The side lengths of three triangles are shown in the table. Which of the triangles is a right triangle?
Answers
Answer:
Triangles I and III are right triangles, because they are similar to a 3-4-5 right triangle.
Step-by-step explanation:
The Pythagorean theorem tells you of the relationship between the sides of a right triangle. A set of integer side lengths that satisfies the Pythagorean theorem is called a Pythagorean triple. There are an infinite number of these, and there are formulas for finding them.
The smallest Pythagorean triple is {3, 4, 5}, and it is generally the first one you learn about. It is special for a variety of reasons. One of them is that it is the only Pythagorean triple that is an arithmetic sequence. Any multiple of a Pythagorean triple is also a set of side lengths that will form a right triangle.
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If we multiply the {3, 4, 5} triple by 2/10, we get {6/10, 8/10, 1}, which matches the side lengths of Triangle I in your list. Multiplying by 1/13 gives {3/13, 4/13, 5/13}, which matches the side lengths of Triangle III in your list. That means both Triangles I and III are right triangles.
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The Pythagorean theorem tells you that a right triangle with sides a, b, and hypotenuse c will satisfy the relation ...
c² = a² +b²
If the triangle is isosceles, such that a=b, then the hypotenuse will be ...
c² = a² +a² = 2a²
c = a√2
In reduced terms, the sides of an isosceles right triangle have the ratios ...
{1, 1, √2}
That is, there is no rational Pythagorean triple that describes an isosceles triangle. Triangle II cannot be a right triangle.
_____
Additional comment
Just so that you can see {3, 4, 5} is a Pythagorean triple, we show you ...
5² = 3² +4² ⇔ 25 = 9 + 16
Other small integer triples that may be seen in math problems are ...
{5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {11, 60, 61}, {12, 35, 37}
Related Questions
A bug is 1.2 cm up a wall and climbs up 1.7 cm each second. Another bug is 30 cm up the wall and climbs down 1.5 cm per second. After how many seconds will the bugs be the same height?
Seconds =
Answers
1.2 cm + ( 9 × 1.7 cm ) = 16.5 cm
30 cm - ( 9 × 1.5 cm ) = 16.5 cm
So the answer is 9 seconds!
Hope this helps :)
Let me know if my answer is incorrect or something :0
Consider the equation 2/x= 5/2x-1. Solve for x
Answers
Answer:
x=1.11651513…,−0.71651513…
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
A.P.E.X.
You pick a card at random. Without putting the first card back, you pick a second card at random.
(the numbers below are the cards)
6
7
8
9
What is the probability of picking a 7 and then picking a number greater than 7?
Write your answer as a fraction or whole number.
Answers
The probability of picking a 7 and then picking a number greater than 7 is 1/6.
What is probability?Probability is the likelihood of the occurrence of an event.
Sample space = {6 or 7 or 8 or 9}
So, favorable outcomes =1( we need 7)
Total outcomes = {6, 7, 8, 9} i.e. 4
So, the probability of picking a 7 in the first pick = 1/4
After the first pick, Sample space = {6 or 8 or 9}
So, favorable outcomes =2( we need 8>7 or 9>7)
Total outcomes = {6, 8, 9} i.e. 3
So, the probability of picking an 8 or 9 in the second pick = 2/3
Total probability = 1/4 * 2/3
Total probability = 1/6
Hence, the probability of picking a 7 and then picking a number greater than 7 is 1/6.
To get more about probability visit:
https://brainly.com/question/24756209
Part B:
The high temperature this Sunday is expected to be 5 degrees warmer than the high temperature this Saturday.
