In matrix from, the system is
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3&-1&-1\\1&1&-1\\1&-1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}[/tex]
The coefficient matrix has eigenvalues [tex]\lambda[/tex] such that
[tex]\begin{vmatrix}3-\lambda&-1&-1\\1&1-\lambda&-1\\1&-1&1-\lambda\end{vmatrix}=-(\lambda-2)^2(\lambda-1)=0\implies\lambda=2_{(2)},\lambda=1[/tex]
(where the subscript denotes multiplicity of the eigenvalue).
[tex]\lambda=2[/tex]:
[tex]\begin{bmatrix}1&-1&-1\\1&-1&-1\\1&-1&-1\end{bmatrix}\vec\eta_1=\vec0[/tex]
[tex]\implies\eta_{1,1}-\eta_{1,2}-\eta_{1,3}=0\implies\eta_{1,1}=\eta_{1,2}+\eta_{1,3}[/tex]
By picking [tex]\eta_{1,1}=1[/tex], we can then set [tex]\eta_{1,2}=1[/tex] and [tex]\eta_{1,3}=0[/tex], and vice versa, to find two corresponding eigenvectors,
[tex]\vec\eta_1=\begin{bmatrix}1\\1\\0\end{bmatrix},\vec\eta_2=\begin{bmatrix}1\\0\\1\end{bmatrix}[/tex]
[tex]\lambda=1[/tex]:
[tex]\begin{bmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{bmatrix}\vec\eta_3=\vec0[/tex]
[tex]\implies2\eta_{3,1}-\eta_{3,2}-\eta_{3,3}=0\implies2\eta_{3,1}=\eta_{3,2}+\eta_{3,3}[/tex]
We obtain [tex]\vec\eta_3[/tex] independent of [tex]\vec\eta_1,\vec\eta_2[/tex] by picking [tex]\eta_{3,2}=\eta_{3,3}=1[/tex], so that the third corresponding eigenvector is
[tex]\vec\eta_3=\begin{bmatrix}1\\1\\1\end{bmatrix}[/tex]
Then the general solution to this system is
[tex]\begin{bmatrix}x\\y\\z\end{bmatrix}=C_1e^{2t}\vec\eta_1+C_2te^{2t}\vec\eta_2+C_3e^t\vec\eta_3[/tex]
[tex]\begin{cases}x=C_1e^{2t}+C_2te^{2t}+C_3e^t\\y=C_1e^{2t}+C_3e^t\\z=C_2te^{2t}+C_3e^t\end{cases}[/tex]
To find the general solution of the given system of differential equations, we can solve each equation separately and obtain the general solution for x(t), y(t), and z(t).
Explanation:The given system of differential equations is:
dx/dt = 3x - y - z
dy/dt = x + y - z
dz/dt = x - y + z
To find the general solution, we can treat each equation separately.
For dx/dt = 3x - y - z, we can rewrite it as:
dx / (3x - y - z) = dt
Integrating both sides gives us:
ln|3x - y - z| = t + C1, where C1 is the constant of integration.
Exponentiating both sides gives us:
|3x - y - z| = e^(t+C1)
Since |3x - y - z| is always positive, we can remove the absolute value signs:
3x - y - z = e^(t+C1)
Now, we can solve the remaining two equations in a similar manner to find y(t) and z(t).
By solving the three equations, we can obtain the general solution for x(t), y(t), and z(t).
Learn more about systems of differential equations here:https://brainly.com/question/33412895
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A 25-foot ladder leans against a wall. The base of the ladder is 15 feet from the bottom of the wall. How far up the wall does the top of the ladder reach?
Answer: 20 feet.
Step-by-step explanation:
Observe the right triangle attached.
You need to find the value of "x".
Then, you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.
In this case, you can identify that:
[tex]a=25ft\\b=15ft\\c=x[/tex]
Substitute these values into [tex]a^2=b^2+c^2[/tex]:
[tex](25ft)^2=(15ft)^2+x^2[/tex]
Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:
[tex]x^2=(25ft)^2-(15ft)^2[/tex]
[tex]x=\sqrt{(25ft)^2-(15ft)^2}[/tex]
[tex]x=20ft[/tex]
ANSWER
20ft
EXPLANATION
The ladder, the wall and the ground formed a right triangle.
