The Pythagorean Theorem and its Converse
6-9
Please answer all questions and solve step by step and please try to show/explain with the least words as possible and use mostly numbers to for explain there can still be some words tho.
Answers
Answer:
Question 6 & 9 is not a right-angled triangle. However, Question 7 & 8 is right-angled triangle.
Step-by-step explanation:
A triangle can be determined to be a right-angled triangle if and only if one of the following conditions is satisfied:
Pythagorean Theorem: If in a triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle. Symbolically, if a, b, and c are the lengths of the sides of the triangle, with c being the length of the hypotenuse, then a^2 + b^2 = c^2.
Angle criterion: If in a triangle, one of the angles is equal to 90 degrees, then the triangle is a right-angled triangle.
Right Angle Mark: If a triangle has a right angle mark (a small square) on one of its angles, then it is a right-angled triangle.
By using any one of the above methods, you can determine whether a triangle is a right-angled triangle or not.
So, Question no 6
Let the distance between three cities be a, b and c i.e. 45 miles, 56 miles and 72 miles.
using Pythagoras theorem,
a^2 + b^2 = c^2
45^2+56^2=72^2
2025+3136=5184
5161=5184
Hence, It's not a right-angled triangle.
So, Question no 7 has three sides a, b and c i.e. 4 ft, 3 ft and 5 ft.
using Pythagoras theorem,
a^2 + b^2 = c^2
4^2+3^2=5^2
16+9=25
25=25
Hence, it's a right-angled triangle.
Question no 8 also have three sides a, b and c i.e. 5 in, 12 in and 13 in.
using Pythagoras theorem,
a^2 + b^2 = c^2
5^2+12^2=13^2
25+144=169
169=169
Hence, it's a right-angled triangle.
Question no 9 also have three sides a, b and c i.e. 9.5 feet, 16 feet and 18.5 feet.
using Pythagoras theorem,
a^2 + b^2 = c^2
9.5^2+16^2=18.5^2
90.25+256=342.25
346.25=342.25
Hence, It's not a right-angled triangle.
Related Questions
2/7 divided by 6 equals?
Answers
Answer: 1/21
Step-by-step explanation: Change 6/1 to 1/6 and multiply
Answer:
Step-by-step explanation
If you've ready any of our fraction walkthroughs before, you'll know we always kick the show off with a quick recap for the kids. The number above the dividing line is the numerator, and the number below the line is the denominator. Simple stuff but sometimes we can all get a little forgetful!
To visualize the question we are trying to solve, let's put 2/7 and 6 side-by-side so it's easier to see:
2
7
÷ 6
So here is the incredibly easy way to figure out what 2/7 divided by 6 is. All we need to do here is keep the numerator exactly the same (2) and multiple the denominator by the whole number:
2
7 x 6
=
2
42
Can it possibly be that simply to divide a fraction by a whole number? Yup. I hate to disappoint you but this might be the easiest problem you've had to solve all day long!
In this particular case there is one slight adjustment we can make. The new fraction we have (2/42) can actually be simplified down to a smaller fraction:
your welcom
6/12 is equal to 1/2 how does the model you shaded in problem 5 show that and solve this one too Write a fraction from the box to complete the expression then complete the model to show the problem
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Answer:
Step-by-step explanation:
1/5=2/10
Some irrational numbers are whole numbers.
All whole numbers are rational numbers. true or false
No integers are irrational numbers. true or false
All integers are rational numbers. true or false
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Answer:
1 false
2 true
3 true
4 true
i need help on the true/false statement i dont get it
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2nd: False
3rd: True
4th: False
In triangle ABC, we have AB = 5, BC = 8, and AC = 7, as shown below:
Calculate: cos(angle A), cos(angle B), cos(angle C)
Please don't post any absurd answers, they will be reported
Answers
The angles are;
A = 60
B = 38
C = 82
What is the cosine rule?The cosine rule is a mathematical formula used in trigonometry to determine the lengths of sides of a triangle, given the lengths of two sides and the measure of the angle between them. The cosine rule states that the square of the length of a side of a triangle is equal to the sum of the squares of the lengths of the other two sides, minus twice the product of the lengths of those sides and the cosine of the angle between them.
