(A) The figure before the reflection is called the preimage. In this case, the preimage is ABC. (B) The figure after the reflection is called the image. In this case, the image is A'B'C'. (C) The outputs for the given inputs are:
Input: A(0,9) Output: A(0,9)
Input: B(-4,4) Output: B'(-8,0)
Input: C(0,4) Output: C(0,4)
(C) The coordinates of the output for each input point can be found by reflecting the input point across the line of reflection. In this case, the line of reflection is the perpendicular bisector of the line segment connecting A and C. For point A, the reflection is itself, so the output is (0,9).
For point B, we can find its reflection as follows: draw the line perpendicular to the line of reflection that passes through B, and find the point where it intersects the line of reflection. This point is the midpoint of the line segment connecting B and its image. The reflection of B is (-8,0), and the output is B'. For point C, the reflection is itself, so the output is (0,4).
Reflection is a type of transformation in geometry where an object is flipped across a line. In this case, ABC was reflected across the line of reflection to form A'B'C'. The line of reflection is the perpendicular bisector of the line segment connecting A and C.
The reflection of a point is the point on the other side of the line of reflection that is equidistant from the line. By applying the reflection rule, we can find the coordinates of the output for each input point.
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y'' + 2y' - y = x.exp(x)
The solution of the differential equation y'' + 2y' - y = xe is found to be [tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]
To solve the differential equation y'' + 2y' - y = xeˣ, we first find the complementary solution by solving the characteristic equation,
r² + 2r - 1 = 0
Using the quadratic formula, we get,
r = (-2 ± √(2² + 4(1)(1))) / 2
r = (-2 ± √6) / 2
So the roots are,
r₁ = -1 - √6/2
r₂ = -1 + √6/2
Therefore, the complementary solution is:
[tex]y_c = Ce^{r_{1}t} + C'e^{r_{2}t}\\y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t}[/tex]
To find the particular solution, we use the method of undetermined coefficients. We assume a particular solution of the form,
y_p = Ax²eˣ + Bxeˣ + Ceˣ
Taking the first and second derivatives, we get,
y'_p = (2Ax + B + A)x eˣ + Beˣ + Ceˣ
y''_p = (4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ
Substituting these expressions into the differential equation, we get,
(4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ + 2[(2Ax + B + A)x eˣ + Beˣ + Ceˣ] - (Ax²eˣ + Bxeˣ + Ceˣ) = xeˣ
Simplifying, we get,
(3Ax² + 4Ax + B)x eˣ = xeˣ
Equating coefficients, we get,
3A = 1
4A + B = 0
Solving for A and B, we get,
A = 1/3
B = -4/3
Substituting these values into the assumed particular solution, we get,
y_p = (1/3)x²eˣ - (4/3)xeˣ + Ceˣ
Taking the first and second derivatives, we get,
y'_p = (2/3)x eˣ - 4/3eˣ + Ceˣ
y''_p = (2/3)eˣ + Ceˣ
Substituting the particular solution and its derivatives into the differential equation and simplifying, We get,
(2/3)xeˣ = xeˣ
This equation is true for all x, so there is no restriction on C. Therefore, the general solution is,
y = y_c + y_p
[tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]
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Complete question - y'' + 2y' - y = xeˣ solve the differential equation.
Please help me please 5th grade math
The length of the given rectangular cuboid is: 9 cm
How to find the volume of the rectangular prism?In geometry, a rectangular prism is defined as a polyhedron with two congruent as well as parallel bases. It is also referred to as a cuboid. A rectangular prism is one that possesses six faces, and then all the faces are located in a rectangle shape and possess twelve edges. Whenever its cross-section along the length, it is referred to as a prism.
The formula for the volume of a prism is given by the formula:
V = L * W * H
Where:
L is length
W is width
H is height
We have that Volume = 432 cm³
Thus:
6 * L * 8 = 432
48L = 432
L = 432/48
L = 9 cm
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not typing itttt cause yes :)
The value of x in the quadrilateral is 70 degrees
To find the value of the fourth interior angle, we can use the fact that the sum of all four interior angles is equal to 360 degrees. We can set up an equation:
85 + 150 + 55 + x = 360
where x is the fourth interior angle we want to find. To solve for x, we can first simplify the left side of the equation by adding the known angles:
290 + x = 360
Then, we can isolate x by subtracting 290 from both sides:
x = 360 - 290
x = 70
Therefore, the value of x when the interior angles of the quadrilateral are 85, 150, and 55 degrees is 70 degrees. This means that the four interior angles of the quadrilateral are 85, 150, 55, and 70 degrees, and their sum is indeed equal to 360 degrees.
