Answers
1. (5, 12, 13) is a Pythagorean triple.
2. (20, 21, 27) is not a Pythagorean triple.
3. Fake triples are (7, 2, 25), (280, 450, 533), and (110, 60, 651)
4. A Pythagorean triple that I know is (3, 4, 5).
5. a.Thus, (6, 8, 10) is also a Pythagorean triple.
b. Thus, (30, 40, 50) is also a Pythagorean triple.
c. Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d. Yes, a Pythagorean triple consisting of three even numbers is (6, 8,
10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
Define Pythagorean theorem?The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right-angled triangle.
1. To prove that (5, 12, 13) is a Pythagorean triple, we need to show that
⇒ 5² + 12² = 13²
⇒ 5² + 12² = 169 (5² = 25 and 12² = 144 and 13² = 169)
Therefore, 5² + 12² = 13², which means that (5, 12, 13) is a Pythagorean triple.
2. To prove that (20, 21, 27) is not a Pythagorean triple.
Assuming that (20, 21, 27) is a Pythagorean triple, we would have:
⇒ 20² + 21² = 27²
⇒ 400 + 441 ≠ 729
Therefore, (20, 21, 27) is not a Pythagorean triple.
3. To find the fakes among the following list of triples, we need to check if there is a whole number solution for the sides of a right-angled triangle with these measurements.
Therefore, the fakes are (7, 2, 25), (280, 450, 533), and (110, 60, 651).
4. A Pythagorean triple that I know is (3, 4, 5).
Scaling up each side by the same amount should still result in a Pythagorean triple, as the relationship between the sides will remain proportional.
5. a) Multiplying each side by 2, we get (6, 8, 10). Verifying Pythagoras' theorem, we have:
6^2 + 8^2 = 36 + 64 = 100
10^2 = 100
Thus, (6, 8, 10) is also a Pythagorean triple.
b) Multiplying each side by 10, we get (30, 40, 50). Verifying Pythagoras' theorem, we have:
30^2 + 40^2 = 900 + 1600 = 2500
50^2 = 2500
Thus, (30, 40, 50) is also a Pythagorean triple.
c) Halving each side of (3, 4, 5), we get (1.5, 2, 2.5). Verifying Pythagoras' theorem, we have:
1.5^2 + 2^2 = 2.25 + 4 = 6.25
2.5^2 = 6.25
Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d) The observation is that scaling up or down a Pythagorean triple by the same amount results in another Pythagorean triple. This is because the sides of a Pythagorean triple are related by the Pythagorean theorem, which is a quadratic equation. Multiplying each side by the same amount simply scales the sides up or down proportionally, while preserving the quadratic relationship.
Yes, a Pythagorean triple consisting of three even numbers is (6, 8, 10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
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1. (5, 12, 13) is a Pythagorean triple.
2. (20, 21, 27) is not a Pythagorean triple.
3. Fake triples are (7, 2, 25), (280, 450, 533), and (110, 60, 651)
4. A Pythagorean triple that I know is (3, 4, 5).
5. a.Thus, (6, 8, 10) is also a Pythagorean triple.
b. Thus, (30, 40, 50) is also a Pythagorean triple.
c. Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d. Yes, a Pythagorean triple consisting of three even numbers is (6, 8,
10. A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
Define Pythagorean theorem?The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right-angled triangle.
1. To prove that (5, 12, 13) is a Pythagorean triple, we need to show that
⇒ 5² + 12² = 13²
⇒ 5² + 12² = 169 (5² = 25 and 12² = 144 and 13² = 169)
Therefore, 5² + 12² = 13², which means that (5, 12, 13) is a Pythagorean triple.
2. To prove that (20, 21, 27) is not a Pythagorean triple
Assuming that (20, 21, 27) is a Pythagorean triple, we would have:
⇒ 20² + 21² = 27²
⇒ 400 + 441 ≠ 729
Therefore, (20, 21, 27) is not a Pythagorean triple.
3. To find the fakes among the following list of triples, we need to check if there is a whole number solution for the sides of a right-angled triangle with these measurements.
Therefore, the fakes are (7, 2, 25), (280, 450, 533), and (110, 60, 651).
4. A Pythagorean triple that I know is (3, 4, 5).
Scaling up each side by the same amount should still result in a Pythagorean triple, as the relationship between the sides will remain proportional.