Let how far up the wall does the top of the ladder reached be x units.
The 25ft ladder is the hypotenuse.
The shorter legs are, 15ft and x ft
Then from Pythagoras Theorem,
[tex] {x}^{2} + {15}^{2} = {25}^{2} [/tex]
[tex] {x}^{2} + 225 = 625[/tex]
[tex] {x}^{2}= 625 - 225[/tex]
[tex]{x}^{2}= 400[/tex]
[tex]x = \sqrt{400} [/tex]
[tex]x = 20ft[/tex]
Therefore the ladder is 20 ft up the wall.
A fireworks company has two types of rockets called Zinger 1 and Zinger 2. The polynomial -16t^2 + 150t gives the height in feet of Zinger 1 at t seconds after launch. The polynomial -16t^2 + 165t gives the height of Zinger 2 at t seconds after launch. If the rockets are launched at the same time and both explode 6 seconds after launch, how much higher is Zinger 2 than Zinger 1 when they explode? 414 ft
90 ft
324 ft
990 ft
Answer:
90 feet
Step-by-step explanation:
If we put t = 6 into both the formulas, we will get the height of each.
Zinger 1:
Height = [tex]-16t^2 + 150t[/tex]
Putting t = 6,
[tex]-16(6)^2 + 150(6)=324[/tex]
Zinger 2:
Height = [tex]-16t^2 + 165t[/tex]
Putting t = 6,
[tex]-16(6)^2 + 165(6)=414[/tex]
The difference in height is 414 - 324 = 90 feet
Solve the system by using a matrix equation
3x-5y=3
3x-4y=3
Answer:
The correct answer is B. (1,0).
Answer: B. (1,0)
Step-by-step explanation:
1. We will use the matrix method to solve this problem.
3 -5 3
3 -4 3
2. Apply to Row2 : Row2 - Row1.
3 -5 3
0 1 0
3. Simplify rows.
3 -5 3
0 1 0
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
4. Apply to Row1 : Row1 + 5 Row2.
3 0 3
0 1 0
5. Simplify rows.
1 0 1
0 1 0
Note: The matrix is now in reduced row echelon form.
6. Therefore,
x=1
y=0
or (1,0).
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An organization consists of 8,684 employees. They decided to conduct a survey about their new vacation policies. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. Assuming a 95% confidence level, which of the following statements holds true?
A. As the sample size is appropriately large, the margin of error is ±0.032.
B. As the sample size is too small, the margin of error is ±0.032.
C. As the sample size is appropriately large, the margin of error is ±0.0265.
D. As the sample size is too small, the margin of error cannot be trusted..
I think the answer is A. am I correct?
A is the correct answer
Answer:
The correct option is A.
Step-by-step explanation:
An organization consists of 8,684 employees. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. It means
[tex]n=884[/tex]
[tex]p=\frac{36}{100}=0.36[/tex]
The value of z-score for 95% confidence level is 1.96.
The formula for margin of error is
[tex]ME=z\times \sqrt{\frac{p(1-p)}{n}}[/tex]
Where, z is z-score at given confidence level, p is sample proportion and n is number of samples.
[tex]ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}[/tex]
[tex]ME=\pm 0.0316425[/tex]
[tex]ME\approx \pm 0.032[/tex]
The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.
For the function below, state the x-coordinate of the x-intercept that is located to the fight of the origin.
[tex]f(x)=x^3-9x[/tex]
Answer:
x = 3
Step-by-step explanation:
It should NOT be "fight of the origin", rather "right of the origin".
Now let's move on to solve the question...
The x-intercept is found by setting the function equal to 0. Thus:
0 = x^3 - 9x
Let's solve this using algebra:
[tex]0=x^3-9x\\0=x(x^2-9)\\0=x(x-3)(x+3)[/tex]
Hence, x = -3 and x = 3
The coordinate that is to the right of the origin is the positive one, so x = 3 is the x-intercept we are looking for.
4.
