======================================================
Explanation:
Let's focus on one point, say the point (3,3).
How far is this point from the vertical line x = -1? That would be 4 units. You can count the spaces or subtract with absolute value.
So to go from (3,3) to the mirror line, we move 4 spaces to the left. Then we'll move another 4 spaces to the left to arrive at the image point (-5,3). The x coordinate shifted over 8 spots but the y coordinate stays the same.
The point (3,6) moves in the exact same way, and the exact same set of distances. It will land on (-5,6).
The point (5,3) needs to move 6 spaces to the left to land on the mirror line. Then another 6 spaces to the left to get to (-7,3).
------------
To summarize:
The point (3,3) moves to (-5,3)The point (3,6) moves to (-5,6)The point (5,3) moves to (-7,3)Each time the y coordinate stays the same for any given point being moved. This makes the two triangles on the same horizontal level together.
Once again, refer to the diagram below for a visual summary. I used GeoGebra to make the drawing. It's a free online tool which I recommend for geometry students.
Six cousins inherited a total of StartFraction 5 Over 8 EndFraction of their great aunt’s assets, which they divided evenly. What fraction of their great aunt’s assets did each cousin inherit?
Answer:
For us to determine the answer to this item, we simply have to divide the given fraction of the great aunt’s property that is to be divided among the cousins by 6.
N = 5/8 / 6
The value of N in the equation is 5/48 or 0.104. Thus, each of the cousins will receive 10% of the great aunt’s property.
Answer:
5/48
Step-by-step explanation:
(5/8) / 6
(1 point) Find \( y \) as a function of \( x \) if \[ x^{2} y^{\prime \prime}+13 x y^{\prime}+36 y=x^{6}, \] \[ y(1)=-3, \quad y^{\prime}(1)=3 \text {. } \] \( y \)
The given differential equation is
x²y″+13xy′+36y = x⁶; y(1) = -3, y′(1) = 3
We have to solve this second-order linear differential equation for y as a function of x.
Given equation is x²y″+13xy′+36y = x⁶
The associated homogeneous equation is
x²y″+13xy′+36y = 0
The auxiliary equation of the associated homogeneous equation ism² + 13m + 36 = 0(m + 9)(m + 4) = 0
So, the roots of the auxiliary equation arem₁ = -9 and m₂ = -4.
Now, the general solution of the associated homogeneous equation is
y = c₁x⁻⁹ + c₂x⁻⁴.
Find a particular solution to the non-homogeneous equation by the method of variation of parameters, such that it satisfies the initial conditions.
For the particular solution, we assume
y_p = u₁(x) x⁻⁹ + u₂(x) x⁻⁴
On differentiating this with respect to x, we get
y_p′ = u₁′(x) x⁻⁹ - 9u₁(x) x⁻¹⁰ + u₂′(x) x⁻⁴ - 4u₂(x) x⁻
Differentiate the above equation with respect to x, we get
y_p″ = u₁″(x) x⁻⁹ - 18u₁′(x) x⁻¹⁰ + 81u₁(x) x⁻¹¹ + u₂″(x) x⁻⁴ - 8u₂′(x) x⁻⁵
Since y_p is a particular solution to the non-homogeneous equation, putting the values of
y_p, y_p', and y_p″ in the equation
x²y″+13xy′+36y = x⁶,
we getu₂(x) = x⁴/2
The value of u₁(x) is
u₁(x) = -x²/2
Substituting the value of u₁(x) and u₂(x) in the general solution of the associated homogeneous equation, we get the particular solution
y_p = -1/2 x² x⁻⁹ + 1/2 x⁴ x⁻⁴
= 1/2 x⁻⁵.
We can now obtain the complete solution of the non-homogeneous equation.
The general solution of the given non-homogeneous equation is
y = y_p + y_c = 1/2 x⁻⁵ + c₁x⁻⁹ + c₂x⁻⁴
where y_c is the general solution of the associated homogeneous equation.
Substituting the initial conditions y(1) = -3 and y′(1) = 3, in the above general solution, we get
-3 = 1/2 + c₁ + c₂and3 = -5/2 c₁ - 4c₂
Solving the above two equations, we getc₁ = -31/40 and c₂ = -27/40
Therefore, the solution of the given differential equation isy = 1/2 x⁻⁵ - 31/40 x⁻⁹ - 27/40 x⁻⁴.