5. a) Multiplying each side by 2, we get (6, 8, 10). Verifying Pythagoras' theorem, we have:
6² + 8² = 36 + 64 = 100
10² = 100
Thus, (6, 8, 10) is also a Pythagorean triple.
b) Multiplying each side by 10, we get (30, 40, 50). Verifying Pythagoras' theorem, we have:
30² + 40² = 900 + 1600 = 2500
50² = 2500
Thus, (30, 40, 50) is also a Pythagorean triple.
c) Halving each side of (3, 4, 5), we get (1.5, 2, 2.5). Verifying Pythagoras' theorem, we have:
1.5² + 2² = 2.25 + 4 = 6.25
2.5² = 6.25
Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d) The observation is that scaling up or down a Pythagorean triple by the same amount results in another Pythagorean triple. This is because the sides of a Pythagorean triple are related by the Pythagorean theorem, which is a quadratic equation. Multiplying each side by the same amount simply scales the sides up or down proportionally, while preserving the quadratic relationship.
Yes, a Pythagorean triple consisting of three even numbers is (6, 8, 10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
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Related Questions
Amanda trains to run a marathon. She must follow a strict schedule to make sure she is ready for the race. She will start her training by running two miles the first week. She wants to run one fewer mile the next week, and then three more miles the week after that. She will continue this pattern during her entire training regimen. Write a sequence for the number of miles that Amanda will run the first 10 weeks of her training. Explain your reasoning.
Answers
The sequence for the number of miles that Amanda will run in the first 10 weeks of her training is
2, 1, 5, 0, 8, 3, 11, 5, 14, 7
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
To find the sequence for the number of miles that Amanda will run in the first 10 weeks of her training, we need to first identify the pattern of increasing and decreasing miles she will run each week.
According to the given information, Amanda will start by running 2 miles in the first week.
In the second week, she will run one fewer mile, so she will run 2 - 1 = 1 mile. In the third week, she will run three more miles than she did in the first week, so she will run 2+3=5 miles.
In the fourth week, she will run two fewer miles than she did in the second week, so she will run 1 - 2 = -1 mile.
However, it doesn't make sense for Amanda to run a negative number of miles, so we can assume that she will take a rest week during the fourth week and not run any miles.
Then, she will resume her pattern of increasing and decreasing miles in the following weeks.
Therefore, we can write the sequence for the number of miles that Amanda will run in the first 10 weeks of her training as follows:
2, 1, 5, 0, 8, 3, 11, 5, 14, 7
To obtain this sequence, we applied the given pattern of running one fewer mile in the second week, followed by three more miles in the third week, and then repeating this pattern. We also accounted for the rest week during the fourth week by inserting a 0 in the sequence.
Hence, the sequence for the number of miles that Amanda will run in the first 10 weeks of her training is
2, 1, 5, 0, 8, 3, 11, 5, 14, 7
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Find the area of the shaded segment of the circle
Answers
I need more info for your problem :
Maybe this could help you :Assume a sector having a radius
Assume a sector having a radius r and a central angle of a degrees.The sector's area will be [tex]A^{2}[/tex] = (a / 360 °)* [tex]\pi[/tex]*[tex]r^{2}[/tex]
The area of an equilateral triangle having a side lenght a is A =( [tex]\sqrt{3}[/tex]/4) * [tex]a^{2}[/tex]
The sum of my digits is equal to 5
My tens digit is not odd
( t - u ) = 1
Keep in mind there are two digits
Answers
The two digits are 3 and 2.
What are numbers?A number is a numerical unit of measurement and labeling in mathematics.
The natural numbers 1, 2, 3, 4, and so on are the first examples.
Number words are a linguistic way to express numbers.
Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.
Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.
The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."
According to our question-
3+2
=5
Hence, The two digits are 3 and 2.
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Which value of n makes the equation true?
-1/2n=-8
O A. -16
OB. -4
O c. 4
O D. 16
Answers
Answer:
D. 16
Step-by-step explanation:
[tex]-\frac{1}{2} n=-8[/tex]
multiply by -2/1 on both sides
[tex](-2)-\frac{1}{2} n=-8(-2)[/tex]
simplify
[tex]n=16[/tex]
Question Progress
Homework Progress
12/
Expand and simplify 2(x + 7) + 3(x + 1)
Answers
Answer:
Step-by-step explanation:
2x + 14 + 3x +3
17 + 5x
x=3.4
Whats the width of a rectangle if the perimeter is 130 ft and the length is 45 but there's no area
Answers
Answer:
Step-by-step explanation:
I hope this helps
What is the sum of the series?