Solve the given system, using the substitution method.
y = 4x – 6
8x – 2y = 14
A.
(14, 12)
B.
(12, 14)
C.
There are an infinite number of solutions.
D.
There is no solution.
3.
Solve the given system, using the substitution method.
y = 3x – 7
6x – 2y = 12
A.
There is no solution.
B.
(12, 14)
C.
(14, 12)
D.
There are an infinite number of solutions.
5.
Solve, using the substitution method.
y + 2x = 7
14 – 4x = 2y
A.
The solution is (1, 5)
B.
The solution is (21, 0)
C.
There are an infinite number of solutions.
D.
There is no solution.
Answer:
4. No solution
Step-by-step explanation:
To solve a system of equations, find the (x,y) solution that satisfies both equations. One method that can be used is substitution. It is done by substituting one function into the other function and simplify.
Substitute y = 4x - 6 into 8x - 2y = 14.
8x - 2(4x - 6) = 14
8x - 8x + 12 = 14
12 = 14 FALSE
Since the variable was eliminated and a false statement was found, there is no solution to this system.
Solve 3 and 5 similarly. If the variable is eliminated again, but a true statement is fund then the solution is infinite. If the variable is not eliminated then substitute it back into one equation to find the other.
Final answer:
Using the substitution method, we find that Problem 4 has no solution (D), Problem 3 also has no solution (A), and Problem 5 has an infinite number of solutions (C).
Explanation:
To solve the given systems of equations using the substitution method, we substitute the expression for y from the first equation into the second equation and solve for x. Once x is found, we plug it back into the first equation to find y.
Problem 4:
Starting with the equations:
y = 4x – 6
8x – 2y = 14
We substitute the first equation into the second equation:
8x – 2(4x – 6) = 14
Solving for x:
8x – 8x + 12 = 14
x = 1/2 (not a solution, as the x terms cancel out)
Since the equation simplifies to 12 = 14, which is not true, we conclude that:
Option D. There is no solution.
Problem 3:
The system appears similar:
y = 3x – 7
6x – 2y = 12
Substitution gives:
6x – 2(3x – 7) = 12
And solving for x:
6x – 6x + 14 = 12
Which simplifies to 14 = 12, another impossibility.
So the answer is:
Option A. There is no solution.
Problem 5:
From our system:
y + 2x = 7
14 – 4x = 2y
We express y from the first equation:
y = 7 – 2x
Substitute it into the second one, and solve for x:
14 – 4x = 2(7 – 2x)
14 – 4x = 14 – 4x
This equation is true for all x; hence, y can be found for any corresponding x and the system has infinite solutions:
Option C. There are an infinite number of solutions.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Twenty percent of candies in a package are red. The rest are another color.
Simulate randomly checking 20 packages for red candies using these randomly generated digits. Let the digits 1 and 2 represent a red candy.
91027 18200 74536 83514
Approximately how many red candies will be in the packages?
Answer:
Step-by-step explanation:
The probability of picking a red candy from a full bag is 0.20.
But we also have experimental information represented by those 20 digits, each of which tells us how many red candies are in each package.
In the 2nd package there is 1 red candy. In the fourth there is 1 red candy (since 2 represents a red candy, just like 1 represents a red candy).
Next, in the 6th and 8th packages there is 1 red candy each. Finally, in the 19th package there is 1 red candy. Now add up these results: the number of red candies is 1 + 1 + 1 + 1 + 1, or 5. This seems to indicate that there will be 5 red candies in the entire 20 packages.
Caution: What I have shared here is MY personal interpretation of what we are being asked.
Roberto's toy car travels at 40 centimeters per second (cm/sec) at high speed and 15 cm/sec at low speed. If the car travels for 25 seconds at high speed and then 45 seconds at low speed, what distance would the car have traveled?
Answer:
1675 cm
Step-by-step explanation:
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (40 cm/s)(25 s) + (15 cm/s)(45 s) = 1000 cm + 675 cm = 1675 cm
Roberto's toy car travels 1000 cm at high speed (40 cm/sec for 25 sec) and 675 cm at low speed (15 cm/sec for 45 sec), totaling 1675 cm.
