One side of a triangle is 6 cm shorter than the base x. The other side is 4 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 43cm?
Answer:
Step-by-step explanation:
x= base
one side= x-6
other side= 4+x
x+x-6+4+x = 43
3x=43+2
x=15 length of base
The length of base is 15 cm.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the base of triangle be x
Length of one side = x- 6
and, length of other side = x+ 4
Now, perimeter of triangle= 43 cm.
x+ x -6 +x +4= 43
3x -2 = 43
3x= 45
x=15
So, x= 15 cm
x-6 = 15- 6 = 9cm
x+ 4 = 15+ 4= 19cm
Hence, the length of base is 15 cm.
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pls help!! will give brainliest answer
A: For this equation you would use distributive property leading you to multiply 3x and 2 by 4 giving you a new expression. 12x + 8 - 2. After this you would just simplify the equation by subtracting 2 from 8 giving you 6. This leading to a new equation, 12x + 6.
B: In order to factor the expression you would need to do the reverse of distributive property, finding the GCF, or greatest common factor between the 16 and the 20b. When you do this you result in getting 4 as your GCF. Afterwards you need to divided the numbers by the GCF. Leading you to get 4(5b-4). This is how you would factor the equation.
Jamie and his two brothers divided A package of 125 toy cars equally how many cars each of them receive
Answer:
125 ÷ 3 = ____
Jamie + 2 brothers = _____
Then divide __ by the number if toy cars. ( 125 )
How many lines of symmetry does a regular polygon with 16 sides have? A. 2 B. 8 C. 32 D. 16
Answer:
16 lines of symmetry.
Step-by-step explanation:
D is your answer!
Hope this helps!!
Option D is correct, 16 lines of symmetry does a regular polygon with 16 sides have.
What is Polygon?a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
Apothem for a regular polygon is a line segment that originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon.
It is perpendicular to the regular polygon's side it touches.
Regular polygons have all sides the same and that apothem bisects the side in two parts, (provable by symmetry).
A regular polygon with 16 sides has a line of symmetry.
It has 16 lines of symmetry as well.
Hence, 16 lines of symmetry does a regular polygon with 16 sides have.
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5/7 divided by 8/9 equals _____
Hey guys I’m having some trouble plz help
I'm pretty sure the answer is 5/16
How do I solve b(x) = 8x; b(x) = -56
Final answer:
To solve b(x) = 8x when b(x) = -56, we set 8x = -56, divide both sides by 8, and get x = -7. No other solutions are necessary, as the given equations are not quadratic but linear.
Explanation:
The problem involves an equation b(x) = 8x and the value b(x) = -56. We need to set these equal to each other to find the value of x that satisfies both conditions. So we have the equation 8x = -56. To solve this, we divide both sides of the equation by 8, giving us x = -7.
To check for other potential solutions, let's consider that b in the quadratic equation ax² + bx + c = 0 may be set to zero. For our equation, b does not appear to be zero, but if it were, we could simplify the equation by factoring out an x.
If the equation were in the form ax² = -c, we could solve for x by taking the square root of -c/a after moving c to the other side and dividing by a. However, in our current problem, this is not necessary since we don't have a quadratic equation but a simple linear one.
Mara carried water bottles to the field to share with her team at halftime . the water bottles weighed a total of 60x^2+48x+24 ounces which factorization could represent the number of water bottles and weight of each water bottle
Answer:
BStep-by-step explanation:
the water temperature at the beach started at 82 degrees and it is rising 0.6 degrees each hour. if the water temperature is now 85 degrees write and solve an equation to find h, the number of hours that have passed
Answer:
5 hours
Step-by-step explanation:
Given: the water temperature at the beach started at 82 degrees and it is rising 0.6 degrees each hour
To Find: If the water temperature is now 85 degrees write and solve an equation to find h, the number of hours that have passed
Solution:
Current water temperature at beach [tex]=82^{\circ}[/tex]
temperature rising rate degrees per hour [tex]=0.6^{\circ}[/tex]
let [tex]\text{h}[/tex] be the hours passed.
