6
Find the length of the hypotenuse in the following figure,
16 km
12 km
Figure not drawn to scale
I
C=
Kilometers
Answers
Answer:
c = 20 Km
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other two sides , that is
c² = 12² + 16² = 144 + 256 = 400 ( take square root of both sides )
c = [tex]\sqrt{400}[/tex] = 20
Related Questions
Alice was having a conversation with her friend Trina, who had a discovery to share:
Pick any two integers. Look at the sum of their squares, the difference of their squares,
and twice the product of the two integers you chose. Those three numbers are the
sides of a right triangle.
a. Write an equation that models this conjecture using the variables x and y.
b. Investigate this conjecture for at least three pairs of integers. Does her trick
appear to work in all cases, or only in some cases? Explain.
c. Use Trina’s trick to find an example of a right triangle in which all of the sides
have integer length, all three sides are longer than 100 units, and the three side
lengths do not have common factors.
BONUS: If Trina’s conjecture is true, use the equation found in part a to prove the
conjecture. If it is not true, modify it so it is a true statement, and prove the new
statement
Answers
Answer:
a. (x² + y²)² = (x² - y²)² + (2xy)²
b. The conjecture works in all cases.
c. Sides of 119, 120, and 169
Step-by-step explanation:
a. Equation that models this conjecture
x² + y² = sum of squares
x² - y² = difference of square
2xy = twice the product of the integers
If these are the sides of a right triangle then
(x² + y²)² = (x² - y²)² + (2xy)²
b. Test the conjecture
(i) Try x = 2, y = 1
(2² + 1²)² = (2² - 1²)² + (2×2×1)²
5² = 3² + 4²
25 = 9 + 16
(ii) Try x = 3, y = 1
(3² + 1²)² = (3² - 1²)² + (2×3×1)²
10² = 8² + 6²
100 = 64 + 36
(iii) Try x = 3, y = 2
(3² + 2²)² = (3² - 2²)² + (2×3×2)²
13² = 5² + 12²
169 = 25 + 144
The conjecture appears to work in all cases.
c. A possible triangle
We must have one side greater than 100. That means,
x² > 100 or x >1 0.
Let x = 12
One side = 12² + y²
The second side = 12² - y²
The third side must have 2xy > 100
24y > 100
y > 4.2
Try y = 5
(12² + 5²)² = (12² - 5²)² + (2 × 12 × 5)²
169² = 119² + 120²
So, one right triangle could have sides of 119, 120, and 169.
Furthermore, these sides have no common factors.
Check:
169² = 119² + 120²
28561 = 14161 + 14400
28561 = 28561
Helppp with this question plzz
Answers
Answer:
306
Step-by-step explanation:
There are 102 triangles, a triangle has 3 sides, each side is 1 cm. 102 x 3=306
Miguel measured a house and its lot and made a scale drawing. The backyard, which is 40 feet wide in real life, is 20 inches wide in the drawing. What scale did Miguel use?
1 inch :
feet
Answers
Answer:
1 inch:2 feet
Step-by-step explanation:
Solve for T
V = x + at
Answers
Answer:
t=V‒x/a
Step-by-step explanation:
V=x+at (add ‒x in both side)
V‒x=x+at‒x
V‒x=at
V‒x/a=at/a
V‒x/a=t
so the formula is t=V‒x/a
What is the domain of the given function?
Answers
Answer:
b or c
Step-by-step explanation:
Carpet Plus installs carpet for $100 plus $8 per square yard of carpet. Carpet World charges $75 for installation and $10 per square yard of carpet. Find the number of square yards of carpet for which the cost including carpet and installation is the same.
Answers
Answer:
12.5 square yards.
Step-by-step explanation:
Let a square yard of carpet = x
The cost of installing a carpet is given by;
100 + 8x
The charge for installation
75 + 10x
The number of square yards of carpet for which the cost including carpet and installation is the same is given by;
100 + 8x = 75 + 10x
100 - 75 = 10x - 8x
25 = 2x
x = 25 / 2
x = 12.5 square yards.