Explanation:To calculate the total distance traveled by Roberto’s toy car, we need to consider the two separate speeds at which the car travels and the time it spends at each speed.
First, we calculate the distance at high speed using the formula distance = speed × time. At high speed, the car travels at 40 cm/sec for 25 seconds, so we multiply these two values to get the distance:
Distance at high speed = 40 cm/sec × 25 sec = 1000 cm
Next, we calculate the distance at low speed, where the car travels at 15 cm/sec for 45 seconds:
Distance at low speed = 15 cm/sec × 45 sec = 675 cm
Finally, we add these two distances together to find the total distance traveled by the toy car:
Total distance = Distance at high speed + Distance at low speed = 1000 cm + 675 cm = 1675 cm
Therefore, Roberto’s toy car would have traveled 1675 centimeters in total.
Which of these statements are true?
A. Both graphs have exactly one asymptote
B. Both graphs have been shifted and flipped.
C. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.
Answer:
Step-by-step explanation:
Given are two graphs. f(x) will have x axis as asymptote while x=2 is asymptote for g(x).
Hence both graphs have exactly one asymptote
First graph passes through (0,2)
f(x) is exponential while g(x) is log.
Both graphs are shifted because f(x) is vertically shifted by 1, while g(x) is horizontally shifted by 3 units to left
In the playoffs, the Algenauts won their division playoff series 3 games to 1 and then beat their arch-rivals the Geometers in the League Championship series 4 games to 2. If the Algenauts won 80% of their home playoff games and 60% of their away playoff games, what percentage of their playoff games were at home?
Answer:
h = 48
Step-by-step explanation:
So they played 48 home games. They won 3/4, so they won 36 and lost 12.
They played 48 away games. They won 2/3, so they won 32 and lost 16.
All tolled, they won 36 + 32 = 68 games and lost 12 + 16 = 28 games.
To calculate the percentage of home playoff games played by the Algenauts, we use a system of equations with the known win rates and number of games played. Solving, we find that approximately 71.43% of their playoff games were at home.
The student is asking about the percentage of home playoff games played by the Algenauts. The Algenauts won 3 division playoff games and then beat their rivals, the Geometers, with a score of 4-2. Given their win rates of 80% for home games and 60% for away games, we can calculate the percentage of games played at home using a system of equations.
Let H be the number of home games and A be the number of away games. Since the Algenauts played a total of 3 + 4 = 7 games, and won 3 + 4 = 7 games, we have the following equations:
H + A = 7 (total games)
0.80H + 0.60A = 7 (total games won)
Solving the system of equations, we get H = 5 and A = 2, meaning 5 out of the 7 games were played at home. Therefore, the percentage of home games is (5/7) * 100, which equals approximately 71.43%.
HELP ASAP PLEASE!!!!!
The answer is A. a=(-1) b=(7)
Answer: A
Step-by-step explanation: simple mafs
WILL GIVE BRAINIEST ANSWER!!
Question: a semi-regular tessellation may have:
A. gaps between shapes
B. overlapping shapes
C. three types of shapes
D. only one type of shape
I think it’s C. three types of shapes
because more than one repeating shape with no spaces or overlapping between shapes
A semi-regular tessellation may have three types of shapes. They do not have gaps between shapes, no overlapping shapes.
What are the semi-regular tessellations?The semi-regular tessellations are the different shapes occupied in a plane with the same behavior and same lengths of sides for each shape. The shapes may be triangles, hexagons, and squares.There are no gaps in between those shapes. So, there is no overlapping of shapes.These are formed by two or more types of regular shapes.Given options:A. Gaps between shapes - false
B. Overlapping shapes - false
C. Three types of shapes - true
D. Only one type of shape - false
Thus, a semi-regular tessellation may have three types of shapes.
Learn more about semi-regular tessellations here:
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64 POINTS AWARDED, PLEASE ANSWER ASAP!!!!!
What is the area of a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)?
