By solving a system of equations we will find that the rate of current in the stream is S = 2 mi/h.
When the motorboat travels downstream, the total velocity will be the velocity of the motorboat in still water plus the velocity of the stream, while if the motorboat travels upstream, we have the velocity of the stream subtracted.
So upstream the speed is:
(14 mi/h - S)
Downstream the speed is:
(14 mi/h + S)
Where S is the rate of current in the stream.
We know that downstream it takes 15 minutes more to travel 12 miles, then we can write the system of equations:
(14 mi/h + S)*T = 12 mi
(14 mi/h - S)*(T - 15 min) = 12 mi
To solve this, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:
T = (12 mi)/(14 mi/h + S)
Replacing that in the other equation we will get:
(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi
Now we can solve this for S. Now we can multiply both sides by (14 mi/h + S).
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)
Also notice that the speeds are in hours, so we can rewrite:
- 15 min = -0.25 h
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)
168 mi^2/h - 12mi*S + 49mi^2/h + 0.25h*S^2 = 168mi^2/h + 12mi*S
- 12mi*S + 49mi^2/h - 0.25h*S^2 = 12mi*S
-24mi*S - 0.25h*S^2 + 49mi^2/h = 0
This is a quadratic equation, the solutions are:
[tex]S = \frac{24mi \pm \sqrt{(-24mi)^2 - 4*(49mi^2/h)*(-0.25h)} }{2*-0.25h} \\\\S = \frac{24mi \pm 25 mi }{-0.5h}[/tex]
We only take the positive solution, so we get:
S = (24 mi - 25 mi)/(-0.5 mi) = 2 mi/h
The rate of current in the stream is 2 mi/h.
If you want to learn more, you can read:
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10(-7y-2z)+4z-2(-8z+6y) simple form
[tex]10(-7y-2z) +4z -2(-8z+6y)\\\\=-70y -20z +4z +16z - 12y\\\\=-82y -4z+4z \\\\=-82y[/tex]
The perimeter of the smallest square is 48 feet. What is the perimeter of the largest square?
Answer:
x > 48
Step-by-step explanation:
There’s nothing told to us or showed to us to answer It So I was only able to answer it with an inequality :(((
sorry if this didn’t help but once again… not enough information :(
help me ! ✬
work due tomorrow. i don’t understand this at all.
there’s 2 questions !
— don’t comment for points.
Answer:
32, 40
Step-by-step explanation:
See the image
Hope that helps! :)
Natural numbers are ? Integers
Answer:
natural numbers are the positive numbers that begins from 1 ...
but integers include natural numbers , it's negative and zero
Question 1
2 pts
A game uses a single 6-sided die. To play the game, the die is rolled one time, with the
following results:
• Even number = lose $7
1 or 3 = win $2
5 = win $8
.
.
Answer:
sorry 400
Step-by-step explanation:
Find the area of the triangle
= (1/2 × 6 × 4) square units
= (3 × 4) square units
= 12 square units
Answer:The area of the triangle is 12 square units.
Hope it helps.
Do comment if you have any query.
=================================================
Explanation/Solution:First, Identify what is the height and base of the triangle.
[tex] \rightarrow [/tex] Height = 4 units
[tex] \rightarrow [/tex] Base = 6 units
[tex] \\ [/tex]
Now to find the area of the triangle, use the formula:
[tex] \rightarrow [/tex] Area = [tex] \sf \frac{Height × Base }{2} [/tex]
Solve.
[tex] \rightarrow [/tex] = [tex] \sf \frac{4 × 6}{2} [/tex]
[tex] \rightarrow [/tex]= [tex] \sf \frac{24 }{2} [/tex]
[tex] \rightarrow [/tex] = 12
Therefore, the area of the triangle is 12 units.
=================================================
#CarryOnLearning
PLEASE HELP!!!
Given various values of the linear functions f (x) and g(x in the table, determine the y-intercept of (f − g)(x).
x −6 −4 −1 3 4
f (x) 20 14 5 −7 −10
g(x) −36 −26 −11 9 14
no links please
Answer:
Building linear equations for f and g, it is found that the y-intercept of (f - g)(x) is of y = 8.------------A linear function has the following format:[tex]y ...
Step-by-step explanation:Use the two points to compute the slope, m, then use one of the points in the form y=m(x)+b to find the value of b.
