The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.
What is integration?Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.
I = ∫ [x / (x² + 1)³] dx
Let x² + 1 = t, then x dx = dt / 2. Then we have
I = ∫ [1 / 2(t)³] dt
I = (1/2) ∫ [1 /(t)³] dt
I = (1/2) [-1 /2t²] + c
I = - (1/4) (1/(x² + 1)²) + c
I = - 1 / 4(x² + 1)² + c
The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.
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Luke says 1/5 +2/5 =3/10 Describe the error .
please solve quickly! (15 points)
Answer:
Step-by-step explanation:
36
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+
3
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2
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x
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3
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2
Ann and leila are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.After 225 miles driven, which car will have less gas remaining?After how many miles will the tanks contain the same amount of gas? If the number of miles driven is less than this, which car will have more gas remaining?
After 180 miles both the cars' tanks contain same amount of gas.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, Ann and Leila are driving separate cars to New York. They begin the trip with full gas tanks.
From the given graph,
After 360 miles Ann's car has 2 gallons of gas.
After 180 miles both the cars' tanks contain same amount of gas.
When they travelled less than 180 miles, Leila's car has more gas.
Therefore, after 180 miles both the cars' tanks contain same amount of gas.
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a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side.
Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.
A triangle's third side must be longer than the difference between the other two sides' lengths and shorter than the total length of the other two sides. The two side lengths in this situation are 18 and 26. The third side must be greater than 8 because the difference between them is 8. The third side must be less than 44 because the total length of the first two sides equals 44. Therefore, the third side length might be any side length between 8 and 44.Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.
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The complete question is
a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side potential lengths range from 8 to 44?
Select all ratios equivalent to 7:6.
The ratios equivalent to 7:6 can be expressed as a) 14 : 12
What does the idea of ratios mean?The concept that will be used here is ratio. The proportion is an equation that demonstrates how two ratios are equivalent, but the notion of ratio defines us to compare two quantities.
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
From the ratios equivalent to 7:6 which can be written as 7/6
Then we consider option A , 14/12 = 7/6 ( divide the denominator and numerator by factor of 2.
Option B; 2 : 18 = 2/18 = 1/9
option C : 28 : 26 = 16/ 13
option D : 30 : 25 = 6/5
Therefore, option A is correct.
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Missing options:
a) 14 : 12
b) 2 : 18
c) 28 : 26
d) 30 : 25
the price of a new car is 23% more than the price of a 3-year old car. if the price of the new car was $12,400, what is the price of the 3-year old car?
Answer: To find the price of the 3-year old car, we need to determine how much less it is than the new car, which is 23% of the price of the new car.
We can start by finding the value of 23% of the price of the new car, which is: $12,400 x 0.23 = $2,832
Now we know that the price of the 3-year old car is $2,832 less than the price of the new car. To find the price of the 3-year old car, we subtract $2,832 from the price of the new car: $12,400 - $2,832 = $9,568
So the price of the 3-year old car is $9,568.
Step-by-step explanation:
now, set up an integral to compute the volume of this solid, then evaluate it to find the volume of the solid: V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx an integral that gives the volume of the solid is:
The volume of the solid is equal to 96 cubic units.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx
= 1/3*∫(24-6x^2-12x)dx
= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4
= 1/3*[(-6)-(-140)-(-136)]
= 1/3*(288)
= 96 cubic units
Set up an integral to compute the volume of the solid.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx
Rewrite the integral with a function of x in terms of a single power of x.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx
= 1/3*∫(24-6x^2-12x)dx
Integrate the function.
= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4
Evaluate the integral to find the volume of the solid.
= 1/3*[(-6)-(-140)-(-136)]
= 1/3*(288)
= 96 cubic units
The volume of the solid is equal to 96 cubic units.
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If the sun is 69° above the horizon, find the length of the shadow cast by a building 91 ft tall. Round your answer to the nearest tenth.
If the sun is 69° above the horizon, the length of the shadow cast by a building 91 ft tall
How to find the length of the shadow?You should understand that the length of the shadow is the distance between a point to the foot of the tenth
This makes an angle of depression, with 69 degrees
Remember that the angle on top of the tenth is 90-69 = 21 degrees
therefore, using the trigonometrical ratio
We have Tan∅ = opposite of adjacent
Tan 21⁰ = x/9
x= 9*tan 21⁰
x = 9*0.3839
The distance is 3.45
Therefore the length of the shadow cast by a building is approximately 3.5 feet long
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(2/5y -8)+ (3/10y+1)
The solution for the expression is (35y - 22)/(5y-8)(10y+1). The solution has been obtained by solving the algebraic expression.
