Given:
A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.
Pilot's speed in still air is 315 miles per hour.
To find:
The speed of the wind.
Solution:
Let the speed of wind be x miles per hour.
Speed with wind = 315+x miles per hour
Speed against wind = 315-x miles per hour
We know that,
[tex]Time=\dfrac{Distance}{Speed}[/tex]
According to the question,
[tex]\dfrac{450}{315+x}=\dfrac{360}{315-x}[/tex]
Divide both sides by 90.
[tex]\dfrac{5}{315+x}=\dfrac{4}{315-x}[/tex]
By cross multiplication, we get
[tex]5(315-x)=4(315+x)[/tex]
[tex]5(315)-5x=4(315)+4x[/tex]
[tex]5(315)-4(315)=4x+5x[/tex]
[tex](5-4)315=9x[/tex]
Divide both sides by 9.
[tex]\dfrac{(1)315}{9}=x[/tex]
[tex]35=x[/tex]
Therefore, the speed of wind is 35 miles per hour.
If two thirds of a number is 56, what is three- quarters of that number?
Answer:
63
Step-by-step explanation: Let n represent the number. If two third of n = 56, n must be 56 times the reciprocal of 2/3 (3/2) 56 time 3/2 = 84. three quarter of 84 is 84 times 3/4 = 63
(first question btw)
please help i will mark brainliest if correct!
Answer:
(3,9)
Step-by-step explanation:
Because the translation moves 1 in the x direction and 4 in the y direction, you just add those to the starting x and y coordinates.
(2+1, 5+4)
(3, 9)
Will give brainliest if correct
Answer:
y=4
x=2
Step-by-step explanation:
y=4
x=2
I think it's right..
Hope I helped!
Answer:
x - intercept = 2
y - intercept = 4
PLEASE HELP ME!! THANK YOU!!
9514 1404 393
Answer:
[-4,3]
Step-by-step explanation:
The domain is the left-right (horizontal) extent of the function. The dots at the end of the continuous line are solid, so the brackets on the interval are square brackets.
The left dot is at x=-4; the right dot is at x=3, so the domain is ...
[-4,3]
Write the equation for a parabola with the focus at
(-1, 4) and the equation of the directrix x = 5.
(x + 1)2 = 3(y-4)
(y-4)2 = 12(x + 1)
(y-2)2 = -3(x – 4)
(y-4)2 = –12(x - 2)
Put the equation 2x+3y=1470 in function notation
Answer:
y = -[tex]\frac{2}{3}[/tex]x + 9
Step-by-step explanation:
Positive negative or no correlation?
Answer:
positive correlation
Answer:
animal
Step-by-step explanation:
4. On the day Alex was born, his father invested $5000 in an account with a 1.2% annual growth rate.
Answer the questions below.
(a) Write a function, A(t), that represents the value
of this investment t years after Alex's birth.
(b) Use your equation to determine how much the
investment will be worth when Alexander turns
21
Answer:
Answer:
A) A(t) = 5000(1 + 0.012)t
B) A(t) = 106260
Step-by-step explanation:
A) 5000 is the initial amount, 1 + 0.012 is the interest rate, and t represents the years.
B) When we plug 21 into the equation, we get 106260.
I hope this helps!
What is the answer to 3z−6/7−2z = 1.2/3.2 ? Please help
Answer:
= 1.23214285
Step-by-step explanation:
please help! no rush though :)
1.6 x 10^5kg and 8 x 10^3kg
(i need it with too but if you can’t it’s all good!)
Answer:
160000 kg and 8000
Step-by-step explanation:
move decimal to the right five times
move decimals to right 3 times
The office manager of First Tech Support borrowed $25,000 to purchase new computers for employees. The bank charges 6 percent interest for 4 years. How much interest will the company pay in all?
$1,200
$1,500
$4,800
$6,000
Answer:
it is 6,000$
Step-by-step explanation:
Answer:
6,000
Step-by-step explanation:
C=5(f-32)/9
Make f the subject of the formula
Give answer in the form of aC+b/c
Answer:
F = [tex]\frac{9C+160}{5}[/tex]
Step-by-step explanation:
Given
C = [tex]\frac{5(F-32)}{9}[/tex] ( multiply both sides by 9 to clear the fraction )
9C = 5(F - 32) ← distribute
9C = 5F - 160 ( add 160 to both sides )
9C + 160 = 5F ( divide both sides by 5 )
[tex]\frac{9C+160}{5}[/tex] = F
6.
Simplify
4√8 + 3√18 √32
Answer:
83.31370849
Step-by-step explanation:
I got you get the 100
The radius of a circle is 5 kilometers. What is the length of a 90° degree arc?
Answer:
s =5*π/2 km
Step-by-step explanation:
arc length s = rθ
where θ =central angle in radians
r = 5km
θ = 90 degrees = 90 degrees/360degrees * 2π = [tex]\frac{1}{4}[/tex](2π) = π/2
s =5*π/2 km
Which of the following points is a solution of y s-Ixl - 1?
O (-1,-3)
O (0,0)
O (1,-1)
Answer: The answer is (-1,-3) :)
Step-by-step explanation:
Mark me as brainlest please
Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below. (0,6) and -1
Answer:
Can't tell
Step-by-step explanation:
Hear me out. There is no graph hear, so I can't answer. Just letting you know
Jaidee invests $2,628 in a retirement account with a fixed annual interest rate of 2.33% compounded 12 times per year. How long will it take for the account balance to reach $3,726.18?
Answer:
The time it will take for the account balance to reach $3,726.18 is 15 months.