Answer:
bro its -4
Step-by-step explanation:
bc f(x) has y-intercept of 2 and g(x) has y-intercept of -6 so 9 (f-g)(x) would be 2-6 = -4
so the answer is actually (0, -4)..
Question: Assume you have a balance of $1000 on a credit card with an APR of 12%, or 1% per month. You start making monthly payments
of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on
the balance for the previous month. The following table shows how you can calculate your monthly balance. Complete and extend the table to
show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit carddebt?
nts
Fill out the table row by row and continue until the last full payment. Round to the nearest cent as needed.
Month
Payment
Expenses
Interest
New Balance
a
urces
0
---
$1000
es
1
$200
$100
$10
$910
4/7
fing
2
$200
$100
ection
3
$200
$100
4
$200
$100
1. The extension of the table to show the month-end balances until full debt settlement is as follows:
Month Payment Expenses Interest New Balance
0 $0 $0 $0 $1,000
1 $200 $100 $10 $910 ($1,000 - $200 + $100 +$10)
2 $200 $100 $9.10 $819.10 ($910 - $200 + $100 + $9.10)
3 $200 $100 $8.19 $727.29 ($819.10-$200+$100+$8.19)
4 $200 $100 $7.27 $634.56 ($727.29-$200+$100+$7.27)
5 $200 $100 $6.35 $540.91 ($634.56-$200+$100+$6.35)
6 $200 $100 $5.41 $446.32 ($540.91-$200+$100+$5.41)
7 $200 $100 $4.46 $350.78 ($446.32-$200+$100+$4.46)
8 $200 $100 $3.51 $254.29 ($350.78-$200+$100+$3.51)
9 $200 $100 $2.54 $156.83 ($254.29-$200+$100+$2.54)
10 $200 $100 $1.57 $58.40 ($156.83-$200+$100+$1.57)
11 $200 $100 $0.58 ($41.02) ($58.40-$200+$100+$0.58)
Data and Calculations:
Credit card balance = $1,000
APR = 12%
Monthly APR = 1%
Monthly payments = $200
Monthly charge = $100
Learn more: https://brainly.com/question/24317087
make the subject x of the formula y = 7x + 4
Answer:
[tex]x = \frac{y - 4}{7}[/tex]
Step-by-step explanation:
[tex]y = 7x + 4 \\\\y - 4 = 7x\\\\\frac{y - 4}{7} = \frac{7x}{7}\\ \\ \frac{y - 4}{7} = x[/tex]
Which situation involves permutations? A. choosing 5 people out of 15 to participate in a survey B. choosing 3 flavors of ice cream out of 15 for an ice-cream sundae C. choosing a dozen flowers out of 30 to create a bouquet D. choosing first second-, and third-place winners in a cooking contest
9514 1404 393
Answer:
D. choosing first second-, and third-place winners in a cooking contest
Step-by-step explanation:
Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.
Cooking contest winners involve permutations.
Suppose that you borrow $16000 for 5 years at 8% toward the purchase of a car. Find the monthly payments and the total interest for the loan.
The total interest on the loan and monthly payments are $64,000 and $ 1,333.3 respectively
The formula for calculating the simple interest is expressed as:
I = PRT
P is the amount borrowed = $16,000R is the rate = 8% = 0.08T is the time = 5 yearsGet the interest;
I = 16,000 * 0.8 * 5
I = $64000
Amount after 5 years = 16000 + 64000
Amount after 5 years = $80,000
Monthly payment = 80000/60months
Monthly payment = $1,333.33
Hence the total interest on the loan and monthly payment are $64,000 and $ 1,333.3 respectively
Learn more on interest here: https://brainly.com/question/10488979
Which of these lenders will make a very short-term loan based on proof of
employment?
A. Title lender
B. Bank
C. Credit union
D. Payday lender
please help me
what is
28a+84b+92c=
Evaluate the expression below if X equals three and Y equals negative 4X- Y -3+(-5y) A 16. B. -50. C. 24. D. 20
nooooooooooooooooooooooooooooo
Find the value of x
(6x-5) (6x+5)
Answer:
-5/6 or 5/6
Step-by-step explanation:
Im assuming you want this equation equal to 0, so (6x-5)(6x+5) would reduce to 36x²-25=0. I would then add 25 to the other since and get
36x²=25, divide the whole thing by 36 to single out x
x²=25/36, which would reduce to x²=5/6.
thus x could be either -5/6 or 5/6
What is 3.59 rounded to the nearest whole number?
