Answer:
s = 18 mph
Step-by-step explanation:
At downstream, time is; t = 11/(s+ 4)
At upstream, time is; t = 7/(s - 4)
Since they both are passed in the same time, then ;
11/(s+ 4) = 7/(s - 4)
Cross Multiply to get;
11(s - 4) = 7(s + 4)
11s - 44 = 7s + 28
11s - 7s = 44 + 28
4s = 72
s = 72/4
s = 18
Answer this question please
help me out and ill give brainliest
Answer:
C
Step-by-step explanation:
Y= MX (The Slope which is Rise/Run) minus 2 (The Y-Intercept).
Please show me step by step how to do this
Answer:
The next three terms of the sequence are 17, 21 and 25.
The 300th term of the sequence is 1197.
Step-by-step explanation:
The statement describes an arithmetic progression, which is defined by following formula:
[tex]p(n) = p_{1}+r\cdot (n-1)[/tex] (1)
Where:
[tex]p_{1}[/tex] - First element of the sequence.
[tex]r[/tex] - Progression rate.
[tex]n[/tex] - Index of the n-th element of the sequence.
[tex]p(n)[/tex] - n-th element of the series.
If we know that [tex]p_{1} = 1[/tex], [tex]n = 2[/tex] and [tex]p(n) = 5[/tex], then the progression rate is:
[tex]r = \frac{p(n)-p_{1}}{n-1}[/tex]
[tex]r = 4[/tex]
The set of elements of the series are described by [tex]p(n) = 1 + 4\cdot (n-1)[/tex].
Lastly, if we know that [tex]n = 300[/tex], then the 300th term of the sequence is:
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 1197[/tex]
And the next three terms of the sequence are:
n = 5
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 17[/tex]
n = 6
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 21[/tex]
n = 7
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 25[/tex]
The next three terms of the sequence are 17, 21 and 25.
The 300th term of the sequence is 1197.
WILL GIVE BRAINLIEST PLEASE HELP ASAP, BEST ANSWER GETES BRAINLIEST. NOT A SCAM AND ITS NOT CAP WHAT SO EVER
Answer:
A. 60 + x = 90
Step-by-step explanation:
Complementary angles add up to 90 degrees so
60 + x = 90
Answer:
The answer is A: 60 + x = 90
Step-by-step explanation:
Complimentary angles are two angles that add up to 90, so the equation 60 + x = 90 is what you need to use to find the complimentary angle. I hope this helps :)
What is the length of AC
A)72
B)8
C)None of these
D)136
E)132
F)96
Seats in a theater are curved from the front row to the back. The front row has 10 chairs, the second has 16 and the third has 22, and so on.
A. Write a recursive rule for this series
B. Write an explicit rule for this series
C. Using the explicit formula, find the number of chairs in row 5
D. The auditorium can hold 17 rows of chairs. Write a sigma notation for this series, and then use either series formula to calculate how many chairs can fit in the auditorium
Answer:
The first term is 10.
The second term is 16
The third term is 22.
We can see that the first term plus 6, is:
10 + 6 = 16
Then the first term plus 6 is equal to the second term.
And the second term plus 6 is:
16 + 6 = 22
Then the second term plus 6 is equal to the third term.
A) As we already found, the recursive rule is:
Aₙ = Aₙ₋₁ + 6
B) The explicit rule is:
Aₙ = A₁ + (n - 1)*6
Such that A1 is the first term, in this case A₁ = 10
Then:
Aₙ = 10 + (n - 1)*6
C)
Now we want to find A₅, then:
A₅ = 10 + (5 - 1)*6 = 34
There are 34 chairs in row 5.
D)
Here we have 17 rows, then we can have 17 terms, this means that the total number of chairs will be:
C = A₀ + A₁ + ... + A₁₆
This summation can be written as:
∑ 10 + (n - 1)*6 such that n goes from 0 to 16.
The formula for the sum of the first N terms of a sum like this is:
S(N) = (N)*(A₁ + Aₙ)/2
Then the sum of the 17 rows gives:
S(17) = 17*(10 + (10 + (17 - 1)*6)/2 = 986 chairs.
There are total 986 chairs in the considered auditorium and there are 34 chairs in the fifth row.
The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex]The explicit rule for this series is: [tex]T_n = 6n + 4[/tex]What is recursive rule?A rule defined such that its definition includes itself.
Example: [tex]F(x) = F(x-1) + c[/tex] is one such recursive rule.
For this case, we're provided that:
Seats in rows are 10 in front, 16 in second, 22 in third, and so on.
10 , 16 , 22 , .....
16 - 10 = 6
22 - 16 = 6
...