Answer:
old post so answering for points
Step-by-step explanation:
a grocery store sells a 6-pack of bottled water for $3.79, a 9- pack for $4.50, and a 12-pack for $6.89. which package cost the least per bottle explain your reasoning ?
Answers
Answer:
Cost per bottle. Therefore cost/bottle. Set 1: 3.79/6=.63 Side note, don’t forget to round each time to the nearest cent. Set 2: 4.50/9=.50 Set 3: 6.89/12=.57 The second package (9-pack for $4.50) is the costs least per bottle.
Step-by-step explanation:
Please help!!
Find the equivalent rate:
300 miles in 20 seconds to miles per minute.
30 miles per min
15 miles per min
3 miles per min
Answers
Step-by-step explanation:
300/20 × 3/3 = 900/60
* 60 sec is 1 min therefore you want to get 60 secs in the denominator. In order to get that, you need to multiply.
900/60 divided by 60/60 is 15/1.
So 300m/20sec = 900m/60sec = 900mpm
If we're to do the same for all then it would be:
30m/20sec = 90m/60sec = 90mpm
15m/20sec = 45m/60sec = 45mpm
3m/20sec = 9m/60sec = 9mpm
Sammy scored an 80% on her math quiz. She answered 12 correctly. How many questions were on her quiz?
Answers
Answer:
15 questions
Step-by-step explanation:
If Sammy got 80%, we can see that 12/15=0.8, and 0.8 as a percentage is 80%.
Hope it helps!!
zachary has six times as many nickels as dimes and four times as many quarters as dimes. zachary has a total of ninety-nine nickels, dimes, and quarters. The total value of the coins is $12.60. How many of each coin does he have?
Answers
Answer:
nickels: 54dimes: 9quarters: 36Step-by-step explanation:
The ratio of nickels to dimes to quarters is given as ...
N : D : Q = 6 : 1 : 4
The total number of ratio units is 6 +1 +4 = 11. The total number of coins is given as 99, so each "ratio unit" must represent 99/11 = 9 coins. That is, the actual coin count ratios are ...
N : D : Q = 54 : 9 : 36
Zachary has 54 nickels, 9 dimes, and 36 quarters.
__
Check
The value of the coins is ...
$0.05 × 54 +$0.10 × 9 +$0.25 ×36 = $2.70 +0.90 + 9.00 = $12.60
A baby is b weeks old. How old will it be in five weeks time
Answers
Answer:
b(5)
Step-by-step explanation:
pls I am not sure
pls I really don't want any bad comment I already feeling bad
Friday’s temperature was 40 degrees and the temperature increased by 130% by Sunday evening. What was the temperature on Sunday evening?
Answers
Answer:
By Sunday evening the temperature would be 92 degrees
Step-by-step explanation:
Find 130% of 40
40 × 1.3 = 52
Add the product to your original temperature (40)
40 + 52 = 92
Please Help Me In Math
Will mark U Brainliest
!!!
#soconfused
Answers
Answer:
[tex]\tt volume=\boxed{6}\: units^3[/tex]
Step-by-step explanation:
[tex]\tt volume=(\frac{9}{2})(\frac{4}{3} )[/tex]
[tex]\tt volume=\frac{36}{6}[/tex]
[tex]\tt volume=6[/tex]
~
Tucker deposited $20,000 in a savings account with simple interest. Five years later, he had earned $14,000 in interest. What was the interest rate? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
the interest rate should be 14%
Vickie conducts a survey of home builders to determine the average cost of building a new home. She samples 10 home builders who are building in the town in which she lives. Under which conditions will her sample be a representative sample? Select two options.
Answers
Complete question is;
Vickie conducts a survey of home builders to determine the average cost of building a new home. She samples 10 home builders who are building in the town in which she lives. Under which conditions will her sample be a representative sample? Select two options:
A) The builders were chosen at random.
B) The population included only builders who build in Vicki’s town.