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Which memory locations are assigned by the hashing function h(k) = k mod 101 to the records of students with the following Social Security numbers?
a) 104578690 b) 432222187
c) 372201919 d) 501338753
The hashing function h(k) = k mod 101 assigns memory locations based on the remainder of the Social Security number (k) divided by 101.
a) For the Social Security number 104578690, h(104578690) = 104578690 mod 101 = 74. So, this record would be assigned to memory location 74.
b) For the Social Security number 432222187, h(432222187) = 432222187 mod 101 = 3. So, this record would be assigned to memory location 3.
c) For the Social Security number 372201919, h(372201919) = 372201919 mod 101 = 46. So, this record would be assigned to memory location 46.
d) For the Social Security number 501338753, h(501338753) = 501338753 mod 101 = 39. So, this record would be assigned to memory location 39.
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Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. 25x2=25y2=6x
25r(cos^2Ф-sin^2Ф)-6cosФ=0
The equation in rectangular coordinates is 25x2=25y2=6x, we need to write in cylindrical coordinates
What is rectangular coordinate system?The rectangular coordinate system consists of two real number lines that intersect at a right angle
In cylindrical coordinate, x=rcosФ
y=rsinФ
z=z
25(rcosФ)^2=25(rsinФ)^2=6rcosФ
25r^2cos^2Ф-25r^2sin^2Ф=6rcosФ
25r^2(cos^2Ф-sin^2Ф)=6rcosФ
25r(cos^2Ф-sin^2Ф)-6cosФ=0
25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required equation in cylindrical coordinates.
Therefore 25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required cylindrical equation
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Points (3, 2) and (7, 2) are on the graphs of both quadratic functions f and g. The graph of f opens downward, and the graph of g opens upward. Which of these statements are true?
1. The graphs of f and g have the same axis of symmetry.
2. The graphs of f and g have the same x-intercepts.
3. The graph of f has a maximum point, and the graph of g has a minimum point.
4. The graph is a result of a reflection of the graph pf g across the x-axis.
Answer: I and III
Step-by-step explanation:
The graphs of f and g have the same axis of symmetry. The graph of f has a maximum point, and the graph of g has a minimum point. The graph is a result of a reflection of the graph pf g across the x-axis. The correct options are 1, 3, and 4.
What is quadratic function?A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.
We can use the fact that the points (3,2) and (7,2) are on the graphs of both functions to find out which of the given statements are true.
Let's start by using the fact that the graphs of the functions f and g pass through the points (3,2) and (7,2).
Since the y-coordinate is the same for both points, we can set the equations of the functions equal to 2 and solve for the unknown coefficients.
For the downward-opening quadratic function f, the equation is of the form:
\(f(x) = a(x - h)^2 + k\)
Where (h,k) is the vertex of the parabola. Since f opens downward, the coefficient a is negative.
Using the point (3,2), we get:
\(2 = a(3 - h)^2 + k\)
Using the point (7,2), we get:
\(2 = a(7 - h)^2 + k\)
Subtracting the second equation from the first, we get:
\(0 = a[(3 - h)^2 - (7 - h)^2]\)
Simplifying this expression, we get:
0 = a[(3 - h + 7 - h)(3 - h - (7 - h))]
0 = a[-4(h - 5)]
Since a is non-zero (otherwise the parabola is not quadratic), we get:
h = 5
Plugging in h = 5 and using one of the equations above, we can solve for k:
\(2 = a(3 - 5)^2 + k\)
2 = 4a + k
k = 2 - 4a
Therefore, the equation of the quadratic function f is:
\(f(x) = a(x - 5)^2 + (2 - 4a)\)
Using the same method for the upward-opening quadratic function g, we get:
\(g(x) = b(x - 5)^2 + (2 + 4b)\)
Where b is positive.
Now, let's check which of the given statements are true:
The graphs of f and g have the same axis of symmetry.
Since the vertex of f is (5, 2 - 4a) and the vertex of g is (5, 2 + 4b), the x-coordinate of the axis of symmetry for both functions is 5. Therefore, statement 1 is true.
The graphs of f and g have the same x-intercepts.
The x-intercepts of f are given by:
\(0 = a(x - 5)^2 + (2 - 4a)\\4a = a(x - 5)^2\)
x - 5 = ±√(4/a)
x = 5 ± 2√(a)
The x-intercepts of g are given by:
\(0 = b(x - 5)^2 + (2 + 4b)\)
-4b = \(b(x - 5)^2\)
x - 5 = ±√(-4/b)
x = 5 ± 2i√(b)
Thus, since a and b have opposite signs, the x-intercepts of f and g are different. Therefore, statement 2 is false.