So consecutive difference is 6
If we take [tex]T_i[/tex] as ith term of the series then:
[tex]T_2 - T_1 = 6\\T_3 - T_2 = 6\\T_4 - T_3 = 6 \\T_5 - T_4 = 6\\\cdots\\T_{n} - T_{n-1} = 6[/tex]
Thus, the recursive rule for the given series is [tex]T_{n} - T_{n-1} = 6[/tex] or [tex]T_n = T_{n-1} + 6[/tex]
From this recursive rule, we can deduce the explicit formula as:
[tex]T_n = T_{n-1} + 6\\T_n = T_{n-2} + 6 + 6\\\cdots\\T_n = T_{n-k} + k \times 6\\T_n = T_1 + 6(n-1)\\T_n = 10 + 6(n-1) \: \rm (as \: T_1 = 10)\\[/tex]
Thus, the explicit rule for this series is [tex]T_n = 10 + 6(n-1)[/tex]
For 5th row, putting n = 5 gives us:
[tex]T_n = 10 + 6(n-1) = 6n + 4\\T_5 = 6(5) + 4 = 34[/tex]
If the auditorium has 17 rows, then total chairs are:
[tex]T = T_1 + T_2 + \cdots + T_{17} = \sum_{n=1}^{17} T_n\\\\T = \sum_{n=1}^{17} (10 + 6(n-1))\\\\T = \sum_{n=1}^{17} (6n + 4)\\\\T = 6\sum_{n=1}^{17} n + \sum_{n=1}^{17}4 = 6\sum_{n=1}^{17} n + 4 \times 17\\\\T = 6\left( \dfrac{17(18)}{2}\right) + 68 = 918 + 68\\\\T = 986[/tex]
(it is because [tex]\sum_{k=1}^n k = 1 + 2 + \cdots + n = \dfrac{n(n+1)}{2}[/tex] )
Thus, there are total 986 chairs in the considered auditorium. There are 34 chairs in the fifth row. The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex] The explicit rule for this series is: [tex]T_n = 6n + 4[/tex].
Learn more about recursive rule and explicit rule here:
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Use the box method to distribute and simplify (2 + 1)(2x - 3). Drag and drop the
terms to the correct locations of the table.
Answer:
2x^2-x-3
(2x)(-3)
(x)
(1)
Step-by-step explanation:
Distribute
(2x^2) (-3x)
(2x) (-3)
Why is convenience sampling biased? a. It takes too long to obtain b. none of the above c. The sample does not represent the population d. is too easy
Answer:
A
Step-by-step explanation:
Answer:
A)
Step-by-step explanation:
Point B has coordinates (1,2). The x-coordinate of point Ais - 11. The distance between point A and
point B is 13 units. What are the possible coordinates of point A?
What is AB?
Triangle ACB is right angle triangle. The length of AC is 12 and BC is 35.
Answer:
the answer is 35
Step-by-step explanation:
because if BC is 35 that means AB will have to be that same because it's a triangle
The required value of AB is 33 units for the given right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Triangle ACB is a right-angle triangle. The length of AC is 12 and BC is 35.
Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
Assume BC is the hypotenuse,
Since this is a right triangle, use the formula AB² + AC² = BC² and substitute values of AC = 12 and BC = 35.
AB² + AC² = BC²
AB² + (12)² = (35)²
AB² + 144 = 1225
AB² = 1225 -144
AB² = 1081
AB = 32.8785
Rounded to two decimal places,
AB = 33 units
Therefore, the required value of AB is 33 units.
Learn more about Pythagoras's theorem here:
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An English teacher reviewed 2/3 of an essay in 1/4 of an hour. At this rate, how many essays can she review in 1 hour?
Answer: 2 2/3
Step-by-step explanation:
Answer:
2 2/3
Step-by-step explanation:
Andrea constructed a triangle. Angle 1 and 3 are the same size and angle 2 has a measurement of 70 degrees. What is the measurement of angle 1 and 3
Answer:
Step-by-step explanation:
By triangle sum theorem,
Sum of all angles of a triangle is 180°.
m∠1 + m∠2 + m∠3 = 180°
(m∠1 + m∠3) + m∠2 = 180°
2(m∠1) + 70° = 180° {Given → m∠1 = m∠3]
2(m∠1) = 110°
m∠1 = 55°
Therefore, m∠1 = m∠3 = 55°
A builder has an 6-acre plot divided into 1 4 -acre home sites. How many 1 4 -acre home sites are there?
Complete question :
A builder has an 6-acre plot divided into 1/4 -acre home sites. How many 1/4 -acre home sites are there?