C) The population included builders who build homes in any town.
D) The population included builders who do not build homes in Vicki’s town.
E) The builders were referred to Vicki by the realtor who will be selling the houses.
Answer:
Options A & B are correct.
A) The builders were chosen at random.
B) The population included only builders who build in Vicki’s town.
Step-by-step explanation:
Looking at the question, we see that Vickie wanted to determine the cost of building a new home in the town in which she lived. Now, she sampled builders who are building in the town in which she lives and thus, it makes the sample more representative.
However, the random method of choosing the builders would help to remove any lingering biases that may arise.
Thus, we can conclude that the builders were chosen at random and that it included only those who build in her town.
Thus, options A & B are correct.
Answer:
A)The builders were chosen at random., B)The population included only builders who build in Vicki’s town.
Step-by-step explanation:
To get an A, you need more than 200 points on a two-part test. You score 109 points on the
first part. How many more points do you need?
Answers
Answer:
91 more points are needed
Step-by-step explanation:
Answer:91
Step-by-step explanation:
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Answers
We know that:
[tex]x - 11 \space\ and \space\ 2x + 8 \space\ are \space\ a \space\ linear \space\ pair. \space\ (Refer \space\ to \space\ attachment.)[/tex]This means that:
[tex](x - 11) + (2x + 8) = 180[/tex]Step-by step calculations:
Open the parenthesis:
[tex](x - 11) + (2x + 8) = 180[/tex]=> [tex]x - 11 + 2x + 8 = 180[/tex]Combine like terms:
=> [tex]x - 11 + 2x + 8 = 180[/tex]=> [tex](x + 2x) + (-11 + 8) = 180[/tex]Simplify the LHS:
=> [tex]3x - 3 = 180[/tex]Add 3 both sides:
=> [tex]3x - 3 = 180[/tex]=> [tex]3x - 3 + 3 = 180 + 3[/tex]=> [tex]3x = 183[/tex]Divide 3 both sides:
=> [tex]\frac{3x}{3} = \frac{183}{3}[/tex]=> [tex]x = 61[/tex]Same side exterior angles are linear pair and have sum 180°
[tex]\\ \rm\Rrightarrow x-11+2x+8=180[/tex]
[tex]\\ \rm\Rrightarrow 3x-3=180[/tex]
[tex]\\ \rm\Rrightarrow 3x=183[/tex]
[tex]\\ \rm\Rrightarrow x=61[/tex]
The distance between slits on a diffraction grating is 0. 60 mm, and one of the angles of diffraction is 0. 30°. The light forms a second-order bright band. How large is the path difference? 1047 nm 1571 nm 3142 nm 6284 nm.
Answers
The path difference will be 1571 nm
What will be the path difference?Now for the constructive interference, the formula is given
[tex]\rm dsin\theta==n\lambda[/tex]
here,
d = is the distance between slits.=060mm
θ = is the angle of diffraction=0.30 Degree
n = is the order of fringe=2
λ = is the path difference.
[tex]\lambda=\dfrac{(dsin\theta)}{n}[/tex] [tex]\lambda=\dfrac{(0.60\times10^{-3}\times sin(0.30)}{2} = 1.57\times10^{-6}[/tex]
Thus path difference will be 1571 nm
To know more about the Diffraction of light follow
https://brainly.com/question/16749356
The answer is C. 3142
3. In Figure 5.37 below, O is the centre of the circle PA and PB are tangents to the circle at A and B, respectively. If m(ZACB)=1150 ,then find: a. m(AB) b. m(ACB) . A o С P B Figure 5.37
Answers
You randomly draw a marble from a bag, record its color, and then replace it. You draw a red marble 3 out of 20 times. What is the experimental probability that the next marble will be red? Write your answer as a fraction, decimal, or percent. The experimental probability that the next marble will be red is
Answers
Answer:
3/20 or 0.15 or 15%
Step-by-step explanation:
Since 3 red marbles were drawn out of 20 outcomes, the probability the next marble will be red is 3/20. If you convert it to a decimal it will be 0.15, and if you convert it to a percent it will be 15%.
