Solution :
Zoe's ball pool is a cylinder with height 20 cm and diameter 90 cm.
Height = 20 cm
Diameter = 90 cm
Calculate :
(a) The Radius of the pool.
Answer :
We are given with Diameter of pool 90 cm.
We know that,
Radius = Diameter/2
Radius = 90/2 = 45 cm.
(b) The circumference of the pool .
Answer :
Circumference = 2 πr
[tex]2 \times \dfrac{22}{7} \times 45 \\ \\ \dfrac{ 44 \times 45}{7} \\ \\ \frac{1980}{7} \\ \\ 282.8 \: cm[/tex]
(c) The area of the base of the pool.
Answer :
Area of base = πr²
[tex] \dfrac{22}{7} \times {(45)}^{2} \\ \\ \frac{22}{7} \times 2025 \\ \\ 22 \times 289.28 \\ \\ 578.56 \: {cm}^{2} \\ [/tex]
(d) The volume of the pool
Answer :
Volume of cylinder = πr²h
[tex] \dfrac{22}{7} \times {(45)}^{2} \times 20 \\ \\ \dfrac{22}{7} \times 2025 \times 2 \\ \\ \dfrac{22}{7} \times 4050 \\ \\ \frac{89100}{7} \\ \\ 12728.57 \: {cm}^{3} [/tex]
Points C , A , and D are located along the edge of a river and point B is on the opposite edge. Use △BCA and △BDA to determine which of the following are possible widths of the river.
Using the two equations, we can determine that the possible widths of the river are 75 m and 90 m.
We can use the properties of triangles to determine the possible widths of the river. Using the triangle △BCA, we can calculate the width of the river using the law of cosines. We know that the angle at C is 90° and the length of side AB is the width of the river. We can calculate the length of side BC using the equation: [tex]BC^2 = AB^2 + AC^2[/tex] - 2(AB)(AC)cos(90°). Similarly, we can use △BDA to calculate the width of the river. We know that the angle at D is also 90° and the length of side AD is the width of the river. We can calculate the length of side BD using the equation: [tex]BD^2 = AD^2 + AB^2[/tex] - 2(AD)(AB)cos(90°). Using the two equations, we can determine that the possible widths of the river are 75 m and 90 m.
the complete question is :
Points C, A, and D are located along the edge of a river and point B is on the opposite edge. The distance between A and D is 40 meters. The distance between C and B is 30 meters. The angles at A and D are both 90 degrees. Use △BCA and △BDA to determine which of the following are possible widths of the river.
a) 60 meters
b) 35 meters
c) 45 meters
d) 50 meters
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Which data set has the largest range?
O A. 14, 19, 18, 35, 32, 38, 40
O B. 102, 105, 103, 110
O C. 5, 6, 75
O D. 1, 9, 2, 5, 4, 19, 2, 4, 3
The data set that has the largest range is C. 5, 6, 75, which is calculated as 75 - 5 = 70.
What is the Range of a Data Set?To find the largest range, we need to calculate the difference between the highest and lowest value in each data set and compare them.
A. For 14, 19, 18, 35, 32, 38, 40, we have:
Range = 40 - 14 = 26
B. For 102, 105, 103, 110, we have:
Range = 110 - 102 = 8
C. For 5, 6, 75, we have:
Range = 75 - 5 = 70
D. For 1, 9, 2, 5, 4, 19, 2, 4, 3, we have:
Range = 19 - 1 = 18
Therefore, data set C has the largest range of 70.
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Find the distance between (3,3) & (5,3)
ASAP HELP!! Find the value of x.
Answer:
42°
Step-by-step explanation:
2x-6=90 2x=84 x=42
PLEASE HELP!!
Given ABC shown in the graph below, XYZ is found according to the following combined transformation function.
Look at both photos below to help answer the question.
The coordinates of triangle XYZ are X(-2,-2), Y(2,4), and Z(-4,8).
Describe Transformation?In mathematics, a transformation refers to a change or modification of an object's position, shape, size, or orientation in a coordinate plane or space. Transformations can be described as functions that map the points or vertices of an object to new positions in the plane or space.
Common transformations include:
Translation: a transformation that moves an object without changing its size, shape, or orientation. Translation involves shifting all points of the object by the same distance in the same direction.
Rotation: a transformation that turns an object about a fixed point or axis by a certain angle. Rotation preserves the size and shape of the object, but changes its orientation.
Scaling: a transformation that changes the size of an object by multiplying the coordinates of each point by a fixed factor. Scaling can either enlarge or reduce an object.