Answer:
40 units^2
Step-by-step explanation:
This is because your figure has a height of 8 and a width of 5. 8*5=40 so there u go! Please mark brainliest
Answer:
Area of rectangle = 40 square units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Area of rectangle = Length * Breadth
To find the length and breadth
Here a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)
Length1 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 7)² + (3 - 3)²] = √5² = 5
Length2 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 12)² + (11 - 3)²] = √8² = 8 units
Therefore Length of rectangle = 8 and
Breadth of rectangle = 5 units
To find the area of rectangle
Area = Length * Breadth
= 8 * 5 = 40 square units
The function F is defined by F(x)= 12 x + 1 2 . Use this formula to find the following values of the function:
F(3)
F(-12)
F(1/3)
F(3/4)
F(k)
F(a/2)
F(x-1)
F(x+h)
Just solving for one of these would be really helpful!
Answer:
Step-by-step explanation:
I will assume that you meant F(x)= 12x + 12. If you meant a fraction, write 1/2.
Then F(3) = 12(3) + 12 = 48
F(-12) = 12(-12) + 12 = -132.
F(1/3) = 12(1/3) + 12 = 4 + 12 = 16
Please verify what you meant. Then I will answer the remaining questions.
[tex]\(F(3) = 48\), \(F(-12) = -132\), \(F\left(\frac{1}{3}\right) = 16\), \(F\left(\frac{3}{4}\right) = 21\), \(F(x) = 12x + 12\).[/tex]
To find the values of the function [tex]\(F(x) = 12x + 12\)[/tex] for the given inputs:
1. F(3): Substitute x = 3 into the function: F(3) = 12(3) + 12 = 36 + 12 = 48.
2. F(-12): Substitute x = -12 into the function: F(-12) = 12(-12) + 12 = -144 + 12 = -132.
3. [tex]\(F\left(\frac{1}{3}\right)\)[/tex]: Substitute [tex]\(x = \frac{1}{3}\)[/tex] into the function: [tex]\(F\left(\frac{1}{3}\right) = 12\left(\frac{1}{3}\right) + 12 = 4 + 12 = 16\).[/tex]
4. [tex]\(F\left(\frac{3}{4}\right)\)[/tex]: Substitute [tex]\(x = \frac{3}{4}\)[/tex] into the function: [tex]\(F\left(\frac{3}{4}\right) = 12\left(\frac{3}{4}\right) + 12 = 9 + 12 = 21\).[/tex]
5. F(k): Substitute x = k into the function: F(k) = 12k + 12.
6. [tex]\(F\left(\frac{a}{2}\right)\)[/tex]: Substitute [tex]\(x = \frac{a}{2}\)[/tex] into the function: [tex]\(F\left(\frac{a}{2}\right) = 12\left(\frac{a}{2}\right) + 12 = 6a + 12\).[/tex]
7. F(x-1): Substitute x = x-1 into the function: F(x-1) = 12(x-1) + 12 = 12x - 12 + 12 = 12x.
8. F(x+h): Substitute x = x+h into the function: F(x+h) = 12(x+h) + 12 = 12x + 12h + 12.
These are the values of the function for the given inputs.
find the volume of the pyramid below.
A. 1200 units^3
B. 1300 units^3
C. 400 units^3
D. 433 units
Answer:
Hence correct choice is C. [tex]Volume=400[/tex] [tex]units^3[/tex]
Step-by-step explanation:
Given that length of the square base of the pyramid a = 10 units
Given that height of the pyramid is h = 12 units
Now question says to find the volume of the given cone.
So plug these values into formula of volume of the square pyramid.
[tex]Volume=\frac{1}{3} a^2h[/tex]
[tex]Volume=\frac{1}{3} (10)^2(12)[/tex]
[tex]Volume=\frac{1}{3} (100)(12)[/tex]
[tex]Volume=\frac{1}{3} (1200)[/tex]
[tex]Volume=400[/tex]
Hence correct choice is C.
Answer:
The correct answer is option C. 400 units³
Step-by-step explanation:
Formula:-
Volume of pyramid = (a²h)/3
Where a - side of base
h - height of pyramid
From the figure we can see a square pyramid
To find the volume of pyramid
here a = 10 units and h = 12 units
Volume = (a²h)/3 = (10² * 12)/3
= 400 units³
What is the range of this data set? 43, 78, 12, 32, 97
Median:
Mean:
Range:
range: 85.
media: 12.
mean: about 52.4
What is the r-value of the following data to three decimal places?
