Solve and show steps. will award brainliest.
For the first question please find the attached diagram.
As per the diagram, P is the upstream point and Q is the downstream point. The distance between P and Q is 22.5 miles.
Let the speed of the boat in the still waters of the lake be represented by S.
Then, when the boat travels upstream, the net speed of the boat will be (S-6) miles per hour because the river flows downstream and thus the speed of the boat will have to be subtracted from the speed of the river.
Now, we know that the relationship between the net speed, distance and time of travel is give as:
Distance = Net Speed x Time of travel
For the upstream ride of the board we know that Distance is 22.5 miles and Net Speed is (S-6). Therefore, the above equation will become:
[tex] 22.5=(S-6)\times T_{1} [/tex] where [tex] T_{1} [/tex] represents the time taken to travel upstream.
We can rearrange the above equation to be:
[tex] T_{1}=\frac{22.5 }{S-6} [/tex]......................(Equation 1)
By similar arguments we know that the downstream speed of the boat is S+6 and the distance travelled is the same and so the time taken to travel downstream (represented by [tex] T_{2} [/tex]) will be:
[tex] T_{2}=\frac{22.5}{S+6} [/tex]................(Equation 2)
Now, we know that the total time of travel should be 9 hours.
This means that: [tex] T_{1}+T_{2}=9 [/tex]............(Equation 3)
Plugging in the values of [tex] T_{1} [/tex] and [tex] T_{2} [/tex] from (Equation 1) and (Equation 2) into (Equation 3), we get:
[tex] \frac{22.5 }{S-6} +\frac{22.5 }{S+6}=9 [/tex]
Simplifying the above we will get a quadratic equation:
[tex] 9S^2-45S-54=0 [/tex]
The roots of this quadratic equation are:
[tex] S=-1 [/tex] and [tex] S=6 [/tex]
Since, speed cannot be negative, [tex] S=-1 [/tex] is out of consideration.
The speed of the boat in the lake is thus [tex] S=6 [/tex] miles per hour.
But we have a problem with S=6 too. The problem is that if S=6, then the boat will not be able to move upstream.
Let us solve problem 2
We are given that: [tex] \frac{x-2}{x+3}+\frac{10x}{x^2-9} [/tex]
We can rewrite it as:
[tex] \frac{x-2}{x+3}+\frac{10x}{(x-3)(x+3)} [/tex]
[tex] \frac{(x-3)(x-2)+10x}{(x-3)(x+3)} =\frac{x^2-5x+6+10x}{(x-3)(x+3)} [/tex]
Now, the numerator can be simplified as:
[tex] \frac{x^2+10x+6}{(x-3)(x+3)} =\frac{(x+3)(x+2)}{(x-3)(x+3)} =\frac{x+2}{x-3} [/tex]
Thus, our final simplified answer is:
[tex] \frac{x+2}{x-3} [/tex]
The restriction on the variable x is that it cannot be equal to either +3 or -3 as that would make the denominator of the original question equal to zero.
Thus, the restriction is [tex] x\neq \pm 3 [/tex]
In order to solve the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them? 2x-4y=5 6x-3y=10 A.Multiply the top equation by -3 and the bottom equation by 2. B.Multiply the top equation by -2. C.Multiply the top equation by -3. D.Multiply the top equation by 3 and the bottom equation by 4.
Answer:
c is correct
Step-by-step explanation:
Estimate the circumference of a circle that has a diameter of 13 yards.
Show the result in yards.
Final answer:
To estimate the circumference of a circle with a diameter of 13 yards, use the formula C = π * d where π is approximated as 3.14. The estimated circumference is 40.82 yards.
Explanation:
To estimate the circumference of a circle that has a diameter of 13 yards, you can use the formula for the circumference of a circle, which is π times the diameter (C = π * d). The value of π (pi) can be rounded to 3.14 for convenience in calculation. Using this rounded value of π:
Circumference = 3.14 * 13 yards= 40.82 yards
Therefore, the estimated circumference of the circle is 40.82 yards.
The length of a rectangle is stored in a double variable named length, the width in one named width. write an expression whose value is the length of the diagonal of the rectangle. submit
(20 points) Find AC, BC, m
Pleasee
Look at the picture below // 99 points // PLEASEE HELPP
What is the y-intercept of the line that is the perpendicular bisector of the segment joining (-3,-4) and (5,10)? express you answer as a mixed number?
What is the domain of the square root function graphed below?
Answer:
x ≥ 0
Step-by-step explanation:
The function is graphed starting at 0 and going up the positive x-axis.
These are numbers that are greater than 0; thus the domain is greater than or equal to 0, or
x ≥ 0
The domain of the function is (d) x >= 0
How to determine the domain?From the graph, we have the following highlight:
The x values of the function starts at 0 and extends the right0 is inclusive of the x valuesSince 0 is inclusive, we make use of the greater than or equal to inequality
Hence, the domain of the function is (d) x >= 0
Read more about domain at:
https://brainly.com/question/10197594
Three times the number of blue marbles exceeds twice the number of red marbles by 18 also five times the number blue marbles is two less than six times number of red marbles how many of each are there
Please guys help me with this question!
helppppppppppppppppppppppppp
Adrien has 4 liters of milk. He drinks y liters each day. If Adrien has x liters of milk left after one week, express d in terms of y.
what is the sum of (5xy + x - 8) and (13x + 2)
Which is a possible expression for the series
–7 + 12 –17 +22 –27
the solutions to the inequality y>-3x+2 are shaded on the grap.which point is a solution?
