If triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us consider the number be x
tripple of a number added to its half part
3x+x/2
Difference between four times the number and 12
4x-12
So tripple of a number added to its half part its equal to the difference between four times the number and 12
3x+x/2=4x-12
6x+x=2(4x-12)
Apply distributive property on RHS
7x=8x-24
Subtract 7x on both sides and add 24
24=x
Hence, if triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.
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A circle has centre C and radius 4 cm.
The diagram shows the circle with a point
D which lies on the circle. The tangent at D
passes through the point E. EC = √65 cm.
Find
a) the size in radians of angle DCE
b) the area of the shaded region
Step-by-step explanation:
EC = 165 cm (Given) Tangent of circle also makes 90°.
a) sind = Perpendicular Hypotenuse = CD = EC 165 => 0 = Sin = 0.519 ~ 0.52 =29.7448 ~ 29.75° =<E
By angle sum property of triangle. <D+<E+ <C = 180°
90° + 29.75 + LC = 180°
<C = 180-90-29.75 = 60.25° <C= 60.25°
<DCE = <C = 60.25 x π/180 = 1.052 radians.
(b) Area of triangle DCE = 1/2 x b x h = 1/2 x ED X 4
ED² + CD² = EC² ED² + 4² = (√65)² => EC² = 65-16 = 49 ED=7
Area = 1/2 x 7 x 4 = 14 cm²
Area of sector a π x 4²x 60.25/360 = 8.4125 cm2
Area of shaded region= Area ADCE Area of sector -
= 14-8.4125 = 5.5875 cm²
(a) <DCE = 1.052 radians b) Area shaded of region = 5.5875cm²
The sum of an integer and seven times next consecutive odd integers -26 find the value of the lesser integer
Answer:
-5
Step-by-step explanation:
Let n = an integer
Let (n+2) = the next consecutive odd integer
n + 7( n + 2) = -26 Distribute the 7
n + 7n + 7(2) = -26
n + 7n + 14 = -26 Combine like terms
8n +14 = -26 Subtract 14 from both sides
8n + 14 - 14 = -26 -14
8n = -40 Divide both sides by 8
n = -5
The next consecutive odd integer would be -3
Consecutive just means the next number.
A marketing research company desires to know the mean consumption of meat per week among males over age 50. They believe that the meat consumption has a
mean of 3.5 pounds, and want to construct a 95 % confidence interval with a maximum error of 0.08 pounds. Assuming a standard deviation of 0.6 pounds, what is
the minimum number of males over age 50 they must include in their sample? Round your answer up to the next integer.
Answer:
we get a required sample size of 122.
Step-by-step explanation:
We can use the following formula to calculate the required sample size:
n = (Z * sigma / e)^2
where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (e.g. for a 95% confidence level, Z = 1.96)
sigma is the standard deviation of the population
e is the maximum error allowed
Plugging in the given values, we get:
n = (1.96 * 0.6 / 0.08)^2 = 121.6
Rounding up to the next integer, we get a required sample size of 122.
The integral 1 π(y2−y4) dy 0 represents the volume of a solid. Describe the solid.
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the y axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.
In the cartesian coordinate system, a plane is divided into four areas by the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.Use washer method:The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.
As we have mentioned, the washer method is an extension of the disk method. This technique is established so that we can also calculate for the volume of the solid returned by rotating the region bounded by two curves over the x and y axis.[tex]$$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$[/tex]
Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.
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•50 POINTS• don’t have to explain.
Answer: 80 degrees
Step-by-step explanation:
Answer:
the remaining angle of triangle is 80° by the sum of triangle is 180.
What is (f + g)(x)?
f(x) = -3x² + 3
g(x) = −3x
Answer:
Step-by-step explanation:
(f.g)(x)=[tex]-3*(-3x)^{2}+3=-27x^{2}+3[/tex]
What is the y-intercept of y= -3x + 6
Answer: 6
Step-by-step explanation:
y = -3x + 6 is the linear equation of the form y = mx + c
where m is the gradient of the graph and c is the y-intercept of the graph.
