Answer:
The rate of the current is 2 mph.
Step-by-step explanation:
When the boat travels upstream we have:
[tex] v_{T_{1}} = v_{b} - v_{c} [/tex]
[tex] \frac{x_{1}}{t_{1}} = v_{b} - v_{c} [/tex]
Where:
[tex] v_{T}[/tex]: is the total speed
[tex]v_{b}[/tex]: is the speed of the boat = 10 mph
[tex]v_{c}[/tex]: is the speed of the current
x: is the distance
t: is the time
And when the boat travel downstream we have:
[tex]v_{T_{2}} = v_{b} + v_{c}[/tex]
[tex] \frac{x_{2}}{t_{2}} = v_{b} + v_{c} [/tex]
Since the boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream we have:
[tex] \frac{x_{1}}{t + 4} = v_{b} - v_{c} [/tex] (1)
[tex] \frac{x_{2}}{t} = v_{b} + v_{c} [/tex] (2)
By adding equation (1) with (2):
[tex] \frac{x_{1}}{t + 4} + \frac{x_{2}}{t} = 2v_{b} [/tex]
[tex] tx_{1} + (t+4)x_{2} - 2v_{b}t(t+4) = 0 [/tex]
[tex] 48t + 24(t+4) - 2*10t(t+4) = 0 [/tex]
By solving the above equation for t we have:
t = 2 h
Now, by entering "t" into equation (2) we have:
[tex] \frac{24 miles}{2 h} = 10 mph + v_{c} [/tex]
[tex] v_{c} = 2 mph [/tex]
Therefore, the rate of the current is 2 mph.
I hope it helps you!
what is : 20.0g of C4H10
Answer:
20 grams of butane
Step-by-step explanation:
C4H10 is butane
What is the LCM (Least Common Multiple) Of 10, 5, and 6?
Answer:
30
Step-by-step explanation:
10= 10 20 30
6= 6 12 18 24 30
5= 5 10 15 20 25 30
Which expression shows the result of applying the distributive property to 9(2+5m)?
18 + 45m
2 + 45m
18 + 5m
11 + 14m
Answer: A: 18 + 45m
Step-by-step explanation:
9(2+5m) = (9 x 2) + (9 x 5m) which gives you: 18 + 45m
Answer:
I think it's 18+45m
Step-by-step explanation:
I just multiplied 9x2 and 9x5.
Graph this inequality:
-15y > 30x - 45
Answer:
Hope this helped
Twelve decreased by twice a number equals -34
Answer:
-22
Step-by-step explanation:
-34+12=-22
PLS HELP I WILL GIVE BRAINLIEST
Answer:
Option 2: y = 6x + -4
Step-by-step explanation:
y = mx + b
y = 6x + -4
Answer:
#2
Step-by-step explanation:
[tex](x^5)(4^3x^7)^0[/tex]
Answer:
=x⁵
Step-by-step explanation:
that the answer
have a great day
24 is 4 times as great as
Pls help
Answer:
6=k
Step-by-step explanation:
pleasee help ill mark brailist and if you can answer a couple of questions
Answer:
B
Step-by-step explanation:
Answer:
48to41, 48:41, 48/41
Step-by-step explanation:
if this is incorrect try
48to41, 48:41, 41/48
A self-serve frozen yogurt store sells servings up to 12 ounces. It charges $0.50 per ounce for a serving between 0 and 8 ounces, and $4 for any serving greater than 8 ounces and up to 12 ounces.
Build the function that models the relationship between the price p(w) and of the weight w of a serving of yogurt.
Answer:
p(w) - - - - - - p = 0.5w ; for 0 < w ≤ 8
p(w) - - - - - - p = 4 ; for w < 8 and w ≤ 12
Step-by-step explanation:
Price, p of weight of a toughurt serving :
p(w) - - - - - - p = 0.5w ; for 0 < w ≤ 8
p(w) - - - - - - p = 4 ; for w < 8 and w ≤ 12
The function that models the relationship is:
p(w) = 0.50w for 0 < w ≤ 8
p(w) = 4w for 8 < w ≤ 12
The self-serve frozen yoghurt store charges:
$0.50 per serving for a serving between 0 and 8 ounces
$4 per serving for any serving greater than 8 ounces and up to 12 ounces.
Let the weight of servings be represented by w
Let the price as a function of the weight be p(w)
For a charge of $0.50 per serving:
p(w) = 0.50w, where 0 < w ≤ 8
For a charge of $4 per serving:
p(w) = 4w, where 8 < w ≤ 12
Therefore, the function that models the relationship is:
p(w) = 0.50w for 0 < w ≤ 8
p(w) = 4w for 8 < w ≤ 12
Learn more on functions here: https://brainly.com/question/10439235
PLEASE HELP!!!!!!!!!!!!!!!!
This triangle can only have one altitude.
A.True
B. False
C.It can have four
Help please.
Answer:
(B) false, because triangle have three altitude.
can someone help me
Answer:
6.6
Step-by-step explanation:
I'm just guessing because it's just adding 1.1 everytime
Kevin has $100 in a savings account that earns 10% annually. The interest is not compounded. How much will he have in 2 years?
If Kelly wakes up after 6:30, then Kelly will be late to
school.
Kelly woke up at 6:45.
