Answer:
a. -5x³ + 29x² - 56x + 15
b. 8x² + 9x + 5
c. 18t³ - 42t² - 14t - 30
d. x³ - 2x² - 5x + 6
e. -2b⁴ + a² + 6b² - 24a
Step-by-step explanation:
a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)
3x³ - 3x² + 15 - 8x³ + 32x² - 56x
-5x³ + 29x² - 56x + 15
b. 7x² + 2x + 5 + x(x + 7)
7x² + 2x + 5 + x² + 7x
8x² + 9x + 5
c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)
10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40
18t³ - 42t² - 14t - 30
d. (x − 1)(x + 2)(x − 3)
(x - 1)(x + 2)
x(x + 2) - 1(x + 2)
x² + 2x - x - 2
x² + x - 2(x - 3)
x(x² + x - 2) - 3(x² + x - 2)
x³ + x² - 2x - 3x² - 3x + 6
x³ - 2x² - 5x + 6
e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)
3a(3a - 2b²) + 2b²(3a - 2b²)
9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)
9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)
(−2a − b²)(2a − b²)
-2a(2a - b²) - b²(2a - b²)
-4a² + 2ab² - 2ab² + b⁴
-4a² + b⁴
2(-4a² + b⁴)
-8a² + 2b⁴
9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴
-2b⁴ + a² + 6b² - 24a
ABC is rotated 90° counterclockwise around the origin to form A'B'C'. Then
AA'B'C' is dilated using a scale factor of with a center of dilation at vertex A'
to form A"B"C". What are the coordinates of A"B"C"? Show your work.
The coordinates of A"B"C" are as follows :
A = 1 1/2,3
B = 1 1/2,0
C = -4 1/2, 3.
What are coordinates?Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. a group of numbers representing a precise place. On graphs, there are typically two numbers: the first one indicates the length along, and the second one indicates the length up or down. For instance, the value of the point (12,5) is 12 units. In general, alphanumeric characters are used to express GPS coordinates, which are a distinctive identifier of a certain geographic location on the globe. Points of intersection in a grid system are referred to as coordinates in this context. Typically, the latitude and longitude coordinates are used to represent GPS coordinates.
Five units up and along.
90degrees clockwise is x, y, y, -x.
A = 1,2
B = 1,0
C = -3, 2.
Times everything by 3/2 now.
A = 1 1/2,3
B = 1 1/2,0
C = -4 1/2, 3.
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Find the distance between each pair of points.
M(-4,9) N(-5,3)
A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.
a. Which information is not needed to compute the bill after tax and tip?
b. What was the total bill?
well, the bill was actually "x", which oddly enough is the 100%, but we also know that the tip was $1.05 and that's 15% of the whole bill plus tax.
so if we know that 1.05 is 15% of "x", what the dickens is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1.05 & 15\\ x& 100 \end{array} \implies \cfrac{1.05}{x}~~=~~\cfrac{15}{100} \\\\\\ 105=15x\implies \cfrac{105}{15}=x\implies 7=x[/tex]
well, as you can see, we know the tax was 8%, but, it doesn't really matter if it had been 25% or who knows, so long we know that 1.05 is 15% of the whole smack.
Create a quadratic inequality with the roots -5 and 2.
Answer:
y=x^2+3x-10
Step-by-step explanation:
.........
Congruent triangles
Please answer this question
A.Congruent triangles)
Solve for X.
Help please!!!
Answer:
x=17
Step-by-step explanation:
2x-3+3x+8=90
5x=85
x=17
:]
Write $5 and $8 in algebra expression
Answer:
5+8=x
step by step explanation
Simplify to create an equivalent expression 10+4(−8q−4)
Answer:
-32q-6
Step-by-step explanation:
Please look at the attachment! Hope this helps! ~~
Answer : -0.3125 + q + 0.5
1) Distribute
10 - 32q - 16
2) Divide all terms by -32
-0.3125 + q + 0.5
Allison's math teacher asked her to write an irrational and rational number. She wrote the following numbers √46 Rational and 5.25 Irrational. Explain if you agree with Allison's identification of rational and irrational numbers.