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Jasper and Corey have saved up a total of $78.00. Jasper has saved 6 dollars more than twice as much as
Corey. How much has Corey saved?
Answer:
24
Step-by-step explanation:
Corey has saved an amount of 24 dollars, if they have saved up a total of $78.00.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's assume that Corey has saved an amount of x dollars.
Given that Jasper and Corey have saved up a total of $78.00.
Jasper has saved 6 dollars more than twice as much as
Corey.
As per the given condition, the algebraic form is:
(6 + 2x) + x = 78.
Rearrange the terms of variables of x in the above equation,
6 + 2x + x = 78
Apply the addition operation,
6 + 3x = 78
Subtract 6 from both sides in the equation,
3x = 72
Now divide both sides by 3 in the equation,
x = 24
Therefore, Corey has saved an amount of 24 dollars.
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PLS HURRY IM TIMED Which statement about a dilation with a scale factor of 3 is true?
Three is added to each side in the pre-image to find the corresponding side length in the image.
Three is subtracted from each side in the pre-image to find the corresponding side length in the image.
Each side in the pre-image is multiplied by three to find the corresponding side length in the image.
Each side in the pre-image is divided by three to find the corresponding side length in the image.
Answer:
Each side in the pre-image is multiplied by three to find the corresponding side length in the image.
Step-by-step explanation:
Hope this helps!!
Answer:
C
Step-by-step explanation:
Each side in the pre-image is multiplied by three to find the corresponding side length in the image.
6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x.
Solving a system of equations, we conclude that the value of x is 28.
How to determine the value of x?
Here we have the quadratic number pattern:
6, 15, x, 45, ...
First, we have that:
15 - 6 = 9
So 9 is the first difference.
Then we will have:
x = 15 + 9 + a
(where a is the second difference, constant of the sequence).
And:
45 = x + 9 + a + a
Then we have a system of equations:
x = 15 + 9 + a
45 = x + 9 + a + a
We can isolate a on the first equation:
a = x - 24
We can replace that in the other equation:
45 = x + 9 + 2a
45 = x + 9 + 2*(x - 24)
Now we can solve that for x:
45 - 9 = x + 2*(x - 24)
36 = 3x - 48
36 + 48 = 3x
84 = 3x
84/3 = x = 28
The value of x is 28.
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The weather in Montana
was - 1° F one night and
12° F the next night. How
much warmer was the
temperature the second
night?
Answer:
13 degrees warmer
Step-by-step explanation:
Answer:
13 degrees Fahrenheit.
Step-by-step explanation:
The temperature started at -1 then raises to 12.
So, it goes -1,0,1,2,3,4,5,6,7,8,9,10,11,12, so it increases by 13 degrees Fahrenheit.
Goedele adds 52g of flour to her cake mix.
This is only 50% of what the recipe told her to add.
How much did the recipe tell her to add?
\(52 \times 2 = 104\)
The recipe told her to add 104 g of flour
//
Proof:
\(104 \times 0.50 = 52\)
Which of the following represents the total area of the figure?
10.663 in2
24.413 in2
28.448 in2
34.335 in2
Answer:
Step-by-step explanation:
1. Area of rectangle = LxB = 4.6X3.15= 14.49
2. Area of right angle triangle= 1/2x base x height = 1/2x 3.3 x 3.15= 5.1975
3. Area of another right angle traingle= 1/2x base x height= 1/2x 3 x (6.3-3.15)*=4.725
add 1+2+3= 24.413 in2
*6.3-3.15 because 3.15 forms part of the rectangle and we want to find the height of the triangle only thus the side of the rectangle is subtracted.
Jeremy needs more soap. He buys 12 bags of soap for 5 dollars. Each bag of soap has x number of bars inside. How many bars of soap does Jeremy have?
Step-by-step explanation:
\(1 \: bag \: has \: x \: bars \\ 12 \: bags \: will \: have \: \frac{12 \times x}{1} \\ = 12x \: bars\)
The mean of five numbers 3, 7, 9, 12, and x is 8. Find the value of x.
