Which set of line segments could create a right triangle? a 15, 30, 35 b 15, 36, 39 c 15, 20, 29 d 5, 15, 30
Answers
Final answer:
By applying the Pythagorean theorem, it's determined that the set of line segments that could create a right triangle is option b. (15, 36, 39), as it's the only set that satisfies the equation a² + b² = c².
Explanation:
The question asks which set of line segments could create a right triangle. To solve this, we apply the Pythagorean theorem, which states for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
For option a (15, 30, 35), applying the Pythagorean theorem: 15² + 30² = 225 + 900 = 1125, which is not equal to 35² (1225).For option b (15, 36, 39), we get: 15² + 36² = 225 + 1296 = 1521, and 39² = 1521, so this set satisfies the Pythagorean theorem.For option c (15, 20, 29), we have: 15² + 20² = 225 + 400 = 625, which is not equal to 29² (841).For option d (5, 15, 30), we get: 5² + 15² = 25 + 225 = 250, which is not equal to 30² (900).Therefore, the set of line segments that could create a right triangle is option b. (15, 36, 39).
Answer:
b. 15, 36, 39
Step-by-step explanation:
You want the set of line segments that could form a right triangle.
Pythagorean triplesA set of 3 integers is a Pythagorean triple if it satisfies the Pythagorean theorem:
a² +b² = c²
The most common primitive triples are {3, 4, 5}, {5, 12, 13}. If two of three numbers match these, but the third does not, a right triangle cannot be formed.
We note that {3, 4, 5} has the smallest first number of any Pythagorean triple, and it is the only triple that is an arithmetic sequence.
ChoicesWe can reduce the given numbers to their lowest form to see if we can determine whether any is a Pythagorean triple:
a. 15 : 30 : 35 = 3 : 6 : 7 . . . . . not a right triangle
b. 15 : 36 : 39 = 5 : 12 : 13 . . . . forms a right triangle
c. 15 : 20 : 29 = 3 : 4 : 5.8 . . . . . not a right triangle
d. 5 : 15 : 30 = 1 : 3 : 6 . . . . not a triangle
__
Additional comment
The attachment shows the values of a² +b² -c² for the different answer choices. That expression will evaluate to 0 if the numbers form a right triangle. If the sum is negative, any triangle formed would be obtuse. As we noted above, choice D values do not even form a triangle.
Other Pythagorean triples commonly seen in algebra problems are ...
{7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {20, 21, 29}
You may also notice that when the two largest numbers differ by 1, the smallest is the root of their sum: 3 = √(4+5), 5 = √(12+13), 7 = √(24+25), and so on. This is another way we can tell {3, 6, 7} is not a Pythagorean triple: 3 ≠ √(6+7).
Related Questions
20. What percent of 392 is 98? 22. 33% of what number is 145? 24, 17 is 40% of what number?
Answers
if we take 392 to be the 100%, what is 98 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 392&100\\ 98&p \end{array}\implies \cfrac{392}{98}=\cfrac{100}{p}\implies p=\cfrac{98\cdot 100}{392}[/tex]
22)
let's say is "x", so if "x" is the 100%, and we know that 145 is the 33%, what the dickens is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 145&33 \end{array}\implies \cfrac{x}{145}=\cfrac{100}{33}\implies x=\cfrac{145\cdot 100}{33}[/tex]
24)
again, if we take "x" to be the 100%, and we know that 17 is 40%, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 17&40 \end{array}\implies \cfrac{x}{17}=\cfrac{100}{40}\implies x=\cfrac{17\cdot 100}{40}[/tex]
how do you factor 30n^2b-87nb+30b?
Answers
I will assume the latter.
b can then be factored out of all three terms, resulting in
b [30n^2 - 87n + 30] = b [ 3 ] [10n^2 - 29n + 10 ]
Can you factor this further?
The surface area of an open-top box with length L, width W, and height H can be found using the formula: A= 2LH + 2WH + LW Find the surface area of an open-top box with length of 7 cm, width 6 cm, and height 3 cm.
Answers
Final answer:
The surface area of an open-top box with a length of 7 cm, width of 6 cm, and height of 3 cm is calculated using the formula and comes out to be 120 cm².
Explanation:
To find the surface area of an open-top box with given dimensions, we use the formula: A= 2LH + 2WH + LW. Substituting in the provided lengths for length (L), width (W), and height (H):
A = 2(7 cm)(3 cm) + 2(6 cm)(3 cm) + (7 cm)(6 cm)
A = 2(21 cm²) + 2(18 cm²) + 42 cm²
A = 42 cm² + 36 cm² + 42 cm²
A = 120 cm²
This gives us the total surface area of the open-top box which is 120 cm².