∑j=152j
Enter your answer in the box.
Answers
Answer:
Hope this helps
Step-by-step explanation:
Sum of series is donated by the for formula below
[tex] \sf \: Sn = \frac{n}{2} [2a + (n - 1)d][/tex]
Example 3,6,9,12,...
Let's say we're finding the sum of the 20 series
n = 20, a = 3, d = 6-3 = 3
Where,
n means number of terms
a means the first term
d means the constant value between terms
S20 = 20/2[2(3) + (20-1)d]
S20 = 10[6+19(3)]
S20 = 60 + 570
S20 = 630
Voila!!
If RT is greater than BA, which correctly compares
angles C and S?
O mzC=mZS
O mzC
O m2C> mZS
O mzC ≥ m/s
Answers
As angle Z is bigger than angle Y and angle C must be greater than angle S, we also cannot say that mzC >mZS. The accurate disparity is: mZS >mZC .
how can you describe angle ?An angle is just a geometric shape made up of two rays or splines that meet at a point in the middle known as the vertex. The angle's sides or legs are the rays or dotted lines that make up the angle. T
he standard unit of measurement for angles is the degree, with 360 degrees being one entire circle. Acute angles are those that are less than 90 °, right angles are those that are exactly 90 degrees, obtuse angles are those that are higher than 90 degrees but much less than 180 degrees, & straight angles are those that are exactly 180 degrees.
given
The right response is "mZC > mZS".
The right side of the figure is longer than the left side if RT is bigger than BA. Angle X is greater than angle W, and angle Z is greater than angle Y as a result.
Angles C and S will have the same measure if the triangles are identical because they are matching angles (they are in the same place in each triangle). We are unsure, nevertheless, whether the triangles are comparable.
We cannot therefore assert that mzC = mZS.
As angle Z is bigger than angle Y and angle C must be greater than angle S, we also cannot say that mzC >mZS. The accurate disparity is: mZS >mZC .
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During a sale, colour pencils were being sold in packs of 24 each and crayons in
packs of 32 each. If you want full packs of both and the same number of pencils
and crayons, how many of each would you need to buy?
Answers
Answer:
96 ÷ 32 = 3 packs of crayons.
Step-by-step explanation:
Find the cross product a ⨯
b. A = 4, 5, 0 , b = 1, 0, 3 verify that it is orthogonal to both a and
b. (a ⨯
b. · a = (a ⨯
b. · b =
Answers
We can verify that a ⨯ (a ⨯ b) is orthogonal to a. We can solve it in the following way.
To find the cross product a ⨯ b, we can use the formula:
a ⨯ b = |a| |b| sinθ n
where |a| and |b| are the magnitudes of vectors a and b, θ is the angle between a and b, and n is a unit vector perpendicular to both a and b, determined by the right-hand rule.
Using the given vectors a and b, we have:
|a| = √(4² + 5² + 0²) = √41
|b| = √(1² + 0² + 3²) = √10
To find the angle between a and b, we can use the dot product:
a · b = |a| |b| cosθ
4(1) + 5(0) + 0(3) = √41 √10 cosθ
Simplifying:
4 = √410 cosθ
cosθ = 4/√410
θ ≈ 77.09°
Now we can find the cross product using the formula:
a ⨯ b = |a| |b| sinθ n
a ⨯ b = √41 √10 sin(77.09°) n
Using the right-hand rule, we can determine that the unit vector n points in the negative z-direction, so n = -k, where k is the unit vector in the positive z-direction.
Thus, we have:
a ⨯ b = -√410 sin(77.09°) k
Evaluating this expression, we get:
a ⨯ b ≈ -0.667i + 1.777j - 3.617k
To verify that this vector is orthogonal to both a and b, we can take the dot product of a ⨯ b with a and b separately. If the dot product is zero, then the vectors are orthogonal.
a ⨯ b · a = (-0.667)(4) + (1.777)(5) + (-3.617)(0) = 0
a ⨯ b · b = (-0.667)(1) + (1.777)(0) + (-3.617)(3) = 0
Since both dot products are zero, we can conclude that the vector a ⨯ b is orthogonal to both a and b.