Answer:
8
Step-by-step explanation:
U literally said x is 8
Answer:
\(8 = \frac{(3 + 7 + 9 + 12 + x)}{5} \\ 8 \times 5 = 31 + x \\ 40 = 31 + x \\ x = 9\)
At Bank A, $600 is invested with an interest rate of 5% compounded annually. At Bank B, $500 is invested with an interest rate of 6% compounded quarterly. Which account will have a larger balance after 10 years? After 20 years?
The Solution:
It is given that
For Bank A:
\(\begin{gathered} P=\text{ \$600} \\ R=5\text{ \% annually} \\ T=10\text{ yrs and T=20 yrs} \end{gathered}\)For Bank B:
\(\begin{gathered} \text{ P=\$500} \\ \text{ R=6\% quarterly} \\ \text{ T=10yrs and 20 yrs} \end{gathered}\)By the formula for the compound interest, we have
\(\begin{gathered} A=P(1+\frac{r}{100\alpha})^{n\alpha} \\ \text{Where} \\ \alpha=\text{ number of periods per annum} \end{gathered}\)For Bank A:
\(\begin{gathered} A=P(1+\frac{r}{100\alpha})^{n\alpha} \\ \text{ In this case,} \\ \alpha=1 \\ P=\text{ \$600} \\ r=\text{ 5\%} \\ n=10\text{ yrs, and 20 yrs} \end{gathered}\)Substituting the corresponding values, we have
\(\begin{gathered} A=600(1+\frac{5}{100\times1})^{(10\times1)} \\ \\ A=600(1+0.05)^{10}=600(1.05)^{10}=977.337\approx\text{ \$977.34} \\ \end{gathered}\)For Bank A for after 20 years:
\(A=600(1.05)^{20}=1591.979\approx\text{ \$1591.98}\)Similarly, for Bank B:
\(\begin{gathered} A=P(1+\frac{r}{100\alpha})^{n\alpha} \\ \text{ In this case,} \\ \alpha=4 \\ P=\text{ \$500} \\ r=6\text{ \%} \\ n=10\text{ yrs, and 20 yrs} \end{gathered}\)Substituting these values in the formula, we get
\(undefined\)how to know if a function has a vertical asymptote
To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.
A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:
Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.
Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.
For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.
In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.
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Could someone help me out thanks!
y= 3x-4
Step-by-step explanation:
do comment on it about your country
your age bye bro
+Suppose g(x) = (x – 4)2 + 5. Which statement best compares the graph ofg(x) with the graph of f(x) = x2?O A. The graph of g(x) is shifted 4 units left and 5 units up.O B. The graph of g(x) is shifted 4 units left and 5 units down.O c. The graph of g(x) is shifted 4 units right and 5 units down.O D. The graph of g(x) is shifted 4 units right and 5 units up.SUBMIT
SOLUTION:
Step 1:
In this question, we are given the following:
Suppose
\(g(x)\text{ = \lparen x-4\rparen}^2\text{ + 5}\)Which statement best compares the graph of g(x) with the graph of:
\(f(x)\text{ = x}^2\)Step 2:
The details of the solution are as follows:
The graphs of the two functions are as follows:
CONCLUSION:
The final answer is:
The graph of g(x) is shifted 4 units right and 5 units up ( OPTION D )
HELP PLS
Which expressions shows a correct way to set up the slope formula for the line that passes through the points (5, 0) and (6, -6)?
Answer:
-6-0
____
6-5
Step-by-step explanation:
its suppose to be a fraction hope it helps please mark brainliest
If 1+1=Flamingo, what does 2+2 equal?
Answer:
octopus
Step-by-step explanation:
because if you break it down one plus one is 2 V equals flamingo but if you get two flamingos two flightless things that would mean octopus yet octopus it's a water creature if his flight was put two flightless birds on water something might happen yes Flamingo plus Flamingo equals octopus
You may need to use the appropriate appendix table to answer this question. Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household (a) What is the probability that a household views television between 5 and 11 hours a day? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (
b) How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. hrs (
c) What is the probability that a household views television more than 3 hours a day?
The solution for question a is 0.7636. The solution for question b is 12.09 hours. The solution for question c is 0.9842. We can show the working in the following manner.
(a) To find the probability that a household views television between 5 and 11 hours a day, we need to find the area under the normal distribution curve between those two values.
We can do this by standardizing the values using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation. Then we can use a standard normal distribution table or calculator to find the area.