If you disagree, provide an example of an irrational and rational number.
x = -4z - 19
y= 5x + z - 4
-5y - z = 25
Answer:
x = 1, y = -4, z = -5
Step-by-step explanation:
Solve the following system:
{x = -4 z - 19 | (equation 1)
{y = z + 5 x - 4 | (equation 2)
{-z - 5 y = 25 | (equation 3)
Express the system in standard form:
{x + 0 y + 4 z = -19 | (equation 1)
{-(5 x) + y - z = -4 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Swap equation 1 with equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{x + 0 y + 4 z = -19 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Add 1/5 × (equation 1) to equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y/5 + (19 z)/5 = -99/5 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Multiply equation 2 by 5:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y + 19 z = -99 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Swap equation 2 with equation 3:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + y + 19 z = -99 | (equation 3)
Add 1/5 × (equation 2) to equation 3:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + 0 y + (94 z)/5 = -94 | (equation 3)
Multiply equation 3 by 5/94:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Add equation 3 to equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y + 0 z = 20 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Divide equation 2 by -5:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Subtract equation 2 from equation 1:
{-(5 x) + 0 y - z = 0 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Add equation 3 to equation 1:
{-(5 x) + 0 y + 0 z = -5 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Divide equation 1 by -5:
{x + 0 y + 0 z = 1 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Collect results:
Answer: {x = 1, y = -4, z = -5
A store owner mixes 2 lbs of candy that cost x dollars pound with 3 lb of candy that costs $1.50 per pound. she sells the mix for $2.50 per pound. how much did the 3lb of the second type cost the owner?
Algebraic equations are mathematical equations that consist of unknown variables. These unknown variables can be represented with any letter of the alphabet.
The cost of 2 pounds(lb) of the first type of candy is $8
Note that: x represents the cost per pound (lb) of the first type of candy
The Algebraic equation for the above statement is given as:
2lb × $x + 3 Ib × $1.50 = $2.50(2lb + 3lb)
2x + 4.5 = 12.5
Collect like terms
2x = 12.5 - 4.5
2x = 8
Divide both sides by 2
2x/2 = 8/2
x = 4
The cost of the 1 pound of first type of candy is $4
The cost of 2 pounds(lb) of the first type of candy is calculated as:
2 x $4
= $8
hope it will be helpful
Mrs. Gomez earns $19.50 per hour and gets a 5% raise. Use compatible numbers to estimate her new hourly rate.
The new hourly rate using compatible numbers is $21.
Given,
The earnings of Mrs. Gomez = $19.50 per hour
She gets a raise of 5%
We have to estimate her new hourly rate by using compatible numbers.
Compatible numbers:
Compatibility in mathematics refers to the mental ease with which a number can be added, subtracted, multiplied, or divided. Compatibility refers to the proximity of the compatible numbers to the real numbers, which facilitates estimation of the solution and simplifies problem-solving.
So,
Compatible number of 19.50 is 20.
The amount raised = 20 × 5/100 = 5/5 = $1
Now, the new hourly rate = 20 + 1 = $21.
That is, the new hourly rate using compatible numbers is $21.
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ANSWER QUICK I WILL GIVE BRAINLIEST
Determine which expression is equivalent to the expression 2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12. 4 over 15 times g plus negative 17 negative 4 over 15 times g plus negative 17 2 over 15 times g plus negative 7 negative 4 over 15 times g plus negative 7
Answer:
-4/15 - 17
negative 4 over 15 plus negative 17
Step-by-step explanation:
2/3g - 5 - 11/15g - (1/5g +12)
Your wording is extremely confusing but I tried :]
-4/15 - 17
is the correct answer (I think)
:]
The required simplified value of the given expression is -4/15 - 17.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12 is given as
= 2/3g - 5 - 11/15g - (1/5g +12)
Adding the alike terms,
= 2/3g -11/15g -1/5g -5 -12
= [10 - 11 -3] /15 g - 17
= -4g/15 -17
Thus, the required simplified value of the given expression is -4/15 - 17.
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Dracula needs to mix 4 quarts of liquid iced tea concentrate with 5.5
quarts of water to make iced tea. He wants to make 66.5 quarts of
iced tea. How much iced tea concentrate will he need?
3=british paintings
t=painting from 2th century
b=british paintings
a painting is chosen at random
work out the probability that it is british
The probability of choosing a painting random and it is British is 0.50.
Given,
The total number of paintings = 30
Then,
x (x - 2) + x + (2x - 8) + 10 = 30x = 3T = Painting from 20th century
B = British paintings
We have to find the probability of choosing a painting random and it is British.
Here,
Probability = British/ Its from 20th century
Probability = n (B and T) / n(T)
= x / (x + x(x-2))
= 3 / (3 + 3(3 - 2))
= 3 / (3 + 9 - 6)
= 3 / 6 = 1/2 = 0.5
Here, the probability of choosing a painting random and it is British is 0.50.