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What is the X-value of 6x-2y=-17
The x value in the linear expression 6x - 2y = -17 is -13/6 when y = 0
Calculating the x value in the linear expressionFrom the question, we have the following parameters that can be used in our computation:
The linear expression 6x - 2y = -17
To determine the value of x in the linear expression, we set y to any value say y = 2 and then calculate the value of x
Using the above as a guide, we have the following:
6x - 2(2) = -17
Evaluate
6x = -13
Divide both sides by 6
x = -13/6
This means that the value of x is equal to -13/6
So, we have (-13/6, 0)
Hence, the ordered pairs of the linear expression is (-13/6, 0)
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Please help here is screenshot!! QUCIK! Algbera
Answer:
Right three
Step-by-step explanation:
Because the translation is applied inside the parentheses, we are shifting the function left/right. To determine whether it is shifted left or right, note that shifting right will have a negative number and shifting left will have a positive number. Since we have a negative number -3, it is shifted right.
Answer:
Step-by-step explanation:
Here if we put [tex]x=3[/tex] then then equation will give 0. Hence it will shift right side three unit .
Final answer: right 3
I will give brainliest and ratings if you get this correct
1. The product of the matrix MG would be [tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36\\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]
2. The values of k₁ = -9; k₂ = -9; t₁ = 0; t₂ = -1
How do we solve for the Matrix product of MG?
The values of the matrix M and G are;
M = [1, 4, 5; G = [2, k₁, -19;
t₁, 3, -1; 1, -4, k₂;
1, t₂, 1] -1, 5, 11]
The product MG will be row 1
1×2 + 4×1 + 5×-1 1k₁+4×-4+ 5×5 1×-19+4k₂+5×11 ⇒1 k₁+9 4k₂+36
Row 2
t₁×2+3×1+-1×-1 t₁k₁+3×-4+-1×5 t₁×-19+3k₂+-1×11 ⇒ 2t₁ k₁t₁-17 3k₂-19t₁-11
Row 3
1×2+t₂×1+1×-1 1k₁+t₂×-4+-1×5 1×-19+t₂k₂+1×11 ⇒ t₂+1 k₁-4t₂+5 k₂t₂-8
Therefore MG =
1 k₁+9 4k₂+36
2t₁ k₁t₁-17 3k₂-19t₁-11
t₂+1 k₁-4t₂+5 k₂t₂-8
G = M⁻¹ should be an identity matrix which looks like
IM = [ 1 0 0
0 1 0
0 0 1 ]
MG and I to find the values of t₁, t₂, k₁, and k₂:
1 = 1, k₁+9 = 0, 4k₂+36 = 0
2t₁ = 0 k₁t₁-17 = 1 3k₂-19t₁-11 = 0
t₂+1 = 0 k₁-4t₂+5 = 0 k₂t₂-8 = 1
k₁+9 = 0 ⇒k₁ = -9
4k₂+36 = 0 ⇒ k₂ = -9
2t₁ = 0 ⇒ t₁ = 0
t₂+1 = 0 ⇒ t₂ = -1
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Can someone help me
Answer:
Y = -½x + 3/2
Y = -3x + 5
Y = 1/4x - 3¼
Step-by-step explanation:
Parallel implies they have the same gradient
Perpendicular implies the gradient is a negative reciprocal of the other.
Probability Digital Escape! puzzle 3 answer
Probability of landing on space with polka dots = 3/8.
Probability of landing on space with stripes = 1/2.
Probability of landing on space with stripes and even numbers = 1/4.
Probability of landing on space with stripes or even numbers = 5/8.
Hence the code is 'AFCH'.
From the definition of Probability we know that,
Probability of event = (Number of Favorable outcomes)/(Total number of outcomes)
Here total number of spaces = 8.
