Answers
Answer:
C. 12, 8, 5
Step-by-step explanation:Side lengths of any triangle must conform to the triangle inequality theorem, which says that the sum of the lengths of any of the two sides of the triangle is greater than the length of the third side.
This means:
a + b > c
a + c > b
b + c > a
Let's check each of the options to see which set are possible lengths for a triangle:
A. 6, 5, 11
6 + 11 > 5 ===> 17 > 5
5 + 11 > 6 ===> 16 > 6
6 + 5 > 11 ===> 11 > 11 (INCORRECT. Does not confirm to tye theorem)
Therefore, this set cannot be possible side lengths for a triangle.
B. 8, 1, 2
8 + 1 > 2 ===> 9 > 2
1 + 2 > 8 ===> 3 > 8 (INCORRECT)
8 + 2 > 1 ===> 10 > 1
This set cannot be possible side lengths for a triangle.
C. 12, 8, 5
12 + 8 > 5 ===> 20 > 5
8 + 5 > 12 ===> 13 > 12
12 + 5 > 8 ===> 17 > 8
All are correct, therefore these are possible side lengths for a triangle.
Related Questions
If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a
Answers
Answer:
Step-by-step explanation:
[tex](a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\[/tex]
Solve for f(-7) plz thanks
Answers
Answer:
12
Step-by-step explanation:
If f(x) = 5 - x
Then f(-7) = 5 - (-7)
f(-7) = 5 + 7
f(-7) = 12
Aaron Lloyd what is a?
Answers
Answer:
Rugby lawyer
Step-by-step explanation:
Aaron is a partner in the firm’s dispute resolution division. He advises clients on a range of litigious and risk related matters, with particular expertise in the areas of corporate misconduct, white collar criminal and regulatory affairs, sports law and employment law. Aaron leads our sports law practice, and is a member of the firm’s health and safety, public law, and organisational integrity teams.
Well regarded by clients for his ability to analyse and strategise complex situations, Aaron is internationally recognised for his ability to implement pragmatic and commercial strategies to minimise risk and create opportunity. This ability has resulted in clients avoiding significant litigation and commercial consequences.
Aaron is an experienced advocate, having argued cases in the District Court, High Court, Employment Court, the Court of Appeal and Supreme Court of New Zealand, along with numerous tribunals.
He is recognised by international legal directories including by Chambers & Partners (Asia Pacific), Who’s Who Legal, Expert Guides, Best Lawyers and Doyles.
Before joining MinterEllisonRuddWatts Aaron practiced as a barrister with Paul Davison QC, and has lectured at the University of Auckland.
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. d) She will have a hard time focusing.
Answers
When you have a clean/ neat workspace, you are more productive.
Martina has 240 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing.
As shown below, one of the sides has length x (in meters).
x
Side along river
(a) Find a function that gives the area Ax of the field (in square meters) in terms of x.
=Ax
(b) What side length x gives the maximum area that the field can have?
Side lengthx:meters
(c) What is the maximum area that the field can have?
Maximum area:square meters
Answers
Answer:
Step-by-step explanation:
Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.
(a) If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is
240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:
240 - x = 2w so
[tex]w=120-.5x[/tex] The area for a rectangle is L * W, so our area using the lengths we have is
A(x) = x(120 - .5x) and we simplify:
A(x) = 120x - .5x² That's the answer to a.
Now for b and c, we will complete the square on this to get the vertex.
Begin by factoring out the -.5:
[tex]A(x)=-.5(x^2-240x)[/tex] Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:
[tex]A(x)=-.5(x^2-240x+14400)+7200[/tex] (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).
The perfect square binomial that results from this is
A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is
(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.
The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,
= x(240-2x)
= 240x - 2x²
Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.
Thus, the required solutions are mentioned above.
