Given:
Speed in still water = 12 miles per hour
Distance travel in upstream = 45 miles
Distance travel in downstream = 45 miles
Total time = 8 hours
To find:
The speed of current.
Solution:
Let the speed of current be x miles per hour.
Speed in upstream = (12-x) miles per hour
Speed in downstream = (12+x) miles per hour
We know that,
[tex]Time=\dfrac{Distance }{Speed}[/tex]
Time to cover 45 miles in upstream = [tex]\dfrac{45}{12-x}[/tex]
Time to cover 45 miles in downstream = [tex]\dfrac{45}{12+x}[/tex]
Total time is 8 hours. So,
[tex]\dfrac{45}{12-x}+\dfrac{45}{12+x}=8[/tex]
[tex]45\left (\dfrac{1}{12-x}+\dfrac{1}{12+x}\right)=8[/tex]
Taking LCM, we get
[tex]45\left (\dfrac{12+x+12-x}{12^2-x^2}\right)=8[/tex]
[tex]45\left (\dfrac{24}{144-x^2}\right)=8[/tex]
[tex]\dfrac{45\times 24}{8}=144-x^2[/tex]
On further simplification, we get
[tex]45\times 3=144-x^2[/tex]
[tex]135=144-x^2[/tex]
[tex]x^2=144-135[/tex]
[tex]x^2=9[/tex]
Taking square root on both sides.
[tex]x=\pm \sqrt{9}[/tex]
[tex]x=\pm 3[/tex]
Speed cannot be negative. So, x=3 only.
Therefore, the speed of the current is 3 miles per hour.
find the coordinates of point S On QR such that the ratio of QS to SR is 1:3 Q(2,5) R(-2,-3)
Answer:
slope or what y2-y1/x2-x1 use the formula
The coordinate of point S such that QS to SR is 1:3 will be (1,3).
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
For example (5,3) here 5 will be for the x and 3 will be for the y.
Another example is (9,0) here 9 is for x and 0 is for y.
Given the coordinate Q(2,5) and R(-2,-3)
The intersection ratio is 1 over 3
The coordinate of point S is given by
x = [1(-2) + 3(2)]/(1+3) ⇒ x = 1
y = [1(-3) + 3(5)]/(1+3) ⇒ y = 3
Hence "The coordinate of point S such that QS to SR is 1:3 will be (1,3)".
For more about coordinates,
brainly.com/question/7869125
#SPJ2
7.5x - 0.8 = 5.6x + 3.95 anybody know? lol
Answer:
X = 2.5.
Step-by-step explanation:
I believe 2.5 should be the solution. Here is how you can solve the equation:
Combine like-terms, First combine the simpler numbers, add 0.8 to 5.6X + 3.95. This should get you the equation: 7.5X = 5.6X + 4.75. Then combine 7.5X and 5.6X by subtracting 5.6X from 7.5X to get the equation: 1.9X = 4.75.
Now, divide 4.75 by 1.9. By dividing these two numbers you should get the equation: X = 2.5.
Hope this helps! Let me know.
Graph y
-2x + 5.
Can someone help me on this plz
Answer:
x axis =2.5 y axis 5
Step-by-step explanation:
you can also use a site called desmos to graph it for u
What is the value of x?
.20
.35
.60
.70
Answer:
20
Step-by-step explanation:
2x=40 so once you divide both sides by 2 you get x=20
Perform the indicated operation. (-3 + 5i) - (7 + 9i) -10 + 4i 4 - 4i -10 - 4i
Answer:
-26-8i does this help?
Step-by-step explanation:
I took what was in the parenthesis and put them together coming out with -10 and -4i. Then I took what was next and started putting the variables together and the numbers together.
Maryanne sells cruise vacations.
She makes a base salary of $2,500 per month plus 5% of the cost of each vacation. This month she sold $80,000 in cruises. What are her total monthly wages?
Enter the correct answer in the box.
$____
Which is the graph of f(x) = (x – 1)(x + 4)?
On a coordinate plane, a parabola opens down. It goes through (negative 1, 0), has a vertex at (1. 75, 6.2), and goes through (4, 0).
On a coordinate plane, a parabola opens down. It goes through (negative 4, 0), has a vertex at (negative 1. 75, 6.2), and goes through (1, 0).
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1. 75, negative 6.2), and goes through (4, 0).
Below is the graph. In other words, the last one is correct.
Answer:
D on edge
Step-by-step explanation:
put the function into desmos
please help as son as possible
Answer:
12 hours
Step-by-step explanation:
Split the 32 in half, and you get 16. Subtract 4 from that, and you get 12. Lily works 12 hours.
Choose the best definition for the following term: substitution
Answer:
In Algebra "Substitution" means putting numbers where the letters are: When we have: x. −
Step-by-step explanation:
The formula 2y = 3x + 6 is used in chemistry. How can this formula be solved for Y?
[tex]2y = 3x + 6\\y = \frac{3}{2}x + \frac{6}{2} = \frac{3}{2}x + 3[/tex]
|-9-3| + (-16:4)
Evaluate the following expressions
Answer:
I got 12 + (-16 :4)
Step-by-step explanation:
if u could subscribe to my friend penny_pg3d, that would be great!
There are 1440 minutes in each day.
Choose the best approximation of the number of minutes in each day.
Answer:
1 * 10^3
Step-by-step explanation:
1440 can be rounded off to the nearest hundred as 1400.
1440 can be rounded off to the nearest thousand as 1000.
1000 = 1 * 10^3
Hana paid $1,200 for the carpet in her living room. The room has an area of 251.2 square feet. What was her unit cost of carpeting in dollars per square foot? Round to the nearest cent.
pls help i am really needing it god bless u if u help me
Step-by-step explanation:
$1,200 divided by 251.2
hope this helps
Lets break this down.