Number of space with polka dots = 3 [space numbered 1, 4, 6]
Number of space with stripes = 4 [space numbered 0, 2, 3, 5, 7]
Number of space with stripes and even numbers = 2 [the space numbered 0 and 2]
Probability of landing on space with polka dots = 3/8 (A)
Probability of landing on space with stripes = 4/8 = 1/2 (F)
Probability of landing on space with stripes and even numbers = 2/8 = 1/4 (C)
So, Probability of landing on space with stripes or even numbers
= Probability of landing on space with polka dots + Probability of landing on space with stripes - Probability of landing on space with stripes and even numbers
= 3/8 + 1/2 - 1/4
= (3 + 4 - 2)/8
= 5/8 (H).
Hence the code will be 'AFCH'.
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Find the height of the tower using the information given in the illustration.
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
(8,-5)(4,7) 1:3 find the partitions the segment with the two given endpoints with the given ratio
The partitions coordinate are (7, -2).
We have the coordinates (8, -5) and (4, 7)
Ratio = 1 :3
Using Section Formula
x = ( 4 + 24)/ 4
x = 28/4
x= 7
and, y= (7 - 15)/4
y = -8/4
y= -2
Thus, the partitions coordinate are (7, -2).
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The probability that a student guesses the correct answer to a four-choice multiple choice question is P(correct) = 0.25. How many correct answers should a student expect to guess on a test with 68 four-choice multiple choice questions?
We can expect a student to guess 17 correct answers on a test with 68 four-choice multiple choice questions with probability 0.25.
Since the probability of guessing the correct answer to a four-choice multiple choice question is 0.25, the probability of guessing an incorrect answer is 1 - 0.25 = 0.75.
We can model the number of correct guesses as a binomial distribution with n = 68 (the number of trials) and p = 0.25 (the probability of success, i.e., guessing correctly).
The expected value of a binomial distribution is given by the formula:
E(X) = n * p
So, in this case, the expected number of correct answers that a student should guess on the test is:
E(X) = 68 * 0.25 = 17
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A dentist office is getting ready to order toothbrushes to give to their patients after checkups. The toothbrush company charges a base cost of $48 to have the dentist's name and address printed on the toothbrushes, regardless of how many are ordered. Each toothbrush will cost $2.58 if the dentist office orders less than 50 toothbrushes. However, if the dentist orders 50 or more toothbrushes, then each toothbrush will only cost $1.24. If the dentist budgets $110 for the order, what is the maximum number of toothbrushes they can purchase?
The maximum number of toothbrushes the dentist can purchase is 50.
Let's denote the number of toothbrushes the dentist orders by "x".
If the dentist orders less than 50 toothbrushes, then the cost of the toothbrushes will be 2.58x.
If the dentist orders 50 or more toothbrushes, then the cost of the toothbrushes will be 1.24x.
There is a base cost of [tex]$48[/tex] for printing the dentist's name and address on the toothbrushes.
The total cost of the order can be expressed as:
Total cost = 48 + (2.58x) for x < 50
Total cost = 48 + (1.24x) for x ≥ 50
The maximum number of toothbrushes the dentist can purchase, given that the budget is [tex]$110[/tex].
So we can set up an equation:
Total cost = 110
For x < 50:
48 + 2.58x = 110
2.58x = 62
x ≈ 24.03
For x ≥ 50:
48 + 1.24x = 110
1.24x = 62
x ≈ 50
The maximize number of toothbrushes, we choose the larger value of x, which is x ≈ 50.
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You deposit $5000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 35 years?
Answer:
50313.28
See the below process
Step-by-step explanation:
Important formulae
A=Total Amount
P=Principal or amount of money deposit
R=Annual interest rate
N=Number of Times compounded per year
T=Time in years
For the formula:
[tex]a \: is \: equals \: to \: p(1 + \frac{r}{n}) \: n - t \\ p \: is \: equals \: to \: 5000 \: dollars \: comma \: r \: s \: equals \: to \: 8\% \: comma \: n \: is \: equals \: to \: 1 \: and \: t \: is \:equals \: to \: 30 \: years \: [/tex]
Solution:
A=5000(1+0.08 /1) to the power 1.30
5000×10.062657
Answer= 50313.28
-Thank You By MrIshaan
Helen is building a rectangular garden in her backyard and she wants to have a fence around it.The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per foot. How many feet of fence panels does she need
Based on the calculations, Helen needs to buy 60 feet of fence panels for her rectangular garden in the backyard
How many feet of fence panels does she needFrom the question, we have the following parameters that can be used in our computation:
The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per footThis means that
Perimeter = 20 yards
By metrric unit of conversion, we have
1 yard = 3 feet
So, we have
Perimeter = 20 * 3 feet
Evaluate
Perimeter = 60 feet
Hence, she needs to buy 60 feet of fence panels
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Guys I’m in 7th grade taking pre ap class for math so for STAAR I’m taking 8th grade math do you guys have any tips? Any Advice for me too remember everything?