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ2
help giving brainilest, heart, and 5 stars
Answers
Answer:
4 = 6
5 = -17
Step-by-step explanation:
4. a² - b / b² - c
a² = 2² = 4
b = -2
4 - (-2) = 4 + 2 = 6
6 / b² - c = 6/4 - 3 = 6/1 = 6
4 = 6
5. -3x² + 2xy + 7
-3x² = -3 * -2² = -3 * 4 = -12
2xy = 2 * -2 * 3 = -4 * 3 = -12
-12 + -12 + 7 = -24 + 7 = -17
5 = -17
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answers
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ [tex]\frac{1}{\sqrt{x^{2} +y^{2} } }[/tex]dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4[tex]\leq x^{2} +y^{2} \leq 9[/tex]
Answers
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
True or False. A rational number can be expressed as the quotient a/b where b ≠ 0
Answers
Answer:
true. A rational number can be expressed as the quotient a/b where b ≠ 0
51.Tandin Dorji was married to five women. First woman had three
daughters and five sons and the youngest wife had two sons. Two
of the remaining wives had one son each. If the ratio of children of
5th wife was 1:3 with the children of other wives. How many
children does Tandin have
Answers
Answer:
Tandin has 16 children.
Step-by-step explanation:
Total of children:
3+5 = 8(first woman)
2(youngest wife)
1 + 1 = 2(two of the remaining wives)
So
8 + 2 + 2 = 12
If the ratio of children of 5th wife was 1:3 with the children of other wives.
Thus the 5th wife has 12/3 = 4 children.
How many children does Tandin have?
12 + 4 = 16
Tandin has 16 children.
Alice wants to estimate the percentage of people who plan
on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.
Answers
Answer:
"[tex]0.6450 < p < 0.723[/tex]" is the right solution.
Step-by-step explanation:
Given:
n = 380
x = 260
Point estimate,
[tex]\hat p = \frac{x}{n}[/tex]
[tex]=\frac{260}{380}[/tex]
[tex]=0.6842[/tex]
Critical value,
[tex]Zc = 1.645[/tex]
Standard error will be:
[tex]S.E = \sqrt{\frac{0.6842(1-0.6842)}{380} }[/tex]
[tex]=0.0238[/tex]
Margin of error will be:
[tex]E = Zc\times S.E[/tex]
[tex]=1.645\times 0.0238[/tex]
[tex]=0.0392[/tex]
hence,
Confidence level will be:
= [tex]\hat p \pm E[/tex]
= [tex]0.6842 \pm 0.0392[/tex]
= [tex]0.6450 < p < 0.723[/tex]
Which is a perfect square?
6’1
6’2
6’3
6’5
Answers
Answer:
6'2
Step-by-step explanation:
Hey community I thank you guys fir your help
Answers
Answer:
A, B, and E.
Step-by-step explanation:
A. 5^x * 5^x
= 5^x+x
=5^(2)(x)
=25^x
B. 5^2x
=5^(2)(x)
=25^x
C. 5*5^2x
=5^1+2x
D. 5*5^x
=5^1+x
E. (5*5)^x
=5^x*5^x
=5^(2)(x)
=25^x
F. 5^2*5^x
=5^2+x
Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answers
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
Manatees can swim in water up to 20 feet deep. Write an expression that represents the depth d, that a manatee can swim
Answers
Answer:
0 ≤ d ≤ 20
Step-by-step explanation:
You mention that Manatees can swim in water up to 20 feet deep. So, this means that the largest depth that he can swim is 20 feet, not more than this. Also, keep in mind that the depth can't be negative, so ----> 0 ≤ d ≤ 20 feet
We want to write an expression (an inequality actually) that defines the depth at which a manatee can swim. The inequality is: 0ft ≤ d ≤ 20ft.
We know that the manatees can swim in water up to 20 feet deep. This represents the maximum deep at which manatees can swim, the minimum is trivial, it would be 0ft (when the manatees are on the surface of the water).
Then we can write the inequality:
0ft ≤ d ≤ 20ft.
This gives the range of possible values of d, depth at which the manatee can swim.
If you want to learn more, you can read:
https://brainly.com/question/17675534
There are 768 beds in a hospital.
Each floor has 64 beds.
How many floors are there?
Answers
Answer:
12 floors
Step-by-step explanation:
768 ÷ 64 = 12.
Answer:
12
Step-by-step explanation:
768 divided by 64 =12
create a graph of 4.95 + 3.99
Answers
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
Can you please help me
Answers
Answer: 1/6
Step-by-step explanation:
Given:
4/9 and 11/18
Solve:
STEP ONE: Make the denominators equal by determining the LCM
LCM = Least Common Multiple
First Five multiples of 9 = 9, 18, 27, 36, 45
First FIve multiples of 18 = 18, 36, 54, 72, 90
As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.
