Choose the set of three sides that correctly matches each description. Each option will be used only once.
Answers
Answers:
30-60-90 triangle = 4, 8, 4*sqrt(3)45-45-90 triangle = 6, 6, 6*sqrt(2)Right triangle, but not special right triangle = 6, 8, 10Triangle but not a right triangle = 7, 8, 10Not a triangle = 7, 12, 19======================================================
Explanation:
The template for a 30-60-90 triangle is that the short leg x leads to hypotenuse 2x, and longer leg x*sqrt(3). If x = 4, then we get the sides 4, 8, 4*sqrt(3) which are the short leg, hypotenuse, and long leg in that order.
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The template for a 45-45-90 triangle is that we have x as the leg length and x*sqrt(2) as the hypotenuse. If x = 6, then we end up with the sides 6, 6, 6*sqrt(2)
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The triangle with sides 6, 8, 10 is a right triangle because a = 6, b = 8, c = 10 makes a^2+b^2 = c^2 true. I'm using the converse of the pythagorean theorem. We don't have a special right triangle because these sides do not fit the templates mentioned in the previous two sections above.
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The triangle with sides a = 7, b = 8, c = 10 on the other hand will not make a^2+b^2 = c^2 true. Note that a^2+b^2 = 7^2+8^2 = 113 which is not the same as 10^2 = 100. However, a triangle is possible because adding any two sides leads to a sum larger than the third side (triangle inequality theorem).
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We cannot form a triangle with sides 7, 12, 19 because the sides 7 and 12 add to 7+12 = 19 but that's not longer than the third side 19.
The triangle inequality theorem says that if you want to form a triangle with sides a,b,c then the following three inequalities must all be true
a+b > c
a+c > b
b+c > a
Related Questions
On selling an article for Rs 2300, a shopkeeper made a profit of 15 %. find the cost price of the article.
Answers
Answer:
Step-by-step explanation:
Sp of an article= Rs 2300
profit%=15%
let Cost Price of an article be X
SP=CP+PROFIT %*CP
2300=X+15/100*X
2300=100X+15X/100
2300*100=115X
230000/115=X
2000=X
Therefore cost price of an article is Rs 2000.
What is the area of a rectangle whose side lengths are o and g?
Answers
Answer:
Area=Base length x Height
Area= O x g.
Two odd numbers are selected at random from integers 11 through 22. Find the
probability that the two numbers are multiples of 3 after replacing first? JUST
SHOW MATH!*
Answers
Probability that the two numbers are multiples of 3 after replacing first
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The odd integers from11 to 22 are
11,13,15,17,19,21
So there are 6 events
Out of these 6 numbers, 2 numbers (15,21) are multiples of 3.
One number out of these 2 numbers can be chosen in 2 ways.
Therefore, favourable number of elementary events = 2.
Required probability =2/6=1/3
Hence 1/3 is the probability that the two numbers are multiples of 3 after replacing first
To learn more on probability click:
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I need help with this question
Answers
-3 -12 -5 in that order
Answer:
-3
-12
-33
Step-by-step explanation:
sorry if i m wrong.
pleaseeeee helppppp!!!!! I have to turn this in...!!!
Answers
Which statement describes the linear graph
Answers
Answer:
B.
Step-by-step explanation:
what is 10^x=1/100?
solve for x
Answers
Answer:
10^x=1/100
10^x=10^-10
x=-10
Step-by-step explanation:
4 – (3 – 5) =
Possible Answers:
A. -4
B. -2
C. 6
D. 12
Answers
Answer:
6
Step-by-step explanation:
4 – (3 – 5) =
PEMDAS says parentheses first
4 – (-2) =
Subtracting a negative is like adding
4 +2
6
Answer:
2-
Step-by-step explanation:
.....................................................................
ILL GIVE YOU BRAINLIEST!!
Answers
Answer:
10[tex]\pi[/tex]
Step-by-step explanation:
Length of arc = [tex]\frac{theta }{360} * 2\pi r[/tex]
= [tex]\frac{150}{360} * 2 \pi * 12\\[/tex]
= [tex]10\pi[/tex]
heya heya heya math question please
thanks in advance :')
Answers
Jennifer invested $400 at 6% interest compounded continuously. Write a model m(t) that represents the money in Jennifer's account in t years. A. B. How much money is in Jennifer's account after 5 years? Round to the nearest cent. C. Approximately when will Jennifer have $800 in her account? Round to the nearest tenth of a year.