Since the transformation function is not provided, I'll assume that D2(ABC) means dilating the triangle ABC with center at the origin and a scale factor of 2.
To find the coordinates of the new triangle XYZ, we can apply the dilation transformation to each vertex of the original triangle:
For vertex A(-1,-1), we multiply its coordinates by the scale factor 2, giving us point X(-2,-2).
For vertex B(1,2), we multiply its coordinates by the scale factor 2, giving us point Y(2,4).
For vertex C(-2,4), we multiply its coordinates by the scale factor 2, giving us point Z(-4,8).
Therefore, the coordinates of triangle XYZ are X(-2,-2), Y(2,4), and Z(-4,8), as shown below:
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Use the data reflected in the graphs above. Which class, if any, has more variability in their data? A) Class A B) Class B C) Neither D) Both show the same variability.
The answer is D but I'm not 100% sure since I don't see the graph
Parts of similar triangles
Find x
The measurement of the side EF in ΔDEF is 13 units.
What's the triangle formula?Tο determine the area οf a triangle, use the fοrmula area = 1/2 * base * height. Determine the height οf the triangle frοm a base side. Then enter the base and height measurements intο the fοrmula.
Because the twο in the figure are similar, we can set up an equatiοn and sοlve fοr the unknοwn value οf x using the prοpοrtiοnality οf cοrrespοnding sides:
As ΔDEF ≅ ΔJHI
Then EF ≅ IH
3x - 2 = x + 8
3x - x = 8 + 2
2x = 10
x = 10/5
x = 5
EF = x + 8
= 5 + 8
= 13
Thus, The measurement of the side EF in ΔDEF is 13 units.
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Which expressions can be used to find each angle measure of a regular polygon with 28 sides? Select all that apply.
The correct answer is the third option: (28 - 2) x 180 / 28.
A regular polygon is what?An -sided polygon with regular sides that are all the same length and symmetrically arranged around a common centre is known as a regular polygon (i.e., the polygon is both equiangular and equilateral).
Every side of a regular polygon with 28 sides is the same length, and every interior angle is the same size.
The formula: gives the sum of the internal angles of a polygon with n sides.
Interior angle total equals (n - 2) x 180 degrees.
Each interior angle of a regular polygon has the same measure, thus we can calculate each interior angle's size by dividing the total of its internal angles by the number of sides. For a regular polygon with 28 sides, the expression to get each angle's measure is as follows:
(28 - 2) x 180 / 28
Simplifying the phrase:
(26 x 180) / 28
For a regular polygon with 28 sides, the shortened expression that may be used to determine each angle measure is:
4680/28
Which is further condensed to:
105*(4/7)
Hence, the appropriate phrase is:
(28 - 2) x 180 / 28 = 4680/28 = 105*(4/7)
As a result, the third option—(28 - 2) x 180 / 28—is the proper response.
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a telephone company makes up its monthly bills as follows: a fixed charge of 800 naira plus a charge proportional to the number of units of call on the telephone. if it charges 2 naira per unit of call, calculate the total charge on
a) 80units
b) 150units
c) 782 units
The total charge for 782 units of call is 2364 naira.
What is a total charge?
Total Charges refers to all payments made by the Customer and all amounts due under the Contract for products and services that the Council has actually provided, regardless of whether the Customer has received an invoice.
We can use the formula:
total charge = fixed charge + charge per unit x number of units
a) For 80 units of call:
total charge = 800 + 2 x 80
total charge = 800 + 160
total charge = 960 naira
Therefore, the total charge for 80 units of call is 960 naira.
b) For 150 units of call:
total charge = 800 + 2 x 150
total charge = 800 + 300
total charge = 1100 naira
Therefore, the total charge for 150 units of call is 1100 naira.
c) For 782 units of call:
total charge = 800 + 2 x 782
total charge = 800 + 1564
total charge = 2364 naira
Therefore, the total charge for 782 units of call is 2364 naira.
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what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
Where m is the distance from A to P and n is the distance from P to B.
What is Length?Length is a measure of distance or size. It is the measurement of the longest dimension of an object, such as a line, segment, or plane. It is commonly used to measure the physical size of objects, as well as the space between them. Length can be measured in many different units, such as meters, feet, or inches. Length is also used to measure the amount of time it takes for something to occur, such as the length of a movie or a song.