Answer:
24 home sites
Step-by-step explanation:
Given :
Total size of land = 6 - acre
Size of each home site = 1/4 acre
Number of home sites obtainable from the 6-acre land :
Total size of land ÷ size of each home site ;
6 ÷ 1/4
6 * 4/1
= 24
Hence, 24 home sites are on the plot of land.
is 12, -15, -18, -21 arithmetic
67 is 42% of what number?
Answer:
28.14
Step-by-step explanation:
I ready linear models choose the line that is the best fit for the data
Answer:
The Answer is lime 2 if not line 4
Step-by-step explanation:
YEp:)
why does the quadratic formula work all the time
the quadratic formula work all the time because it is suitable for every equation.
PLEASE HELP WILL MARK BRAINLIEST HELP QUICK!!
Answer: Your Answer would be A
Step-by-step explanation:
Pls helpppp and thank you
Osing Trig to Find a Side Apr 06, 5:40:44 PM In AOPQ, the measure of ZQ=90°, the measure of Z0=26°, and QO = 4.9 feet. Find the length of PQ to the nearest tenth of a foot. P (hypotenuse) X (opp. of 20) 2009 Q 4.9
Answer:5.4
Step-by-step explanation:
I NEED HELP WITH MATH PLS
screenshot is posted below
Answer: The correct answer is A or B
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Step-by-step explanation:
Need someones help on this!
please helpppp which function h(x) results when g(x) is translated 7pi/8 units right and one unit down????
Answer:
The second option
Step-by-step explanation:
Find the volume of an oblique circular cylinder that has a radius of five feet and a height
of three feet
Answer:
235.5 cubic feet
Step-by-step explanation:
The volume v of a circular cylinder whose base radius is r and height h is given as
v = πr^2h
where π is 22/7 or 3.14
Given that the radius is five feet and the height is three feet
the volume v = 3.14 *5^2 * 3
= 235.5 cubic feet
The volume of the oblique circular cylinder is 235.5 cubic feet
Drag the operations signs to make the number sentence true. Use each operation sign once. +–×÷ 4 (3 2) 6 1 = 14
Answer: its 4x(3+2)-6÷ 1=14
Step-by-step explanation: in the picture
5
7
9
4
In percents?
Answer:
Convert the decimal to a percentage by multiplying the decimal by
100 .
500%
700%
900%
400%
A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few years. Write an equation representing the relationship, where x is time in years, and y is the number of songs available.
Answer: y = (3^(x-1))*1500
Step-by-step explanation:
We want the relationship
y = f(x)
where y is the number of songs, and x is the number of years.
We know that in the first year, x = 1, the site has 1,500 songs.
The next year, x = 2, the number of songs is tripled, then we will have:
1,500*3 = 4500 songs.
The next year, x = 3, we will have: 3*(3*1500) = (3^2)*1500.
when x = 4, the number is tripled again:
3*(3^2)*1500 = (3^3)*1500
We already can see the pattern, for the year x, the site will have:
y = (3^(x-1))*1500 songs.
This is the equation we are looking for.
I can't figure it out
Answer:
V = 17,371.8
Step-by-step explanation:
V = π r^2 h
V = π (12)^2 (38.4)
V = 17,371.75073729
V = 17,371.8
You have to calculate the area of the base of the cylinder (the circle) by using the formula π r^2, r = the radius of the circle. You are squaring the r because r^2 = diameter. The formula to get the area of a circle is π r ^2. To get the volume you need to multiply the area of the circle by the height of the cylinder. All together the total formula to get the volume of a cylinder is π r^2 h
3-6 x (34 divided by 30)2
Answer:
3-6
Step-by-step explanation:
The expression 3⁻⁶ × (3⁴ ÷ 3⁰)² value is 9 which is 3².
To simplify the given expression: 3⁻⁶ × (3⁴ ÷ 3⁰)², let's break it down step by step:
First, let's simplify the exponent expressions within the parentheses:
3⁴ = 81 (because 3⁴ = 3 × 3 × 3 × 3 = 81)
3⁰ = 1 (because any number raised to the power of 0 is 1)
Now, we can rewrite the expression with the simplified exponents:
3⁻⁶ × (81 ÷ 1)²
Next, simplify the division within the parentheses:
81 ÷ 1 = 81
Now, the expression becomes:
3⁻⁶ × 81²
Simplify the exponent:
81² = 6561 (because 81 × 81 = 6561)
Now, the expression becomes:
3⁻⁶ × 6561
1/729 × 6561
6561/729
dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 9:
729/81
We get 9 which is equal to 3².
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What does this equal to
|9-14|
Answer:
5
Step-by-step explanation:
An absolute value is NEVER negative.
|9 - 14| = |-5| = 5
Answer: 5