What is algebraic expression?
An algebraic expression is one that uses variables, constants, and algebraic operations (addition, subtraction, etc.).
The four primary categories of expressions are as follows:
A monomial expression is one with only one term.These expressions have two terms and are called binomial expressions.Expressions with three terms are known as trinomial expressions.The terms in polynomial expressions are numerous.We are given
⇒(2/5y -8)+ (3/10y+1)
⇒(2(10y+1) + 3(5y -8))/(5y-8)(10y+1)
⇒(20y + 2 + 15y - 24)/(5y-8)(10y+1)
⇒(35y - 22)/(5y-8)(10y+1)
Hence, the solution for the expression is (35y - 22)/(5y-8)(10y+1).
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A bakery used 30% more sugar this month than last month.If the bakery used 560 kilograms of sugar lost month,how much did it use this month?
728 kilograms of sugar is used in this month.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a bakery used 30% more sugar this month than last month.
Let us convert 30% to decimal.
Divide 30 by 100
30/100=0.3
the bakery used 560 kilograms of sugar last month we have to find the amount of sugar used this month.
Now multiply 30% of 560
0.3×560
168.
So now 560+168=728 is the amount of sugar used this month.
Hence, 728 kilograms of sugar is used in this month.
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Can someone explain to me why the answer is 90 and not 1080? I think it has to do with the inches and ft. But I don’t remember how you solve it.
Answer:
You are correct
Step-by-step explanation:
You are correct sir. They want the answer in feet, so everything on that triangle has to be converted into feet.
There are 12 inches in a foot. If we do 108/12 we get 9 feet.
A barn is 100 feet long and 40 feet wide (see figure attached). A cross section of the roof is the inverted catenary given below.
y = 31 - 10(e^(x/20) + e^(-x/20))
Find the number of square feet of roofing on the barn. (Round your answer to the nearest whole number.
The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)
What is integration ?
Integration is a fundamental concept in calculus. It refers to the process of finding the integral of a function, which gives the total amount of change of a quantity over a given interval. The process of integration is the reverse of differentiation, which is the process of finding the rate of change of a quantity. The symbol for integration is ∫.
A barn is 100 feet long and 40 feet wide.
Find the first derivative of the given function:
dy/dx = -10[1/20e^x/20 - 1/20 e^-x/20]
1 + (dy/dx)^2 = 1/4[e^x/20 - e^-x/20]^2
The arc length:
= ∫ √1/4[e^x/20 - e^-x/20]^2 dx
After solving the above integration:
= 20(e - 1/e)
The roofing = 100(20(e - 1/e))
= 4701 square feet,
The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)
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How the expressions are equivalent
Equivalent equations are algebraic equations that are having identical roots or solutions
What are Equivalent Expressions?Equations in algebra with the same roots or solutions are said to be equivalent. An analogous equation is one that is created by adding or removing the identical number, symbol, or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
To determine which complex expression is the simple expression's equivalence:
Give any coefficients a distribution:
a(bx±c)=abx±ac
X-terms and constants should be combined with any other like terms on either side of the equation.Put the terms in the same order, with the x-term typically coming before the constants.The two phrases are equal if and only if each of their terms is the same.To know more about Equivalent expressions, refer to:
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in the x y coordinate plane, which of the following points must lie on kx + 3y + 6 if k = -1/2
Answer:
honestly, I got no idea. I can tell you though - go us Desmos kid. it'll help you more than any person in this platform.
don't thank me
Step-by-step explanation:
Desmos
use Desmos
Find the equation of this line.
y =
x +[]
Simplify the fractional part.
Answer:
y = 1/3x +2
Step-by-step explanation:
when x =o, y=2
when x= -6, y=0
so slope is always the difference between the Ys divided by diff b/w the Xs
so the slope is (2-0)/(0-(-6)) = 1/3
the intercept by definition is when x=0, so it's 2
so Y = 1/3 X +2
Sarah ordered 37 shirts that cost $9 each. She can sell each shirt for $16. She sold 30 shirts to customers. She had to return 7 shirts and pay a $3 charge for each returned shirt. Find Sarah's profit.