Answer:
its 4 ezy
Step-by-step explanation:
please mark as brainlists
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.07 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
93.684
Step-by-step explanation:
They just give a 5% bonus to the price of the lunch
please help with t his question
Answer: 15 inches
Step-by-step explanation:
15 × 1 ÷ 12 = 1.25 ft
1.25 ft = 1.25 × 12 = 15 in
- C C) C.P = Rs 20, profit Rs 2, S
.P. -
Answer:
[tex]cp = p + sp \\ \\ cp = 2 + 20 \\ \\ cp = 22[/tex]
3^4x-1=15
Need help with this log question
Answer:
x=16/81
Step-by-step explanation:
3^4x-1=15
81x-1=15
81x=15+1
81x+16
divide both sides by 81
x=16/81
An oil company estimates that only 1 well in 20 will yield commercial quantities of oil. Assume that successful drilled wells represent independent events. If 5 wells are drilled, find the probability of obtaining a commercially successful well for the following number of times. (Round your answer to six decimal places.) exactly 1
Please please help please help me please please help me
Answer:
y = -6/7x - 10/7
Step-by-step explanation:
(-4,2) and (3,-4)
Slope: - 6/7
Take any point: (-4,2)
y-intercept: 2 - (- 6/7)(-4) = -10/7
Need helpPlzzzzzzzzzzzzzzzz
Answer:
2
Step-by-step explanation:
−3 2/3=x−1 1/4 pls help
Answer:
- 2 5/12Step-by-step explanation:
−3 2/3 = x − 1 1/4x = - 3 2/3 + 1 1/4x = - 2 - 2/3 + 1/4x = - 2 - 8/12 + 3/12x = - 2 - 5/12x = - 2 5/12How do you write as an expression of inequality, then solve it?
Twice a number is more than the sum of that number and 8
Answer:
2x > x + 8
x > 8
Step-by-step explanation:
(Twice a number) (is more than) (the sum of that number and 8)
2x > x + 8
2x > x + 8
Subtract x from both sides
x > 8
The quotient of b and -6 is 18
The quotient is the result obtained by dividing one quantity by another.
This means that b/-6 = 18
b = 18*-6
b = -108
Answer:
b = -108
Step-by-step explanation:
Given the mathematical expression, "The quotient of b and -6 is 18":
We could represent the given mathematical expression as follows:
b ÷ -6 = 18 or [tex]\frac{b}{-6} = 18[/tex] .
In the fraction form, [tex]\frac{b}{-6} = 18[/tex] , multiply both sides by -6 to eliminate the denominator on the left-hand side. It will also isolate b:
[tex]\frac{b}{-6} = 18[/tex]
[tex](-6)(\frac{b}{-6}) = 18(-6)[/tex]
b = -108
In order to double-check whether we have the correct value for b, simply substitute its vlaue into the equation:
[tex]\frac{-108}{-6} = 18[/tex]
18 = 18 (True statement).
The value of b = -108, hence, the quotient of -108 and -6 is 18.
Anne and chima are to share a sum of money in ratio 4:1.Anne obtains #6000.what is chima's share?
Answer:
Chima would obtain 1200
the x-coordinate is zero and the y-coordinate is positive choose the location
Answer:
(0,5)
Step-by-step explanation:
A positive number is a number higher than 0. The x-coordinate is the first number, and the y coordinate is the second number. Plug in any random positive y coordinate to get your point.
(x,y)
(0,1)
(0,2)
(0,3)
The area of a rectangle is 24 square inches. Determine both dimensions if the length is 6 inches less than three times the width
Answer:
width is 4 inches
length is 6 inches
Step-by-step explanation:
the length is 6 inches less than three times the width
l = 3w - 6
a = l * w
a = (3w - 6)w
a = 3w^2 - 6w
area of the rectangle is 24 square inches
3w^2 - 6w = 24
subtract 24 from both sides
3w^2 - 6w - 24 = 0
Divide both sides by 3
w^2 - 2w - 8 = 0
Factor
(w - 4)(w + 2) = 0
w = {-2, 4}
disregard the negative root since measurement must be positive
w = 4
l = 3w - 6
l = 3(4) - 6
l = 6
Write a story that can be representd by the equation y=x+1/5x
Answer:
I sorry but I don't get this question