c^2 = a^2 + b^2 - 2abCos C
7^2 = 5^2 + 8^2 - 2(5 *8) Cos C
49 = 25 + 64 - 80 CosC
-40 = -80 CosC
Cos C = 0.5
C = 60°
b^2 = a^2 + c^2 - 2ac Cos B
5^2 = 8^2 + 7^2 - 2(8 *7) Cos B
25 = 64 + 49 - 112Cos B
Cos B = 38
C = 180 - (60 + 38)
A = 82
Learn more about cosine:https://brainly.com/question/29114352
#SPJ1
Sebastian is making gingerbread cookies and lemon bars for a holiday party. He needs 2.5 times as much sugar for the bars as he needs for the cookies. If his gingerbread cookie recipe calls for 1.5 cups of sugar, how much sugar does Sebastian need for the lemon bars?
Answers
Answer:
3.75 cups of sugar
Step-by-step explanation:
if he needs 2.5 times as much sugar as 1.5 cups of sugar, he needs
2.5x1.5= 3.75 cups of sugar
Can someone please explain??
Answers
Answer:
Step-by-step explanation:
divide by 6
2k+8=-8
subtract 8 in both sides
2k=-16
divide by 2
k=-8
equal to -8
In order to solve for k you always want to try and isolate the variable (trying to get only k on one side of the equal sign). You can start of by distributing 6 into the numbers in the parenthesis. So 6 times 2k is 12k and 6 times 8 is 48. So in reality, you now have 12k+48= -48. Then you can subtract 48 from the left side to cancel it out. Note: you would not add 48 to cancel out the -48 on the right because you need a number on both sides of the equal sign. So once you subtract -48 from one side you must do it to the other so -48-48 is -96. Now you have 12k=-96. All you have to do now is cancel out the 12k but dividing since it is the inverse of multiplying. Divide 12 from both sides and -96 divided by 12 is -8.
So your answer is k=-8
Khalil read 88 pages in 2 2/3 hours. At what rate, in pages per hour, did he read? At what rate, in pages per hour, did he read?
First, reason down from 2 2/3 to 1/3 Enter all values as fractions (proper or improper) or whole numbers. You will need to convert mixed numbers to improper fractions.
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Answer:24 im pretty sure
Step-by-step explanation:
Please help me with this!
If you answer this correctly, I will give you thanks, a 5-star rating, and brainliest!
Answers
Answer: A
The
Step-by-step explanation:
what is it? i don't get it
Answers
Answer:
The part of the whole was not converted to a decimal or fraction
Step-by-step explanation:
700 is not 35% of 20.
This can be concluded with the product not being calculated properly to calculate 35% of 20.
We first need to turn 35% (whole number) into a decimal of 0.35 to figure out the percentage.
so the actual calculation:
0.35x20
= 7
Correct the error:
ANS: 7 is 35% of 20.
Answer:
B; 7
Step-by-step explanation:
35% = 0.35 (decimal form)
Therefore: 0.35 x 20 = 7
PLEASE HELP 65 POINTS
Answers
Answer:
1. 40π
2. 7
3. It's probably wrong because you didn't screenshot the whole chart.
help with this topic pls
Answers
The second one is = False
The third one is = True
The fourth one is = True
————————————————————————————————————————————
This is because integers are negatives and positives whole numbers.
Rational numbers are numbers or decimals that repeat, or numbers/decimals that terminate/end.
Irrational numbers are numbers or decimals that doesn’t repeat and goes on and on forever. Irrational numbers could be Pi = 3.14159265….
Hopefully this helped. If you have any questions, please ask me! Have a great day!
Find 62% of 50. Show your work or explain how you arrived at your answer.
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Please help!! (I added a screenshot)
Answers
i am postitive its 40
Help me pls. This is a grade
Answers
Answer: He should knit at least 25 scarfs.
Step-by-step explanation:
can you please mark me brainliest?
[tex]a) \frac{cups.of.flour}{cookie} \\b) cups\\c) \frac{cookies}{cups.of.flour} \\d) cookies\\e) cookies[/tex]
Answers
Answer:
A). 1/8
B). 5 cups
C). 8/1
D). 40 cookies
E). 0 cookies
Angles
6-10
Please answer all questions and solve step by step and please try to show/explain with the least words as possible and use mostly numbers to for explain there can still be some words tho.
Answers
Answers for pictures 1, 2, &3
Question 1: P = 35 degrees
It is given to us that angles N and P are complementary.
