Using the properties of Isosceles triangles and right-angled triangles, it can be deduced that LM = NO given that angles ONL = MLN and O and M are right angles.
Explanation:The given question is about proving equivalency of lines in a geometric figure. Given the figure has the angles ONL and MLN that are equal and O and M are right angles. Given these conditions, using the properties of triangles especially the Isosceles Triangle (where two sides are equal), we can conclude that LM = NO.
To prove this assumption, we incorporate the following facts: In an isosceles triangle, the angles opposite to equal sides are equal. Hence, if ONL = MLN, it implies that NO = LM. Additionally, if angles O and M are right angles, it signifies that the triangles formed are right angled triangles. Therefore, using the property of isosceles right angled triangles, the sides opposite to equal angles are equal.
Based on these facts and the properties of geometric concepts [Isosceles Triangle, Pythagorean theorem and right angled triangles], we can confidently conclude that LM = NO. This proves that given the conditions in the problem, the lines LM and NO are equal in length.
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Given that ONL=MLN and O and M are right angles, we can say that triangles ONL and MLN are congruent right-angled triangles. Therefore, according to the property of congruent triangles, the sides opposite the equal angles in these triangles (i.e., LM and NO) should also be equal to each other.
Explanation:The question involves proving the equivalence of two lines in a geometric configuration, LM and NO, where two angles, ONL and MLN, are given as equal and O and M are right angles. This is quite a typical problem in Geometric Proof, an important topic in High School Mathematics.
To solve this, we need to apply the properties of triangles and the concept of congruent triangles. Since ONL and MLN are given as equal angles and O and M are right angles, we know that triangle ONL and MLN are right-angled triangles. In a right-angled triangle, if one angle is equal, then the other angles will be equal because the summing of angles in a triangle is 180 degrees.
Because we have now two right-angled triangles with their respective angles equal (ONL = MLN and NOM = LNM), they must be congruent triangles by the Angle-Angle (AA) criterion for congruency. This implies that the sides opposite the equal angles in these two triangles should also be equal. So, LM = NO in these triangles.
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For a cylinder open at one end with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 44 cm3.
To find the dimensions of a cylinder with one open end that minimizes its surface area given a volume of 44 cm³, use calculus and the formulas for the cylinder's volume and surface area. The solution results in radius r ≈ 1.34 cm and height h ≈ 9.87 cm.
Explanation:For a cylinder open at one end, the surface area is given by the formula A = πr² + πrh, where r is the radius and h is the height.
The volume of a cylinder is given by the formula V = πr²h. Given that V=44 cm³, we can write the volume equation as h = V / (πr²).
Substituting this into the surface area equation, we get A = πr² + πr(V / (πr²)) = πr² + V/r.
We want to minimize the surface area, so we take the derivative of A with respect to r, set it equal to zero and solve for r.
Doing this gives us: dA/dr = 2πr - V/r² = 0 => r = cuberoot(V/2π).
Substituting V=44 cm³ into this, we get r = cuberoot(22/π) ≈ 1.34 cm.
Substituting r back into h = V / (πr²), we derive that h = 44 / (π * (1.34)²) ≈ 9.87 cm.
Therefore, the dimensions that will minimize the surface area of the cylinder given that the volume is 44 cm³, are approximately r = 1.34 cm and h = 9.87 cm.
This is a classic problem of optimization in calculus.
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A cell phone company charges a monthly fee plus $0.25$0.25 for each text message. The monthly fee is $30.00$30.00 and you owe $59.50$59.50. Write and solve an equation to find how many text messages xx you had.An equation is
Complete the indirect proof to show that two supplementary angles cannot both be obtuse angles. given: angle1 and angle2 are supplementary. prove: angle1 and angle2 cannot both be obtuse. assume that two supplementary angles can both be obtuse angles. so, assume that angle1 and angle2 are obtuse. then mangle1 > 90° (equation 1) and mangle2 > ° (equation 2) by the definition of angles. adding the two inequalities, mangle1 + mangle2 > ° (equation 3). however, by the definition of supplementary angles, mangle1 + mangle2 = (equation 4). so equation 3 contradicts the given information. this means the assumption is , and therefore angle1 and angle2 both be obtuse.
The proof was completed by assuming that two supplementary angles could both be obtuse, which would mean that their sum is more than 180°. This contradicts the definition of supplementary angles, where their sum should always be exactly 180°, and hence proves that two supplementary angles cannot both be obtuse.
Explanation:To complete the indirect proof, we start by assuming that two supplementary angles, let's call them angle1 and angle2, can indeed both be obtuse angles. An obtuse angle is defined as an angle which measures more than 90°. Therefore, if both angle1 and angle2 are obtuse, they would each measure more than 90°, meaning that their sum (angle1 + angle2) would measure more than 180°.
However, the definition of supplementary angles is such that their sum should always be exactly 180°. Therefore, we reach a contradiction in our assumed scenario: the sum of angle1 and angle2 cannot be both more than 180° (by our assumption that they are both obtuse) and exactly 180° (by the known definition of supplementary angles).
This contradiction means that our initial assumption was incorrect, thus completing the proof. In other words, two supplementary angles cannot both be obtuse, as it would contradict the definition of supplementary angles.
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A barrel of oil contains 42.0 gallons. how many liters is this? (1 gal = 3.785 l)
Final answer:
A 42.0-gallon barrel of oil is equivalent to 158.97 liters, calculated by multiplying the number of gallons by the conversion factor of 3.785 liters per gallon.
Explanation:
To discover out how numerous liters are in 42.0 gallons of oil, given that 1 gallon is proportionate to 3.785 liters, you'd perform the taking after calculation:
Multiply the number of gallons by the conversion factor from gallons to liters.
42.0 gallons × 3.785 liters/gallon = 158.97 liters.
Therefore, a barrel of oil, which contains 42.0 gallons, is equivalent to 158.97 liters.
Factor the expression over the complex numbers.
x^2+50
Answer:
[tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Step-by-step explanation:
The factorization is in the form (x-a)(x-b) where a,b are zeros of the equation [tex]x^{2} +50=0[/tex].
[tex]x^{2} =-50[/tex]
[tex]x =\sqrt{-50}[/tex]
[tex]x =\sqrt{50}i = 5\sqrt{2}i[/tex] and [tex]x =-\sqrt{50}i = -5\sqrt{2}i[/tex]
So, the factorization is [tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Complex numbers are numbers with real and imaginary part.
The factorized expression is [tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
The expression is given as:
[tex]\mathbf{x^2 + 50}[/tex]
Set to 0
[tex]\mathbf{x^2 + 50 = 0}[/tex]
Subtract 50 from both sides
[tex]\mathbf{x^2 = -50}[/tex]
Take square roots
[tex]\mathbf{x = \sqrt{-50}}[/tex]
Expand
[tex]\mathbf{x = \sqrt{25 \times -2}}[/tex]
Take square roots of 25
[tex]\mathbf{x =\pm 5\sqrt{-2}}[/tex]
Expand
[tex]\mathbf{x = \pm5\sqrt{2 \times -1}}[/tex]
Split
[tex]\mathbf{x =\pm 5\sqrt{2} \times \sqrt{-1}}[/tex]
In complex numbers,
[tex]\mathbf{\sqrt{-1} = i}[/tex]
So, we have:
[tex]\mathbf{x = \pm5i\sqrt{2}}[/tex]
So, we have:
[tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
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A public interest group hires students to solicit donations by telephone. After a brief training period students make calls to potential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 80% of them give up their jobs in their first two weeks of employment. The group hires 7 students, which can be viewed as a random sample.
which property is illustrated the following statement? 3z+4=4+3z
Answer:
Commutative additive property.
Step-by-step explanation:
Given : 3z+4=4+3z
To find : which property is illustrated the following statement.
Solution : We have given
3z + 4 = 4 + 3z.
Commutative additive property : a + b = b + a .
Example : 2 + 3 = 3 +2 = 5.
Hence this the commutative additive property 3z + 4 = 4 + 3z.
Therefore, Commutative additive property.
what is the perimeter of a polygon with sides measuring; (a) cm,(a+1) cm;(a+2) cm and 3(a+3)?
524127 Add mathematical signs (+, -, ), (*, /) in between all or some oft he above digits so the result of the created mathematical equation will be 100
Find the measure of ∠D if ∠A = 5 2 x + 30 ∠B = 7 2 x + 40 ∠C = 9 2 x + 10 ∠D = 5 2 x + 20
For anyone who needs the measure itself, it's 70.
The function, f(x)=45/x models the volume of a gas in a balloon under xx units of pressure at a constant temperature. Which best describes the domain of f(x) ?
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how do you factor 2x^3+5y^3
If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is
The probability of heads on the fifth trial is still 0.5, just like any other coin flip.
Explanation:The probability of heads on the fifth trial is still 0.5, just like any other coin flip. The outcome of each coin flip is independent of the previous flips, so each trial has the same probability of resulting in heads or tails.
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Question 8 the price of a cup of coffee was $2.55 yesterday. today, the price fell to $2.40 . find the percentage decrease. round your answer to the nearest tenth of a percent. %
the difference between the measures of two supplementary angles is 42. find both
Answer:
69 and 11, took me 1 hour to slove this
Step-by-step explanation:
Write an equation for each
1. 10
2. 12
4. 16
6. 20
Last Saturday there were 1486 people at a cinema. There were about the same number of people in each of the 6 theaters. Between which 2 numbers does the number of people fall?
John has 6 green marbles and 4 purple marbles. He chooses a marble at random, writes down its color, and then puts the marble back. He performs this process 5 times. What is the probability that he chooses exactly two green marbles?
The probability that John chooses exactly two green marbles is calculated using the binomial probability formula and is found to be 720/3125.
To solve this problem, we can use the binomial probability formula because John is performing independent trials of the same experiment and he is interested in the probability of exactly two successes (picking a green marble) in a specific number of trials (5).
The binomial probability formula is: [tex]P(X = k) = (n choose k) \times p^k \times (1-p)^{n-k[/tex]
For John's case:
n = 5 (since he is picking 5 marbles).
k = 2 (he wants exactly two green marbles).
p = 6/10 or 3/5 (because there are 6 green marbles out of a total of 10 marbles).
Using the formula, the probability that John picks exactly two green marbles is:
[tex]P(X = 2) = (5 choose 2) \times (3/5)^2 \times (2/5)^{5-2[/tex]
Calculating further:
[tex]P(X = 2) = 10 \times (3/5)^2 \times (2/5)^3 = 10 \times 9/25 \times 8/125 \\P(X = 2) = 720/3125[/tex]
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat? what would a proportion be for this problem?
Patty has 8 flowerpots, and she wants to plant a different type of flower in each pot. There are 11 types of flower available at the garden shop. How many different ways can choose the flowers?
There is a large bag with marbles in it. there are 23 red ones, 16 black ones, 5 blue ones, 17 orange ones, 4 white ones, and 15 purple ones. juanita reaches in without looking and selects one marble. what is the probability that it is purple? 1 15 1 80 7 3 16
There are 4 dogs, 6 cats, a rooster and 8 pigs on a farm. What is the ratio of pigs to all the other animals?
Answer:
Its 8:11 because theres eleven animals and 8 pigs
Step-by-step explanation:
How to multiply fractions with a mixed number?
1=logx solve this equation for x. Round your answer to the nearest hundred.
A stock value doubles every 42 days. If the stocks start out with $5.00, what will the value of the stock be in 18 weeks?
A.)$125.00
B.)$15.00
C.)$30.00
D.)$40.00
Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Determine the minimum number of whole days it will take for him to be able to spell at least 75 words.
Peter needs 33 whole days to be able to speak 75 words.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Peter begins his kindergarten year able to spell 10 words.
He is going to learn to spell 2 new words every day.
Assuming no. of days it will take him to be able to spell at least 75 words
is d.
∴ The inequality that represents this scenario is 2d + 10 ≥ 75.
2d ≥ 65.
d ≥ 32.5 but it will take him 33 whole days to learn 75 words.'
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The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).
What is the perimeter of the polygon to the nearest tenth of a unit?
15.3 units
16.9 units
17.5 units
17.9 units
The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.
Further explanation:
The distance between the two points can be calculated as follows,
[tex]\boxed{{\text{Distance}}=\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}}[/tex]
Given:
The coordinates of the vertices of the polygon are [tex]\left({ - 2, - 2}\right),\left( {3, - 3}\right),\left( {4, - 6}\right),\left( {1, - 6}\right)[/tex] and [tex]\left( { - 2, - 4}\right).[/tex]
Explanation:
Consider the points as A [tex]\left( { - 2, - 2} \right), B\left( {3, - 3} \right), C\left( {4, - 6} \right), D\left( {1, - 6} \right)[/tex] and [tex]E\left({ - 2, - 4} \right).[/tex]
The distance between point A and point B can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( { - 3 + 2}\right)}^2}}\\ &= \sqrt {25 + 1}\\&= \sqrt {26}\\&= 5.2\\\end{aligned}[/tex]
The distance between point B and point C can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( { - 6 + 3} \right)}^2}}\\&= \sqrt {{1^2} + 9}\\&= \sqrt {10}\\&= 3.17\\\end{aligned}[/tex]
The distance between point C and point D can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left({1 - 4} \right)}^2} + {{\left( { - 6 + 6}\right)}^2}} \\&=\sqrt {{3^2} + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]
The distance between point D and point E can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 2 - 1}\right)}^2} + {{\left( { - 4 + 6}\right)}^2}}\\&= \sqrt{ - {3^2} + {2^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.61\\\end{aligned}[/tex]
The distance between point E and point A can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 + 2} \right)}^2} + {{\left( { - 4 + 2} \right)}^2}}\\ &= \sqrt {{0^2} + {2^2}}\\&=\sqrt4\\&= 2\\\end{aligned}[/tex]
The perimeter of the polygon can be calculated as follows,
[tex]\begin{aligned}{\text{Perimeter}}&= 5.12 + 3.17 + 3 + 3.61 + 2\\&= 16.9\\\end{aligned}[/tex]
Option (a) is not correct.
Option (b) is correct.
Option (c) is not correct.
Option (d) is not correct.
The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.
Answer:
here is the answer
Step-by-step explanation:
The probability of tossing three coins simultaneously and obtaining two heads and one tail is
2(x+14)+(2x-14)= do you know this
The simplified form of the expression 2(x+14)+(2x-14) is 4x + 14.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
An expression,
2(x+14)+(2x-14).
Simplifying,
2(x+14)+(2x-14),
= 2x + 28 + 2x - 14
= 4x + 28 - 14
= 4x + 14
Therefore, the solution is 4x + 14.
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