Which of the following are possible side
lengths for a triangle?
A. 8, 5, 7
B. 10, 3, 7
C. 9,5, 15
Answer:
A yes B No C Yes
Step-by-step explanation:
The length of the third side is greater than the difference and less than the sum of the two smallest sides.
8, 5, 7 Using the 5 and 7 the third side is > (7 - 5) and < (5 + 7)
the third side is > 2 and < 12 so 8 is OK
10, 3, 7 Use the two smallest number: 3 and 7
the third side is > (7 - 3) and < (3 + 7)
the third side is > 4 and < 10 No it is 10
9, 5, 15 Use the two smallest number 9, 5
the third side is > (9 - 5) and < (9 + 5)
the third side is > 4 and < 14 Yes
Answer:
A. 8, 5 , 7
Step-by-step explanation:
the other guy who answered gave two yes's so I chose one and A. was correct.
12. After 80 years of 5.8% interest compounded monthly, an account has $102,393.44. What was the
original deposit amount?
Answer:
12195508,42
Step-by-step explanation:
A(1-R) NA is the depositR is the % presentN is the time period (exponent)A(1-5.8%)80=102,393.44An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
What is meant by deposit?A deposit is money held at a bank. A deposit is a monetary transaction in which money is transferred to another party for safekeeping.A deposit is money placed in a bank account. Deposits are classified into two types: demand deposits and time deposits. Checking, savings, and money market accounts are all examples of demand deposit accounts. Certificates of deposit (CD) and individual retirement accounts are examples of time deposit accounts.Therefore,
Assume that each year has 52 weeks: then compounding occurs.
n = 52 × 80n
times and the rate for each compounding is
[tex]$i=\frac{5.8 \%}{52}=\frac{0.058}{52}$[/tex]
If the original deposit amount is
PV
then the future value
FV
is equal to
[tex]$$F V=P V \cdot(1+i)^n=P V \cdot\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}$$[/tex]
We know the future value (which is given as $ 102,393.44), so calculating the present value is simple:
[tex]P V=F \frac{V}{(1+i)^n}=\frac{\$ 102,393.44}{\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}}[/tex]
The simplest way to compute this is to use a calculator:
[tex]$P V \approx \$ 991.45 .$$[/tex]
We can simplify this expression with great precision just for fun. It is well known that
[tex]$\left(1+\frac{1}{n}\right)^n \rightarrow e$[/tex]
which easily implies that
[tex]$\left(1+\frac{a}{n}\right)^n \rightarrow e^a$[/tex]
Here,
[tex]$$\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}=\left(\left(1+\frac{0.058}{52}\right)^{52}\right)^{80} \approx\left(e^{0.058}\right)^{80}=e^{0.058 .80}=e^{4.64}[/tex]
That is, [tex]P V \approx F V e^{-4.64}$.[/tex]
Hence, An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
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In an A.P. if Tₚ = q and Tq = p, then find the rth term.
Please solve this problem
Formula:
We know that
nth term of the AP is Tn = a+(n-1)d
Where, a = First term
d = Common difference
n = number of terms
Now,
Given that
pth term of the A.P. = Tp = q
⇛a + (p-1)d = q
⇛(p-1)d = q - a
⇛d = (q-a)/(p-1) →→→→(i)
and
qth term of the A.P. = Tq = p
⇛a + (q-1) d = p
⇛ (q-1)d = p-a
⇛ d = (p-a)/(q-1) →→→→(ii)
From Eqn(i) and Eqn(ii)
⇛(q-a)/(p-1) = (p-a)/(q-1)
On applying cross multiplication then
⇛(q-a)×(q-1) = (p-a)×(p-1)
⇛q²-q-aq+a = p²-p-ap+a
⇛q²-q-aq = p²-p-ap
⇛ap-aq = p²-p+q-q²
⇛a(p-q) = (p²-q²)-(p-q)
⇛a(p-q) = (p+q)(p-q)-(p-q)
⇛ a(p-q) = (p-q){(p+q)-1}
On cancelling (p-q) both sides then
⇛a = (p+q-1) →→→→Eqn(iii)
On Substituting the value of a in Eqn(ii) then
⇛ d = [p-(p+q-1)]/(q-1)
⇛d = (p-p-q+1)/(q-1)
⇛d = (-q+1)/(q-1)
⇛d = -(q-1)/(q-1)
⇛d = -1
We have,
a = p+q-1 and d = -1
Now, rth term of the AP
⇛ Tr = a + (r-1)d
⇛Tr = (p+q-1)+(r-1)(-1)
⇛ Tr = p+q-1+(-r+1)
⇛ Tr = p+q-1-r+1
⇛ Tr = p+q-r
Therefore, Tr = p+q-r
Answer: rth term of the given A.P. is p+q-r
Answer:
rth=q+p+qxp
Step-by-step explanation:
rth= 3 of the T and Tq added together and joined.