Lydia purchased a 15 cup bag of pasta. the suggested serving is 3/4 cup per person. how many servings are in a 15 cup bag of pasta
Answers
To find out how many servings are in a 15 cup bag of pasta when serving size is 3/4 cup per person, divide 15 by 3/4, which equals 20 servings.
Firstly, convert the mixed fraction into an improper fraction for easier division: 3/4 remains the same since it is already a proper fraction.
Now, carry out the division: 15 ÷ (3/4)
= 15 × (4/3) (You multiply by the reciprocal of 3/4)
Then, multiply the numbers:
= 15 × 4 ÷ 3
= 60 ÷ 3
= 20
Therefore, there are 20 servings in a 15 cup bag of pasta when the serving size is 3/4 cup per person.
After a discount of 10%, the price of a pair of jeans, including tax, was $69.62. The following equation can be used to find x, the price of the pair of jeans without the discount:
x - 0.1x + 0.07(x - 0.1x) = 69.62
What is the price of the pair of jeans without the discount?
A-$70.58
b-$72.29
c-$74.86
d-
Answers
First, we need to multiply all numbers that contain variable x
x -0.1 x + 0.07x - 0.007x = 69.62
0.963 x = 69.62
After this, we just need to find the value of x
x= 69.62 / 0.963
x = 72.29
The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?
Answers
This function can be called b(t(h)), or b(h).
Consider the function b(t), or bacteria as a function of temperature.
b(t) = 20t² - 70t +300
This describes the number of bacteria, given the temperature.
t(h) described the temperature as a function of time, specifically hours after refrigeration:
t(h) = 2h + 3
Since the time h can tell us the temperature t, and the temperature t can tell us the # of bacteria b, we can create a function that tells us the number of bacteria, b, given hours following refrigeration, h.
To do this, we plug t(h) in for every t in the b(t) function:
b(t(h)) = 20 (2h+3)² - 70(2h+3) + 300
We can also call this function b(h), since we now can express b as a function of h.
Simplify the function:
b(h) = 20 (4h²+12h+9)-14h-210+300
b(h) = 80h² +100h +270
The Answer is B
b(t) = 20t² - 70t + 300
t(h) = 2h + 3
Therefore
b(h) = 20(2h + 3)² - 70(2h + 3) + 300
= 20(4h² + 12h + 9) - 140h - 210 + 300
= 80h² + 240h + 180 - 140h - 210 + 300
= 80h² + 100h + 270
Answer: b(h) = 80h² + 100h + 270
What is 2r+7+r=? I'm not sure
Answers
Combine like terms.
(2r + r) + 7
Simplify.
3r + 7
~Hope I helped!~
Enjoy!!!
If (7^2)x = 1, what is the value of x? Explain your answer.
If (7^0)x = 1, what are the possible values of x? Explain your answer.
Answers
(7^2)x = 1
7^2 = 49
49x = 1
x = 1/49
(7^0)x=1
7^0 = 1 (anything raised to 0 = 1)
1x = 1
x = 1
What point in the feasible region maximizes the objective function constraints: x>=0 y>=0 -x+3>=y y<=1/3 x+1 Objective function: C=5x-4y Please explain!
Answers
Answer:
So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)
Step-by-step explanation:
When you graph all of the constraint functions, the vertices of the shape that is made are at the points above. Now you plug those points into the function equation C=5x-4y and see where you get a max or min.
(0,1)
(1.5,1.5)
(0,0)
(3,0)
(1,1)=C=1
(1.5,1.5)=C=1.5
(0,0)=C=0
(3,0)=C=15
So, the maximum of C is 15 at (3,0) and the minimum value is 0 at (0,0)
An airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 276 tickets.
a. what is the expected number of ticket holders that will fail to show for the flight?
Answers
2.76*4=11 rounded
11 people will fail to show
The expected number of ticket holders that will fail to show for the flight is 11.
Given that,
There is a fail percentage of 4%.There are 267 seats.And, the 276 airline tickets are sold.Based on the above information,
= 276%
= 2.76
Now the number of ticket holders who fail for presenting the flight should be
[tex]= 2.76\times 4[/tex]
= 11
Therefore we can conclude that the expected number of ticket holders that will fail to show for the flight is 11.
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Hello, I am taking Quantitative methods for business, which has a lot of excel based mathematics and I was wondering if anyone could help. Here is the question:
Refer to the table that illustrates customer’s complaints about a manufacturing company.
A. What is the probability a customer complained during the guarantee period?
B. What is the probability that a customer complained about an electrical problem or a mechanical problem?
Table is included in attachment. Also Thank you!!!