For 5 hours of viewing: z = (5 - 8.35) / 2.5 = -1.34
For 11 hours of viewing: z = (11 - 8.35) / 2.5 = 1.06
Using a standard normal distribution table, we find that the area to the left of -1.34 is 0.0918, and the area to the left of 1.06 is 0.8554. So the area between -1.34 and 1.06 is:
0.8554 - 0.0918 = 0.7636
Therefore, the probability that a household views television between 5 and 11 hours a day is 0.7636.
(b) To find the number of hours of television viewing that a household must have in order to be in the top 3% of all television viewing households, we need to find the z-score that corresponds to the top 3% of the distribution. We can then use the formula z = (x - μ) / σ to solve for x.
Using a standard normal distribution table, we find that the z-score that corresponds to the top 3% of the distribution is approximately 1.88. Therefore:
1.88 = (x - 8.35) / 2.5
Solving for x, we get:
x = 1.88 * 2.5 + 8.35 = 12.09
Therefore, a household must view at least 12.09 hours of television per day to be in the top 3% of all television viewing households.
(c) To find the probability that a household views television more than 3 hours a day, we need to find the area under the normal distribution curve to the right of 3. We can use the same formula as in part (a) to standardize the value and then use a standard normal distribution table or calculator to find the area.
For 3 hours of viewing: z = (3 - 8.35) / 2.5 = -2.14
Using a standard normal distribution table, we find that the area to the left of -2.14 is 0.0158. So the area to the right of 3 is:
1 - 0.0158 = 0.9842
Therefore, the probability that a household views television more than 3 hours a day is 0.9842.
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Misty must pack 365 candles into 15 boxes. Each box must contain an equal number of candles. How many candles does she have left over? (use long division to find the remainder)
A) 1
B) 3
C) 5
D) 7
The answer is 5 because you can fit 365 into 15 24 times and then that would equal 360 and then you have 5 left over.
15x24=360 365
- 360
____
5
Answer:
C
Step-by-step explanation:
10 can go into 365 10 times leaving 5 left over.
h-4/j = k for j solve for the indicated variable
Answer:
j = -4/(k - h)
Step-by-step explanation:
h - 4/j = k
use inverse operation
h - 4/j = k
-h -h
-4/j = k - h
*j *j
-4 = j( k - h )
/( k - h ) /( k - h )
-4/( k - h ) = j
PLEASE HELP I WILL MARK BRAINLIEST
helppppppppppp OMG pleaseee
Answer:
It is
1/c^93
Step-by-step explanation:
At the Throw Factory, the assembly line produces 122 baseballs in a batch. The baseballs are packaged in boxes with 11 each. If 8 batches are made in one day, how many baseballs will be leftover at the end of it?
The baseballs produced in a day would fill 88 boxes and there would be 8 baseballs leftover.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
The assembly line produces 122 baseballs in a batch, If 8 batches are made in one day hence:
Total baseballs produced = 8 batches * 122 balls per batch = 976 balls
Each box contain 11 baseballs each, hence:
number of boxes = 88 boxes and 8 baseballs remaining
The baseballs produced in a day would fill 88 boxes and there would be 8 baseballs leftover.
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What can you say about the end behavior of the function f(x) = -4x^6 +6x^2-52?
The true statement about the end behavior of f(x) is (b)
How to determine the end behavior?The equation of the function is given as;
f(x) = -4x^6 +6x^2-52
The leading coefficient of the above function is
Leading coefficient = -4
-4 is less than 0 i.e. negative
This means that options (a) and (c) are false
Also;
The ends of even functions face the same direction, and not opposite directions.
Hence, the true statement about the end behavior of f(x) is (b)
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Examine the graphs and match each one with the correct coordinate rotation. You should match one graph with one rule.
what is the number for running shoes
Answer:
It's actually quite simple. Shoes that end with lower numbers (40, 50 & 60) deliver the highest stability. Numbers in the middle (70 & 80) are designed for light stability or neutral runners and the highest numbers (90 & 00) are your competition and lightest models.
Answer:
You didn't explain
Lionel's table group drank 1 liters of juice with their pizza. How many milliliter
did they drink? Show your work.
Answer:
1,000 milliliters
Step-by-step explanation:
1 liter = 1,000 milliliters
So, 1 * 1,000 = 1,000
Answer: 1,000 milliliters
Step-by-step explanation: 1 liter = 1,000 milliliters
Can any kind soul help me ASAP!
Answer:
the answer is B
x = 1
Step-by-step explanation:
the symmetry is in the middle of the curve like a mirror and the equation of the mirror or symmetry line is x=1