Perform the indicated operations/solutions.
1. 12-7+45÷15x11=
2. 16x2+12-18÷9-4=
What is 25+25-100+25+25
Answer: 0
Step-by-step explanation: when you add 25+25 it is equal to 50. when you subtract 100 from 50 it gives you -50. when you add 25+25= 50 so you add that -50 and 50 and it gives you zero (im not very good at explaining hope it helped)
the ordered pair (2, - 3) has a solution to which of the following inequalities?
What is the second number in the sequence?
Answer:
Step-by-step explanation:
Let "n" be the second odd number in the sequence
(n - 2) + n + (n + 2) + (n + 4) + (n + 6) = 135
5n + 10 = 135
5n = 125
n = 25
23 + 25 + 27 + 29 + 31 = 135
50 POINTS FOR EACH PERSON PLSSSSS HELP!!!!!
∫[tex]x^{\frac{3}{2} }[/tex]㏑(x) dx
Answer:
Look at images below ^^
Step-by-step explanation:
I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.
If a person walks 1/3 mile in 15 minutes, how far will that person walk in one hour?
Answer: 1 1/3 miles
Step-by-step explanation:
Since we know that an hour is 60 minutes, and 60 divided by 15 = 4, then we can multiply 1/3 times 4 to get the total number of miles in 60 minutes.
1/3 X 4 = 4/3
4/3 = 1 1/3
Therefore, the answer is 1 1/3 miles.
Therefore, in an hour, a person will walk 4/3 mile.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
x=9
Step-by-step explanation:
since the triangles are similar, the sides are all in proportion. This means that:
[tex] \frac{uw}{eg} = \frac{uv}{fg} [/tex]
Now we can just sub in the sides:
[tex] \frac{91}{13} = \frac{56}{x - 1} [/tex]
simplify the first fraction
[tex] \frac{7}{1} = \frac{56}{x - 1} [/tex]
Now we can cross multiply
56=7(x-1)
56=7x-7
63=7x
Therefore:
×=9
HELP! I don't understand
Answer:
Step-by-step explanation:
its suppolsy the hardest question in math
Answer:
E
Step-by-step explanation:
[tex]\sqrt{\dfrac{64}{49}} = \dfrac{\sqrt{64}}{\sqrt{49}} = \dfrac 87[/tex]
Answer:
E
Step-by-step explanation:
Your classmate is telling you how they plan to become financially secure.
Which of the following factors can help him do so?
A saving money
B investing money
C both saving and investing money
D neither saving nor investing money
Answer:
savind and investing money
Try changing these improper fractions to mixed numbers.
16/5?
( teach me how to solve this please!)
Answer:
3 1/5
Step-by-step explanation:
The improper fraction 16/5 is called improper because the top number(the numerator) is bigger than the bottom number(the denominator) we "fix" this by dividing and creating a mixed number (it is called mixed because there is a whole part and a fraction part):
As 16÷5 >>> doing this division gives you 3 wholes and 1/5 leftover. We write this as
3 1/5 (in handwriting the three is big and the 1/5 is a fraction, it is the mixed number they are asking you for)
A plane traveled 960 miles each way to Jakarta and back. The trip there was with the wind. It took 10 hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?