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In a survey of 1,900 people who owned a certain type of car, 855 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer: 45%
Step-by-step explanation: 45% of 1,900 is 855
What is the
range?
Help meeeeeee
In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by quantity y plus 16 end quantity squared over 400 plus x squared over 144 equals 1 and Comet H is modeled by quantity y plus 13 end quantity squared over 144 minus x squared over 25 equals 1 comma where all measurements are in astronomical units.
Part A: What are the vertices for the path of Comet E? Show your work. (4 points)
Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points)
Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points)
The vertices of the path of the comet E are; (-12,0) and (+12,0) as it is moving an elliptical path.
What are the vertices of the path of the comet E?Comet 'E' is modeled by
((y + 16)²)/400 + (x²)/144 = 1
This is an equation of an ellipse. So, the path traveled by Comet E will be an elliptic path.
Comparing with the equation of ellipse;
((y - k)²)/(b²)+ ((x - h) ²)/(a ²) = 1
whose; Centre is (h,k) and Vertex is (h±a, 0)
On Comparing Centre (h, k), h= 0 and k = -16,
a²=144
a = 12
b²=400
b=20
So, Centre (0, -16),
The Vertex (-12,0) and (+12,0)
So, the vertices of the path of the comet E are; (-12,0) and (+12,0).
Part B: The path of Comet H has been modeled as; a horizontal hyperbola.
Thus, The Comet H travels closer to the sun.
Part C: The sun represents the one of the foci of both the Comet E and Comet H.
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Draw the graph of each circle given its equation below.
Step 1:
First, write the general equation of a circle
[tex]\begin{gathered} (x-a)^a+(y-b)^2=r^2 \\ r\text{ is the radius} \\ (a,\text{ b) is the center} \end{gathered}[/tex]Step 2:
Question 1
[tex]\begin{gathered} x^2+y^2\text{ = 121} \\ x^2+y^2=11^2 \\ \text{radius r = 11} \\ \text{center = (0 , 0)} \end{gathered}[/tex]Question 2
[tex]\begin{gathered} (x-2)^2+y^2\text{ = 64} \\ (x-2)^2+y^2=8^2 \\ \text{Center = (2, 0)} \\ r\text{ = 8} \end{gathered}[/tex]Question 3
[tex]\begin{gathered} (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = 36} \\ (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = }6^2 \\ \text{Center = (-}\frac{3}{2}\text{ , -}\frac{5}{8}) \\ r\text{ = 6} \end{gathered}[/tex]Question 4
[tex]\begin{gathered} (x-1)^2+(y+7)^2\text{ = 9} \\ (x-1)^2+(y+7)^2\text{ = }3^2 \\ \text{Center = (1, -7)} \\ r\text{ = 3} \end{gathered}[/tex]Question 5
[tex]\begin{gathered} (x+8)^2+(y-3)^2\text{ = 7} \\ (x+8)^2+(y-3)^2\text{ = (}\sqrt[]{7})^2 \\ \text{Center = (-8, 3)} \\ \text{radius r = }\sqrt[]{7} \end{gathered}[/tex]Use the table to answer the question. HELP PLS
Number of cases ordered
1
3
5
10
Number of rolls of paper towels
12
36
60
120.
A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair.
The constant of proportionality when the restaurant is placing an order for paper towels is 12.
How to calculate the value?It should be noted that the constant of proportionality simply means the ratio that is important to show the proportional relationship between the two given values.
This will be illustrated as:
y = kx
y = Number of paper roll
x = Number of cases ordered
From the table, this will be:
y = kx
12 = k × 1
k = 12
Therefore, the constant of proportionality is 12.
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Plot the intercepts to graph the equation.
2x-3y=6
Answer:
y - intercept is (0,2)
x - intercept is (3,0)
Step-by-step explanation:
This is standard form.
Let x = 0
2x + 3y = 6
2(0) + 3y = 6
3y = 6 Divide both sides of the equation by 3
y = 2
The y intercepts is (0,2)
Let y = 0
2x + 3(0) = 6
2x = 6 Divide both sides of the equation by 2
x = 3
The x intercept is (3,0)
Answer:
x-intercept (3, 0)
y-intercept (0, -2)
Step-by-step explanation:
Finding the intercepts:At x-intercept the y = 0. The line passes the x-axis.
2x -0 = 6
2x = 6
x = 6 ÷ 2
x = 3
x-intercept (3, 0)
At y-intercept, x = 0 . The line passes y-axis.