Complementary angles means the sum of the angles = 90 degrees.
Because angles N and M are supplementary, meaning they = 180 degrees, you can subtract angle M from 180.
180 - M = N
180 - 125 = 55
N = 55 degrees
Now that we know N = 55 degrees, we subtract that from 90 degrees to find P for N + P = 90 degrees, so if we subtract 55 from 90 we will get the value of angle P.
90 - N = P
90 - 55 = 35
P = 35 degrees!
Question 2: Option 4
We are trying to figure out which angles are congruent to one another.
We can rule out option one, for angles 1 & 4 are supplementary meaning their sum = 180 degrees.
The same applies for options 2 & 3, leaving us with the correct answer, option 4. We can make sure this is true because angles 3 & 5 are alternate interior angles, and alternate interior angles of parallel lines are congruent.
Question 3: x = 5
The three different angles add up to 180 because they are a straight angle.
First, we need to find out what 9 and 10 are equal to.
To do so, we can subtract 85 from 180.
180 - 85 = 9x + 10x
9x + 10x = 95
Now that we have an equation, we can simplify to find the value of x.
9x + 10 = 95
19x = 95
Divide by 19 on each side to isolate the variable x
x = 5
Hope this helps!
Please help. I WILL make first person to answer brainliest.
Requirments:
Very simple explanation
Answer
No step by steps.
Thank you
Also sub to Graystillplays bc he is GOATED and hilarious
Answers
Answer:
1st term: 5m 2nd term:9
coefficient= 5
constant=9
Step-by-step explanation:
Answer:
Step-by-step explanation:
1st term: 5m 2nd term:9
coefficient= 5
constant=9
yw it is easy
Select the statement that correctly explains how to use the benchmark fraction one half to compare the fractions three eighths and six tenths.
three eighths is greater than six tenths because three eighths is greater than one half and six tenths is less than one half.
three eighths is equal to six tenths because three eighths is equal to one half and six tenths is equal to one half.
six tenths is less than three eighths because six tenths is less than one half and three eighths is greater than one half.
six tenths is greater than three eighths because six tenths is greater than one half and three eighths is less than one half.
Answers
Answer:
Step-by-step explanation:
b
this is important!! im trying to help my friend out with homework
Answers
Answer:
im sure its 12
Step-by-step explanation:
can someone help me with these
Answers
question 2: five goes into forty-one 8 times, so put the 8 to the left of “r”. multiply 5 x 8 = 40, and put the 40 below the 41. subtract 41-40= 1, meaning the 1 is what you put to the right of “r”.
question 3: six goes into twenty-seven 4 times, so put the four above the 27. multiply 6 x 4 = 24, so put the 24 below the 27. subtract 27-24= 3, meaning 3 is the number that goes to the right of “r”
Answer:
8.2
4.5
6.5
Step-by-step explanation:
Please Help!!
The equation and the tables represent two different functions. Use the equation and the table to answer the questions. This table represents C as a function of A.
Answers
Your first answer is correct, the 2nd one is wrong though. If you look at the table when c is 21 a is 5. The next one is 15 because if you plug 5 in the equation you get 15. Not sure about the third question I think c is right though. For the last one -3 is incorrect and should be 0, 12 is fine and 10 should be 5.
mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh!!!
Answers
Answer:
Step-by-step explanation:
(51-8)/51 = 43:51
Answer: what he said
Step-by-step explanation: XD
You can read 52 pages per hour. You read for an hour and a half. How many pages have you read? Explain or show how you know
Answers
Answer:
78 pages
Step-by-step explanation:
You can read 52 pages per hour and therefore in half an hour you can read:
52/2 = 26 pagesFor an hour and half you read:
52 + 26 = 78 pages1. 52 divided by 2 = 26 (this is how long you can read in a half an hour)
2. 52+26= 78 (this is how long you can read in an hour and a half)
I tried to explain as best as i could i hope this helps
A circle has an area of 144πcm². Calculate the circumference of the circle leaving your answer in terms of π
Answers
The circumference of the circle is 24π cm.
The area of a circle is given by the formula:
A = πr²
where A is the area of the circle and r is the radius.
