminium [tex](Al)[/tex] atom = 143 pm
Radius of Aluminium [tex](Al^{3+})[/tex] atom = 54 pm
Change is the radius = Radius of Aluminium [tex](Al)[/tex] atom - Radius of Aluminium [tex](Al^{3+})[/tex] atom = 143 -54 = 89
Now to find % Change is the radius we will divide Change is the radius by Radius of Aluminium [tex](Al)[/tex] atom and multiply by 100 we get
% Change is the radius = [tex]\frac{\textrm{Change is the radius}}{\textrm{Radius of Aluminium (Al) atom}} \times 100 = \frac{89}{143}\times100= 62.23\%[/tex]
Hence there was 62.23% change in radius as the ion formed.
What is the solution set of 4x^2-36= 0?
(-3)
(3)
(-3,3)
Answer:
(-3, 3).
Step-by-step explanation:
4x^2-36= 0
4x^2 = 36 Taking square roots of both sides:
2x = +/- 6
x = +/- 3.
Answer:
(-3, 3)
Step-by-step explanation:
The equation is:
[tex]4x^2-36=0[/tex]
to clear for x, first we move the -36 to the right as a +36 (or you can also say that we add 36 to both sides):
[tex]4x^2=36[/tex]
dividing by 4:
[tex]x^2=36/4\\x^2=9[/tex]
taking the square root:
[tex]x=[/tex] ± [tex]\sqrt{9}[/tex]
we add the ± because a square root has two solutions, a positive one, and a negative one.
Then we get:
[tex]x=[/tex] ± 3
The solutions are -3 and +3
which is represented in the option (-3, 3)
20 points!!!
What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
y+3=4(x+1)
y+1=4(x+3)
y−3=4(x−1)
y−1=4(x−3)
Answer: y+3 = 4( x + 1)
Step-by-step explanation:
The equation in point slope form is given as :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) , where m is the slope
slope = 4
point given : (-1,-3)
Using the formula :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
and substituting the value , we have
y - (-3) = 4 (x -{-1} )
y+3 = 4( x + 1)
Friends go on a trip. Jeff drove 1/2 of the trip and Jason Joe 1/4 of the trip.Susan and Sharon divided the rest of the drive equally.If the entire trip was 168 miles, how many miles did Sharon Drive?
Answer:
21 miles
Step-by-step explanation:
Jeff drove [tex]=\dfrac{1}{2}[/tex] of the trip
Jason Joe drove [tex]=\dfrac{1}{4}[/tex] of the trip
Together Jeff and Jason Joe drove [tex]=\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}[/tex] of the trip
All trip [tex]=1[/tex]
Remaining trip [tex]=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}[/tex]
Susan and Sharon divided the rest of the drive equally, so
Susan drove = Sharon drove [tex]=\dfrac{1}{4}:2=\dfrac{1}{4}\cdot \dfrac{1}{2}=\dfrac{1}{8}[/tex] of the trip.
The entire trip was 168 miles, then
Sharon drove [tex]=\dfrac{1}{8}\cdot 168=21\ miles[/tex]
Richard paints a picture on a rectangular canvas that is 3 feet by 2.64 feet. What is the area in Richards painting?
Answer:
7.92 Feet
Step-by-step explanation:
Since area is Length × Height in comparison to perimeter being Length + Length + Height + Height, the equation is simply:
3 × 2.64 = 7.92 Feet
Final answer:
The area of Richard's painting is calculated by multiplying the length of 3 feet by the width of 2.64 feet, which equals 7.92 square feet.
Explanation:
To calculate the area of Richard's rectangular painting, we use the formula for the area of a rectangle, which is the product of its length and width. In this case, the length of the canvas is 3 feet and the width is 2.64 feet. So, the calculation to find the area will be as follows:
Area = Length × Width
Area = 3 feet × 2.64 feet
Area = 7.92 square feet
Therefore, the area of Richard's painting is 7.92 square feet.
mrs. white buys a used car for $3,000 she makes monthly payments of $300 until the car is paid for. mr. brown buys a used car for $2,400 his makes a monthly payment of $300 until the car is payed for. find and compare the rate of change and the inital value
Answer:
Initial value for Mrs. White is $600 more than Mrs. Brown.
The rate of change is same for both.
Step-by-step explanation:
Cost of car purchased by Mrs. White = $3,000
Rate at which she pays for the car = $300 per month
Cost of car purchased by Mrs. Brown = $2,400
Rate at which she pays for the car = $300 per month
So,
Initial value for Mrs. White was =$3,000
Initial values for Mrs. Brown was =$2,400
difference in initial values [tex]=3000-2400[/tex] =$600
∴ Initial value for Mrs. White is $600 more than Mrs. Brown.
Rate of change of payment due for Mrs. White = $300 per month
Rate of change for payment due for Mrs. Brown = $300 per month
∴ The rate of change is same for both.
Since Mrs White had a higher initial value than Mrs Brown and both having same rates of change, therefore Mrs. White will take a longer time to pay the due.
Help with question 1 please.
Answer:
x is more than or equal to 35
A net force F acts on a mass m and produces an acceleration a. What mass would accelerate at a rate 8a if the force is decreased to F/2?