water temperature at the beach after hour [tex]\text{h}[/tex] be
[tex]= 82+0.6\text{h}[/tex]
Therefore,
equation for water temperature after [tex]\text{h}[/tex] [tex]\text{hour}[/tex] is
[tex]= 82+0.6\text{h}[/tex]
When water temperature is [tex]85^{\circ}[/tex]
[tex]85=82+0.6\text{h}[/tex]
[tex]0.6\text{h}=85-82[/tex]
[tex]0.6\text{h}=3[/tex]
[tex]\text{h}=\frac{3}{0.6}[/tex]
[tex]\text{h}=5[/tex] [tex]\text{hours}[/tex]
therefore it will take [tex]5[/tex] [tex]\text{hours}[/tex] to reach temperature [tex]85^{\circ}[/tex]
Initial temperature = 82°
Rate of temperature rise = 0.6° per hour
Final temperature = 85°
The equation which describes the relationship :
Final temperature = Initial temperature + (rate × number of hours)
Number of hours = h
Mathematically, the relationship can be written as :
85 = 82 + 0.6h
Solving for h :
Subtract 82 from both sides :
85 - 82 = 0.6h
3 = 0.6h
Divide both sides by 0.6
3/0.6 = h
h = 5
Hence, the temperature will be 85° after 5 hours
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For every $50.00. Michael earns, he saves $5. for the future. How much money will he have saved when he earns a total of $500.
Question 6 options:
A. He will have saved $25.
B. He will have saved $150.
C. He will have saved $500.
He will have saved $50.
The answer is D
This is because if for every $50 he saves $5, and he has saved a total of $500, you can set up a proportion to find out how much money he has saved at that point.
The proportion is as follows:
50/5 == 500/x
x is equivalent to the amount of money he has saved
You can cross multiply to get the following equation:
50x == 2500
To isolate x, you must divide both sides by 50, giving you an answer of:
x = 50
This is the same as option D
Explain how to use compensation to find the difference of 30000 and 6985
Compensation is the process of reformulating an addition, subtraction, multiplication, or division problem to one that can be computed more easily mentally.
We will use compensation to find the difference of 30,000 and 6985.
Since, we have to evaluate 30,000 - 6,985
Let us add '15' to 6985,
6,985 + 15 = 7,000
Let us add '15' to 30,000
30,000 + 15 = 30,015
Now, we have to subtract 30,015 and 7,000
= 30,015 - 7,000
= 23,015
Therefore, the difference of 6,985 from 30,000 is 23,015.
The strategy of compensation involves adjusting numbers to make calculations easier. In the case of finding the difference between 30000 and 6985, you would adjust 6985 to 7000, subtract it from 30000 to get 23000, then add back the 15 you added to 6985 at the beginning. The result is 23015.
Explanation:In mathematics, compensation is a strategy where you adjust one of the numbers to make the equation easier to solve. Pivotally, you make the same adjustment to the other number so as not to change the overall result.
Let's use this strategy to find the difference between 30000 and 6985
First, round up the smaller number, 6985, to a easier number to subtract from 30000, which is 7000.Next, calculate the difference between the original number 6985 and the rounded number 7000, which is 15.Then, subtract the rounded number 7000 from 30000, which gives you 23000.Finally, add back the 15 you adjusted in Step 2, which gives you 23015.So, through the use of compensation the difference between 30000 and 6985 is 23015.
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a theater has 144 seats. the theater sells tickets for $6 per adult and $4 per child. if the theater sold out on friday night and earned $660, how many adult tickets and child tickets were sold friday night?
a theater has 144 seats. the theater sells tickets for $6 per adult and $4 per child
Let x be the number of adult tickets
and y be the number of child tickets
Total number of tickets sold is 144
x + y = 144 -----------> equation 1
the theater sells tickets for $6 per adult and $4 per child and earned $660
6x + 4y = 660 ----------> equation 2
Solve for x and y
x + y = 144
y = 144 - x
Now plug it in second equation
6x + 4y = 660
6x + 4(144 - x) = 660
6x + 576 -4x = 660 (combine like terms)
2x + 576 = 660 (subtract 576 from both sides)
2x = 84 (divide by 2)
x= 42
Number of adult tickets = 42
y = 144 - x
y = 144- 42= 102
Number of child tickets = 102
The theater sold 42 adult tickets and 102 child tickets on Friday night, calculated by setting up and solving a system of equations based on the total seats and revenue.