Sarah's profit, given the shirts sold, the cost of the shirts, and the shirts returned, can be found to be $ 126
How to find the profit ?First, find Sarah's cost :
= Cost to buy the shirts + cost to return the shirts
= ( 37 x 9 ) + ( 7 x 3)
= 333 + 21
= $ 354
The revenue made from selling the shirts was :
= 30 x 16 per shirts
= $ 480
Sarah's profit is therefore:
= 480 - 354
= $ 126
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Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
The rate at which the water flow from the given volume is 21.72 in³/sec
What is rate at which the water flowTo find the rate at which water is being drained from the container, we first need to find the rate at which the water level is falling and then use that to calculate the volume of water being drained per unit of time.
We know that the surface level is falling at a rate of 0.9 inches per second and that the container has the shape of an inverted right circular cone. The volume of a cone is given by the formula:
V = (1/3) * π * r^2 * h
Where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.
We can use this formula to find the volume of the container when the water level is 8 inches. The radius at this point is 6 * (8/10) = 4.8 inches and the height is 8 inches.
V = (1/3) * π * (4.8 inches)^2 * 8 inches = 193.02 inches³
Now that we know the volume of the container when the water level is 8 inches, we can use the rate at which the water level is falling (0.9 inches per second) to find the rate at which the water is being drained.
The rate at which water is being drained = rate of change of volume / rate of change of height = dV/dt = dV/dh * dh/dt = -dV/dh * dH/dt
Where dV/dh is the derivative of volume with respect to height, dH/dt is the rate of change of height.
-dV/dh = -(1/3) * π * (4.8 inches)^2 = -24.13 in³
dH/dt = -0.9 inches/sec
The rate at which water is being drained = -dV/dh * dH/dt = -24.13 * -0.9 inches/sec = 21.72 in³/sec
So the rate at which water is being drained from the container is 21.72 in³/sec
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The question is based on the following table, which provides information on the production of a product that requires one variable input.
Input Total Product
0 0
1 5
2 20
3 32
4 42
5 50
6 55
7 58
8 58
9 56
With the addition of the seventh unit of input, the marginal product is
Answer: The marginal product is the change in total product that results from an additional unit of input. With the addition of the seventh unit of input, the marginal product can be calculated as follows:
Total product when 7 units of input is used: 58
Total product when 6 units of input is used: 55
Marginal product = Total product when 7 units of input is used - Total product when 6 units of input is used
Marginal product = 58 - 55 = 3
So with the addition of the seventh unit of input, the marginal product is 3 units.
Step-by-step explanation:
Diya earned a 36 out of 80 on a test. Her teacher offered extra credit that would allow Diya to double her score. What score could she earn if she completes the extra credit?
Diya could earn 72 marks out of 80 after getting the extra credits.
What are extra credits in School?Teachers employ extra credit for a variety of reasons. For example, it may be felt that students who are highly capable may benefit from an additional challenge that might not be suitable as required work for all students. Extra credit may also be used as a way to allow a student to improve their grade after a weak performance earlier in a course. In both of these cases, extra credit can promote differentiated instruction by factoring in optional work in the assessment of student performance.
Given here: Diya scores 36 out of 80 on a test.
Also, her teacher gives her extra credit with which she could double her marks.
If Diya doubles her marks then her total marks would be 72
Therefore the increase in her marks is 72-36=36
She could earn another 36 credits.
Thus her score after the extra credit is equal to 72
Hence, Diya could earn 72 marks out of 80 after getting the extra credits.
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Select the correct answer. An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B? A. 8 units B. 6 units C. 5 units D. 3 units
Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Find the plane determined by the intersecting lines.
L1 x= -1 + 3t y = 2+2t z=1-t
L2 x=1-4s y=1+2s z=2-2s
In a plane, intersecting lines are any two or more lines that cross each other. The point of intersection is the common point shared by all intersecting lines.
What are Intersecting Lines?In a plane, intersecting lines are those that cross one another three times or more. The point of intersection is the shared location between all intersecting lines that exists on all intersecting lines.Point O represents the point of intersection where lines P and Q meet in this instance.Specifications of intersecting linesWhen two or more lines intersect, they always do so at the same location.Any angle may be used to intersect the lines. Always more than 0° and less than 180° is the angle that is generated.Vertical angles are created by two intersecting lines. There is a common vertex between the opposing vertical angles (which is the point of intersection).Vertical angles a and c are equivalent in this case. Additionally, b and d have equal vertical angles and are vertical angles.A plus D equals a straight angle of 180 degrees.To Learn more About intersecting lines refer To:
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X+6y=-2 show ur work
The equation when making x the subject is X = -2 - 6y
How to make x the subjectTo do this, we would have to take the values that are in the left hand side to the right hand side. When we do this, the signs on the left hand side would have to change
X+6y=-2
we have to take +6y to the right hand side.