Hence,
m = -3
c = 6
y-intercept of the graph = c
= 6
What is the log value of log2?
The log value of log2 is 1Log2 is defined as the logarithm base 2. This means that the logarithm of any number x is equal to the power to which the base 2 must be raised to produce x.
In other words, log2(x) = y, where 2^y = x.
Therefore, when x = 2, 2^y = 2. This means that the logarithm of 2 is equal to 1, since 2^1 = 2.
Therefore, the log value of log2 is 1.
Log2 is an important mathematical concept that is used to calculate the logarithm of a number. Logarithms are used in a variety of fields, including mathematics, physics, engineering, and computer science. Log2 is the logarithm with a base of 2, which means that the logarithm of any number x is equal to the power to which the base 2 must be raised to produce x. To calculate log2 of a number, the formula is log2(x) = y, where 2^y = x. This means that the logarithm of 2 is equal to 1, since 2^1 = 2. Therefore, the log value of log2 is 1. Log2 is often used to calculate logarithms of numbers that are not powers of 2, such as log2(3) = 1.5849. Log2 can also be used to calculate logarithms of numbers with decimals, such as log2(1.5) = 0.5849. Log2 can also be used to calculate exponents, such as 2^3 = 8.
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A gardener uses a tray of 6 conical pots to plant seeds. Each conical pot has a radius of 3 centimeters and a depth of 8 centimeters. About how many cubic centimeters of soil are needed to plant the full tray
The volume of a cone is one-third of the product of the area of the base times the height, i.e. Now multiply that by the number of cones: 6 * 75.40 cm^3 = 452.40 cm^3.
What is Volume of a Cone?The volume of a cone is one-third of the product of the area of the base times the height, i.e.(1/3)π(r^2)*h = (1/3)π(3cm)^2 *(8cm) = 75.40 cm^3Now multiply that by the number of cones: 6 * 75.40 cm^3 = 452.40 cm^3.Then the answer is 452 cm^3The total surface area of a cone is the sum area of its circular base and the curved surface. The curved surface area of a cone is given by the formula: Total surface area = Area of Curved Surface + Area of Circular Base. TSA = π ✕ r ✕ l + π ✕ r² or, TSA= π ✕ r ✕ (l + r) square unitsThe formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the conTo learn more about Volume of a Cone refers to:
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HELP ASAP
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes. What does the number 3 represent in this equation?
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 3 times of the time, increased.
Given,
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes.
The number '3' is constant term, which basically represents the the distance covered by the snail, in terms of time or, the rate of increment of distance is terms of time.
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 1/3 of the time, increased.
For example if the snail is moving for 1 unit time, the t will be considered as 1. so, the d will be 3*1 = 3, i.e. 3 unit distance will be covered by the snail in 1 unit time.
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The staff at Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of six hours per day. The mowing and raking typically takes four hours and an average of twenty-four bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves
Assuming the bags are filled at a constant rate, the average time it takes to fill one bag of leaves is 5 minutes.
To calculate the average time it takes to fill one bag of leaves, we need to know the total amount of time spent filling bags and divide that by the number of bags filled.
First, we know that the staff works an average of six hours per day. Since mowing and raking typically take four hours, we can assume that the remaining two hours are spent filling bags.
To find out how long it takes to fill one bag, we divide the total time spent filling bags by the number of bags filled. In this case, it would be:
(2 hours) / (24 bags) = 0.083 hours (or 5 minutes)
So the average time it takes to fill one bag of leaves is 5 minutes.
It's important to note that this is an average time and may not reflect the exact time it takes for each bag to be filled. Factors such as the size of the bag, the type of leaves being filled, and the skill level of the staff could all affect the time it takes to fill a bag.
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Cedro bought five games and eight songs for a total cost of $22. 87. Benita bought seven songs and four games for a total cost of $18. 89. The cost of their purchases can be represented by the following equations: 5g + 8s = 22. 87 and 7s + 4g = 18. 89 where g is the cost of each game and s is the cost of each song purchased. What was the cost of each game and each song purchased?
The purchasing cost of each game costs $1.55 and each song costs $1.89 according to the given equation.
What are variables?A variable is a symbol or character that represents a value or set of values in mathematics and computer programming that can change and take on different values depending on the context.
The given problem can be solved using a system of equations.
The first formula, 5g + 8s = 22.87, represents the total cost of games and songs purchased by Cedro.
The second formula, 7s + 4g = 18.89, represents the total cost of games and songs purchased by Benita.
5g = 22.87 - 8s
g = (22.87 - 8s)/5.
We can now substitute this expression for g into the second equation and solve for s. So we have:
7s + 4((22.87 - 8s) / 5) = 18.89
On expanding and solving this equation for s we get:
7s + (91.48 - 32s) = 18.89
32s + 7s = 73.59
39s = 73.59
s = 1.89
By substituting the value of s into the equation 5g = 22.87 - 8s gives
5g = 22.87 - 8(1.89)
5g = 22.87 - 15.12
5g = 7.75
g = 1.55
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What is the coefficient form of X³ 2 *?
Let x= the co-efficient of x^2. So the co-efficient of given function is x=1.
Define co-efficient.
The term "coefficient" refers to a number or symbol that multiplies another number or symbol (used as a mathematical variable).
Write an example of co-efficient.
An amount multiplied by a variable is known as a coefficient. As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
Let x= the co-efficient of x^2 So the co-efficient of given function is x=1.
The term multiplied with x^3 is the co-efficient of this expression. As there is not term with x^2 so it is 1.
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Division of mixed numberrss
Answer:
1. 99/104
2. 4/3
3. 6/5
4. 52/25
5. 57/58
6. 33/100
7. 1/2
8. 8/5
9. 4
10. 4/3
hope this helps any
If you have 10 friends and make two equal teams, what fraction do you use?
Reflect shape A in the line y = -x.
Answer:
pentagon
Step-by-step explanation:
pentagon...................................
jacks meeting stared at 2:45 pm and ended at 5:25 pm how long did the meeting last
Jacks meeting lasted for 160 min or 2 hrs 40 min.
What is Time?Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.
Given is that jacks meeting stared at 2:45 pm and ended at 5:25 pm.
The time for which the meeting lasted can be written as -
{i} = 2:45 pm
{i + 60 minutes} = 3:45 pm
{i + (2 x 60) minutes} = 4:45 pm
{i + (2 x 60 + 40) minutes} = 5:25 pm
{f} = 5 : 25 pm
The meeting lasted for -
2 x 60 + 40
160 minutes
or
2 hours 40 minutes
Therefore, Jacks meeting lasted for 160 min or 2 hrs 40 min.
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The distance between a 16 feet long chord and the center of a circle is 15 feet. Compute the diameter of the circle
The diameter of the circle is 30 feet
To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.
So, we can write the equation:
diameter^2 = radius^2 + (distance between chord and center)^2
We know the radius is half the diameter, so we can substitute that in:
diameter^2 = (diameter/2)^2 + (15)^2
And we can solve for the diameter:
diameter^2 = diameter^2/4 + 225
diameter^2 = diameter^2/4 + 225
4diameter^2 = diameter^2 + 900
3diameter^2 = 900
diameter^2 = 900/3
diameter = sqrt(900/3)
So the diameter of the circle is 30 feet.
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9) Express the roots of the equation 2x² + 4x + 5 = 0 in simplest a + bi form.
2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.
What is the quadratic equation of 2x² 3x 5 0?Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.
Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.
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Lionel purchases 1-pound bags of each of the five seeds and nuts shown in the table. Of the following, which best approximates the average (arithmetic mean) number of calories per bag?