Anything would help my test is on Wednesday
To memorize knowledge there are several tips that can help us. Some are: Repeat some knowledge from time to time to memorize them.
How to memorize knowledge?To memorize knowledge there are several methods that can be useful when we need to learn something difficult. In this case, we must use some methods that can help us such as:
Practice Spaced Repetition: Spaced repetition is a memorization technique that involves repeating information at specific intervals.Create associations: Try to associate the information you are trying to memorize with something you already know.Use visualization: Visualization is a technique that consists of creating mental images of the information that you are trying to memorize.Learn more about memorization in: https://brainly.com/question/762011
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Calculate the price of a zero-coupon bond that matures in five years if the market interest rate is 7.50 percent. (Assume semiannual
compounding and $1,000 par value.)
Multiple Choice
Based on the information given, the price of the zero coupon bond is $692.04.
How to solveTo calculate the price of a zero coupon bond, we need to use the following formula:
[tex]\sf P =\dfrac{F}{1+r\div n}^{(nt)[/tex]
Where:
P = price of the bondF = face value of the bondr = annual interest raten = number of compounding periods per yeart = time to maturity in yearsAlso, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.
Plugging in the values into the formula, we get:
[tex]\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}[/tex]
[tex]\sf P = \dfrac{1000}{(1.0375)^{10}}[/tex]
[tex]\sf P = \dfrac{1000}{1.4450}[/tex]
[tex]\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)[/tex]
Therefore, the price of the zero coupon bond is $692.04.
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what is 10x10 to the second power of 10
Answer:
10 * 10^10 is equal to 100,000,000,000
The perimeter of the pentagon below is 64 units. Find the length of side AB
Step-by-step explanation:
If this is a regular pentagon , it has FIVE sides of equal length
64 ÷ 5 = 12.8 units = AB
The net below shows a square pyramid. What is the lateral surface area?
The lateral surface area of the pyramid is 112 sq. in.
The correct answer is an option (B)
From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.
The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.
Using the formula of the area of triangle, the lateral surface area would be,
A = 4 × (1/2 × base × height)
A = 4 × (1/2 × 8 × 7)
A = 4 × (4 × 7)
A = 4 × 28
A = 112 sq. in.
This is the required lateral surface area.
The correct answer is an option (B) 112 in²
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Find the complete question below.
The net below shows a square pyramid. What is the lateral surface area? A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2
Hey guys i need your help please
The matrix after the row operation is:
[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]
We have,
We use the operation R1 → R1/9.
This will give us,
Row 1 values will change to 9/9, 4/9, -9/9
So,
1, 4/9, -1
Now,
[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]
Thus,
The matrix after the row operation is:
[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]
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A GROUP OF 6 ADULTS PAY A TOTAL OF $105 FOR THEIR ADMISSION TO A MUSEUM. EACH PERSON HAS A COUPON FOR $5 OFF THE REGULAR ADMISSION PRICE. THEY WANT TO KNOW WHAT THE REGULAR ADMISSION PRICE IS FOR ONE ADULT.
LET A EQUAL THE REGULAR ADMISSION PRICE. WRITE AN EQUATION THAT REPRESENTS THE SITUATION
The regular admission price for one adult is $17.50.
We have,
Let's first determine the total cost of admission after the coupons have been applied.
Since each person has a coupon for $5 off, the total discount for the group is $5 x 6 = $30.
The total cost of admission after the discount.
$105 - $30
= $75.
Let A be the regular admission price.
Since each person paid the same price after the discount, we can set up the following equation:
6(A - $5) = $75
We subtract $5 from the regular price A because that is the amount of the coupon discount.
We can simplify the equation as follows:
6A - $30 = $75
6A = $105
A = $17.50
Therefore,
The regular admission price for one adult is $17.50.
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Analyze the diagram below and complete the instructions that follow.
Find cos 45°.