Note: The dot product of a vector and its own cross product is always zero, which can be used to verify that a ⨯ (a ⨯ b) is orthogonal to a. In this case, we have:
a ⨯ (a ⨯ b) = (4, 5, 0) ⨯ (-0.667, 1.777, -3.617)
= -17.07i - 6.248j - 12.005k
(a ⨯ (a ⨯ b)) · a = (-17.07)(4) + (-6.248)(5) + (-12.005)(0) = 0
Thus, we have verified that a ⨯ (a ⨯ b) is orthogonal to a.
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What do I do I’m confused
Answers
Graph the image of T(10, – 2) after a reflection over the x-axis.
Answers
Answer:
To graph the image of T(10, -2) after a reflection over the x-axis, you simply need to flip the point vertically so that it lies on the opposite side of the x-axis.
The x-coordinate of the point will stay the same, and the y-coordinate will change sign.
Starting with the point T(10, -2), reflect it over the x-axis to obtain the image point T'(10, 2), which is 10 units to the right of the y-axis and 2 units above the x-axis.
So the graph of T(10, -2) after a reflection over the x-axis is the point T'(10, 2), as shown in the following diagram:
|
|
|
|
|
------T'(10, 2)
|
|
------x-axis------
|
|
|
|
|
|
|
Note that the x-axis is the line that runs horizontally through the middle of the diagram, while the y-axis is the line that runs vertically through the middle of the diagram. I hope this helps.
Which model best represents the relationship between time and volume?
OA linear model would best represent the relationship because scatterplot A is fairly linear.
O An exponential model would best represent the relationship because scatterplot B is fairly linear.
A power model would best represent the relationship because scatterplot C is fairly linear.
A linear model would best represent the relationship because scatterplot C is fairly linear.
Answers
The answer is C: A power model would best represent the relationship because scatterplot C is fairly linear.
What is a power model?In this the rate of change of the dependent variable is proportional to the power of the independent variable. In other words, when the independent variable increases, the dependent variable increases at a rate that is proportional to the power of the independent variable. This type of model is often used to describe phenomena such as population growth, economic growth, and physical processes such as diffusion.
When looking at the graph of scatterplot C, it is clear that the relationship between time and volume follows a power model.
The data points in the graph are fairly linear, meaning that as the log of time increases, the log of volume increases at a rate that is proportional to the power of the log of time.
This indicates that a power model would best represent the relationship between time and volume, making C the correct answer.
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Answer:
the obvious
Step-by-step explanation:
Natalie uses a
50
%
50% off coupon when she buys a camera. The original price of the camera is
$
46. 00
$46. 0. How much money does Natalie save by using the coupon?
Answers
Answer: Amount Saved = $23 (answer). In other words, a 50% discount for a item with original price of $46 is equal to $23 (Amount Saved).
Step-by-step explanation:
What is the measure of each exterior angle of a regular decagon
Answers
Answer: Hence, a regular decagon has each exterior angle 36∘ and each interior angle as 144∘.
Smith's Produce sells packages of pre-cut vegetables. The company has a tolerance level of less than or equal to y grams for a 250-gram package. Which graph could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x?
Answers
The answer of the given question based on the graph could be used to determine the variance levels that would result in a package of vegetables is histogram.
What is Histogram?A histogram is a bar graph-like representation of data that groups data into ranges, called bins, and displays the frequency of data within each bin. In this case, the x-axis of the histogram would represent the weight of the vegetable packages, and the y-axis would represent the frequency of packages that fall within each weight bin.
To determine variance levels that would result in package of vegetables being rejected because of its weight, histogram would need to be constructed based on tolerance level of company. The histogram would show distribution of package weights, and any packages that fall outside of the acceptable weight range would be considered rejected. By analyzing the histogram, the company could determine the variance levels that would result in package rejection and make necessary adjustments to their production process.
A histogram would be the most appropriate graph to use in this situation to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x.
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the graph that could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x, is a normal distribution curve with a mean of 250 grams and a standard deviation of y.
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).
To determine the graph that could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x, we need to understand the tolerance level of the company.
The company has a tolerance level of less than or equal to y grams for a 250-gram package. This means that any package of vegetables that weighs less than 250-y grams or more than 250+y grams will be rejected.
To graph this, we can plot the weight of the package on the x-axis and the probability of the package being rejected on the y-axis. The graph will have a normal distribution curve with a mean of 250 grams and a standard deviation of y.
Therefore, the graph that could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x, is a normal distribution curve with a mean of 250 grams and a standard deviation of y.