To solve the problem, we need to set up a system of equations based on the information provided. The total number of seats is 144, and the total revenue from selling out on Friday night is $660. Let A represent the number of adult tickets sold and C represent the number of child tickets sold. Therefore we have the following equations:
A + C = 144 (since all seats were sold)6A + 4C = 660 (which reflects the total revenue from ticket sales)Now we can solve this system of equations. Multiplying the first equation by 4, we get 4A + 4C = 576. Subtracting this from the second equation cancels out the C, leaving us with 2A = 84, or A = 42. Plugging this into the first equation gives us C = 144 - 42, or C = 102.
Therefore, the theater sold 42 adult tickets and 102 child tickets on Friday night.
are all even numbers composite?
Yes. All even numbers are composite. However digits - 2, 4, 6, and 8 - do not count, since a number must be greater than 9.
Yes all even numbers are composite because they have more than 1 factor
what gose into 2 14 fractions
round 483 to the nearest ten
Answer:
480
We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.
We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.
If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
FOUR QUESTIONS!! TYSM IF YOU ARE ANSWERING THIS!! TYSM!!!
Write an equation of the line passing through the given point that is parallel to the given line for the following: (I put a picture bc it’s easier for me and hopefully for you)
THANK YOU SO SO MUCH !!!!
Answer:
17. Equation : [tex]y=-x-1[/tex]
18: Equation: [tex]y=\frac{1}{2}x+8[/tex]
19: Equation: [tex]y=3x-6[/tex]
20: Equation: [tex]y=\frac{1}{3}x-2[/tex]
Step-by-step explanation:
Using the Slope-Intercept Form for the following questions:
Equation of line: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
17. A(3, -4), [tex]y=-x+8[/tex]
First substitute the slope from the original line [tex]y=-x+8[/tex] (i.e. -1 in this case) into the equation of line.
[tex]y=(-1)x+b[/tex] .....(1)
Now, substitute the given point A(3,-4) in the equation (1), we have;
[tex]-4=(-1)\cdot (3)+b[/tex]
[tex]-4=-3+b[/tex]
[tex]-4+3=b[/tex]
∴[tex]b=-1[/tex]
Substitute the value of b=-1 in the Slope-Intercept form i.e, [tex]y=-x+(-1)[/tex]
[tex]y=-x-1[/tex]
Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=-x-1[/tex].
18. A(-6, 5) , [tex]y=\frac{1}{2}x -7[/tex]
First substitute the slope from the original line [tex]y=\frac{1}{2}x -7[/tex] (i.e. [tex]\frac{1}{2}[/tex] in this case) into the equation of line.
[tex]y=\frac{1}{2} x+b[/tex] .....(1)
Now, substitute the given point A(-6, 5) in the equation (1), we have;
[tex]5=\frac{1}{2} \cdot (-6)+b[/tex]
[tex]5=-3+b[/tex]
[tex]5+3=b[/tex]
∴[tex]b=8[/tex]
Substitute the value of b=8 in the Slope-Intercept form i.e, [tex]y=\frac{1}{2}x+8[/tex]
[tex]y=\frac{1}{2}x+8[/tex]
Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=\frac{1}{2}x+8[/tex].
19. A(2,0), [tex]y=3x-5[/tex]
First substitute the slope from the original line [tex]y=3x-5[/tex] (i.e. 3 in this case) into the equation of line.