Step-by-step explanation:
The information provided is:
Jaidee invests $2,628 in a retirement account With a fixed annual interest rate of 2.33% Compounded 12 times per year, i.e. compounded monthly.Final account balance: $3,726.18The formula of compound interest (compounded monthly) is:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]
Compute the value of t as follows:
[tex]3726.18=2628\times (1+\frac{0.0233}{12})^{12t}\\\\\frac{3726.18}{2628}= (1.00194167)^{12t}\\\\1.41787671= (1.00194167)^{12t}\\\\\log(1.41787671)= 12t\times \log(1.00194167)\\\\12t=\frac{\log(1.41787671)}{\log(1.00194167)}\\\\t=14.99995\\\\t\approx 15[/tex]
Thus, the time it will take for the account balance to reach $3,726.18 is 15 months.
NEED ANSWER ASAP THE TEST IS TIMED!!!!!!!
Find the slope of the line that contains the two points (6, -2) and (-3, 1).
Answer:
5/-1
Step-by-step explanation:
y1-y2/x1-x2
What's the opposite of -1.5 and 3/4?
Answer:
1.5
- 3/4
Step-by-step explanation:
To find the opposite of a number, you just have to either add or remove a negative sign.
- 1.5 is negative, so the opposite of negative 1.5 is positive 1.5 or 1.5
3/4 is positive, so the opposite of positive 3/4 is negative 3/4 or - 3/4
I Hope That This Helps! :)
Answer:
1.5
- 3/4
Step-by-step explanation: CREDIT TO GUY ABOVE!
A truck can be rented from Company A form $130 a day plus $0.30 per mile. Company B charges $50 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
160 miles
Step-by-step explanation:
Company A form $130 a day plus $0.30 per mile
Company A = 130 + 0.30x
Company B charges $50 a day plus $0.80 per mile
Company B = 50 + 0.80x
Where,
x = number of miles
Equate the cost of company A and company B
130 + 0.30x = 50 + 0.80x
Collect like terms
130 - 50 = 0.80x - 0.30x
80 = 0.50x
Divide both sides by 0.50x
x = 80 / 0.50
= 160
x = 160 miles
The number of miles in a day at which the rental costs for Company A and Company B are the same is 160 miles
Use the Binomial Theorem/Pascal's Triangle to expand (2a + 2b)^5
Answer:
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
============================================================
Explanation:
Let's use Pascal's Triangle
In the row that starts with 1,5,... we have the values 1,5,10,10,5,1
These will be the coefficients of the terms.
Let x = 2a and y = 2b
We want to expand out (x+y)^5
Using pascals triangle, we get the following expansion
(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5
The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.
Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.
At this point, we plug in x = 2a and y = 2b
Since this will clutter things a bit, I'll do it term by term
1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^55x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^210x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^35x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^41x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5So in the end, the expression (2a+2b)^5 expands out to
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.
Answer: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex].
Using Pascal's triangle we get:
[tex](x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5[/tex]
Here, x = 2a and y = 2b
So the terms become:
[tex]1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\[/tex]
Hence: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex]
Learn more: https://brainly.com/question/13769924
(1,-19),(-2 -7) finnd the slope to this equation
Answer:
slope is 4
Step-by-step explanation:
5x - 2y = 26 y + 4 = x
Dave wants to put a row of tiles in his kitchen. The row has to be 3 meter long. Each tiles is a square, with 25 cm sides. How many tiles does he need?
Answer:the answer is b or c
Step-by-step explanation:
Determine the value of x.
Edward wanted to buy a skateboard. The original price of the skateboard was $90. The store was having a sale where everything in the store was markdown 35%, or 35% off. What was the price of the skateboard after the markdown or discount?
Answer:
$58.5Step-by-step explanation:
Step one:
Given data
original price of Skate board= $90
Also there was a 35% discount on the original price.
the idea now is to find what 35% of $90 is.
=(35/100)*90
=0.35*90
=31.5
hence 35% of $90 is $31.5, the discounted price is $31.5
Step two:
The markdown price is the original price- the discounted price
90-31.5= $58.5
Therefore the price of the skateboard is $58.5
can't figure this out
Answer:
2.55%
Step-by-step explanation:
You have 11 years to make $500, To do this, take the 11 and multiply it by the percentage, after that, do $2000 divided by 11 x (percentage) answer. Then you will have the difference, which should roughly equal $556, which is slightly over $500 but you can't have it under so this is the best answer.
a store sells jump ropes. each jump rope costs the same amount. during a sale, the store reduces the price of each jump rope by $1.25. jada spends $15.08 on 2 jump ropes at the sale price.
Answer:
she spent $7.45 on each rope at the sale price. The original price would have been $8.70
Step-by-step explanation:
I am given that p || q. ∠1 and ∠4 are supplementary angles because they form a linear pair, so m∠1 + m∠4 = 180°. ∠4 and ∠8 are also supplementary because of the Same-Side Interior Angles Postulate, so m∠4 + m∠8 = 180°. You can substitute m∠4 + m∠8 for 180° in the first equation above. The result is m∠1 + m∠4 = m∠4 + m∠8. After subtracting m∠4 from each side, I see that m∠1 = m∠8.
Answer:
3
Step-by-step explanation:
Replace 8 with 3
Cz angle 4 is equal to 8
Angle 4+Angle 3 is 180⁰
And angle one is equal to angle three
X
GEOMETRY The sum of the measures of
the angles of a triangle is 180°.
Find the missing measure.
35°
45
Answer:
Step-by-step explanation:
Sum of all three angle in a triangle=180
Given angles are 35°,45°
Let the remaining angle =x
So 35 +45+X=180
X=180-80
X=100°
Remaining angle =X=100° is the answer