When the positive sign crosses the equal sign it becomes negative
X = -2 - 6y
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X+6y=-2 show ur work make x the subject
8-3(4-4)+2*4*6 :< i need help man
Answer:
[tex]\sf 56[/tex]Step-by-step explanation:
[tex]\sf 8-3(4-4)+2*4*6[/tex]
[tex]\sf 8-(3)(0)+(2)(4)(6)[/tex]
[tex]\sf 8-0+(2)(4)(6)[/tex]
[tex]\sf 8+(2)(4)(6)[/tex]
[tex]\sf 8+(8)(6)[/tex]
[tex]\sf 8+48[/tex]
[tex]\sf 56[/tex]
QUICK!!! WHAT IS -2 2/5 times -1/3
(Please show work)
Environmentalists want to estimate the percent of trees in a large forest that are infested with a certain beetle. The environmentalists will select a random sample of trees to inspect. Which of the following is the most appropriate method for creating such an estimate? A two-sample z-interval for a population proportion A one-sample interval for a sample proportion A one-sample 2-interval for a population proportion A two-sample z interval for a difference between sample proportions A two sample 2-interval for a difference between population proportions
A two-sample z-interval for a population proportion. This method is used to create an estimate of the percentage of trees in a large forest that are infested with a certain beetle by taking a random sample of trees to inspect.
A two-sample z-interval for a population proportion is the most appropriate method for creating an estimate of the percent of trees in a large forest that are infested with a certain beetle. This method involves taking a random sample of trees from the forest and inspecting them to determine the proportion of infested trees. The sample size chosen should be large enough to provide a reliable estimate of the proportion of trees in the population that are infested. A two-sample z-interval is then used to calculate a confidence interval for the population proportion, which can be used to estimate the overall percent of trees in the forest that are infested with the beetle. This method can provide a reliable estimate of the percent of trees in the forest that are infested with the beetle, allowing environmentalists to make informed decisions regarding management of the forest.
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ACTIVITY: Writing an Inequality
Work with a partner. In 3 years, your friend will still not be old enough
to apply for a driver's license.
a. Which of the following represents your friend's situation?
What does x represent? Explain your reasoning.
x + 3 < 16
x + 3 ≤ 16
x + 3 > 16
x+3≥ 16
The inequality that represents the situation in this problem is given as follows:
x + 3 < 16
How to define the inequality?The inequality symbols are given as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.In three years, your friend's age is given as follows:
x + 3.
To apply for the driver's license, an age of 16 is needed, and your friend will be younger than 16, as he/she cannot apply, hence the inequality is:
x + 3 < 16
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Which of the following is a property of an isosceles trapezoid? Choose ALL that apply.
Four right angles
Two pairs of parallel sides
Diagonals are congruent
Diagonals are perpendicular
The properties of isosceles trapezoid are
Two pairs of parallel sidesTwo pairs of parallel sidesWhat is isosceles trapezoid?The lengths of the left and right sides of an isosceles trapezoid are equal or identical hence the base angles are likewise equal.
Because lengths of the left and right sides are equal and base angels are equal, the diagonals are equal
Other types of trapezoid include
The right trapezoid has two right angles.Its non-parallel sides are of identical length, making it an isosceles trapezoid.It does not have equal angles or sides, making it a scalene trapezoid.generally all trapezoid have two sides that are parallel to each other
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Rosa gasto 11.52 en 8 collares de dulces para cada una de sus dos amigas cuánto costó cada collar
Answer:
1.44
Step-by-step explanation:
11.52/8=1.44
Quadrilateral EFGH is a rhombus.
Which additional fact would prove that
EFGH is a square?
O A) EG ~ FH
O BEG 1 FH
O C) EG bisects LFEH
O DILFEH ~ LFGH
The additional fact that would prove that
EFGH is a square is D) IFLEH ~ LFGH.
What is a quadrilateral?A quadrilateral is a plane figure with four edges and four corners, also known as vertices. The quadrilateral's four vertices or corners all have angles.
If a quadrilateral is a rhombus, that means opposite sides are congruent, but it does not mean that all angles are congruent. In order to prove that EFGH is a square, we need to show that all angles are congruent. The statement "IFLEH ~ LFGH" implies that all angles in the quadrilateral are congruent, since it states that opposite angles are congruent, which is one of the defining characteristics of a square. Therefore, statement D is the correct answer.
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True or false? A hair clip is 1 4/7 inches long. A paper clip is 5/6 inches long. The two items are about the same length.