[tex]y=3x+b[/tex] .....(1)
Now, substitute the given point A(2, 0) in the equation (1), we have;
[tex]0=3\cdot (2)+b[/tex]
[tex]0=6+b[/tex]
∴[tex]b=-6[/tex]
Substitute the value of b=-6 in the Slope-Intercept form i.e, [tex]y=3x+(-6)[/tex]
[tex]y=3x-6[/tex]
Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=3x-6[/tex]
20. A(3, -1), [tex]y=\frac{1}{3}x+10[/tex]
First substitute the slope from the original line [tex]y=\frac{1}{3}x +10[/tex] (i.e. [tex]\frac{1}{3}[/tex] in this case) into the equation of line.
[tex]y=\frac{1}{3} x+b[/tex] .....(1)
Now, substitute the given point A(3, -1) in the equation (1), we have;
[tex]-1=\frac{1}{3} \cdot (3)+b[/tex]
[tex]-1=1+b[/tex]
[tex]-1-1=b[/tex]
∴[tex]b=-2[/tex]
Substitute the value of b=-2 in the Slope-Intercept form i.e, [tex]y=\frac{1}{3}x+(-2)[/tex]
[tex]y=\frac{1}{3}x-2[/tex]
Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=\frac{1}{3}x-2[/tex].
Simplify -8y^3(7y^2-4y-1) PLEASE HELP
Hey!
Alright, according to P.E.M.D.A.S., the first step to solving this expression is to distribute.
Original Expression :
[tex]\displaystyle\ -8y^{3} (7y^{2} -4y-1)[/tex]
New Expression {Distributed Old Expression} :
[tex]\displaystyle\ -(56y^{5} -32y^{4} -8y^{3} )[/tex]
Now all you have to do is simplify the parenthesis.
Old Expression :
[tex]\displaystyle\ -(56y^{5} -32y^{4} -8y^{3} )[/tex]
New Expression {Simplified} :
[tex]\displaystyle\ -56y^{5} + 32y^{4} + 8y^{3}[/tex]
So, since the expression can no longer be simplified, the final answer is...
Hope this helps!
- Lindsey Frazier ♥
Solution :
Given expression [tex]-8y^{3}(7y^{2}-4y-1)[/tex]
To simplify this expression, first we need to know about the Distributive property.
Distributive Property: [tex]a\times(b+c+d)=(a\times b)+(a\times c)+(a\times d)[/tex]
Given expression [tex]-8y^{3}(7y^{2}-4y-1)[/tex]
Applying Distributive property on this expression:
[tex]\Rigtharrow -8y^{3}(7y^{2}-4y-1)=((-8y^{3})\times7y^{2})+((-8y^{3})\times(-4y))+((-8y^{3})\times(-1))[/tex]
[tex]= -56y^{5}+32y^{4}+8y^{3}[/tex]
Hence, the simplified form of the expression [tex]-8y^{3}(7y^{2}-4y-1)[/tex] is [tex]-56y^{5}+32y^{4}+8y^{3}[/tex].
Use the objective function P = 50x + 80y to calculate the profit at each point. (0, 5) P = (1, 12) P = (4, 10) P =
Answer :
The profit at point (0,5) is, 400
The profit at point (1,12) is, 1010
The profit at point (4,10) is, 1000
Step-by-step explanation :
Coordinates : It is a set of values which show an exact position on a graph.
There are two variables or coordinates that are x-coordinate and y-coordinate.
As we are given that function:
[tex]P=50x+80y[/tex]
where,
P = profit
x and y are the coordinates.
(1) Now we have to calculate the profit at point (0,5).
[tex]P=50x+80y[/tex]
x = 0 and y = 5
[tex]P=50\times 0+80\times 5[/tex]
[tex]P=0+400[/tex]
[tex]P=400[/tex]
The profit at point (0,5) is, 400
(2) Now we have to calculate the profit at point (1,12).
[tex]P=50x+80y[/tex]
x = 1 and y = 12
[tex]P=50\times 1+80\times 12[/tex]
[tex]P=50+960[/tex]
[tex]P=1010[/tex]
The profit at point (1,12) is, 1010
(3) Now we have to calculate the profit at point (4,10).