Answer:
The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]
Step-by-step explanation:
Given as :
The net force = F Newton
The mass of the object = m kg
The acceleration = a m/s²
Now, As The force is define as the product of mass and velocity
So, F = m × a
Now, Again , if the acceleration = 8 a
and The force decrease to [tex]\frac{F}{2}[/tex] = 0.5 F
So, Let The mass = M
∵ F = m × a
∴ mass = [tex]\frac{\textrm Force}{\textrm acceleration}[/tex]
Or. M = [tex]\frac{\textrm 0.5 F}{\textrm 8 a}[/tex]
or, M =0.0625 × [tex]\frac{F}{a}[/tex]
∴ M = 0.0625 × m = [tex]\frac{m}{16}[/tex]
so, The mass = [tex]\frac{m}{16}[/tex]
Hence The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex] Answer
Final answer:
According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). If the force is decreased to F/2, the mass that would accelerate at a rate 8a can be found by rearranging the equation and solving for mass.
Explanation:
According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), expressed as F = ma.
If the force is decreased to F/2, the new force is now (F/2). To find the mass (m) that would accelerate at a rate 8a, we need to rearrange the equation as follows:
(F/2) = m * (8a)
To solve for the mass (m), we divide both sides of the equation by (8a), which gives us:
m = (F/2)/(8a)
Therefore, the mass that would accelerate at a rate 8a when the force is decreased to F/2 is (F/2)/(8a).
(2x^3-4x^2-3x-9) by x-3
Answer:
2x² + 2x + 3
Step-by-step explanation:
x = 3 is a zero of both the numerator and the denominator, so the denominator will factor completely into the numerator with no remainder. Using grouping to factor:
(2x³ − 4x² − 3x − 9) / (x − 3)
(2x³ − 4x² − 6x + 3x − 9) / (x − 3)
(2x (x² − 2x − 3) + 3x − 9) / (x − 3)
(2x (x − 3) (x + 1) + 3 (x − 3)) / (x − 3)
2x (x + 1) + 3
2x² + 2x + 3
To use long division instead, see image.
A sphere has a diameter of 10 in. What is the volume of the sphere?
v= 125 in.
©
0
v= 500 in
v = 590 x in.
0
v - 4000 x in.
0
Answer:
The volume of sphere is 500 in³
Step-by-step explanation:
Given:
Diameter of sphere is 10 in.
Now, to find the volume we need radius.
Radius(r) = half of the diameter
[tex]r=\frac{10}{2}[/tex]
[tex]r=5[/tex]
And, now putting the formula to get the volume of sphere:
[tex]volume(v)=\frac{4}{3}\pi r^{3}[/tex]
Putting the value of π = 3.
[tex]v=\frac{4}{3} \times 3.14\times 5^{3}[/tex]
[tex]v=1.33\times 3.14\times 125[/tex]
[tex]v=522.025[/tex]
So, the volume is 522.025 in³.
By estimating the value the volume is 500 in³.
Therefore, the volume of sphere is 500 in³.
Answer:
B
Step-by-step explanation:
for those that didnt understand like me
The table shows the age and finish time of ten runners in a half marathon.
Identify the outlier in this data set. Drag into the table the ordered pair of the outlier and a reason why that point is an outlier.
Answer:
Left box: Outlier in this data set is (57,132)
Right box: because the finish time looks faster than expected for the age.
Step-by-step explanation:
As per the given table shows the [tex]age[/tex] and [tex]finish \ time[/tex] of [tex]10[/tex] runners.
It is clear that people of age around [tex]35[/tex] are finishing at around [tex]142 \ minutes[/tex]
and person with older age takes longer to finish.
One person of age [tex]57[/tex] finishes in [tex]175 \ minutes[/tex] , that looks as expected.
Another person of same age [tex](57)[/tex] finishes it too fast which is unexpected.
Therefore [tex](57,132)[/tex] is an outlier, because it looks a faster finish as per expected.
Answer:
The left box = (57 , 132)
The right box= The finished time is expected for the age.
Step-by-step explanation:
Which of the following is a step in simplifying the expression (see first image)
(the second image is the options for multiple choice)
Please be serious and don't joke around! <3 I really need help.
Answer:
D) (x^-3*y^-12)/(x^15*y^-15)
Step-by-step explanation:
If you simplify that further, then you'll get x^(-18)*y^3.
What is
[tex]8 - 8x[/tex]
One of the solutions to the equation 5x^2+bx+12=0 is − 4/5 . Find the other solution.
Answer:
-3 is the other solution.
Step-by-step explanation:
As, [tex]\frac{-4}{5}[/tex] is One of the solutions of the equations , So, it should satisfy the equation.
Putting [tex]\frac{-4}{5}[/tex] in equation 5[tex]x^{2}[/tex] + bx + 12 = 0 ,
We get,
5×[tex]\frac{-4}{5}[/tex]×[tex]\frac{-4}{5}[/tex] + b×[tex]\frac{-4}{5}[/tex] + 12 = 0.
5×[tex]\frac{16}{25}[/tex] + [tex]\frac{-4b}{5}[/tex] + 12 = 0.
After solving , 16 - 4b + 60 = 0.
4b = 76
b = 19.
So, the equation is 5[tex]x^{2}[/tex] + 19x + 12 = 0.
After factorizing , 5[tex]x^{2}[/tex] + 15x + 4x + 12 = 0.
5x(x+3) + 4(x+3) = 0
(5x+4)(x+3) = 0
Clearly the roots of the equation are -3 and [tex]\frac{-4}{5}[/tex] .
So, the other solution is -3.