Answer:
Wind speed = 40 km/hr
Speed of the plane in still air = 280km/hr
Step-by-step explanation:
Formula to use
Distance = Rate multiplied by Time
D = R × T
Speed of the plane in still air = a
Speed of the wind = b
Plane with the wind (tailwind) is a + b where the time = 3hours
Plane against the wind is a - b, where the time = 4hours
This would give us 2 equations
3 × (a+ b) = 960
3a + 3b = 960 ...... Equation 1
4 × (a- b) = 960
4a - 4b = 960 ........ Equation 2
Solve this like you would with system of equations:
We solve the equation using elimination method.
Mulitply equation 1 by 4 and equation 2 by -3
4 × (3a + 3b = 960)
12a + 12b = 3840 ..... Equation 4
-3 × (4a- 4b = 960)
-12a + 12b= -2880 ........ Equation 5
Therefore we have
12a + 12b = 3840 ..... Equation 4
-12a + 12b= -2880 ........ Equation 5
24b = 960
b = 960÷ 24
b = 40
Wind Speed = 40km/hr
To find the speed of air, we use equation 2
4a - 4b = 960 ........ Equation 2
Substituting 40 which is wind of speed for b in equation 2 we would have
4a - 4(40) = 960
4a - 160 = 960
4a = 960 + 160
4a = 1120
a = 1120 ÷ 4
a = 280
The speed of the small plane in still air is 280 km/hr
I want a way to solve such a problem
Answer: please calculate the answer.
Step-by-step explanation:\\ Bro use this formula (sum of all numbers of the question) \ no. of seen numbers.
Arithmetic mean = ( 24+124+243+...) \ 12
Solve the inequality below for z.
8z+3>3z-17
A.z>-4
B.z<-14/5
C.z<-4
D.z>-14/5
Therefore, the solved inequality is z > -4.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
HURRY!
Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)} write the set of ordered pairs representing ƒ -1.
Select one:
a. {(1, 2), (3, 2), (4, 3)}
b. {(2,1), (3, 2), (4, 3)}
c. {(2, 1), (2, 3), (3, 4)}
The set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1, which is the correct answer that would be an option (C).
What is an ordered pair?An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.
Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)}
According to option (A),
The set of ordered pairs is {(1, 2), (3, 2), (4, 3)}
This represents ƒ -3,
According to option (B),
The set of ordered pairs is {(2,1), (3, 2), (4, 3)}
This represents ƒ -2,
According to option (C),
The set of ordered pairs is {(2, 1), (2, 3), (3, 4)}
This represents ƒ -1,
Thus, the set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1.
Hence, the correct answer would be option (C).
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2. Scholarships The probability that Samantha will be accepted by the college of her choice and
obtain a scholarship is 0.35. if the probability that she is accepted by the college is 0.65.
Find the probability that she will obtain a scholarship given that she is accepted by the college.
(4 pts)
The probability that she will obtain a scholarship given that she is accepted by the college is 0.54.
Given that the probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35, to determine, if the probability that she is accepted by the college is 0.65, the probability that she will obtain a scholarship given that she is accepted by the college, the following calculation must be performed:
0.65X = 0.35 X = 0.35 / 0.65 X = 0.538
Therefore, the probability that she will obtain a scholarship given that she is accepted by the college is 0.54.
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Determine if a relation is a function {(-1,5), (2, 7), (-3,2), (-1, 1)}
Answer:
Step-by-step explanation:
A relation is only a function if ALL the x-values (the first number in the pairs) ONLY have one partner.
Check that -1
At first that -1 is paired up with a 5 in the ordered pair (-1, 5) but then later... that -1 is down there hanging out with a 1 in the last ordered pair (-1, 1).
This means that this relation (all the pairs lumped together) is NOT a function. Just because of that -1 pairing up with more that one partner.
Write an equation of the line in slope-intercept form. 2. 3. (0, -1) (0.4) 2 3 4 5 * 86 (4, -2) -6 (-5, -3)
I MARK BRAINLIEST AND 50 points!!! find the magnitude of the resultant. forces of 92.6 lb and 118 lb act on an object. the angle between the forces is 75.2°.
a) 208 lb
b) 130 lb
c ) 168 lb
d) 150 lb
Answer:
This a vector addition problem and you need to know the law of cosines and law of sines to solve this problem.