Therefore, if the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2), the x- and y- coordinates of point P would be:
x= [2/3(x2 -x1) +x1
y = [2/3](y2 - y1) +y1
This equation can be used to calculate the coordinates of any point P on a directed line segment from A to B such that P is a fraction of the length of the line segment from A to B. By setting the fraction equal to 2/3, we can calculate the coordinates of point P that is 2/3 the length of the line segment from A to B. This can be useful in a variety of applications, such as computer graphics, game design, and engineering. For example, this equation could be used to calculate the coordinates of a point on a line segment that is an exact distance from the two endpoints, or to calculate the coordinates of a point that is a certain percentage of the distance between the two endpoints.
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The coordinates of point P such that it is 2/3 the length of the line segment from A to B are (4, -2). Therefore, the correct option is d-(3,-2).
What is Length?Length is a measure of distance or size. It is the measurement of the longest dimension of an object, such as a line, segment, or plane. It is commonly used to measure the physical size of objects, as well as the space between them. Length can be measured in many different units, such as meters, feet, or inches.
Given the coordinates of the points A, B and P, we can calculate the x- and y- coordinates of point P such that it is 2/3 the length of the line segment from A to B.
To do this, we need to use the following formula: x = [m/m+n](x2 -x1) +x1, y = [m/m+n](y2 - y1) +y1, where m is 2/3, n is 1/3, x1 and y1 are the x- and y-coordinates of point A, and x2 and y2 are the x- and y-coordinates of point B.
In this case, m = 2/3, n = 1/3, x1 = 2, y1 = -1, x2 = 4, y2 = -3.
Therefore, plugging these values into the formula we get:
x = [2/3](4 -2) +2 = 4
y = [2/3](-3 - (-1)) + (-1) = -2
Therefore, the coordinates of point P such that it is 2/3 the length of the line segment from A to B are (4, -2). Therefore, the correct option is d-(3,-2).
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What is the meaning of "the underlying set"?
The underlying set of a group is the set of elements that are being operated on using the binary operation specified in the definition of the group.
What is a set?A set is a collection of distinct objects, which can be anything from numbers, letters, or even other sets.
According to question:In the context of the definition of a group, the "underlying set" refers to the set of elements that are used to define the group. In other words, it is the set of objects or elements that are being combined or operated on using the binary operation specified in the definition.
For example, if we define a group using the set of integers (G = {...,-2,-1,0,1,2,...}) and the binary operation of addition, then the underlying set of the group is the set of integers. Each element in the set of integers is an element of the group, and the binary operation of addition is used to combine two elements of the to create a new element within the group.Similarly, if we define a group using the set of real numbers greater than zero (G = {x | x > 0}) and the binary operation of multiplication, then the underlying set of the group is the set of positive real numbers. Each element in the set of positive real numbers is an element of the group, and the binary operation of multiplication is used to combine two elements of the to create a new element within the group.
In summary, the underlying set of a group is the set of elements that are being operated on using the binary operation specified in the definition of the group.
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the great zlatan ibrahimović always scores a goal if he manages to take no less than six shots in a game (and sometimes he scores even without shooting). the following is a probability distribution of the number of shots zlatan ibrahimović must make to score a goal:
No. of shots Probability of scoring
0 0.02
1 0.13
2 0.34
3 0.32
4 0.16
5 0.02
6 0.01
(A). Calculate the expected ( mean) number of shots he takes to score a goal ?
(B). Calculate the standard deviation of the distribution.
a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.
b) The standard deviation of the distribution is 2.46.
How are the expected number and standard deviation computed?The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.
The formula for the mean is given as E(x) = ∑x P(x).
On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.
No. of shots Probability Expected Squared Squared Deviation
of scoring No. of shots Deviation x Probability
0 0.02 0 9.6721 0.193442
1 0.13 0.13 8.8804 1.154452
2 0.34 0.68 5.9049 2.007666
3 0.32 0.96 4.6225 1.4792
4 0.16 0.64 6.1009 0.976144
5 0.02 0.1 9.0601 0.181202
6 0.01 0.6 6.3001 0.063001
The expected (mean)
number of shots = 3.11 6.055107
Standard Deviation = Square root of 6.055107 = 2.46
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Which of the following is NOT a use of the perpendicular bisector?
A.Finding center of a circle given points on the circle.
B.Drawing a square.
C.Drawing a triangle with two equal sides lengths (isosceles triangle).
D.Finding the circumference ofthe a triangle.
Drawing a square is NOT a use of the perpendicular bisector.
What does perpendicular bisector mean?
A line that bisects another line segment into two equal-sized segments by crossing it perpendicularly might be said to be a perpendicular bisector. The midpoint of a line segment is traversed by a perpendicular bisector. A ruler and a compass are needed to build it. The line segment that is being divided is bisected at an angle of 90° on both sides.
What use serve perpendicular bisectors?