Using the line c = 2t - 89, how many more cups of lemonade should Lin expect to sell on Sunday than
Answers
Answer:
Lin should expect to sell 10 cups more
Step-by-step explanation:
The line c = 2t − 89 relates the cups Lin expect to sale (c) with the high temperature of the day (t)
If high temperature on Saturday is t1, then high temperature on Sunday is (t1+5)
Cups sold on Saturday are: 2t1 − 89
Cups sold on Sunday are: 2(t1+5) − 89 = 2t1 + 10 - 89
Cups sold on Sunday - Cups sold on Saturday:
2t1 + 10 - 89 - (2t1 − 89) = 2t1 + 10 - 89 - 2t1 + 89 = 10
What is the value of x?
(3x – 14)
x
[4(x – 9)°
Enter your answer in the box.
Next
Answers
22
pretty sure we are doing the same test
Willie had 55 baseball cards after trading with his friends. He traded 5 cards for one special card. Lee gave him 11 cards for a Mickey Mantel card. How many cards did Willie start with?
Answers
Answer:
49 baseball cards.
Step-by-step explanation:
First you want to add 5 cards to the 55 for the 5 he traded for the one. You get 60. Then subtract the 11 cards that he was given for the 1. You end up with 49 baseball cards.
What the square area with side length of 3/5 units
Answers
Answer:
9/25 units^2
Step-by-step explanation:
AREA(Square) = side * side = 3/5 *3/5 = 9/25 square units
Answer: 9/25 units ^2 :)
What would the equation be? First to ACTUALLY answer will be marked brainliest!! Plz and thank you
Answers
Answer:
y = 0.50 + 8
Step-by-step explanation:
The slope is .50 and the y-intercept is 8
y-int is the initial cost before adding toppings.
slope represents the cost of each topping.
What is the value of x in log2 (x) – 3 = 1?
Answers
Answer:
2^2
Step-by-step explanation:
2^2-3=1
Hope this helps!
Answer:
it is 2^2
Step-by-step explanation:
i did the iready diagnostic
The graph below shows the hours students spent studying and their science test scores.
Hours Spent Studying vs. Science Test Scores
A graph has hours spent studying on the x-axis and test score on the y-axis. A line has a regression equation of y = 3.1 x + 40.5.
A student gets a score of 70 on the test. Based on the trend line in the scatter plot, how much time did the student spend studying?
3.1 hours
4.5 hours
9.5 hours
40.5 hours
Answers
Answer:
(c) 9.5 hours
Step-by-step explanation:
The equation of the trend line predicts a score based on study hours. Here, we're asked for the inverse relation: finding a number of study hours based on a given score.
Inverse relationWe can solve the equation for x in terms of y:
y = 3.1x +40.5
y -40.5 = 3.1x . . . . subtract 40.5
(y -40.5)/3.1 = x . . . . divide by the coefficient of x
This tells us the number of hours spent studying for a particular score.
ApplicationUsing y=70, we find the number of study hours to be ...
x = (70 -40.5)/3.1 = 29.5/3.1 ≈ 9.516 ≈ 9.5
The student spent about 9.5 hours studying.
Bailey tossed a coin 10 times. the results were 7 heads and 3 tails. What is the best comparison between the theoretical and experimental probability of tossing heads?
Answers
Answer:
The theoretical probability is greater than the experimental probability.
The best comparison between the theoretical and experimental probability of tossing heads: The theoretical probability is equal to the experimental probability.
The theoretical probability of tossing heads can be calculated as the ratio of the number of favorable outcomes (heads) to the total number of possible outcomes (heads or tails). In a fair coin, this probability is 0.5 or 50%.
The experimental probability is determined by the outcomes observed in the experiment. In this case, Bailey observed 7 heads out of 10 tosses, which gives an experimental probability of 7/10 =0.7 or 70%.
Comparing the theoretical probability (0.5 or 50%) with the experimental probability (0.7 or 70%), we find that they are not exactly the same but quite close.
Given that the experimental probability is based on a limited number of trials (10 tosses), it may not perfectly match the theoretical probability. However, with more trials, the experimental probability tends to approach the theoretical probability.
Hence, the best comparison between the theoretical and experimental probability of tossing heads is that they are approximately equal.
Which of the following functions is equal to cos(90 - a)
A. Sec(a)
B. Tan(90 - a)
C. Csc(90 - a)
D. Sin (a)
Answers
Answer:
i think C
Step-by-step explanation:
Answer:
It's D sin(a)
Step-by-step explanation:
Which function is growing the fastest?
A) cubic C) linear
B) exponential D) quadratic
Answers
Answer: (C) the linear
Step-by-step explanation:
at x = 3 the y-value ... is growing
Answer:
Step-by-step explanation:
The rate of growth (the slope of the transformed curve) is first higher than for an exponential function, but later it goes down. ... Initially, the quadratic function grows much faster. The function x² grows from 0 to 1 in finite time, while the exponential function takes from minus infinity to 0.
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answers
Answer:
The area of the shaded region is 42.46 cm2
Step-by-step explanation:
Answer:
5 x 5 = 25
25 x 3.14 = 78.5
11 x11 = 121 - 78.5 = 42.5
42.5 cm
Step-by-step explanation:
y= 3x - 7
Complete the missing value in the solution to the equation.
(1, )
Answers
Answer:
(1, -4)
Step-by-step explanation:
y = 3x-7
Let x = 1
y = 3(1) -7
y = 3-7
y = -4
hi help me right now i am dunb
Answers
If the perimeter of a square is 14d+28 centimeters, what is the length, in centimeters, of each side of the square?
Answers
Answer:
Each side is (7/2d +4) cm
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side length
14d +28 = 4s
Divide each side by 4
14d/4 +28/4 = 4s/4
7/2d +7 = s
Each side is (7/2d +4) cm
what 3 numbers can be multiplied to make 106
Answers
Answer:
1 x 106 = 106
2 x 53 = 106
53 x 2 = 106
106 x 1 = 106
Step-by-step explanation:
(happy to help)
Answer:
1 x 106 = 106
2 x 53 = 106
53 x 2 = 106
106 x 1 = 106
Give me Brainliest Plz
can someone help me w #10 and #11
Answers
Answer:
10. Expanded vertically by 3, shifted left 2 and up 4.
11. Shifted right 6 and up 7.
Step-by-step explanation:
This sort of question involves matching patterns. You need to know what the various transformations look like, and what that means for a specific parent function.
Here are the transformations used in this problem:
f(x -a) . . . . shift f(x) to the right by "a" unitsf(x) +a . . . . shift f(x) up by "a" unitsa·f(x) . . . . . vertically scale f(x) by a factor of "a"For these problems, the parent function is f(x) = 1/x.
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10. The multiplier of 3 in the numerator (3/x) means the function has been scaled vertically (expanded) by a factor of 3.
The replacement of x with x+2 means the function has been shifted to the right by -2 units. That is the same as shifted left 2 units.
The addition of 4 to the function value means the function has been shifted up by 4 units.
__
11. We note the numerator is still 1, so there is no vertical expansion. The replacement of x with x-6 means a right shift by 6 units. The addition of 7 to the function value means a shift up by 7 units.
Dean's class took a field trip to the art museum. They left school at 11:45 A.M. It took them 45 minutes to drive to the museum. They stayed at the museum for 1 hour and 30 minutes. What time was it when Dean's class left the museum?
Answers
Answer:
2:00 p.m.
Step-by-step explanation:
driving to the museum is 12:30
then they sped 1 hour and 30 minutes
Jennifer buys a block of clay for an art project. The block is shaped like a cube with edge lengths of 12 inches.
a. Jennifer uses one piece of the cube to make spheres that have a diameter of 4 inches. How many spheres can she make?
b. Jennifer wants to keep the other piece of the cube for a future project. What is the area of the newly exposed surface from the wire cut?