STEP TWO: Compare the size and determine the greater one.
4/9 = (4 × 2) / (9 × 2) = 8/18
11/18 = 11/18
Since 11 > 8, therefore, 11/18 is greater than 8/18
STEP THREE: Find the difference between the two fractions.
11/18 - 4/9
=11/18 - 8/18
=(11 - 8) / 18
= 3 / 18
= 1/6
Hope this helps!! :)
Please let me know if you have any questions
Big sleds must hold 3 children and small sleds must hold 2 children. If 17 children want to go sledding at the same time, how many of each type of sled is needed?
Answers
Answer:
5 big sleds and 1 small sled
Given a sphere with radius r, the formula 4 r2 gives
O A. the volume
O B. the surface area
O c. the radius
O D. the cross-sectional area
Answers
Answer: surface area
Step-by-step explanation:
Find the lengths the missing side
Answers
Answer:
Short leg = x
Longer leg = 12
Hypotenuse = y
Short leg = 4√3
longer leg = 12
Hypotenuse = 8√3
Answered by GAUTHMATH
Add the first 12 terms of this sequence:
15, 45, 135, 405, 1215, ...
Answers
Answer:
Step-by-step explanation:
a₁ = 15
a₂/a₁ = 45/15 = 3
a₃/a₂ = 135/45 = 3
...
It is a geometric sequence with a common ratio r=3.
Sum of first 12 terms = a₁·(1-r¹²)/(1-r)
= 15·(1-3¹²)/(1-3)
= 15·(-531,441)/(-2)
= 3,985,800
PLEASE HELP ASAP
Solve the inequality [tex]\sqrt[3]{x+4} \ \textgreater \ \sqrt[2]{-x}[/tex]
A) x < 2
B) x > 2
C) x > –2
D) x < –2
Answers
Zoe earns 22.50 per hour plus 3% commission on sales. last week she worked 34 hours and made sales totalling 15280. Calculate her pay for the week.
Answers
Answer: $1,223.40.
Step-by-step explanation:
Since she earns $22.5 per hour, for 34 hours, she would earn:
$22.5 × 34 = $765
She earn 3% of her sales, therefore find 3% of $15,280:
$15280(3%) = $15280(0.03) = $458.4
Add them together:
$765 + $458.4 = $1223.4
9514 1404 393
Answer:
$1,223.40
Step-by-step explanation:
Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.
Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40
Pay = $1,223.40
Zoe's pay for the week is $1,223.40.
The length of the hypotenuse of a 30 -60 -90 triangle is 32. What are the lengths of the legs?
Answers
Answer:
16, 16(sqrt3)
Step-by-step explanation:
30-60-90 triangles follow a rule where the hypotenuse is 2 times the shortest leg, and the longer leg is sqrt3 times the shorter leg.
So, the sides are x, 2x, and (sqrt3)x.
If 2x = 32, then x = 16.
Therefore the two legs are 16 and 16(sqrt3)
you can search up 30-60-90 triangle for more information
Describe what is the most difficult part of solving equations, for you personally.
Answers
What do you personaly feel like is most dificult.
For me its rembering minus signs
Cho hình hộp chữ nhật ABCD A B C D
Answers
Answer:
A B C D
A×B×C×D
3×3×3×6
162
A canoeist paddled down a river a distance of 2 miles in 45 minutes. Paddling up-stream on his return, it took him 90 minutes. Find the rate of the canoe in still water.
Answers
When f(x) =-3 what is x?
Answers
Answer:
D or -1
Step-by-step explanation:
It says that f(x) is equal to -3.
f(x) is the same as y-values, and x is the same as the x-values on a coordinate grid because x is the independent variable, meaning y is the dependent variable, where f(x) depends on the value of x to find y.
So if y is -3, it can be found on the graph on the 4th line, so x = -1 when y = -3
Mike wants to buy a scooter worth R10000 but cannot afford so he opts for the hire purchase agreement which requires a 13% deposit and a 24 equal monthly installments at a rate of 15% per annum compounded monthly
A.How much will his deposit be?
B.calculate how much does he still need to pay after the deposit
C.calculate the monthly installment
Answers
Answer: I think the answer is A
Step-by-step explanation:
