Answer:
45
Step-by-step explanation:
When you're completing the square you're adding (b/2)^2 which in this case is (-5)^2 or 25. This is because when you rewrite it as a square binomial you write it in the form (x+(b/2))^2 which is going to result in x^2+b+(b/2)^2. Since you need to reach 25 you need to add 45 since the last value is at -20.
Answer:
25 to both sides
Step-by-step explanation:
Group x² and x terms
(x² - 10x ) - 20
complete the square
(x² - 10x +25 ) -20 -25
(x-5)² -45
A delivery of 5 large boxes and 3 small boxes has a total mass of 137 kilograms. A delivery of 2 large boxes and 6 small boxes has a total mass of 128 kilograms. What is the mass of each type of box?
Answer:
Large boxes are 18.25 kg
Small boxes are 15.25 kg
Step-by-step explanation:
This is a system of equations. You need to set up each equation first.
I am assigning x to be big boxes and y to be small boxes.
5x + 3y = 137
2x + 6y = 128
To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.
-2 ( 5x + 3y = 137)
2x + 6y = 128
Distribute the -2 to everything in the parentheses in the first equation.
-10x - 6y = -274
2x + 6y = 128
Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:
-8x = -146
Solve for x by dividing by -8.
x = 18.25
Now plug that into one of the original equations.
2(18.25) + 6y = 128.
36.5 + 6y = 128 Subtract 36.5 from each side
-36.5 -36.5
6y = 91.5 Divide by 6 to solve
y = 15.25
What is the product of (6x^2 − 8)(9x^2 – x + 1)?
[tex](6 {x}^{2} - 8)(9 {x}^{2} - x + 1) \\ 54 {x}^{4} - 6 {x}^{3} + 6 {x}^{2} - 72{x}^{2} + 8x - 8 \\ 54 {x}^{4} - 6 {x}^{3} - 66 {x}^{2} + 8x - 8[/tex]
Hope it helps
please give brainliest
Find the missing length given that GH is a midsegment of the trapezoid. Base 42 and midpoint 26
The missing length is 14 unit.
The Trapezoid Midsegment segment theorem states that the length of midsegment of trapezoid is half the sum of the length of its two parallel sides of the trapezoid.
In a trapezoid, Midsegment = 1/2 × ( Sum of two bases of the trapezoid )
Here, The midsegment GH is given by 26.
One of the bases = 42
Let, another base be x
Then we have to use the formula of mid segment to find the another base of the trapezoid
∴ GH = 1/2 × (42+x)
⇒ 26 = 1/2 × (42+x)
⇒ 56 = 42+x
⇒ x = 56-42
⇒ x = 14
So, the missing length = 14 unit
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What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7
Answer:
D. x = 7
Step-by-step explanation:
NOTE : there should be an equal sign somewhere in the given expression.
suppose the equation is the following:
3(x-4)-5 = x-3
………………………………………………………
3(x - 4) - 5 = x - 3
⇔ 3x - 12 - 5 = x - 3
⇔ 3x - 17 = x - 3
⇔ 3x - 17 + 17= x - 3 + 17
⇔ 3x = x + 14
⇔ 2x = 14
⇔ x = 14/2
⇔ x = 7
What is the solution to the system of equations?
2x + 4y = 12
y = 1/4x - 3
A. (–1, 8)
B. (8, –1)
C. (5, 1/2)
D. (1/2, 5)
Explain how the shapes shown have been sorted.
Two groups of shapes. In group A, one shape has four equal side lengths of three, and no right angles. The opposite sides are parallel. Two shapes have two pairs of opposite equal side lengths. One shape has side lengths of four and eight. The other side lengths are three and two. Opposite sides are parallel, and there are no right angles. In group B there are three four sided shapes. One has opposite equal side lengths of seven and four and four right angles. One shape has four equal side lengths of three and four right angles. One shape has one set of opposite parallel sides and one right angle. None of the side lengths in the last shape are equal.
Answer:
There are different kinds of shapes. The shapes have been sorted below:
The shape that has one shape has four equal side lengths of three, and no right angles is rhombus.The opposite sides are parallel is parallelogram .Two shapes have two pairs of opposite equal side lengths is a parallelogram.A shape that has side lengths of four and eight is quadrilateral and octagon.Opposite sides are parallel, and there are no right angles is a parallelogramHeptagon has opposite equal side lengths of sevenQuadrilaterals and triangle shape has shape has four equal side lengths of three and four right angles.Trapezoids has one set of opposite parallel sides and the shape that has one right angle is right-angled triangles.None of the side lengths in the last shape are equal is scalene triangle.What do you understand by the term shapes?The term shape is a word that connote the form or dimensions of an object and also their outline.
It is made up of outer boundary and also outer surface. Most of everything in the world today do have shape.
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Please help!!!!!!!!!!!!!!!!!1
Answer:
f(x)=(x+4)(x+2)
Step-by-step explanation:
Factor x^2−6x+8 using the AC method.
Please help me!!!!!! Geometry
Marsha has 132 books.
They are divided
equally between three
shelves. Each book
weighs 0-2 kg.
How much weight
does each shelf
support?
Answer:
Step-by-step explanation:
=132/3
=44 books per shelf
since maximum weight of a book is 2kgs,
=44(2)
=88
To show - 7 on the number line, from zero, we have to move 7 units in which direction?
Answer:
7 units to the left.
Step-by-step explanation:
On the number line , the number will always decrease when we move towards the left, and likewise will always increase when we move towards the right. In this case since the number is moving from 0 to -7, it is definitely decreasing therefore we will move 7 units to the left.
Find the measure of the remote exterior angle. m∠x=(198−5n)°m∠y=(5n+37)°m∠z=(n+7)°
The value of the angle ∠x will be ∠x = 128°. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle is given below.
The sum of the two interior angle is equal to the third exterior angle.
m∠x = (198 − 5n)°
m∠y = (5n + 37)°
m∠z = (n + 7)°
We know that
∠x = ∠y + ∠z
198 - 5n = 5n + 37 + n + 7
11n = 154
n = 14
Then the value of the angle ∠x will be
∠x = 198 – 5 × 14
∠x = 128°
Then the correct option is C.
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Find X = Find Y= please help ty :)
Answer:
X = 125° and Y = 75°
Step-by-step explanation:
Y = 75° because the line the bisects two parallel lines. When this happens, the angles at the corners are identical.
To find the value of "X", I first found the value of the last angle in the triangle. I found this by performing the following:
180° - 55° - 75° = 55°
The value of this missing angle is 55°. To find "X", I subtracted this value from 180°. I did this because lines always equal 180°
180° - 55° = 125°
You find a wooden shelf 4½ feet long. You want to cut it to make two smaller shelves. One will be 1¼ feet long, the other, 2⅜ feet long. Is the uncut shelf long enough? Explain your answer.
The length of the uncut shelf is not long enough.
Given a wooden shelf 4½ feet long.
The length of two small shelves is 1¼ and 2⅜ feet long respectively.
To find an uncut shelf long enough or not subtract shelf's piece length from the total length of the wooden shelf length.
The length of an uncut shelf can be calculated as:
⇒1¼ + 2⅜+x= 4½
⇒5/4 + 19/8 + x = 9/2
To solve this equation make variable and constant different sides.
⇒x= 9/2-5/2-19/8
⇒x=2-19/8
⇒x=-3/8
The length of the uncut shelf is -3/8 feet, which is not valid (∵ Length cannot be negative).
∴ The length of the shelf is not long enough.
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This is all the questions I need answers to:
A two-digit locker combination has two non-zero digits and no two digits are the same. Event A is defined as choosing an even digit for the first number, and event B is defined as choosing an odd digit for the second number.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
A. 4/9
B. 1/2
C. 5/9
D. 5/8
A locker combination consists of two non-zero digits, and each combination consists of different digits. Event A is defined as choosing an even number as the first digit, and event B is defined as choosing an even number as the second digit.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 1/6
B. 5/18
C. 1/2
D. 5/9
A jar contains 5 red marbles and 8 white marbles.
Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
If two marbles are drawn from the jar, one after the other without replacement, what is P(A and B) expressed in simplest form?
A. 3/13
B. 10/39
C. 5/12
D. 8/13
A bag contains 5 blue marbles, 8 green marbles, 4 red marbles, and 3 yellow marbles.
Event A = drawing a green marble on the first draw
Event B = drawing a blue marble on the second draw
If Jasmine draws two marbles from the bag, one after the other and doesn’t replace them, what is P(B|A) expressed in simplest form?
A. 2/19
B. 1/6
C. 4/19
D. 5/19
A jar contains 3 pink balls, 6 blue balls, and 3 red balls.
Event A = drawing a red ball on the first draw
Event B = drawing a pink ball on the second draw
If two balls are drawn from the jar, one after the other without replacement, what is P(A and B) expressed in simplest form?
A. 3/44
B. 4/9
C. 3/11
D. 1/4
House numbers along a street consist of two-digit numbers. Each house number is made up of non-zero digits, and no digit in a house number is repeated.
Event A is defined as choosing 8 as the first digit, and event B is defined as choosing a number less than 6 as the second digit.
If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?
A. 1/9
B. 5/72
C. 5/8
D. 2/3
House numbers along a street consist of two-digit numbers. Each house number is made up of non-zero digits, and no digit in a house number is repeated.
Event A is defined as choosing 8 as the first digit, and event B is defined as choosing a number less than 6 as the second digit.
If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?
A. 2/7
B. 5/14
C. 5/13
D. 6/13
A two-digit locker combination is made up of two non-zero digits. Digits in a combination are not repeated and range from 3 through 8.
Event A = choosing an odd number for the first digit
Event B = choosing an odd number for the second digit
If a combination is chosen at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 1/5
B. 3/14
C. 5/18
D. 2/5
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.
Event A = the first digit is an odd number
Event B = the second digit is an odd number
If a combination is picked at random with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
A. 3/8
B. 3/7
C. 1/2
D. 4/7
There are 15 tiles in a bag. Of these, 7 are purple, 5 are black and the rest are white.
Event A = drawing a white tile on the first draw
Event B = drawing a purple tile on the second draw
If two tiles are drawn from the bag one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 1/5
B. 1/3
C. 7/15
D. 1/2
I know theres a lot here but please hurry :) thx 100 points to the first person to answer all correctly! thx :)
The is probability P(B|A) expressed in simplest form is 1/2 (Option B) See computation below.
How do we derive the above?P (A) = [[tex][\mathrm{C}_{5}^{1} \mathrm{C}_{8}^{1}]/ \mathrm{A}_{9}^{2}[/tex]
= ('5 x 8)/(9 x 8)
P (A) = '5/9
P (AB) = [tex][\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1}]/ \mathrm{A}_{9}^{2}[/tex]
= ('5 x 4)/(9 x 8)
= '5/18
P(B|A) = P (AB)/P(A)
= ('5/18)/('5/9)
P(B|A) = 1/2
How do we derive P(A and B) in the simplest form?From the above we already have P (AB)
this is given as
P (AB) = [tex][\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1}]/ \mathrm{A}_{9}^{2}[/tex]
= ('5 x 4)/(9 x 8)
P(AB) = '5/18
How do we derive P(A and B) in the simplest form where a jar contains 5 red marbles and 8 white marbles?Note that:
Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
P(A) = 8/13; while
P (B) = (5/12) because the first marble was not replaced, thus reducing th sample to 12.
Thus
P(A and B) = P(A)*P(B) = 8/13 * 5/12
P(A and B) = 10/39 (Option B)
If Jasmine draws two marbles from the bag, one after the other and doesn’t replace them, what is P(B|A) expressed in simplest form?Event A - Probability of Drawing a Green Marble is 8/20
Event B - Probability of Drawing a Blue Marble is 5/19
Thus P(B|A) = (8/20) * (5/19)
= [tex]\frac{8 * 5 }{20 * 19}[/tex]
= 40/380; divide numerator and denominator by 20
P(B|A) = 2/19 (Option A)
Event A = Probability of Drawing a red ball = 3/12
Event A = Probability of Drawing a pink ball without replacing the read in Event A = 3/11
Thus P (B and A) =
3/12 x 3/11
P (B and A) = 3/44 (Option A)
If a house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?The conditions given are as follows:
The house number comprises of nonzero digits and are of two digits ranging from 1 to 9.As per the condition, the First digit 8 can be selected in 9 ways; and Second digits is less than 6 can be selected in waysThe sum total of ways thus is
9 x 8
= 72 ways........X
Recall that
Event A is defined as selecting 8 as the first numeral
The only way to select this is one way
Event B is defined as choosing a number less than 6 as the second digit, that is 1, 2, 3, 4, 5
Thus, the possible number of ways to fill second digit = 5/8
Thus, the possible number of ways to form two digits 'AnB' =
('AnB') = 1 x 5 = 5 .................y
Hence Probability (AnB) = 5/72 (Option B)
Given that the non-zero digits are in a combination are not repeated and range from 3 through 8, thus the odd numbers between 3 and 8 are:
3, 5, 7
total numbers is 3, 4, 5, 6, 7, 8
Hence; Event A = choosing an odd number for the first digit = 3/6
Event B = choosing an odd number for the second digit (recall that the numbers are not repeated) = 2/5
= [tex]\frac{2*3}{3*6}[/tex]
= 6/30
= 1/5 (Option A)
If a combination is picked at random with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
Event A = the first digit is an odd number
Event B = the second digit is an odd number
The numbers from 2 to 9 are:
2,3,4,5,6,7,8,9
The odd numbers between 2 and 9 are:
3,5,7,9
P (A) = 4/8
P (B) = 3/7
P(B|A) = (3/7)/(4/8)
P(B|A) = 3/7
Event A = drawing a white tile on the first draw
Event B = drawing a purple tile on the second draw
P(B|A) = (P(AnB)/P(A)
|n| = 15 * 14 = 210
| A| = 3*14 = 42
| AnB| = 3*7 = 21
P (A) = 42/210 = 6/30
P (AnB) = 21/210 = 1/10
P(B|A) = (1/10)/6/30)
P(B|A) = 1/10 * 30/6
P(B|A) = 30/60
P(B|A) = 1/2 (Option D)
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_3x_13 =_7x+15 what is the an
Answer:
x = -7Step-by-step explanation:
_3x_13 =_7x+15 what is the anSWER?
assuming that the underscore is a minus and you are looking for the x value.
-3x - 13 = -7 + 15
-3x = -7 + 15 + 13
-3x = 8 + 13
-3x = 21
x = -7
---------------
check
-3 * (-7) - 13 = -7 + 15
21 - 13 = 8
8 = 8
the answer is good
Decide whether each number is written in standard notation or scientific notation.
Number
Type of notation
3000
Select ...
Select ...
4.2 × 104
Select ...
Select ...
1.05 × 10–7
Select ...
Select ...
0.0013
Select ...
Select ...
6,500,000
Select ...
Select ...
6.2 × 1019
Select
The answers are as follows:
3000- standard notation
4.2*10 raised to 4 - scientific notation
1.05 × 10 raised to power –7 - scientific notation
0.0013 - standard notation
6,500,000 - standard notation
6.2 × 10 raised to power 19 - scientific notation
Concept: Standard notation is a way of writing a number so it is easier to read. It is often used for very large or very small numbers.
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
In the given questions,
3000- standard notation
4.2*10 raised to 4 - scientific notation
1.05 × 10 raised to power –7 - scientific notation
0.0013 - standard notation
6,500,000 - standard notation
6.2 × 10 raised to power 19 - scientific notation
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Which piece of additional information can be used to prove that △rst ~ △vut? rt = st 3st = ut ∠r ≅ ∠v ∠v ≅ ∠u
The option third ∠R ≅ ∠V is correct because line segment RS and UV are parallel which is crossed by a transversal RV.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have given two triangles:
Triangle RST and Triangle VUT
AS we can see Line segment RS and UV are parallel.
Which is crossed by a transversal RV.
The angle SRV = Angle RVU
Thus, the option third ∠R ≅ ∠V is correct because line segment RS and UV are parallel which is crossed by a transversal RV.
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Answer:
c
Step-by-step explanation:
An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup. Which expression should be used to find the amount of the markup?
48 dollars (0.55)
48 dollars (55)
48 dollars (0.55) + 48 dollars
48 dollars (55) = 48 dollars
The amount of the markup is $48 + $48 (0.55) .
Option (C) is correct .
What is Markup Price?Mark up refers to the value that a player adds to the cost price of a product. The value added is called the mark-up. The mark-up added to the cost price usually equals retail price.
As given
An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup.
55% is written in the decimal form .
= 55/100
= 0.55
Markup price = 0.55 × wholesale price of item .
= 0.55 × $48
= $48 (0.55)
Price of item after markup = Wholesale price of item + Markup price
= $48 + $48 (0.55)
Thus, the amount of the markup is $48 + $48 (0.55) .
Option (C) is correct .
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Answer:The answer is A
Step-by-step explanation:
Edg 2022 (sometimes the verified ones are wrong)
If T(x) = x + 0.14x, then find the value of T(290).
The value if T(290) is 330.6
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Given:
T(x) = x + 0.14x
T ( 290)= 290+ 0.14* 290
= 290+ 40.6
= 330.6
Hence, the value of T(290) is 330.6.
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help me out asap!please and thank you
Answer:
c. (5, -2)
Step-by-step explanation:
as we can clearly see, the 4th vertex has to be on the positive side of x.
therefore, all answer options with negative x are out.
(2, -5) is almost at D (-1, 5). that cannot be right for a rectangle.
that leaves only c as right answer.
FYI - how to get this without predefined answer portions ?
the x- difference of B to A is 4 (from -5 to -1). the x-difference from D to C must be the same (4). 1 + 4 = 5.
so, x of D must be 5.
the y- difference of B to A is 3 (from 3 to 6). the y-difference from D to C must be the same (3). -5 + 3 = -2.
so, y of D must be -2.
What's the circumference of a circle with a diameter of 18 inches? Use 3.14 for I. T What's the circumference of a circle with a diameter of 18 inches ? Use 3.14 for I. T
Answer:
56.52 inches
Step-by-step explanation:
pi is the ratio of the circumference to the diameter so you can simply multiply the diameter by pi to get the circumference which is 3.14 * 18 = 56.52
Marquis wrote the linear regression equation y = 1.245 x minus 3.684 to predict the cost, y, of x songs purchased. marquis spent $40 on songs. which is the best estimate of the number of songs that marquis purchased? 29 32 35 46
Answer:
35
Step-by-step explanation:
1. Write the equation
y = 1.245x - 3.684
2. Set y = 40, since that is the cost of the songs he purchased.
40 = 1.254x - 3.684
3. Add 3.684 to both sides
43.684 = 1.254x
4. Divide by 1.254
x = 35.0875502
Answer:
Answer is C.) 35
Step-by-step explanation:
In the figure below, what is the value of x°?
Answer:
1
Step-by-step explanation:
x to the zeroth power is always 1
Answer:
Step-by-step explanation:
90 - 20 = 70
So now do 5 times x and that's also equal to 70
70.x =11
please help me its help.
The answer will be 81.
Step-by-step explanation:
just multiple by 3
Answer:
81
Step-by-step explanation:
the people told secrion has a sequence of multiplyung by 3 if you continue the sequence you will get to 81
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer: 26 inches is equivalent to 660.4 millimeters.
Step-by-step explanation:
You will multiply the inches by the conversion.
[tex]26in*25.4mm=660.4mm[/tex]
Therefore, the answer is 660.4 millimeters.
I hope this helps!! Pls mark brainliest :)
Can you answer this question
Step-by-step explanation:
Hi There! Let me help you :)
[tex] = 6.6.6.3.3[/tex]
[tex] = 6(1 + 1 + 1).3(1 + 1)[/tex]
[tex] = 6(3).3(2)[/tex]
Area of a triangular prism
Answer:
if you mean the formula it is (1/2) · b · (6 · h + sqrt(3) · b)
Step-by-step explanation:
Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T.
Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l?
Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m.
Use the compass to construct a circle centered at Q through point P.
Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q.
Use the compass to construct a circle centered at P through point Q.
Mark this and return
Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. The correct option is C.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
Since the given parallel line has equation y = 2x + 2 , thus its slope is 2 and thus, the slope of the needed line is 2 too.
The next step that Gerald should take is Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Hence, the correct option is C.
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If the center of the small gear is rigidly attached to the center of a bicycle wheel with a radius of 10 inches, how many inches will the bicycle travel with a single rotation of the large gear? the small gear has a radius of 2 inches.
The distance traveled is 62.8 inches.
How many inches will the bicycle travel with a single rotation of the large gear?
We know that the gear is rigidly attached to the center of the wheel. This means that in one complete rotation of the gear, we also have a complete rotation of the wheel.
Then the distance that the bicycle travel with a single rotation of the gear is equal to the circumference of the wheel, which is:
C = 2*pi*R
Where pi = 3.14 and R is the radius, which we know is 10inches.
Then:
C = 2*3.14*10in = 62.8in
The distance traveled is 62.8 inches.
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a) Write 2 expressions for the area of the shaded region.
b) Find the length of the shaded region if the perimeter is 48cm.
c) Find the area of the shaded region if perimeter is 48cm.
Answer:
(a)9×3=37' 97 and 8 are factors of 37