Two vector forces of 80lbs and 70 lbs act on an object at 40 degree angle between them.
The magnitude of the resultant force can be found by applying the law of cosines:
c2 = a2 + b2 - 2abcos140°
where a = 80, b = 70 and c is the resultant force vector you are asked to find
Once you find the magnitude of the resultant force, then you can find the angle it makes wrt the 70lb force using the law of sines:
sinα/a = sin140°/c
where α is the angle opposite side a, or the angle between the resultant and the 70lb vector that you are asked to find. so it would be 140lbs
Step-by-step explanation
Find two numbers whose sum 7500 and whose product is the maximum value.
(Round your answer to the nearest whole number.)
Blank = 1
Blank = 2
The two numbers whose sum is 7500 and whose product is a maximum value are 3750 and 3750.
Let the two numbers be x and y.
Since their sum equals 7500,
x + y = 7500 (1)
Their product f(x,y) = xy (2)
We desire to maximize the product.
From (1), x = 7500 - y
Substituting x into (2), we have
f(x,y) = xy
f(x,y) = (7500 - y)y
f(y) = 7500y - y²
To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.
So, df(y)/dy = d(7500y - y²)/dy
f'(y)/dy = d(7500y)/dy - dy²/dy
f'(y)/dy = 7500 - 2y
Equating it to zero, we have
7500 - 2y = 0
7500 = 2y
y = 7500/2
y = 3750
To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.
So, f"(y) = d(7500 - 2y)dy
f"(y) = 0 - 2
f"(y) = -2 < 0.
So, y = 3750 gives a maximum for f(y) = f(x, y)
Since x = 7500 - y
Substituing y = 3750 into the equation, we have
x = 7500 - 3750
x = 3750
So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.
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W/5+20=22. How do I do this
Answer:
W = 10
Step-by-step explanation:
W / 5 + 20 = 22
W / 5 - 20 = 22 - 20
W / 5 = 2
W * 5 = 2 * 5
W = 10
Step-by-step explanation:
[tex] \frac{w}{5} + 20 = 22 \\ \\ \frac{w}{5 } = 22 - 20 \\ \\ \frac{w}{5} = 2 \\ \\ w = 5 \times 2 \\ \\ w = 10[/tex]
Which of the following quadrants of the standard (x,y) coordinate plane contain points on the graph of the equation 6x – 3y = –9 ?
A. l and lll only
B. l, ll and lll only
C. l, ll and IV only
D. I, II and IV only
E. II, IIIand IV
Using linear function concepts, it is found that the correct option is:
B. l, ll and lll only
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope.b is the y-intercept.If the slope is positive.
The function goes through quadrants I and III.If the intercept is positive, it also goes through quadrant II.If the intercept is negative, it also goes through quadrant IV.If the slope is negative:
The function goes through quadrants II and IV.If the intercept is positive, it also goes through quadrant I.If the intercept is negative, it also goes through quadrant III.In this problem, the equation is:
[tex]6x - 3y = - 9[/tex]
Placing it into the standard format:
[tex]3y = 6x + 9[/tex]
[tex]y = \frac{6}{3}x + \frac{9}{3}[/tex]
[tex]y = 2x + 3[/tex]
Both slope and intercept are positive, hence, quadrants I, II and III, option B.
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2x-y=3
X+y=3
Slove equations algebraially
What is that answer Share 126 gallons of petrol between Steve and Dave in the ratio 2:5
Factor the following expression. Type x^2 for 22 as needed. If it is not factorable, type unfactorable.
22-8x+16
Answer:
63
Step-by-step explanation:
you divide and add then subtract
you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much will each pay if they share in paying the total bill
Answer:
x+y=12.96, or 12.96=y=x then you can solve for x and then the other half of the total is the other amount
Find the measure of angle m
Answer:
36
Step-by-step explanation:
Any triangle have 180 degrees in total.
So 60 + 84 + angle M = 180
144 + angle M = 180
180 - 144 = angle M
angle = 36