Answers
Answer:
11.5 years
Step-by-step explanation:
Given data
Principal= $400
Rate= 6%
For the compound interest at time t, the expression is given as
A= P(1+r)^t
Substitute
A= 400(1+0.06)^t
A=400(1.06)^t
B. How much money is in Jennifer's account after 5 years
put t= 5
A=400(1.06)^5
A=400*1.338
A=$535.2
C. Approximately when will Jennifer have $800 in her account
A=$800
P=$400
r=6%
t= ln(A/P)/r
t= ln(800/400)/0.06
t= ln(2)/0.06
t= 0.6931/0.06
t=11.551
Hence the time is about 11.5 years
Use the equation below to find c, if a = 39 and b= 27.
c=180-a-b
c=0
X
5 ?
Answers
Answer:
the answer is 114
Step-by-step explanation:
Select the correct answer from the drop-down menu.
Consider this system of linear equations:
y- x= -13
-4x + 3y = -51
The solution of the system of equations is
Reset
Next
Answers
Answer:
y - x= - 13 -------(1)
- 4x + 3y = -51 -------(2)
(1) => y = - 13 + x
Substitute y in (2)
- 4x + 3( - 13 + x) = -51
- 4x - 39 + 3x = -51
- x = -51 + 39
- x = -12
x = 12
Substitute x in (1)
y = - 13 + x = -13 + 12 = - 1
x = 12, y = -1
what is the domain of the relation enter each value on the same line separated by commas. consider the relation { (9,1), (4,5), (6,2), (8,6), (1,2)}
Answers
Answer:
D = {1, 4, 6, 8, 9}
Step-by-step explanation:
A relationship maps elements from a set (the domain, the set of the inputs) into elements from another set (the range, set of the outputs).
Such that the usual notation is: (x, y)
this says that the relationship maps the element x into the element y.
In this case, we have the relation:
" { (9,1), (4,5), (6,2), (8,6), (1,2)}"
The inputs are the first value for each pair, then the set of the inputs (also called the domain) is:
D = {9, 4, 6, 8, 1}
And we can rewrite this in order to get:
D = {1, 4, 6, 8, 9}
HELP ME PLEASEESWSAS
Solve the following equation for x.
2 + x^2 = 47
6.7
b. 7
22.5
d. 47
Answers
Answer:
6.7
Step-by-step explanation:
x² = 45
x = 6.7
is the answer
Please help me!
Find the indicated sum for each sequence.
S9 of –9, 36, –144, 576, ...
Answers
Answer:
the answer is to multliply it by -4
Item 23 Find the sale price. Original price: $50 Discount: 15% Item 23 Find the sale price. Original price: $50 Discount: 15%
Answers
Answer:
$42.50
Step-by-step explanation:
discount reduces the price of the good
discount value = 15% x 50 = 0.15 x 50 = 7.5
sales price = 50 - 7.5 = 42.50
If you live in a rectangular city that is 1 mile along the southern border and contains 1000 people, what is the density of people in the city?
Group of answer choices
A. We cannot calculate this value.
B. 1000 people per square mile
C. 1 person per square mile
D. 100 people per square mile
Answers
Answer:
A. We cannot calculate this value.
Step-by-step explanation:
Had it on my test c:
We cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.
What is population density?It is defined as the ratio of the population to the total area. The population density represents the average number of people living on each square unit.
We have:
If you live in a rectangular city that is 1 mile along the southern border and contains 1000 people,
As we know,
population density = number of people/area of the region
As we have a rectangular city,
The area of the city = length×width
Width is not given so we cannot find the area of the region.
Thus, we cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.
Learn more about the population density here:
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A hockey goalie got shot on 18 times . She saved 10 of the shots . Which ratio represents the amount of shots that went in to the amount of shots she saved ?
Answers
========================================================
Explanation:
She saved 10 shots out of 18 total, so that means 18-10 = 8 shots went in.
That forms the ratio 8:10 where we list the amount of shots that went in, followed by a colon, then the amount of shots that were saved. The order is important. From here, we divide both parts of the ratio by 2. The ratio 8:10 fully reduces to 4:5
Effectively, this means that for every 4 shots that went in, there were 5 shots that were blocked.