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What is the measure of each interior angle of a regular octagon? 45º 60º 120º 135º
Answers
The measure of each interior angle of a regular octagon is 135°.
An octagon is an eight-sided polygon with eight interior angles, and a regular octagon is an eight-sided polygon with eight interior angles of equal measure (congruent angles) and eight sides of equal length (congruent sides).
An octagon is composed of eight angles that sum to 1080 degrees.
The sum of the interior angles of a polygon with n sides is (n-2)×180°.
To get the interior angle, you must divide the sum of the interior angles by the number of sides.
A regular octagon has eight sides, so to find the measure of each interior angle of a regular octagon, divide the sum of
the interior angles by eight.
Sum of interior angles = (n-2)×180°
= (8-2)×180°
= 6 × 180°
= 1080°
Measure of each interior angle of a regular octagon = 1080°/8= 135°
Therefore, the measure of each interior angle of a regular octagon is 135°.Answer: 135°.
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Answer: The answer is D 135º
Step-by-step explanation: it is show below
while bowling with freinds, bradly rolls a stirke in 8 out o f10 frames. what is the experimental probabillty that bradly will role a stike in the first frame of the next game?
Answers
The experimental prοbability οf Bradley rοlling a strike in the first frame οf the next game is alsο 0.8 οr 80%.
What is prοbability?The likelihοοd οr chance that an event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 indicates an imprοbable event and 1 indicates a certain event. A given event's prοbability is determined by dividing the number οf pοssible οutcοmes by the number οf ways the event cοuld οccur.
The experimental prοbability is the ratiο οf the number οf times an event οccurs tο the tοtal number οf trials.
In this case, Bradley rοlls a strike in 8 οut οf 10 frames, sο the experimental prοbability οf him rοlling a strike in a single frame is 8/10 οr 0.8.
Hence, each frame is independent οf the οthers, the experimental prοbability οf Bradley rοlling a strike in the first frame οf the next game is alsο 0.8 οr 80%.
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Gene bought 144.65 ounces of flour and she uses 0.5 ounces of it to make biscuits how much is left 
Answers
Answer:
After making biscuits, Gene would have 144.15 ounces of flour left
True or false? To begin an indirect proof, you assume the inverse of what you
intend to prove is true.
OA. True
OB. False
PLEASE HELP ASAP
Answers
Answer:
the answer is A. true
Step-by-step explanation:
I had this question before
Abby tosses one penny and Babby tosses two pennies. What is the probability that Babby gets the same number of heads that Abby gets?
Answers
Babby has a 3/4 probability of obtaining the same number of heads as Abby.
What is probability?Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
The probability of an event happening is determined by probability: P(A) = f / N.
Probability and odds are related, but probability determines what the odds are.
So, the formula for probability is:
P(E) = Favourable events/Total events
Now, insert values:
Babby can get:
TT, HH, HT, TH
Abby will only get: H or T
Then,
P(E) = Favourable events/Total events
P(E) = 3/4
Therefore, Babby has a 3/4 probability of obtaining the same number of heads as Abby.
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(HELP!!) Express the trig ratios as fractions in simplest terms.
Answers
The answers for the following questions and fill uos are given below respectively.
Define the term trigonometry?Study of correlations between triangles' sides and angles is the focus of the mathematical field of trigonometry.
It solves mathematical problems, especially those involving geometric shapes and motion, by using the properties of triangle angles and sides.
We can use the given side lengths of the right triangle KJL to determine the trigonometric ratios:
sin K = opposite/hypotenuse = KJ/LK = 9/10
cos L = adjacent/hypotenuse = KJ/LK = 9/10
To express these trig ratios as fractions in simplest terms, we can simplify each fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. Therefore:
sin K = 9/10
cos L = 9/10
Since sin K is the ratio of the opposite side (KJ) to the hypotenuse (LK), it corresponds to angle K. Similarly, cos L is the ratio of the adjacent side (KJ) to the hypotenuse (LK), it corresponds to angle L.
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The ratio of the opposing side (KJ) to the hypotenuse is called sin K, which is equivalent to angle K. (LK). Cos L is the ratio of the neighboring side (KJ) to the hypotenuse and is related to angle L. (LK).
Define the term trigonometry?The area of mathematics known as trigonometry focuses on the analysis of relationships between shapes' sides and angles.
It uses the characteristics of triangle angles and sides to answer mathematical problems, particularly those involving geometric shapes and motion.