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?
Answer:
c
Step-by-step explanation:
The average monthly amount Isabella has spent on gasoline since 1990 is shown in the table. Use the data in the table to complete the statements. Let x be the number of years since 1990. The year 2005 corresponds to an x-value of . The function that best models the data, with numerical values rounded to the nearest hundredth, is f(x) = x + 22.08. Models have their limitations. For which year would this model not make sense to use?
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Divide the following polynomial and then place the answer in the proper location on the grid. Write your answer in order of descending powers of y.
(y 3 - y 2 + y + 3) ÷ (y + 1)
THE ANSWER IS:
y^2-2y+3
The reason I included the correct answer is that this question has not been asked yet and I figured that someone might need to know this. Feel free to answer the question and get the points! :)
Answer:
y²-2y+3
Step-by-step explanation:
We write the dividend, y³-y²+y+3, under the box and the divisor, y+1, to the left of the box.
We first divide y³ by y; this is y². We write this above the box, over -y². We multiply the divisor by y²:
y²(y+1) = y³+y²
This goes under the divisor. We then subtract:
(y³-y²)-(y³+y²) = -2y². We then bring down the next term, y; this gives us -2y²+y.
We then divide -2y² by y; this is -2y. This goes above the box beside the y² in the quotient. We then multiply the divisor by -2y:
-2y(y+1) = -2y²-2y
We now subtract:
(-2y²+y)-(-2y²-2y) = 3y. We bring down the last term, 3; this gives us 3y+3. We divide 3y by y; this is 3. This goes beside the -2y in the quotient. We then multiply this by the divisor:
3(y+1) = 3y+3. We then subtract: (3y+3)-(3y+3) = 0
This makes the quotient y²-2y+3.
The graph of the function g(x) is shown on the coordinate plane below. For what value of x does g(x)=0
Answer:
the answer is 6 on algebra nation
Step-by-step explanation:
Table a shows the average low temperatures recorded in a city during the first three months of the year. table b shows the average low temperatures recorded in the city during the next four months of the year. what is the difference in the medians of the two sets of data?
a.1
b.4
c.5
d.13 12)
This is not enough information, sorry
Perform the requested operation or operations.
f(x) = 7x + 6, g(x) = 4x^2
Find (f + g)(x). (5 points)
7x + 6 + 4x^2
28x3 + 24x
7x + 6 - 4x^2
seven x plus six divided by four x squared.
it took team tool bella 2 1/3 hours to hike 4 2/3 miles. whats their average speed in mph
The dimensions of a triangle are shown below. If the height of the triangle is increased by a factor of 4, which statement will be true about the area of the triangle?
Answer:
The area will increase by a factor of 4
Step-by-step explanation:
4 * 4 = 16
IT'S UP THERE STEVE (Like on family feud)
you plan to take $450 U.S on a trip to South Africa. How many rands is this if one U.S dollar equals 3.70 rands ?
822 rands
1,216 rands
1,665 rands
8,222 rands
Given:
one U.S dollar equals 3.70 rands. To find how many rands does 450 U.S dollars equal to, we need to multiply 450 with 3.70
Solution:
[tex] 1 \; U.S \; dollars \; = \; 3.70 \; rands\\ \\ 450\; U.S\; dollars= 450 \times 3.7 \; rands=1665 \; rands [/tex]
Conclusion:
1665 rands equals $450.
Using the fafsa, you can apply for
The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. What is the annual percent of decay? A) 1.19% B) 2.19% C) 3.19% D) 4.19%
Answer:
The answer is D.Step-by-step explanation:
If the object starts with a value [tex]V_0[/tex], and a annual percent of decay d, after a year the value will be
[tex]V_1 = V_0 * d[/tex]
after 2 years, taking now [tex]V_1[/tex] as the starting value
[tex]V_2 = V_1 * d = V_0 * d * d [/tex]
[tex]V_2 = V_0 * d^2 [/tex]
and so on, after n years the value will be:
[tex]V_n = V_0 * d^n[/tex]
Now, in 1997 the value was $9500, in 2012 the value was $5000. Between 1997 and 2012 there are 15 years, so, our equation will be:
[tex] \$5000 = \$ 9500 * d^{15}[/tex]
Working it a little
[tex] \frac{\$5000}{\$ 9500} = d^{15}[/tex]
[tex] (\frac{\$5000}{\$ 9500})^{1/15} = d[/tex]
[tex] (0.5263})^{1/15} = d[/tex]
[tex] 0.9581 = d[/tex]
This mean that, after a year, the value will be at 95.81 %, this is, a decay rate of 4.19%.
what is equivalent to (3^6/y^-5)^2
write an equation that represents the situation in the table?
x: y:
6 122
10 170
15 230
28 336
Dylan works 30 hours a week. His hours are decreased by 20%. How many hours does he now work each week?
Answer:
He now work 24 hours each week
Step-by-step explanation:
Dylan works 30 hours a week. His hours are decreased by 20%.
The number of work hours 30 is decreased by 20%
we need to find 20% of 30
[tex]30 \cdot \frac{20}{100} =6[/tex]
So number of hours should be decreased by 6
[tex]30-6= 24[/tex]
he now work 24 hours each week
Find the distance from A to C.
Answer:
√74
Step-by-step explanation:
a^2 + b^2 = c^2
7^2 + 5^2 = c^2
49 + 25 = c^2
74 = c^2
√74 = √c^2