A line that cuts through the junction of two adjacent line segments at a right angle is known as a perpendicular bisector. With this in mind, we may state that a perpendicular bisector always splits a line segment in its middle. The word "bisect" itself refers to an even or uniform division.
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Find the resistance in a 1238 watt circuit with 120 volt electricity passing through it.
The resistance in the circuit is 11.63 ohms
What is resistance?Resistance is the opposite of the flow of current. It can also be defined as the ratio of square of voltage to the power of a circuit. It is measured in ohms.
The factors that affects the resistance of a conductor are;
1. temperature
2. length of the wire
3. Area of the wire
4. Nature of the wire
power = V²/R
R = V²/P
P = 1238 W
v = 120
R = 120²/1238
R = 14400/1238
R = 11.63 ohms
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is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x is first angle
y is second angle
and z is third angle
Step-by-step explanation:
This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.
Whats the the sum of x and 2
The sum of x and 2 is equal to x + 2.
What is value?Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.
This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.
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Traveling 65 miles/1 hr, how many minutes will it take to drive 125 miles ?
It would take approximately 115.38 minutes to drive 125 miles at a rate of 65 miles/hour.
How many minutes will it take to drive 125 miles?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given that, the speed or rate is 65 miles/1 hr, how many minutes will it take to drive 125 miles.
First, we need to find the time it takes to travel 125 miles at a rate of 65 miles/hour.
We can use the formula:
Speed = Distance ÷ time.
time = distance / rate
time = 125 miles / 65 miles/hour
time = 25/13 hours
Now we can convert hours to minutes by multiplying by 60:
= 25/13 hours × 60 minutes/hour
= 115.38 minutes
Therefore, the required time is approximately 115.38 minutes.
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How many zeroes (real or imaginary) does f ( x ) = x 2 + x − 2 have?
Answer:
2 real zeros at x = - 2 , x = 1
Step-by-step explanation:
f(x) = x² + x - 2
to find the zeros let f(x) = 0 , that is
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 1 = 0 ⇒ x = - 1
there are 2 real zeros , x = - 2 and x = 1
A store sells water bottles in large and small sizes. There are 24
large water bottles and 18 small water bottles on display in the
store. The manager of the store wants there to be 3 large water
bottles on display for every 2 small water bottles. Should the
manager make any changes to the current display? Explain.
Answer:
Yes, the manager should make changes to the current display. There should be 36 large water bottles and 36 small water bottles, which would be a 3:2 ratio. To achieve this, the manager should add 12 more large water bottles to the display.
evaluate if r = 7. r - 12 =?
Answer:
if r is 7 then the answer is -5
if r is 7 then the answer is -5Step-by-step explanation:
if r is 7 then the answer is -5Step-by-step explanation:r-7=-5 because r is =to 7 so if you subtract 12 from 7 the answer you will get is -5
Convert 1.374 to a percent. Do not add any additional values to the number.
Answer:
137.4%
Step-by-step explanation:
Why is the second open interval on which the function is decreasing (0, infinity) and not (0, -infinity) if it’s going down? (Photo attached)
Therefore , the solution of the given problem of function comes out to be the function's behavior on that range because it is not specified for negative values of x.
What does the term function actually mean?The midterm exam will include questions on design, geometry, numbers, each division, as well as actual and hypothetical geographic places. A piece of work describes the connections between variable elements that cooperate to produce the same outcome. A utility is a structure made up of numerous unique parts that work together to create unique outcomes for each input.
Here,
Given that the function in the graph you supplied is undefinable for negative values of x, its domain is (0, infinity).
Therefore, referring to the function as declining on the interval is illogical. (0, -infinity).
As we travel from right to left on the interval, we can observe that the function's values are indeed decreasing. (0, infinity).
We refer to this interval as the function's declining one because of this.
On the interval, we could state that the function is decreasing.
(-infinity, 0). However, in this specific instance, we are unable to discuss the function's behavior on that range because it is not specified for negative values of x.
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Find value of X and then Y. Not drawn to scale
Answer:
x=66 and y=63
Step-by-step explanation:
The middle triangle is isosceles
57+57+x=180
114+x=180
x=66
Left triangle is equilateral (all angles =60)
60+57+?=180
117+?=180
?=63
Right triangle is isosceles
?=y
y=63
A flower bed is 2 meters wide and 3 meters long.What is the area of the flower bed i square feet? Round your converted dimensions and your final answer to the nearest hundredth show your work.
