Answer:
7 mph
Step-by-step explanation:
Let x mph be the canoeist's rate in still water.
The speed of the current in a stream is 2 mph, then
the canoeist's rate upstream is x-2 mph;the canoeist's rate downstream is x+2 mph.The distance covered is 22.5 miles.
The time to go upstream [tex]\dfrac{22.5}{x-2}[/tex] hours.
The time to go downstream [tex]\dfrac{22.5}{x+2}[/tex] hours.
It takes a canoeist 120 minutes (= 2 hours) longer to paddle 22.5 miles upstream than to paddle the same distance downstream, then
[tex]\dfrac{22.5}{x-2}-\dfrac{22.5}{x+2}=2\\ \\22.5\left(\dfrac{1}{x-2}-\dfrac{1}{x+2}\right)=2\\ \\22.5\cdot \dfrac{x+2-x+2}{(x-2)(x+2)}=2\\ \\\dfrac{22.5\cdot 4}{x^2-4}=2\\ \\x^2-4=22.5\cdot 2\\ \\x^2-4=45\\ \\x^2 =49\\ \\x=\pm 7[/tex]
The canoeist's rate cannot be negative, then his rate in still water is 7 mph.
Final answer:
To find the canoeist's rate in still water, we set up equations using the time taken to travel 22.5 miles upstream and downstream, with the current's rate given as 2 mi/hr. A time difference of 2 hours between both directions yields a quadratic equation which can be solved to determine the canoeist's rate in still water.
Explanation:
To determine the canoeist's rate in still water, we first need to find the rates traveling upstream and downstream. Let's denote the canoeist's rate in still water as r (in miles per hour), and the rate of the current as 2 mi/hr. When the canoeist paddles upstream, the effective rate is r - 2 mi/hr and when paddling downstream, the effective rate is r + 2 mi/hr.
Given the distance is 22.5 miles in both directions, we can set up two equations:
1) Time upstream = Distance / (r - 2),
2) Time downstream = Distance / (r + 2).
The problem states that it takes 120 minutes (or 2 hours) longer to paddle upstream than downstream, so we have:
Time upstream = Time downstream + 2 hours.
Plugging in the equations from above gives us:
22.5 / (r - 2) = 22.5 / (r + 2) + 2.
Solving this equation, we multiply through by (r - 2)(r + 2) to get rid of the fractions, resulting in:
22.5(r + 2) = 22.5(r - 2) + 2(r² - 4),
which simplies to a quadratic equation we can solve for r.
Therefore, the rate of the canoeist in still water is approximately 3.65 miles per hour.
can someone help me do this problem please
|2x-4|=22
Answer:
2x-4 = 22
2x = 26
x=13 check |26-4|=22
-(2x-4) = 22
-2x+4 = 22
-2x = 18
x=-9 Check |-18 -4| = |-22| = 22
Answer:
x=13
Step-by-step explanation:
Finding the answer to this is very simple actually. you can actually solve this problem without the || because x has to be a positive value for this to work. 2x-4=22 can be done by adding 4 to both sides and getting the answer 26. Isolate the variable by dividing both sides by 2 to get x=13
A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a straight river bank instead of fencing as one side of the rectangle, as shown in the figure.
The farmer can determine the dimensions of the fenced area by solving the formula L + 2W = 180 feet, where L is the length of the fenced region along the river bank and W is the width.
Explanation:This is a classic application of the perimeter of a rectangle in the field of Mathematics. If the farmer is using part of a straight river bank instead of fencing for one side of the rectangle, then he only needs fencing for the other three sides. The formula to calculate the perimeter of a rectangle is 2(length) + 2(width), but since one side is not fenced, it is length + 2(width) in this case.
If we assume the length (L - along the river bank) and width (W) of the rectangular area, then the equation can be expressed as:
L + 2W = 180 feet
This formula can help the farmer calculate the dimensions of the fenced area needed in order to use his materials most effectively. He needs to solve this equation to find the values of length and width that add up to 180 feet.
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Identify the x-intercept.
1) y= 1/5x + 3
2) y= 6x - 7
3) y= -8/3x + 9
Answer:
Step-by-step explanation:
the x-intercept when y = 0
1 ) 1/5 x +3 =0 1/5x = - 3 so : x = -15
2) 6x -7 = 0 6x = 7 so ; x =7/6
3) -8/3x +9 = 0 -8/3 x = -9 so : x =27/8
|b|+b^3;b=-2 evaluate the expression
Answer:
-6
Step-by-step explanation:
[tex] | - 2| = 2 \\ {( - 2)}^{3} = ( - 2)( - 2)( - 2) = ( - 8) \\ \\ | - 2 | + {( - 2)}^{3 } = 2 - 8 = - 6[/tex]
To evaluate the expression |b|+b^3 when b=-2, substitute -2 for b, evaluate |b| and b^3 separately and then add the results.
Explanation:To evaluate the expression |b|+b^3 when b=-2, we substitute -2 for b in the expression.
The absolute value of a number is that number's distance from zero on a number line, regardless of which direction. This means that the absolute value of any negative number is its positive equivalent. Thus, |b| is the same as |-2|, which equals 2.