Answers
The probability that a customer complained during the guaranteed period is given by the number of costumers that complained during the guarantee period devided by the total number of students.
Therefore, the probability that a customer complained during the guaranteed period is [tex] \frac{1,890}{3,000} = \frac{63}{100} [/tex]
Part B:
The probability that a customer complained about an electrical problem or a mechanical problem is given by the sum of the probability that the customer complained about an electrical problem or the probability that the customer complained about a mechanical problem.
Therefore, the probability that a customer complained about an electrical problem or a mechanical problem is [tex] \frac{900}{3,000} + \frac{1,050}{3,000} = \frac{1,950}{3,000} = \frac{13}{20} [/tex]
Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?
Answers
f(x) = 3 (x + 4) (x - 6)
Now expand the parenthesis using the notable product
f(x) = 3 (x^2 - 2x - 24)
Now use distributive property:
f(x) = 3x^2 - 6x - 72
As you see it has leading coefficient 3 and you can demonstrate that the roots are - 4 and 6.
Answer: f(x) = 3x^2 - 6x - 72
The sum of any two consecutive prime numbers is also prime
Answers
Say the primes 7 and 11. Adding them gets us 7+11 = 18. This counter example disproves the initial claim since 18 = 9*2 = 6*3 making 18 composite (not prime)
In general, if we let p and q be two primes such that q > p > 2 and q is the next prime after p, then p and q are both odd. If any of them were even then they wouldn't be prime (2 would be a factor)
Adding any two odd numbers together leads to an even number
Proof:
p = 2k+1 where k is some integer
q = 2m+1 where m is some integer
p+q = 2k+1+2m+1 = 2(k+m) + 2 = 2(k+m+1) which is in the form of an even number
That proof above shows us that adding any prime larger than 2 to its next prime up leads to an even number. This further shows us that the claim is false overall. It is only true if you restrict yourself to the primes 2 and 3, which add to 5. Otherwise, the claim is false.
Help with #30 Please!
Answers
40 x 0.0039 = 0.0000975% chance
It is a exteremely low chance that those that left against medical advice.
Which means the others have a exteremely high percentage, of 99.0061% and 99.0000025% chance
hope this helps
Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?
Answers
6 rolls of dimes = $30.
6 rolls of quarters = $60.
Answer:
7 roll of quarter and 4 roll of dimes.
Step-by-step explanation:
Let x be the number of rolls of quarters and y be the number of rolls of dimes,
Given,
Total rolls = 11
⇒ x + y = 11 ------(1),
Also, the total value of $ 90 in which Each roll of quarters has a value of $10 and each roll of dimes has a value of $5.
⇒ 10x + 5y = 90 ------(2),
Equation (2) - 5 × Equation (1),
We get,
5x = 90 - 55
⇒ 5x = 35 ⇒ x = 7
From equation (1),
7 + y = 11 ⇒ y = 4
Hence, the number of roll of quarters = 7,
And, the number of roll of dimes = 4
what is an angle between a side of a polygon and the extension of its adjacent side
Answers
here's an example. hope it helps!
The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.
Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.
What is factor out the coefficient of the variable of 4h-3
Answers
4h - 3 = 4[h - 3/4]
Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the northeast?
Answers
The probability is 0.187 or 18.7% that the restaurant chosen at random is in the north east and is located in a city with a population over 500,000.
To find the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east, we really want to know the quantity of cafés that meet these two rules and are situated in the north east.
Let's look for this information using the table:
Northeast Midwest South West More than 500,000 Over 500,000 110 95 178 66 Less than 500,000 53 39 38 9 The table indicates that 110 restaurants are located in the north east of the United States in cities with more than 500,000 residents. In this manner, the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east is:
P(Northeast and North of 500,000) = 110/588 = 0.187
Thus, the likelihood is 0.187 or 18.7% that the café picked aimlessly is in the north east and is situated in a city with a populace more than 500,000.
The sum of two integers is greater than 12. One integer is 10 less than the other. What are the values of the integers?
Answers
x plus y is greater than 12
x + y > 12
One of the integers is ten less than twice the other one
x = 2y -10
Time to start solving:
(2y-10) + y > 12
2y + y > 12 + 10
3y > 22
3y=24
y=8
Now its time to find the value of x:
x=2(8) - 10
x=16-10
x= 6
6 + 8 > 12, 6+8 is greater than twelve.
In conclusion we can wrap up that 6 and 8 are the least value integers.
69.5 is What precent of 85?