0 - 3y = 6
-3y = 6
y = 6 ÷ (-3)
y = (-2)
y-intercept (0 , -2)
Plot these two points in the graph and join the points.
Angel buys cookies and lemons at the store.
He pays a total of $29.80.
He pays a total of $6.25 for the cookies.
• He buys 5 bags of lemons that each cost the same amount.
How much does each bag of lemons cost?
The cost of each bag of lemons is $4.71
Let y represent the cost of lemon
Angel pays $29.80 for both the cookies and lemon
He pays a total of $6.25 for the cookies
He buys 5 bags of lemons
The equation can be expressed as
6.25 + 5y= 29.80
collect the like terms
5y= 29.80-6.25
5y= 23.55
divide by the coefficient of y which is 5
y= 23.55/5
y= 4.71
The result of y from the equation is 4.71
Hence each bag of lemon costs $4.71
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(3,-8) with a slope of -1
Answer:
See below
Step-by-step explanation:
Point slope form
y - - 8 = (-1)(x -3) re-arrange
y + 8 = -x+3
y = -x - 5
if f(x)=8-5x find f(4-+3)
The required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given function ,
f(x) = 8 - 5x
put x = 4
f(4) = 8 - 5(4)
f(4) = 8 - 20
f(4) = -12
Again,
put x = 3
f(3) = 8 - 5(3)
f(3) = 8 - 15
f(3) = -7
Thus, the required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.
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Which equation has the solution x= 9? Select each correct answer. 4 + 5x = 18 0 24 - 2x – 13 DE O +7=8 – 0 3x + 2 = 25 81 si - 3 = 6 3 = V 2x - 3= 15
Equations with solution x = 9 are:
81/x - 3 = 6
2x - 3 = 15
Explanation:To determine the equation whose result ives x = 9, we need to solve each of the equation in the question
a) 4 + 5x = 18
5x = 18 - 4
5x = 14
x = 14/5
This is not x = 9 (option is wrong)
b) 24 - 2x = 13
24 - 2x + 2x = 13 + 2x
24 = 13 + 2x
24 - 13 = 2x
11 = 2x
x = 11/2
This is not x = 9 (option is wrong)
c) x/3 + 7 = 8
x/3 = 8 - 7
x/3 = 1
x = 3(1) = 3
This is not x = 9 (option is wrong)
d) 3x + 2 = 25
3x = 25 - 2
3x = 23
x = 23/3
This is not x = 9 (option is wrong)
e) 81/x - 3 = 6
81/x = 6 + 3
81/x = 9
81 = 9x
x = 81/9
x = 9
This equation has the sloution x = 9
f) 2x - 3 = 15
2x = 15 + 3
2x = 18
x = 18/2
x = 9
This equation has the sloution x = 9
C is the center of the circle with a diameter whose endpoints are the points A(-2, 1) and B(6, 9).
What is the equation of circle C?
well, the midpoint of segment AB is the center of the circle, so
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]
now since we know AB is the diameter, so half that distance AB is its radius, so
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]
[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]
The cost of Sara’s Cell Phone is $200 plus $45 per month.
How much will she spend on the cell phone in 3 years?
…. If Sara spent $1500, how long would she have had the phone?
(Use Cost ((y=mx+b))
Answer: The cost of her phone is $1,820.
45*12=540 per year
540*3=1,820 every 3 years.
She would have had the phone between 2 and 3 years if she had spent 1,500.
At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.
F represents the fee (in dollars) for climbing d meters.
F=110+0.12d
What is the increase in price for every 100 meters climbed?
Answer:
$12
Step-by-step explanation:
You want to know the price increase per 100 meters if the fee for climbing d meters is ...
f = 110 + 0.12d
Rate of changeThe rate of change indicated by the coefficient of d in the equation is 0.12 for each unit of d. Then the amount of change for 100 units of d is ...
0.12(100) = 12
The price increases by $12 for every 100 meters climbed.
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Given f(x) = -x - 1, find ƒ (1).
Answer:
You've gotta be kidding me...It's easy come on
-2 is the answer
Step-by-step explanation:
f(x)= -x-1 JUST SUBSTITUTE 1 FOR X
f(1)= -(1)-1
f(1)= -2
write the polynomial in standard given the following zeros: x=0,i\sqrt(2),-i\sqrt(2)
The polynomial is x³ + 2x
If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.
That is, a, b and c are roots of the polynomial, then the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.
Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc
Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.
So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).
Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x
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