A. -0.811
B. 0.811
C. 0.901
D. -0.901
Answer:
-0.9007 it would be D. if I'm right
Step-by-step explanation:
X Values
∑ = 34
Mean = 6.8
∑(X - Mx)2 = SSx = 140.8
Y Values
∑ = 54
Mean = 10.8
∑(Y - My)2 = SSy = 164.8
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -137.2
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -137.2 / √((140.8)(164.8)) = -0.9007
Meta Numerics (cross-check)
r = -0.9007
Answer: Your answer is D. -0.901 !
AP CALC HELP!!! Worth 38 points. AP Calc AB differental FRQ
Answer:
5a. approximately 6 grams remain after 2 seconds
5b. The graph shown cannot be a solution. The solution has negative slope everywhere.
5c. y = 50/(t+5)
5d. The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)
Step-by-step explanation:
5a. The tangent line has the equation ...
y = f'(0)t +f(0)
Here, that is
y = -0.02·10²·t +10 = 10 -2t
Then at t=2, the value is ...
y = 10 -2·2 = 6 . . . . grams remaining
__
5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.
__
5c. The equation is separable so can be solved by integrating ...
∫y^-2·dy = -0.02∫dt
-y^-1 = -0.02t +c . . . . for some arbitrary constant c
Multiplying by -50 gives ...
50/y = t + c . . . . for some constant c
We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...
50/10 = 0 +c = 5
Then, solving for y, we get ...
y = 50/(t+5)
__
5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.
PLEASE HELP! If you apply the changes below to the quadratic parent function, f(x) = x2, what is the equation of the new function?
Shift 1 unit right.
Vertically stretch by a factor of 5
Reflect over the x-axis
Answer:
Step-by-step explanation:
By the way, please use the symbol " ^ " to indicate exponentiation:
f(x) = x^2
Shifted 1 unit to the right, we get g(x) = (x - 1)^2
Vertically stretched by a factor of 5, we get h(x) = 5(x - 1)^2
Reflected over the x-axis: j(x) = -5(x - 1)^2
Answer:
The correct option is A.
Step-by-step explanation:
The quadratic parent function is
[tex]f(x)=x^2[/tex]
The translation is defined as
[tex]g(x)=k(x+a)^2+b[/tex] .... (1)
Where, k is vertical stretch, a is horizontal shift and b is vertical shift.
If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5
Substitute a=-1 and k=5 in equation (1).
[tex]g(x)=-5(x+(-1))^2+(0)[/tex]
[tex]g(x)=-5(x-1)^2[/tex]
Therefore the correct option is A.
The last 30 times that Eric has played his video game he has scored over 100,000 points 40% of the time. What prediction can you make about the next 15 times Eric plays his video game?
Answer:
A)
He will score over 100,000 points 4 times.
B)
He will score over 100,000 points 6 times.
C)
He will score over 100,000 points 8 times.
D)
He will score over 100,000 points 12 times.
Step-by-step explanation:
Answer is B
Answer:
B) He will score over 100,000 points 6 times.
Step-by-step explanation:
I got it correct on USATP.
Hope this helps!
From: Aug1e
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
-4a^2 -7a^2 - 2ab +3ab +9b^2 -5b^2
11a^2 + ab +4b^2
Step-by-step explanation:
Answer:
-11a^2+ab+4ab^2
Step-by-step explanation:
Solve using a proportion.
Answer:
t = 24 yards
Step-by-step explanation:
Since the trapezoids are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{t}{c}[/tex] = [tex]\frac{u}{d}[/tex]
Substitute in given values
[tex]\frac{t}{0.4}[/tex] = [tex]\frac{15}{0.25}[/tex] ( cross- multiply )
0.25t = 6 ( divide both sides by 0.25 )
t = 24
-1 3/7 x (-3 2/3)=?
Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
Answer:
(x,y) = (-2, 0)
and
(x,y) = (2.5, 2.25)
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equations.