Saved shots: 10
Shot in: 8
8:10 -> 4:5 (simplified)
when the crispy rice treats cool, mrs.williams cuts them into 30 equal pieces. she gives two-fifths of the treats will mrs.willimas take to school.
a. 18 treats
a. 19 treats
c. 14 treats
d. 16 treats
Answers
Answer:
18 treats
Step-by-step explanation:
If she gives 2/5 of 30 = 12
so 3/5 of 30 is 18 (also 30-12 =18)
Oscar rides his skateboard 58
5
8
mile in 14
1
4
hour. How fast, in miles per hour, does he ride his skateboard?
Answers
Answer:
about 4.1 miles per hour
Azlyn can ride her horse 15.2 miles per hour. She is in an endurance race that is 76 miles
long! How long should this race take her to complete?
Answers
Step-by-step explanation:
Remember, math is a language
when you see per think fractions
15.2 miles per hour = 15.2 miles / 1 hour
since this is a fraction, Units can cancel just like numbers
To cancel miles and be left with hours rearrange the fraction
1 hour / 15.2 miles
then multiply by 72 miles
[tex] \frac{1hour}{15.2miles} \times 72miles[/tex]
the miles cancel and youre left with hours!
so youd write and solve 72 / 15.2
The value of which of these expressions is closest to e?
Answers
Answer:
the answer is D
Step-by-step explanation:
Got it wrong on the A*pex test D is the correct answer
1+(1/30)30
simplify 5^-2
please help me! i don't know how to do it and its due today
Answers
0.04
jndjnwjnc jwnfjnjwfjn jn jnwjnj njnfjbfwhijfkwb jnj nwjnjfjwkf n
please answer this question
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
[tex]\frac{3}{7}[/tex] a × - [tex]\frac{21}{15}[/tex] b ( cancel 3 and 15 and 7 and 21 )
= a × - [tex]\frac{3}{5}[/tex] b
= - [tex]\frac{3}{5}[/tex] ab
(b)
3xy(5x²y² - 4yz) ← multiply each term in the parenthesis by 3xy
= 15x³y³ - 12xy²z
Molly and her friends just dined at a restaurant and left a tip of $20.54, which was equal to exactly 30% of the total bill. What was the total bill in dollars? Round your answer to two decimal places.
Answers
Answer:
68.47
Step-by-step explanation:
30%=0.3
20.54/0.3=68.4666……
A cone has a height of 10 millimeters and a radius of 6 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Answer:[tex]376.80\ mm^3[/tex]
Step-by-step explanation:
Given
The height of the cone is [tex]h=10\ mm[/tex]
The radius of the cone is [tex]r=6\ mm[/tex]
Volume of cone is given by
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Insert the values
[tex]\Rightarrow V=\dfrac{1}{3}\times 3.14\times 6^2\times 10\\\\\Rightarrow V=376.80\ mm^3[/tex]
Thus, the volume of the cone is [tex]376.80\ mm^3[/tex]
Please help me this is due tomorrow thank you
Answers
Answer:
The answer is option B.
Step-by-step explanation:
Answer: D
Step-by-step explanation:
The histogram shows driving to work so A even though it looks like it may fit there is no way to assume they don’t drive at all
Hope this helps
The owners of a large pet store have determined that 65\ee, percent of their customers own dogs. They select 151515 customers at random to survey. Let DDD be the number of customers they survey who have dogs.What type of variable is DDD
Answers
Answer:
D is a binomial random variable with [tex]p = 0.65, n = 15[/tex]
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they have dogs, or they do not. The probability of a customer having a dog is independent of any other customer. This means that D is a binomial random variable.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
65% of the customers have dogs:
This means that [tex]p = 0.65[/tex]
15 customers:
This means that [tex]n = 15[/tex]
What type of variable is D?
D is a binomial random variable with [tex]p = 0.65, n = 15[/tex]
Answer:
binomial
Step-by-step explanation:
Solve -2y+1=y-5
Y=6
Y=-6
Y=-2
Y=3
Answers
Answer:
y=2
Step-by-step explanation:
-2y+1=y-5
Add 2y to each side
-2y+2y+1=y+2y-5
1 = 3y -5
Add 5 to each side
1+5 = 3y-5+5
6 = 3y
Divide each side by 3
6/3 = 3y/3
2 =y
Answer:
y=2
Step-by-step explanation:
Move y to the other side by subtracting by y on both sides:
-y-2y+1=y-y-5
-3y+1=-5
Move the 1 to the other side by subtracting by 1 on both sides:
-3y+1-1=-5-1
-3y=-6
Divide -3 on both sides to eliminate the -3 on y
-3y/-3=-6/-3
y=2