Answers
6950 ÷ 85 = 81 percent
Kareem runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Answers
x 44 min
-------- = ------------
6 mi 55 min
Reduce this to x/6 = 1/11. Then 11x = 6, and x = 11/6 miles, or 1 5/6 miles.
55x = 264 => 4.8 miles in 44 minutes.
The sum of three consecutive integers is 90. Find the integers
Answers
The sum of three consecutive integers is 90. So you know that 3 numbers that are next to each other in numerical order equals 90.
First step: Make an equation:
Let's take x as the smallest of the three numbers.
[tex]x +(x+1)+(x+2)=90[/tex]
2nd step: Open the brackets:
[tex]x+x+1+x+2=90[/tex]
3rd step: Simplify:
[tex]3x+3=90[/tex]
4th step: Keep similar integers on one side of the equation
[tex]3x+3-3=90-3[/tex]
5th step: Solve for x:
[tex]3x=87[/tex]
[tex]\frac{3x}{3} =\frac{87}{3}[/tex]
[tex]x=29[/tex]
So if the numbers are consecutive, they have to be next to each other.
Answer: 29, 30, 31
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How l can write a brief summary about measurement for 3rd grade
Answers
You'd be best off by limiting your scope to a couple of familiar situations:
Weighing a piece of chocolate
Having your height and weight measured by the school nurse
Counting the number of coins in your pocket
Getting a rough measure of how well you have learned new material by checking how many questions you got right out of the whole test.
what percent of 176 is 17.6
Answers
To find 100% percent sure, multiply 17.6 *10
17.6 * 10 = 176
1. We assume, that the number 176 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 176 is 100%, so we can write it down as 176=100%.
4. We know, that x is 17.6% of the output value, so we can write it down as x=17.6%.
5. Now we have two simple equations:
1) 176=100%
2) x=17.6%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
176/x=100%/17.6%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 17.6% of 176
176/x=100/17.6
(176/x)*x=(100/17.6)*x - we multiply both sides of the equation by x
176=5.6818181818182*x - we divide both sides of the equation by (5.6818181818182) to get x
176/5.6818181818182=x
30.976=x
x=30.976
now we have:
17.6% of 176=30.976
you earn $70 per week mowing lawns one week you work 10 hours during the week and spend $20 on gasoline for your mower how much do you earn each hour
Answers
$50
------------------- = $5 per hour
10 hours
What is the smallest natural number that has three distinct prime factors in its factorization?
Answers
there are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each row
Answers
Write the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
A) y + 6 = -1(x – 5)
B) y – 6 = -1(x + 5)
C) y + 6 = 1(x – 5)
D) y – 6 = 1(x + 5)
Answers
[tex]y - y_1 = m(x - x_1)[/tex]
We need to find the slope. To find the slope we can use the following formula:
[tex]\frac{y_2 - y_1}{x_2 - X_1}[/tex]
Use the points (-5, 6) and (0, 1) and plug it into our slope formula and solve:
[tex]\frac{1 - 6}{0 - (-5)}[/tex]
[tex]\frac{-5}{5} = -1[/tex]
So our slope is -1 which means m = slope = -1
Now that we have our slope lets create the point slope form
Our point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex] Remember
m = slope = -1. Also, we are going to use the point (-5,6).
First insert the m = slope = -1 number where m is located
[tex]y - y_1 = -1(x - x_1)[/tex]
Next, insert the -5 from (-5,6) where [tex]x_1[/tex] is located and the 6 from (-5,6) where [tex]y_1[/tex] is located.
[tex]y - y_1 = -1(x - x_1)[/tex]
[tex]y - 6 = -1(x - (-5))[/tex]
Now simplify
[tex]y - 6 = -1(x - (-5))[/tex]
[tex]y - 6 = -1(x +5)[/tex] <-------Answer
The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\((-5, 6)\) and \((0, 1)\)[/tex]
Calculate the slope m:
[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]
Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
Now, simplify and compare with the given options:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
Sara bought two pounds of strawberries for $5.12. What is price in dollars per ounce of strawberries 1 pound =16 ounces
Answers
In an eye color study, 25 out of 50 people in the sample had brown eyes. in this situation, what does the number .50 represent?
Answers
The number .50 in the context of this question represents the proportion (or probability) of people in the sample who have brown eyes. It's calculated by dividing the count of individuals with brown eyes by the total number of individuals in the sample.
Explanation:In this context, the number .50 represents the proportion or probability of people with brown eyes in the sample. This number is obtained by dividing the number of people with brown eyes (25) by the total number of people in the sample (50).
Hence, .50 means there is a 50% chance that a randomly selected person from the sample will have brown eyes. This is often used in the field of statistics where proportions are utilized to represent probabilities of outcomes.
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