In this problem, we know that the area of the circle is 144π cm^2. Substituting this value into the formula, we get:
144π = πr²
Dividing both sides by π, we get:
r² = 144
Taking the square root of both sides, we get:
r = 12
Therefore, the radius of the circle is 12 cm.
The circumference of a circle is given by the formula:
C = 2πr
Substituting the value of r, we get:
C = 2π(12)
Simplifying, we get:
C = 24π
Therefore, the circumference of the circle is 24π cm.
To learn more about the circumference of the circle,
https://brainly.com/question/20489969
Answer:
Therefore, the circumference of the circle is 24π cm.
Step-by-step explanation:
A circle's circumference is the distance around its outside.. It is similar to the perimeter of other shapes such as squares. Consider it to be the line that defines the shape.
The circle's circumference is 24 cm.
The area of a circle is:
A = πr²
where A denotes the circle's area and its radius.
In this problem, we know that the area of the circle is 144π [tex]cm^2.[/tex] Exchange this value into the formula, and we get.
144π = πr²
Divide π by both sides, and we get:
r² = 144
Take the square root on both sides, and we get:
r = 12
The radius of the circle is 12cm.
The circumference of a circle is:
C = 2πr
Exchange the value of r, we get:
C = 2π(12)
Finally, we get:
C = 24π
Therefore, the circumference of the circle is 24π cm.
To learn more about circumference of the circle,
https://brainly.com/question/28912364
To learn more about radius of the circle,
https://brainly.com/question/13449316
A burrito company uses the function C(x) = 1.74x2 to calculate the number of calories in a tortilla with a diameter of x inches.
a) Find the average rates of change for the function over the intervals 6 < x < 8 and 9 < x < 11.
b) Interpret the average rates of change.
c) What does the difference in the average rates of change mean in terms of the situation?
Answers
Answer:
7 and 11 are the rates
Step-by-step explanation:
trying to help a friend out with homework (again) can someone give an answer
Answers
Answer:
126cm³
Step-by-step explanation:
In order to find the volume of the cube, you must multiply all three units together. So we would multiply 7·6·3=42·3=126. Then since we multiplied 3 units together, our final answer is 126cm³
Answer:
Hello!!! :)))
A=2(wl+hl+hw)=2·(3·6+7·6+7·3)=162
Answer: 162 cm2
Hint when finding the surface area it will be [tex]cm^{2}[/tex], [tex]in^{2}[/tex] , [tex]ft^{2}[/tex] , etc.
whyyyyyyyyyyy mattttttttttttth!!!
Answers
Answer:the third one
Step-by-step explanation: 0.45 is just 45/100
Answer:
C.
Step-by-step explanation:
Can you click the crown on this answer please? Thanks!
HELP ASAP PLSSS
SMALL BOX Unit Rate
DOLLAR PER OUNCE?
_______
LARGE BOX Unit Rate
DOLLAR PER OUNCE?
_______
SMALL BOX Unit Rate
OUNCES PER DOLLAR?
_______
LARGE BOX Unit Rate
OUNCES PER DOLLAR?
_______
The SMALL BOX/LARGE BOX is a better buy because it costs MORE/LESS dollars per ounce.
The SMALL BOX/LARGE BOX is a better buy because you receive MORE/LESS ounces per dollar.
Answers
2) Large box is $0.41 per ounce
3) Small box is 2.63 ounce per dollar
4) Large box is 2.44 ounce per dollar
5) The SMALL BOX is a better buy because it costs LESS dollars per ounce
6) The LARGE BOX is a better buy because you receive MORE ounces per dollar
Hope this helped!
Find the equation of the axis of symmetry of the parabola. Each box in the grid represents 1 unit.
Answers
Answer:
The line x=b2a will serve as the parabola's axis of symmetry.
Detailed explanation:
Graph the parabola y=x2−7x+2 .
To get the values of a, b, and c, compare the equation with y=ax2+bx+c.
In this case, a=1, b=7, and c=2.
To write the axis of the symmetry equation, use the coefficient values.
The line x=b2a serves as the axis of symmetry for a quadratic equation of the form y=ax2+bx+c. Therefore, x=(7)2(1) or x=72 is the equation of the axis of symmetry of the given parabola.
To determine the vertex's y coordinate, change x=72 in the equation.
y=(72)2−7(72)+2 =494−492+2 =49 − 98 + 84 =−414
The vertex's coordinates are (72, 414) as a result.