Secondly, b^3 means b multiplied by itself twice. So (-2)^3 equals -2*-2*-2 which is -8.
First, we evaluate |b|. The absolute value of -2 is 2, so |b| = 2.
Next, we evaluate b^3. (-2)^3 = -8.
Finally, we add the two results together: 2 + (-8) = -6.
Therefore, when b=-2, the expression |b|+b^3 evaluates to -6.
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What is the cube of the difference of 40 and a number
Answer:
(40-y)^3
Step-by-step explanation:
Make the unknown y
(40-y)^3
Answer:
The difference can be expressed as
y=x³+120x²-4800x+64000
Or
y=(40-x)³
Step-by-step explanation:
Step one
To solve the problem problem let us first initialize the number to be x
By breaking the statement into component parts and implementing
Step two
1. The difference between 40 and the number
=(40-x)
2. The cube of the difference
= (40-x)³
Let us equate the expression to y
y=(40-x)³
Step three
Expanding the expression we have
y= (40-x)(40-x)(40-x)
Opening bracket we have
y=(1600-40x-40x+x²)(40-x)
y=64000-1600x-
1600x+40x²-1600x+40x²+40x²-x³
y=x³+120x²-4800x+64000
Enter the numerical coordinates of the vertices of quadrilateral ABCD in the table. (Point A has been done for you.) Then predict the numerical coordinates of the vertices of quadrilateral A′B′C′D′ as the figure translates four different ways: 7 units up, 1 unit down, 4 units to the right, and 3 units to the left.
Answer:
Step-by-step explanation: Edmentum Answer
Answer:
Step-by-step explanation: I got it wrong lol
Select the prime number and multiply by 1000
4. 6. 7. 8. 15. 21
7 is the prime number.
7 × 1000 = 7000
What is 14/18 as decimal
Answer:
14/18 = 0.778
Step-by-step explanation:
14 divided by 2 = 7
18 divided by 2 = 9
7/9 is the same as 7 divided by 9
= 0.778
The decimal equivalent of [tex]\( \frac{14}{18} \)[/tex] is approximately 0.777777777777778.
To convert [tex]\( \frac{14}{18} \)[/tex] to a decimal, one divides 14 by 18. This can be done by hand or with a calculator. When dividing 14 by 18, the result is a repeating decimal where the digit 7 repeats indefinitely. This repeating decimal can be represented as 0.777777777777778 when rounded to the nearest 10th decimal place.
Alternatively, one can simplify the fraction [tex]\( \frac{14}{18} \)[/tex] before converting it to a decimal. By dividing both the numerator and the denominator by their greatest common divisor, which is 2, the fraction simplifies to [tex]\( \frac{7}{9} \)[/tex]. When 7 is divided by 9, the result is again the repeating decimal 0.777777777777778.
In summary, [tex]\( \frac{14}{18} \)[/tex] simplifies to [tex]\( \frac{7}{9} \)[/tex] and as a decimal, it is approximately 0.777777777777778.
for every 8 candles that you sell you raise $96 you raise $288 how many candles did you sell
Jason burned 1,400 calories Friday playing 1 hour of basketball and canoeing for 2 hours. On Saturday, he spent 2 hours playing basketball and 3 hours canoeing and burned 2,500 calories. How many calories did he burn per hour when playing basketball?
Answer: He burned 800 calories per hour playing basketball.
Step-by-step explanation:
Let be "b" the amount of calories per hour Jason burned playing basketball and "c" the amount of calories per hour Jason burned canoeing.
Set up a system of equations:
[tex]\left \{ {{b+2c=1,400} \atop {2b+3c=2,500}} \right.[/tex]
You can apply Elimination Method:
Multiply the first equation by -3.Multiply the second equation by 2.Add these equations.Finally, solve for "b".Therefore, you get:
[tex]\left \{ {{-3b-6c=-4,200} \atop {4b+6c=5,000}} \right.\\.............................\\b=800[/tex]
What is 4/3 - (-3/4)
Answer:
0 I think
Step-by-step explanation:
Answer:
25/12 or 2 1/12
Step-by-step explanation:
4/3 - (-3/4) =
= 4/3 + 3/4
= 16/12 + 9/12
= 25/12
= 2 1/12
How to write 12 ten thousands 8 thousands 14 hundreds 7ones
Answer:
129,407.
Step-by-step explanation:
12 ten-thousands = 12*10000=120,000.
8 thousands = 8*1000=8000;
this gives us 120,000+8,000=128,000.
14 hundreds = 14*100=1400;
this gives us 128,000+1,400=129,400.
7 ones = 7*1=7;
this gives us 129,400+7=129,407.
Answer:
12,000 8,000 1,400 7
Step-by-step explanation:
I hope u get a tutor if u dont know how to do this I hope this helps
what is
[tex] \sqrt{180 } [/tex]
simplified?
Answer:
Step-by-step explanation:
I don't know exactly how simplified it will be, but you can get the square root smaller.