A. Kelly will arrive early to school
B. Kelly will be late to school.
C. Kelly will be on time to school.
D. Kelly will catch the bus to school.
Answer:She’ll be late to school
Step-by-step explanation:
a rectangular tree lot must have a perimeter of 100 yards and an area of at least 500 square yards. Describe the possible lengths of the tree lot
Answer:
36.18 yd and 13.82yd
Step-by-step explanation:
Area of the rectangular tree = Length * Width
A = LW
perimeter of the rectangular tree = 2(L+W)
Given
Area = 500 square yards and
perimeter = 100yards, then;
100 = 2L+2W
50 = L+W .... 1
500= LW ... 2
From 1, W = 50-L
Substitute into 2;
LW =500
L(50-L) = 500
50L-L² = 500
L²-50L + 500 = 0
Factorize
L = 50±√50²-4(500)/2
L = 50±√2500-2000/2
L = 50±√500/2
L = 50±22.36/2
L = 72.36/2 and 27.64/2
L = 36.18 and 13.82
Hence the possible lengths of the tree lot are 36.18 yd and 13.82yd
Write 63/100 as a decimal
Answer:
it is 0.63
Step-by-step explanation:
plz give me a brainliest plz
For what value of a must LMNO be a parallelogram?
Answer:
a = 2.5
Step-by-step explanation:
For LMNO to be a parallelogram then opposite sides are congruent, so
ON = LM , that is
8b - 1 = 4b + 7 ( subtract 4b from both sides )
4b - 1 = 7 ( add 1 to both sides )
4b = 8 ( divide both sides by 4 )
b = 2
Then
MN = 2b + 1 = 2(2) + 1 = 4 + 1 = 5 , so
2a = 5 ( divide both sides by 2 )
a = 2.5
Thus
For LMNO to be a parallelogram , a = 2.5
The value of a that makes LMNO a parallelogram is 5/2.
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
In a parallelogram, the opposite sides are parallel and equal.
This means,
4b + 7 = 8b - 1
7 + 1 = 8b - 4b
8 = 4b
b = 2
Now,
2a = 2b + 1
2a = 2 x 2 + 1
2a = 4 + 1
2a = 5
a = 5/2
Thus,
The value of a is 5/2.
Learn more about parallelograms here:
https://brainly.com/question/1563728
#SPJ5
HELP PLS QUICK
(03.03 LC)
Look at points C and D on the graph:
What is the distance (in units) between points C and D? Round your answer to the
nearest hundredth. (5 points)
Answer:
[tex]\displaystyle d \approx 7.07[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian planeCoordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point C (-2, 0)
Point D (3, 5)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(3+2)^2+(5-0)^2}[/tex][√Radical] (Parenthesis) Add/Subtract: [tex]\displaystyle d = \sqrt{(5)^2+(5)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25+25}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{50}[/tex][√Radical] Simplify: [tex]\displaystyle d = 5\sqrt{2}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 7.07107[/tex]Round: [tex]\displaystyle d \approx 7.07[/tex]
Natilie invested $200 in a savings account that earned 4% simple interest each year. She invested for
two years without adding or taking money from her account.
A. How much INTEREST has she made? (I=PRT or Interest = Principal x Rate x Time
B. How much money does she have in total? Show work for both
Answer:
16.32 made in interest
216.32 in total
Step-by-step explanation:
Need help again, I hate this lol
Answer:
4x+64
Step-by-step explanation:
Perimeter is the sum of all sides so you add all of the expressions together. Then combine like terms, x+x+2x, and 14+14+36. Combine them and you get 4x+64.
What is the y-intercept: y + 2 - X= 0
A storekeeper increased the price of snack by 20%. If the price of a snack (after the increase) is 3.25, what is the original price?
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS!!!
What is the factored form of each expression?
24. 20x + 35y
F. 4x + 7y, G. 5xy(4 + 7), H. 5(4x + 7y), I. (20 + 35) · (x + y)
25. 24x + 64y
A. 4(6x + 16y), B. 8(3x + 8y), C. 8xy(3 + 8), D. 3x +
Answer them both please! This is due in 2 minutes!!
Answer:
The answers are H and A, let me know in a comment if you want me to explain it
WILL GIVE BRAINLIEST find area
Answer:
[tex] 60 \: {cm}^{2} [/tex]
Step-by-step explanation:
[tex]A = \frac{1}{2} (14 + 6) \times 6 \\ \\ = \frac{1}{2} \times 20 \times 6 \\ \\ = \frac{1}{2} \times 120 \\ \\ = 60 \: {cm}^{2} [/tex]
Write an inequality to match this statement: -7 is located to the right of -10. **Hint** You need to use shift and the comma button or the period button to make the greater than or less than sign. *
please tell the answer and explain how to get it
Answer:
-7 > -10
Step-by-step explanation:
We just have to compare these two numbers. When you're comparing two negative numbers, the smaller number is the bigger one. Ex. -3 is bigger than -6, so we can say that -3 > -6 (-3 is greater than -6). This means that -7 is larger than -10, which allows you to say that -7 > -10.
which of the following equations has a greater rate of change than what is shown in the graph?
A. y = 65x + 100
B. y = 85x
C. y=50x + 150
D. All of the above
Answer:
B
Step-by-step explanation:
change of a = 65
b = 85
c = 50
==> (B) is correct one.
yo i’m stuck hahahelp ASAP -4 3/8 - (-1 1/4)
Answer:
I hope this helps
Step-by-step explanation:
-3 1/8
311,305,299... find the 32nd term
Answer:
Step-by-step explanation:
It is an arithmetic sequence with common difference = -6
32nd term = 311 - 31(6) = 125
I NEED UR HELP ILL BE BRAINLISTING YALL!
A market stall holder bought a variety of coloured 'hoodies' to sell. Each hoodie costs the stall holder $20 and she intends to sell them to the public at a mark up of 65%
1) calculate the value of the markup on each hoodie.
Answer: $13
Step-by-step explanation:
The markup would be 65% of 20
65% as a decimal is 0.65
0.65*20= 13
The new price would be $33, the markup would be $13