The trigonometric ratios can be calculated using the side lengths of the right triangle KJL as given:
sin K = opposite/hypotenuse = KJ/LK = 9/10
cos L = adjacent/hypotenuse = KJ/LK = 9/10
We can simplify each fraction by dividing the numerator as well as the denominator by their greatest common factor, which is 1 in this instance, to express these trig ratios as fractions in the simplest possible terms.
sin K = 9/10
cos L = 9/10
Sin K correlates to angle K because it is the ratio of the opposite side (KJ) to the hypotenuse (LK). Similar to cos L, which correlates to angle L, cos L is the ratio of the adjacent side (KJ) to the hypotenuse (LK).
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How do you find the surface area for this? Anything helps, thank you!
Answers
Answer:
99
Step-by-step explanation:
Take the whole shape apart, now, multiply every part on it using the formulas for each.
The area of the two triangle parts is 7.5+7.5=15
the side on the left would be found by doing 5*6=30
the middle side would be 6*6=36
and the right side would be 6*3=18
Add it all up to get 15+30+36+18=
15+66+18=
81+18=
99
Please help! Homework due tonight and I have yet to figure out this answer!
The perimeter of a garden is 20 feet. The area of the garden is 26 square feet. Draw this garden and label its length and width.
Answers
Answer:
The maximal area of the rectangle with the perimeter of 20 feet is 5*5 = 25 square feet.
So, the area can not be 26 square feet.
Step-by-step explanation:
wement of the progress bar may be uneven because questions can be worth more or less (including zero) depes
What is the slope of the line that contains the points (2, 5) and (4, -3)?
Answers
Answer: 75
Step-by-step explanation:
7+5=75
Find the volume of the rectangular prism.
10 m
Not drawn to scale.
21 m³
42 m³
240 m³
480 m³
Answers
2. Minor arc PQ in circle O below is 27. If angle PQO is 45°, what is the area of the shaded region?
Α) 2π
B) 4
C) 8
D) 16
Answers
The radius of the circle is approximately 16 units.
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
Here, ∠PQO = 45° So, ∠QPO = 45° (because OP = OQ radius)
So, central angle is 90°
The formula of arc length of a circle is :
arc length = [tex]\frac{central angle}{360} * (2\pi r)[/tex] ; here, the radius of the circle is r
Substituting the values we get:
27 = (90/360) x (2πr)
r = 54/π
Therefore, the radius of the circle is approximately 17.1 units.
by using radius we can find any area in circle.
So, nearby option D. is correct 16 units.
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. Create a box plot using 28, 34, 40, 24, 44, 49, and 32 as the data
ps: can you please draw a diagram and upload the pic here? i need it ASAP
Answers
Minimum: 24
Maximum: 49
Median: 34
First quartile: 28
Third quartile: 44
There are no outliers from the given data. The IQR is 16.
Here’s a drawing:
Hope this helps!
Consider parallelogram ABCD.
A parallelogram A B C D has the following angles labeled. D left parenthesis 85 plus y right parenthesis degrees, B left parenthesis 3 y minus 15 degrees right parenthesis degrees. The sides are labeled x minus 8 and 40 minus 2 x.
Which equation is made true by the opposite angles theorem?
A.
x − 8 = 40 − 2x
B.
40 − 2x = 85 + y
C.
x − 8 = 3y − 15
D.
3y − 15 = 85 + y
Answers
An equation which is made true by the opposite angles theorem include the following: D. 3y − 15 = 85 + y.
What is a parallelogram?In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.
According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:
(3y − 15)° = (85 + y)°
Next, we would determine the value of y as follows;
(3y − 15)° = (85 + y)°
3y - y = 85 + 15
2y = 100
y = 100/2
y = 50.
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Answer:
Step-by-step explanation:
the answer is [3y-15=85+y]
there are 4 baseball games during the week. the probability of a rainout is 10% for each game. assuming the weather each day is independent, what is the probability for at least one rainout
Answers
The probability that at least one game will be rained out during the week is 0.3439
To calculate the probability of at least one rainout, we need to calculate the probability that all four games will be played and then subtract it from 1.
The probability that a game will not be rained out is 1 - 0.1 = 0.9.
Therefore, the probability that all four games will be played is
= 0.9 x 0.9 x 0.9 x 0.9
Multiply the numbers
= 0.6561
So the probability that at least one game will be rained out is
= 1 - 0.6561
Subtract the numbers
= 0.3439
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