This is pretty easy, if you just think about it, all we have to do is............. DIVIDE!
So what IS, 1200 by 251.2??
the answer is to your question 4.8
What value of c makes the polynomial below a perfect square? X2+5x+C
A. 25/2
B. 25/4
C. 5/4
D. 5/2
Answer:
I think the answer is c = 25/4
Step-by-step explanation:
For the function f(x) = 0.25 (x - 1) (x + 7) identify the vertex.
Answer:
Mark brainly then I will answer..
Which factor pair has a product of 75?
A) 25 and −3
B) −15 and 5
C) −75 and 1
D) −25 and −3
Answer:
D)-25 and -3
Step-by-step explanation:
-25 × -3
25×3(minus,minus cut)
=75
How does the value of the digit 3 in the number 63,297 compared to the value of the digit 3 in the number 60,325?
Answer:
The value of digit 3 in 63,297 is in the thousands place while the digit 3 in the number 60,325 is in the hundreds place
Hope this helps!
Olivia planted 25 tomato plants but only 20 produce tomatoes what percentage of the plants did not produce tomatoes?
answer:
1.25 %
explanation:
25 - 20 = 5 (5 plants didn't produce)
25 ÷ 100 × 5 = 1.25 %
Helppppp!!!!!!!!!!!!!!
Answer:
pour the water out
Step-by-step explanation:
Answer:
the answer is 1.8
Step-by-step explanation:
100 POINTS!!!!!!!!!!! ( I NEED FAST ANSWERS ) The table below shows Karen's distance during the
marathon. Between which hours does Karen run the fastest?
Answer:
Between 6 and 9 hours.
Reason: the slope increases during 6-9 hour period.
The altitude of Death Valley California is 282 ft below sea level of hot air balloon is launched From The Bottom Of Death Valley and Rises at a rate of 10 ft per second after 12 seconds balloon Captain lower the balloon 15 ft what is the altitude of a hot air balloon after being lowered
Answer:
177 ft below sea level.
Step-by-step explanation:
Initial altitude of the hot air balloon = 282 below sea level
Rate of rise of balloon = 10 ft / second
Time = 12 seconds
Total rise in 12 seconds = Rate of rise of balloon [tex]\times[/tex] Time
[tex]\Rightarrow 10 \times 12[/tex] = 120 ft
Now, we will have to subtract to find the new altitude.
New altitude = 282 - 120 = 162 ft
Now, it is given that balloon Captain lowers the balloon 15 ft.
To find the final altitude, we will have to add it to the previous altitude.
Therefore, the final altitude = 162 + 15 = 177 ft below sea level
I need help!!!!with this math question
The elivation of city A is 60 feet above sea level; the elevation of city C is 12 feet above sea level. The elevation of city D is 1/2 of the elevation of city c. How do you represent the elevation, in feet, of city d?
Answer:
The elevation of city d is 6 feet
brainliest??
HELPPPP ASAPP WILL MARK BRAINLIST
Which sequence of transformation results and figures that are similar, but not congruent?
A. Reflected across the X axis, then dilated by a factor of 1/3
B. Rotated counterclockwise 90° then translated six units to the left
C. Translated to units down, then reflected across the Y axis
D. Reflected across the Y axis then translated seven units to the left
Can someone help me
Answer:
Answer I think 2 is it
...........
What is the answer to this?
Find the length of RS with endpoints R(4,5) and S(-1, – 4).
Answer:
[tex]d=\sqrt{106}[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in your 2 coordinates into the distance formula to find distance d:
[tex]d=\sqrt{(-1-4)^2+(-4-5)^2}[/tex]
[tex]d=\sqrt{(-5)^2+(-9)^2}[/tex]
[tex]d=\sqrt{25+81}[/tex]
[tex]d=\sqrt{106}[/tex]
Erica was deducted 450 points while she was playing a
video game. She was deducted 30 points each time. How
many times was she deducted 30 points? Work this problem
out on paper or your white board. Then snap a picture of your work
using the camera tool.
Answer:
15
Step-by-step explanation:
hope this helps
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 10 hours of burning, a candle has a height of 17 centimeters. After 21 hours of burning, its height is 12.6 centimeters. What is the height of the candle after 14 hours?
Answer:
The height of the candle after 14 hours is 15.4 centimeters
Step-by-step explanation:
A linear function is a polynomial function of the first degree of the form:
f(x)= m*x + b or y= m*x + b
where m is the slope of the function and b is the ordinate at the the y-intercept.
In this case height=m*time + b
Given two points of the line, point 1 (x1, y1) and point 2 (x2, y2), we can find the equation of the line or linear function.
You must first find the slope of the line using the expression:
[tex]m=\frac{y2 - y1}{x2 - x1}[/tex]
In this case you know the two points are (x1, y1)= (10,17) and (x2, y2)=(21,12.6)
So the slope is:
[tex]m=\frac{12.6-17}{21-10}[/tex]
m= -0.4
Now you find the value of b, replacing m in the equation, the values of x and y by the values of the coordinates of one of the points and solving for b to obtain its value.
Replacing (x1, y1)= (10,17) and m=-0.4 in the expresion y=m*x+b:
17= -0.4*10 + b
and solving you get:
17= -4 + b
17 + 4= b
21= b
So: height= -0.4*time + 21 where the height is expressed in centimeters and the time in hours.
To calculate the height of the candle after 14 hours, you simply replace the time by 14:
height= -0.4*14 + 21
height= 15.4
The height of the candle after 14 hours is 15.4 centimeters
Solve:
m
m
Fine m
Graph is in picture :)
Answer:
50
Step-by-step explanation:
if you take 138 witch equals the whole angle and subtract the second part of the abngle 88 we get 50 equaling the unknown angle