Answer:
64.58
Step-by-step explanation:
1 meter is 3.28084 so 3 meters is 9.84252 because you multiply it by 3 or add them to each other 3 times. 2 meters is 6.56168 because you multiply it by 2 or add them to each other. now that you have 6.56168 and 9.84252 multiply them with each other and you get 64.5834666336 but it was said to round to nearest hundredth so since the 3 in front of the 8 is not a 5 and above the answer is 64.58 and not 64.89
Pls help Which function models the area of a rectangle with side lengths of 2x – 4 units and x + 1 units? What is the area when x = 3?
Answer:
Step-by-step explanation:
The area A of a rectangle is given by the formula:
A = length × width
In this case, the length is 2x - 4 units and the width is x + 1 units. So the function that models the area of the rectangle is:
A(x) = (2x - 4)(x + 1)
Expanding this expression, we get:
A(x) = 2x^2 - 2x - 4x + 4
A(x) = 2x^2 - 6x + 4
To find the area when x = 3, we can substitute x = 3 into the function:
A(3) = 2(3)^2 - 6(3) + 4
A(3) = 18 - 18 + 4
A(3) = 4
Therefore, when x = 3, the area of the rectangle is 4 square units.
20 POINTS ANSWER FOR BRAINLIST
Multiply. Final answer needs to be in Standard
Form. Two different methods need to be shown.
You can choose between Area Model, Distributive
Property and FOIL.
(3x − 4)(2x − 1)
Answer:
Method 1: Distributive Property
To multiply (3x - 4) and (2x - 1), we can use the distributive property:
(3x - 4)(2x - 1) = 3x(2x) + 3x(-1) - 4(2x) - 4(-1)
= 6x^2 - 3x - 8x + 4
= 6x^2 - 11x + 4
Therefore, the final answer in standard form is 6x^2 - 11x + 4.
Method 2: FOIL
To multiply (3x - 4) and (2x - 1), we can use the FOIL method:
(3x - 4)(2x - 1) = 3x(2x) + 3x(-1) - 4(2x) - 4(-1)
= 6x^2 - 3x - 8x + 4
= 6x^2 - 11x + 4
Therefore, the final answer in standard form is 6x^2 - 11x + 4.
complete part A and B
The corresponding point on the graph is (9, 21). This point is within the normal respiratory rate region, which is defined by the system of linear inequalities. Therefore, model breakdown has not occurred.
The given problem involves the normal respiratory rates of children aged 3 to 15 years. The respiratory rate, measured in breaths per minute, is represented as a function of age using a system of linear inequalities. The graph depicts a normal respiratory rate region that models the respiratory rate ranges shown in the table. The problem requires us to identify a specific point on the graph that corresponds to a respiratory rate of 21 breaths per minute for a 9-year-old child. The ordered pair (9, 21) represents the corresponding point on the graph.
Further, we need to determine if this point lies within the normal respiratory rate region or if model breakdown has occurred. The system of linear inequalities defines the normal respiratory rate region, and we can determine if the point (9, 21) satisfies these inequalities. In this case, the point (9, 21) lies within the normal respiratory rate region and satisfies the system of linear inequalities. Therefore, model breakdown has not occurred, and the given model is an appropriate approximation of the normal respiratory rate region for children aged 3 to 15.
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Please help. Deeply appreciated
By using the Pythagorean theorem we know that the given triangle is not a right triangle.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2.
The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.
The smallest and most well-known triplets are (3,4,5).
So, we have the values already,
Now, calculate as follows:
3² + 4² = 6²
9 + 16 = 36
25 ≠ 36
Hence, the given triangle is not a right triangle.
Therefore, by using the Pythagorean theorem we know that the given triangle is not a right triangle.
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Type the correct answer in the box. Use numerals instead of words.
The cone and cylinder below both have a height of 11 feet.
The cone has a radius of 3 feet.
The cylinder has a volume of 310.86 cubic feet.
Complete the statements using 3.14 for pi. Any non-integer answers in this problem should be entered as decimals rounded to the nearest hundredth.
The volume of the cone is [?]
cubic feet.
The radius of the cylinder is [?]
feet.
The ratio of the volume of the cone to the volume of the cylinder is 1:[?]
.
the length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.
Length of rectangle in cm:
Width of rectangle in cm:
Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).
Formula to find the area of a rectangle is given by-
[tex] \small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length\times Width }}}}\\[/tex]
On substituting the values-
[tex] \:\:\:\:\:\:\longrightarrow \sf {Area_{(rectangle)} = X \times \bigg(X-9\bigg)}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6\times \bigg(X-15\bigg)=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) \times \bigg(X+6\bigg) =0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\[/tex]
Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.