(PLS HELP)The diameter of a cylindrical water tank is 12 ft, and its height is 17 ft. What is the volume of the tank?
Use the value 3.14 for л, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
Answers
Answer: The volume is equal to 1922.65.
Step-by-step explanation:
Diameter is 12 ft, height is 17 ft.
V = πr2h
V = πr2h = π·62·17≈ 1922.65
The volume of the tank is approximately 1814 cubic feet.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
The formula for the volume of a cylinder is:
V = πr²h
where V is the volume, r is the radius, h is the height, and π is a constant equal to approximately 3.14.
We are given the diameter of the tank, which is 12 feet.
The radius is half the diameter, so:
r = 12/2 = 6 feet
We are also given the height of the tank, which is 17 feet.
Substituting these values into the formula, we get:
V = πr²h
V = 3.14 × 6² × 17
V ≈ 1814
Therefore,
The volume of the tank is approximately 1814 cubic feet.
Learn more about cylinder here:
https://brainly.com/question/15891031
#SPJ2
need this asap so if you know it please let me know quickly
Answers
Answer:
Step-by-step explanation:
-20d + 12
4(d + 9) - 8(-3d - 3)
4d + 36 - 24d - 24
4d - 24d + 36 - 24
-20d + 12
Please assist!!!! No links
Answers
Answer:
The choice C.
Step-by-step explanation:
[tex] {( \frac{ {2}^{ - 10} }{ {4}^{2} } )}^{7} = \frac{ {(2}^{ - 10}) ^{7} }{ {( {4}^{2}) }^{7} } = \frac{ {2}^{ - 10 \times 7} }{ {4}^{2 \times 7} } = \frac{ {2}^{ - 70} }{ {4}^{14} } \\ \\ = \frac{1}{ {2}^{70} \times {4}^{14} } [/tex]
due today
please help
Answers
Answer:
Hiking
Step-by-step explanation:
Given: Kayaking burns 4.5 calories per minute
The slope of the graph is 5
You can use rise over run to figure out the slope. Or you may have noticed the order pair (1,5)
This means hiking burns 5 calories per minute, which is greater than 4.5
The perimeter of a rectangular pool is 246 m.
If the width of the pool is 52 m, what is its length?
Answers
P=L+L+W+W
W= 52
So 52+52= 104
246-104= 142
Since that’s the two L added up divide by 2
142/2= 71
71+71+52+52= 246
Mr. Campbell decides that too many students are getting a pass on homework. He adds 10 yellow marbles to the jar. Tell whether each part of the probability model does or does not change.
The sample space change.
Each event within the sample space change. The probability of each event
change.
Answers
Answer:
The new probability of drawing a red marble is ()=.
Step-by-step explanation:
The sample space change. Each event within the sample space change. The probability of each event changes.
please answer this
9²+5x2+ 1³
Answers
Just need to add them up
Answer: your answer would be 92 .
Step-by-step explanation: all you have to do is add . hope this helped <3 .
What is the value of x in the equation -5/8x=-160
Answers
Answer:
x=256
Step-by-step explanation:
Answer:
x=256
Step-by-step explanation:
What value belongs next to the 1 in the table? What does it mean in this context?
Answers
Answer:
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
Step-by-step explanation:
The value next to 1 in the table above = number of dimes we have in 1 quarter.
Let the value next to 1 be "x".
That is:
1 quarter = x dimes
If 4 quarters = 10 dimes, then,
Cross multiply to find, how many dimes, x is equal to.
Thus:
1*10 = 4*x (cross multiplication)
10/4 = 4x/4 (dividing both sides by 4)
2.5 = x
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
how do i do 21 divided by 18
Answers
Answer:
Hello~Step-by-step explanation:
[tex]21 \div 18[/tex]
if you will use calculator you'll simply get the answer 1.16666667but simply you can put 1.1666