(1 pound = 16 ounces)
A)150
(B)250
C) 1,500
D) 2,500
The best approximate average (arithmetic mean) number of calories per bag is equal to: D) 2,500.
What is an arithmetic average?In Mathematics, an arithmetic average is sometimes referred to as arithmetic mean and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the arithmetic average for the number of calories per bag?Mathematically, the arithmetic average for the number of calories per bag can be calculated by using the following formula:
Arithmetic average = [F(x)]/n
Next, we would determine the total number of calories and then convert to ounces:
Total number of calories, F(x) = 198 + 80 + 159 + 166 + 185
Total number of calories, F(x) = 788 calories.
Note: 1 pound = 16 ounces.
Total number of calories, F(x) = 788 calories × 16 ounces
Total number of calories, F(x) = 12,608 calories.
Now, we can calculate the arithmetic average for the number of calories per bag:
Arithmetic average = [F(x)]/n
Arithmetic average = 12,608/5
Arithmetic average = 2,521.6 ≈ 2,500.
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PLS PLS HELP ASAP!!! ILL GIVE BRAINIEST AND 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS
Answer:
F and C
Step-by-step explanation:
CUZ AAS means angle angle side
Answer:
see explanation
Step-by-step explanation:
for the triangles to be congruent by the angle- side- angle (ASA postulate )
if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle ( included side is the side between the vertices of the two angles ) , then the triangles are congruent.
given
∠ B ≡ ∠ D and AB ≡ PD
then the included sides are AB and PD
the other 2 angles for congruency are ∠ A ≡ ∠ P
-----------------------------------------------------
By the AAS postulate
If two angles and a non included side of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent
for AAS then ∠ C ≡ ∠ F
Please help me lol
8=t/-3+4
Answer:t=-12
and if want step by step just look the equation up on the internet and it will be there step by step
Simplify.
8-3(4-2x)
i’ll mark brainliest :)
Answer:
-4 + 6x.
Step-by-step explanation:
8 - 3(4 - 2x)
= 8 - 12 + 6x
= -4 + 6x.
The correct answer is 6x - 4
Simplify :
8 - 3(4 - 2x)
8 - (12 - 6x) (using BODMAS rule)
8 - 12 - (-6x)
( 8 -12) + 6x
-4 + 6x
= 6x - 4
A customer purchased 1/4 pound of ham, 1 1/2 pounds of turkey, 1 pound of roast beef, and 3/4 pound of bologna. Approximately what will the customer pay for the purchase before sales tax?
A customer purchased 1/4 pound of ham, 1 1/2 pounds of turkey, 1 pound of roast beef, and 3/4 pound of bologna. Therefore, the customer pay for the purchase before sales tax is $22.
Sales tax:
A sales tax is a tax paid to a governing body on the sale of certain goods and services. Laws generally allow sellers to collect taxes from consumers at the time of purchase. When a tax on goods or services is paid by consumers directly to the governing body, it is usually called a use tax. Laws often provide excise and use tax exemptions for certain goods or services, such as: food, education, medicine, etc. Value Added Tax (VAT) charged on goods and services is related to sales tax.
For Example:
I am shopping at The Clothing Boutique and would like to estimate the total after tax before checking out. After counting the total price of the items in the cart, the total is $100. Sales tax in this county is 9.5%, so you charge 9.5% (100 x 0.095) of $100.
According to the question:
The purchase before sales tax:
= 1/4 × $5.99 + 1 1/2 × $4.99 + 1 × $6.99 + 3/4 ×2.99
= $1.5 + $7.5 + $6.99 + $5.24
= $21.23 ≈ $22
Therefore, the customer pay for the purchase before sales tax is $22.
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ind the general solution of the given differential equation. dr / d theta + r sec theta = cos theta
r = ___
r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.
Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.
r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)
The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.