[tex]P=50x+80y[/tex]
x = 4 and y = 10
[tex]P=50\times 4+80\times 10[/tex]
[tex]P=200+800[/tex]
[tex]P=1000[/tex]
The profit at point (4,10) is, 1000
1.22 on a candy bar, $1.48 on yogurt, $7.98 on a pizza, and $2.79 on bread. If she pays with a $20 bill, how much change will she receive? Explain how you got your answer.
Answer:
She'll receive $6.53.
Step-by-step explanation:
First add everything she purcahsed.
1.22 + 1.48 + 7.98 + 2.79 = 13.47
Then subtract that from how much she paid.
20 - 13.47 = 6.53
So 6 dollars and 53 cents.
Hello!
To find the total amount of change we need to combine the total cost of everything first and then subtract that from 20!
$ 1.22+ $ 1.48+ $ 7.98+$ 2.79 = $ 13.47
$ 20.00 - $ 13.47 = $ 6.53
The answer to question is that she will recieve $6.53 in change if she pays with a $20 bill. If you need anymore clarification feel free to ask! Hope this helps.
which expression has a value of 27
Hello there!
The answer should be the first option A.
16-(-11)
16+11
Answer⇒=27
10-17
10+-17
Answer⇒=-7
-15-(-12)
-15+12
Answer⇒=-3
-25-2
-25+-2
Answer⇒=-27
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
Option a, 16-(-11), is the expression that has a value of 27.
To find the expression that has a value of 27, we can evaluate each option:
Let's evaluate each expression to determine which one equals 27:
a. 16−(−11)
Applying the rule that subtracting a negative number is the same as adding its positive counterpart:
16+11=27
Therefore, a equals 27.
b. 10−17
Subtracting 17 from 10:
10−17=−7
This does not equal 27.
c. −15−(−12)
Similar to the first expression, subtracting a negative is the same as adding its positive counterpart:
−15+12=−3
This does not equal 27.
d.−25−2 Subtracting 2 from -25:
−25−2=−27
This does not equal 27.
Hence, after evaluating each expression, the correct choice that equals 27 is option a: 16−(−11)
Therefore, option a, 16-(-11), is the expression that has a value of 27.
Complete Question:
which expression has a value of 27.a.16-(-11) b.10-17 c.-15-(-12) d.-25-2
find the next two terms 1/8, 2/7, 1/2, 4/5
Susie earned $66.70 in 9.2 hours.how much did she earn in per hour
To find out how much she earned per hour you want to divide.
$66.70/9.2 = $7.25
Susie earned $7.25 per hour.
Hope this Helps!!
Susie earns $7.25 per hour.
To determine how much Susie earns per hour, you need to divide her total earnings by the number of hours worked. Given that Susie earned $66.70 in 9.2 hours, you can calculate her hourly rate as follows:
Hourly Rate = Total Earnings / Hours Worked
Hourly Rate = $66.70 / 9.2 hours
Hourly Rate = $7.25 per hour (rounded to two decimal places)
Thus, Susie earns $7.25 per hour.
which expressions are equivalent to 2(4f+2g)
Answer:
8f + 4g
Step-by-step explanation:
Distribute the 2 to all terms within the parenthesis
2(4f) = 8f
2(2g) = 4g
8f + 4g is your expression
~Senpai
HELP ME ASAP PLEASE!!
Emma throws an object upward from a hill that is 64 feet high. The object has an initial velocity of 48 feet per second. The function y = -16x2 + 48x + 64 represents the height of the object, y, in terms of the time elapsed after the object is thrown, x.
What statements about this function are true?
A. The function is a linear function.
B. The function is a nonlinear function.
C. The function has a constant rate of change.
D. The function does not have a constant rate of change.
E. The function is a decreasing function.
Answer:
oh b this is a hard question
Step-by-step explanation:
i will answer it gimme a few mins to learn this things
Answer:
Options B and D are correct.
Step-by-step explanation:
The given equation is :
[tex]y= -16x^{2}+48x+64[/tex]
We can see that it is a quadratic equation.
Hence it is non linear.
The rate is dependent on x, so it does not have a constant rate of change also.