Please see the attached image below, to find more information about the graph
s
The equations are:
y1 + 4 = x^2
y1 = x^2 - 4
y2 - x = 2
y2 = x +2
The intersection of the two graphs correspond to
(x,y) = (-2, 0)
and
(x,y) = (2.5, 2.25)
Cards numbered 1 through 20 are mixed up and placed in a bag. Milan chooses one of the cards without looking.
What is the probability that Milan chooses a card with a number 12 or greater?
3/5
4/5
9/10
9/20
Answer: 9/20
Step-by-step explanation:
Easy!!!
If f(x) = x^2 I horizontally compressed to g(x) which could be the equation of g(x)?
A. [tex]g(x) =( \frac{1}{5} x)^2[/tex]
B. [tex]g(x) = x^2+5[/tex]
C. [tex]g(x) = (5x)^2[/tex]
D.[tex]g(x) = (x-5)^2[/tex]
Answer: Option C.
Step-by-step explanation:
For a parent function [tex]f(x)=x^2[/tex], you have these transformations:
If [tex]f(x)=c(x^2)[/tex] and [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor "c".
If [tex]f(x)=c(x^2)[/tex] and [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]0 <c <1[/tex] then the graph is stretched horizontally by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]|c| > 1[/tex] then the graph is compressed horizontally by a factor "c"
In this problem we have the function [tex]f(x)=x^2[/tex] and we know that this is horizontally compressed to g(x), then the transformation is:
[tex]f(x)=(cx)^2[/tex] and the factor must be [tex]|c| > 1[/tex]
You can observe that the option that shows this form is the option C. Therefore, the equation of g(x) is:
[tex]g(x) = (5x)^2[/tex]
Where [tex]|5| > 1[/tex]
A horizontal compression of the function f(x) = x² is represented by the function g(x) = (5x)², where x is multiplied by a constant greater than 1, causing the function to be 'squeezed' together along the x-axis.
Explanation:The question is asking for a horizontal compression of the function f(x) = x². A horizontal compression occurs when we multiply the x by a constant greater than 1 inside the function parentheses. This affects the rate at which the function grows horizontally.
A good way to visualize this is by thinking of the x-axis being 'squeezed' together. Given the choices, the function that represents a horizontal compression of f(x) = x² is C: g(x) = (5x)². In this case, we are multiplying x by a constant (5), thus compressing the function horizontally compared to the original function.
Learn more about Horizontal Compression here:https://brainly.com/question/28968436
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How do I find X for this problem? I’m stuck
Corresponding sides of the two triangles occur in a ratio with one another. In particular, you have the relationship
[tex]\dfrac6{6+x}=\dfrac{10}{15}=\dfrac y{y+4}[/tex]
We only need the first two parts to solve for [tex]x[/tex]:
[tex]\dfrac6{6+x}=\dfrac{10}{15}\implies6\cdot15=10(6+x)\implies90=60+10x\implies30=10x[/tex]
[tex]\implies\boxed{x=3}[/tex]
Translate this sentence into an equation.
The product of Delia's score and 5 is 65
Use the variable d to represent Delia's score.
Answer:
Step-by-step explanation:
Delia's score X 5 = 65
d X 5 = 65
5d=65
The sentence 'The product of Delia's score and 5 is 65' translates into the equation '5d = 65', where 'd' represents Delia's score.
Explanation:The given sentence, 'The product of Delia's score and 5 is 65', can be translated into an equation as follows:
Replace 'the product of Delia's score and 5' with '5d' (since 'product' implies multiplication)Replace 'is' with '=' (as '=' is the mathematical symbol for 'is')Replace '65' with '65'So, the translated equation is: 5d = 65. Here, 'd' represents Delia's score.
Learn more about Equation Translation here:https://brainly.com/question/29244302
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The weight of an object on a particular scale 155. 2lbs the measured weight May very from the actual weight by the most 0.4 lbs what is the actual weight of the objects
Answer:
154.8-155.6
Step-by-step explanation:
155.2-.4=154.8 or maybe its more in that case the most it could be is 155.2+.4=155.6