A 1
NI-
2
45°
B. √√√2
2
Answer:
cos(45°) = √2/2
B is correct.
if 1 cm is 20 km then how many km equals 9 cm
Find the value of x if log6 36 = x
Answer:
The answer for x is 2
Step-by-step explanation:
write the equation
log6(36)= x
rewrite the equation as, x = log6(36) [ formula used; logb x=y; x=y^b]
so, x^6=36
x^6=2^6[ 36=2^6=2*2*2*2*2*2]
thus, x=2
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12. ABC-A'B'C' is a reflection. Use this to answer the questions below.
(A) Which figure is the preimage?
(B) Which figure is the images
(C) What are the coordinates of the output?
Input. Output
A(0,9). A
B(-4,4) B
C(0,4). C
(A) The preimage is ABC.
(B) The image is A'B'C'.
(C) The coordinates of the output are:
A(0,9) reflects over the line of reflection to A'(0,-9).
B(-4,4) reflects over the line of reflection to B'(4,-4).
C(0,4) reflects over the line of reflection to C'(0,-4).
In geometry, a reflection is a type of transformation where a figure is flipped over a line, called the line of reflection. In this problem, ABC-A'B'C' is a reflection, which means that it is a transformation of a figure where each point of the original figure has a corresponding point in the reflected figure such that the line of reflection is the perpendicular bisector of the line segment joining each point to its corresponding point.
A) The preimage is the original figure, which is ABC.
B) The image is the reflected figure, which is A'B'C'.
C) The coordinates of the output are:
A(0,9) reflects over the line of reflection to A'(0,-9).
B(-4,4) reflects over the line of reflection to B'(4,-4).
C(0,4) reflects over the line of reflection to C'(0,-4).
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please help with this question
Answer:
Step-by-step explanation: Here if we put [tex]x=0[/tex] then we will get initial temperature. That is [tex]T_0=70+20=90[/tex].
The temperature will cools down [tex]70(0.8)^{10}+20=27.52(approx)[/tex].
So the final temperature after 10 minutes will be :[tex]90-27.52=62.48(approx)[/tex].
Final Answer: The temperature is 62.48 degree Celsius.
The National Sporting Goods Association collects data through surveys on the sales of sporting goods. A mathematician for the association used the data for the years 2003 to 2009 to create the function shown where x is the number of years since 2003 and g is the amount of the sales of golf equipment, in millions, of dollars
g(x)=-40(2x+7)(x-10)
Based on the context, what is the best constraint on x?
The constraint of x for the function g(x) = -40(2x + 7)(x - 10) is given by, 0 [tex]\le[/tex] x [tex]\le[/tex]6.
Given that the function is,
g(x) = - 40(2x + 7)(x - 10)
where x stands for the number of years since the year 2003
and g(x) stands for the amount of sales of golf equipment in million dollar unit.
The mathematician used the data for the year span of 2003 - 2009.
Min of x = Number of years since 2003 when the year is 2003 = 2003 - 2003 = 0
Max of x = Number of years since 2003 when the year is 2009 = 2009 - 2003 = 6
So the constraint of x is, 0 [tex]\le[/tex] x [tex]\le[/tex] 6.
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20 points PLS HELPP marking as BRAINLIST
Answer:
25% probability
Step-by-step explanation:
2x2=4
1x1=1
1 out 4 is shaded red
1 out of 4 is 1/4 which is 25%
Emily's score for a Mathematics test was 5% higher than her score for an English test. If Emily scored 84 points for the Mathematics test, how many points did she score for the English test?
Answer:
80 points
Step-by-step explanation:
If score in English is x points and score in math is 5% higher then score in math
y = x + 0.05x
where 0.05 = 5% expressed as decimal
0.05x refers to the 5% increase in score
y = math score
y = x(1 + 0.05)
y = 1.05x
Given score in math = 84 this becomes
84 = 1.05x
x = 84/1.05
x = 80
So Emily's score in English was 80 points
What's the value of x in the figure?
A) 33°
B) 57°
C) 76°
D) 78°
Answer:
x = 78°
Step-by-step explanation:
Line q pass through the parallel line of s and r so their alternet interior angles are equal. the alternet interior angles of 135° is 57°+ x so they are equal .
57° + x = 135°
x = 135° - 57°
x = 78°
So the answer is D, 78°