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For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the image below for Part A, Part B, and Part C.
Two triangles: GHI and JKL
Both have one similar angle but different side lengths
Part A: Sharon says the triangles above are similar using the AA Postulate. Is she correct?
Part B: Explain the answer from Part A.
Part C: If HI=7, find KL. Show your work.
Please Help!
The triangle given is similar to using SAS. Sharon is wrong and the value of KL is 14.
What are the triangle similarity criteria?there are three types of triangle similarity criteria known. those are
AA: Two pairs of corresponding angles are equal.SSS: Three pairs of corresponding sides are proportional.SAS.: Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.Given, two Triangle ΔGHI and ΔKLJ. Also, we can see in the figure That ratio of there two known sides is equal and they both have a similar angle.
the ratio of two sides of given triangles
4/8 and 5/10
hence, the ratio of both the side is equal that is 1/2
from the SAS theorem:
Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
thus, given triangles are similar.
Since the Ratio of all three sides would be equal.
hence, HI / KL = 1/2
the third side of the triangle JKL, KL is 14.
Therefore, The given triangle is comparable to using SAS. Sharon is mistaken; The value of KL is 14.
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Can you form a triangle with side lengths 8 9 and 17?
No, you cannot form a triangle with side lengths 8, 9, and 17. The sum of any two sides of a triangle must be larger than the remaining side. 8 + 9 = 17, which is not larger than 17.
1. A triangle is a three sided polygon with three angles and three sides.
2. In order to form a triangle, the sum of any two sides of the triangle must be larger than the remaining side.
3. To test if a triangle can be formed with side lengths 8, 9, and 17, we need to add two of the sides together and see if the result is larger than the remaining side.
4. 8 + 9 = 17, which is not larger than 17, so a triangle cannot be formed with side lengths 8, 9, and 17.
5. Therefore, you cannot form a triangle with side lengths 8, 9, and 17.
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he distribution of the diameters of a particular variety of apples is approximately normal with a standard deviation of 0.2 inches. How does the diameter of an apple at the 34th percentile compare with the mean diameter
Using the normal distribution, we have that diameters at the 0.34th percentile are 0.2 standard deviations, that is, 0.127 inches above the mean.
Which of the following can be true about an event's probability?Probability is the likelihood that a particular experiment result will appear a certain number of times. It cannot be less than zero or greater than one. A 100% chance of an outcome occurring exists if the outcome is 1, for example. If the result is greater than 1, there is a greater chance that it will occur.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
It measures how many standard deviations the measure X is from the mean.
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
34th percentile is X when Z has a p-value of 0.34, so X when Z = 0.6331.
It means that the diameter is 0.44 standard deviations = 0.6331x0.2 = 0.127 inches above the mean.
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Sergio purchased 4 items for $1.50 each. Sales tax was 8.25%. What was the total price?
please explain if you can, thxs!
Answer:
6.495.Step-by-step explanation:
The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.
The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.
So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.
Using a pencil
, pair of compasses and ruler, construct a triangle with sides 7cm,5cm and 6cm.
Measure the size of the angle between the 5cm and 7cm sides to the nearest degree.
The angle between the 5cm and 7cm sides to the nearest degree should measure approximately 71 degrees.
To construct a triangle with sides 7cm, 5cm and 6cm, start by drawing a straight line of 7cm length using the ruler. Next, use the compasses to draw an arc from one end of the line, with a radius of 5cm. Then, draw another arc from the same point of the line, with a radius of 6cm. Where the arcs intersect, draw a straight line connecting them to complete the triangle.
To measure the size of the angle between the 5cm and 7cm sides, use the compasses to draw a small arc from the vertex of the angle, and measure the angle using the ruler. To ensure accuracy, divide the angle into smaller, easier-to-measure angles. Repeat the process until the angle is measured to the nearest degree. In this case, the angle between the sides of 5cm and 7cm is approximately 71 degrees.
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