Answers
Answer:
Volume of block Jennifer bought:
V = side^3 = 12 x 12 x 12 = 1728 (in3)
Volume of sphere Jennifer wanted to make:
V = (4/3) x pi x radius^3 = (4/3) x pi x (4/2)^3 = 33.5 (in3)
a, The number of spheres she can make:
N = 1728/33.5 = 51.58 = ~51
b, The area of remaining clay after she made a sphere:
A = 1728 - 33.5 = 1694.5 (in3)
Hope this helps!
:)
Element X decays radioactively with a half life of 10 minutes. If there are 510 grams
of Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 21 grams?
Answers
Answer:
46 minutes
Step-by-step explanation:
If AC = 20 and BC = 17 what is the radius
Answers
The radius of the circle is 10.5.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
AC = 20 and BC = 17
From the figure,
We apply the Pythagorean theorem.
So,
AC² = BC² + AB²
Substituting,
20² = 17² + AB²
AB² = 400 - 289
AB² = 111
Now,
Radius = AB
So,
AB = √111
AB = 10.535
Rounding to the nearest tenth.
AB = 10.5
Thus,
The radius of the circle is 10.5.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
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In the diagram, line x|| line y. Find the angle measures below.
Answers
Answer:
<1 = 95
<2 =85
Step-by-step explanation:
<1 = 95
They are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
<1 + <2 = 180 since they form a straight line
95+ <2 =190
Subtract 95 from each side
95-95+<2 =180-95
<2 =85
Please help on math.
Answers
Answer:
Total area= 207 ft^2
Step-by-step explanation:
You can divide the figure to make 2 big rectangles.
The first has a base of 15 ft and a height of 15 ft
A1 = b * h
A1= 15 ft * 9 ft A1= 135 ft^2
The second has a base of 12 ft and a height of 6 ft
A2= b*h
A2= 12 ft * 6 ft
A2= 72 ft^2
Total area= A1+A2= 135 ft^2 + 72 ft^2
Total area= 207 ft^2
Solve for d. 8d − 6 = 7d
Answers
Answer:1d
Step-by-step explanation:
Step-by-step explanation:
Bringing like terms on one side
8d - 7d = 6
d = 6
A store sells two types of coffee: House blend and Premium blend. Each bag of House blend contains 3 pounds of Type A beans and 2 pounds of Type B beans. Each bag of Premium blend contains 7 pounds of Type A beans and 3 pounds of Type B beans. The store can use at most 105 pounds of Type A beans and at most 60 pounds of Type B beans. Each bag of House blend sells for $6 and each bag of Premium blend sells for $10. How many bags of each type of coffee should the store make in order to maximize its revenue? What is the maximum revenue?
Answers
Answer:
do 3 dived by 2 they the awnser times seven then add 105 then multiply 60 then carry the 3 then add 10 and 6 then add 16 to the awnser and boom!
Step-by-step explanation:
Which represents the solution(s) of the equation x2 = 64?
A) x =
8
Eliminate
B) x = ±
8
C) x = −
64
D) x = ±
64
Answers
Answer:
A) x=8
Step-by-step explanation:
it can not be B because -8^2 = -64. it can't be either C or D because 64^2 = 4096 and doesn't equal 64.
Answer:
A
Step-by-step explanation:
Which of the following relations is a function?
A.
(2, 1), (-2, 4), (-5, 1), (2, -5)
B.
(-5, 4), (-2, 6), (-5, 3), (7, 2)
C.
(-5, 1), (-2, -5), (2, 5), (7, 1)
D.
(-5, 1), (-2, 4), (2, -5), (-2, 6)
Answers
Answer:
the answer is C
Step-by-step explanation:
The temperature at 4:00 P.M. was − 12°C. By 11:00 P.M. the temperature had dropped 14°C. What was the temperature at 11:00 P.M.?
Answers
Answer:
-26
Step-by-step explanation:
If the temperature dropped by 14 degrees than it decreased by 14, which means we subtract:
-12-14= -26