We can check this :
At x= 0, y = 64
At x=1, y = [tex]-16+48+64=96[/tex]
Hence, the function does not have a constant rate of change.
So, the answer is :
B. The function is a nonlinear function.D. The function does not have a constant rate of change.4x + 7 = 3 do you know how to do this?
your work 14 hours last week a d earned a total of $96 befor taxes. your job as a lifeguard pays $8 per hour and your job as a chashier pays $6 per hour. how many hours did you work at each job
You would have worked 6 hours as lifeguard and 8 hours as cashier.
8(14 - y) + 6y = 96
112 - 8y + 6y = 96
112 - 2y = 96
-2y = -16
y = -16/-2 = 8
You worked 8 hours as a cashier. since the total hours worked is 14 we know you worked as a lifeguard for 6 hours.
The high school football team has a fundraiser selling t-shirts. It cost the team an initial $150 for the shirt order plus an additional $2 per shirt. The team sold the shirts for $10 per shirt. What is the the football team's profit equation, p(x), where x represents the number of shirts?
Answer:
[tex]P(x)=8x-150[/tex]
Step-by-step explanation:
Let
x-----> the number of shirts
we know that
The equation of the cost is equal to
[tex]C(x)=2x+150[/tex]
The equation of the sell is equal to
[tex]S(x)=10x[/tex]
The equation of the profit is equal to
[tex]P(x)=S(x)-C(x)[/tex]
substitute the values
[tex]P(x)=10x-(2x+150)=8x-150[/tex]
URGENT!! GEOMETRY TANGENT LINES, FIND THE VALUE OF X. PLEASE EXPLAIN, BRAINLIEST GIVEN!!
the length of a rectangle is 5 in. less than 3 times its width. If the perimeter of the rectangle is 54 in. find the length and width.
Answer: length = 19 inches and width = 8 inches
Step-by-step explanation: To solve this problem, our first task is to set up variables.
Since the length of the rectangle is 5 inches less than 3 times its width, we can set up variables to represent this.
Variables
X ⇒ width
3x - 5 ⇒ length
To help set up our equation, I will draw a picture of the rectangle labeling the widths X and the lengths 3x - 5.
Going back to the original problem, the second sentence states that the perimeter of he rectangle is 54 inches. Remember that the perimeter is the distance around the rectangle.
Based on the picture I provided, our equation will read as followed.
X + X + (3x -5) + (3x - 5) = 54
8x - 10 = 54 ← simplify on the left side of the equation
+10 +10 ← add 10 on both sides
8x = 64
÷8 ÷8
X = 8
Therefore, the width of our rectangle is 8 inches and the length of our rectangle is (3 x 8) - 5 or 19.
"the perimeter of a rectangle is 42 centimeters. the length of the rectangle can be represented by (x+4), and the width can be represented by (2x-7). what are the dimensions of this rectangle in centimeters"
The dimensions of the rectangle that has a perimeter of 42 cm are:
length = 12 cm
width = 9 cm
Recall:
The perimeter of a rectangle is given as:
Perimeter = 2(length + width)Given the following:
Length of rectangle = [tex](x+4)[/tex]Width of rectangle = [tex](2x-7)[/tex]Perimeter of rectangle = 42 cmTherefore:
[tex]2((x + 4) + (2x -7)) = 42[/tex]
Open the bracket[tex]2(x + 4 + 2x -7) = 42[/tex]
Add like terms[tex]2(3x -3) = 42\\\\6x - 6 = 42\\\\[/tex]
Add 6 to both sides[tex]6x - 6 + 6 = 42 + 6\\\\6x = 48\\[/tex]
Divide both sides by 6[tex]x = 8[/tex]
Find the dimensions of the rectangle by plugging in the value of x
[tex]length = (x+4) = 8 + 4 = 12 $ cm\\\\width = (2x - 7) = 2(8) - 7 = 9 $ cm[/tex]
Therefore, the dimensions of the rectangle that has a perimeter of 42 cm are:
length = 12 cm
width = 9 cm
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