180: 2*2 * 3*3 *5
For every pair of prime factors you can take 1 of the pair outside the the square root and throw the other one away
sqrt(2*2*3*3*5) = 2 * 3 * sqrt(5) = 6*sqrt(5)
transform pls in fraction (transformati in fractie pls) 3,(7)
Answer:
The fraction number is [tex]\frac{34}{9}[/tex]
Step-by-step explanation:
we have
[tex]3.777...[/tex]
This is a repeating decimal (a decimal that has a digit, that repeat over and over and over again without ever ending)
Convert to fraction number
Let
[tex]x=3.777...[/tex]
[tex]10x=37.777...[/tex]
we know that
[tex]10x-x=37.777...-3.777...[/tex]
[tex]9x=34[/tex]
[tex]x=\frac{34}{9}[/tex]
therefore
The fraction number is [tex]\frac{34}{9}[/tex]
how many vertical asymptotes does the graph of this function have? f(x)=5/3x(x+1)(x-7)
Answer:
The graph of the function has three vertical asymptotes
Step-by-step explanation:
we have the function
[tex]f(x)=\frac{5}{3x(x+1)(x-7)}[/tex]
we know that
To find the vertical asymptotes of a rational function, simply set the denominator equal to 0 and solve for x.
so
[tex]3x(x+1)(x-7)=0[/tex]
The values of x are x=-1,x=0, x=7
using a graphing tool
see the attached figure to better understand the problem
therefore
The graph of the function has three vertical asymptotes
Answer:
3. The answer is 3
Step-by-step explanation:
11.3 divided by 100
Find the quotient:
32) 8,736
Answer:
273
Step-by-step explanation:
8736÷32=273
273×32=8736
Let's assume that bacteria doubles every 10 minutes. If a culture begins with exactly
30 bacterial cells, how many bacteria will be present after 1 hour?
A 960 Bacteria
B 1000 Bacteria
C 1520 Bacteria
D 1920 Bacteria
Greetings!
First off, we should know that there are 60 minutes in an hour. Therefore, the first step we will need to do, is divide 60 by 10.
60 ÷ 10 = 6
As shown above, we now know we will have to double the number 6 times. If we start with 30, this will be our first problem.
(1) 30 + 30 = 60
And so on and so forth...
(2) 60 + 60 = 120
(3) 120 + 120 = 240
(4) 240 + 240 = 480
(5) 480 + 480 = 960
(6) 960 + 960 = 1920
And after our sixth time we have our answer:
1920 bacteria
Hope this helps!
~Fluerie
What is the quadratic equation to this question
Answer:
f(x) = 4x − 12
Step-by-step explanation:
It's not quadratic. It's linear. Each time x increases by 1, f(x) increases by 4. So the slope is 4. The y-intercept (when x=0) is -12. The equation of the line is therefore:
f(x) = 4x − 12
Estimate 29.14 x 5.2
Answer:
About 151.500
Step-by-step explanation:
Actual answer is 151.528 Just go with mental math.
Next number in the sequence 1 4 9 16 25
The next number in the sequence is 36.
Starting from 1, the number increases by 3, 1 + 3 = 4. But the next number, the number it's being increased by increases by 2. 3 + 2 = 5, 4 + 5 = 9. And again, 5 + 2 = 7, 7 + 9 = 16. And again. 7 + 2 = 9, 16 + 9 = 25. Therefore, it is increased to + 11, and the next number is 36.
I hope this helped, and you have a great day!
Answer:
36
Step-by-step explanation:
1² = 1 2² = 43² = 94² = 165² = 256² = 36divide line segments
please help me with this thanks a lot please I dont really understand show work :)
tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,
[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}[/tex]
Worth 13 Points!
write each rational number in the form a/b ( <---- this is when i got confused ), where a/b are integers.
1. 0.3 _______
2. 2 7/8 ____
3. -5 _____
4. 16 _____
5. -1 3/4 _____
6. -4.5 _____
7. 3 _____
8. 0.11 ____
Answer:
7 is rmthe correct answer as it's value is 3 the answer is on no 7.
Simplify: -3(4x - 5)
12x -15
12x + 15
-12x + 15
Simplify: -5x + 8 - 11x - 12
-16x - 4
16x + 4
16x - 4
2(4x - 8) - 10
8x + 26
8x - 26
-8x - 26
Answer:
[tex]8x - 26 \\ -16x - 4 \\ -12x + 15[/tex]
Step-by-step explanation:
2(4x - 8) - 10
8x - 16 - 10
|_______|
8x - 26
-5x + 8 - 11x - 12
___ ___ _____ ____
___ ____
-16x - 4
-3(4x - 5)
-12x + 15
For the third and first exercises, you just use the Distributive Property, and for the second exercise, all you are doing is combining like-terms.
I am joyous to assist you anytime.
the number 3456 is divisible by which single-digit numbers?
Answer:
1, 2, 3, 4, 6, 8, 9
The number 3456 is divisible by the single-digit numbers 2, 3, 4, 6, and 8.
Explanation:The number 3456 is divisible by the single-digit numbers 2, 3, 4, 6, and 8.
To determine if a number is divisible by another, we check if the remainder is 0 when dividing the number being tested by the potential divisor. In this case, for example, if we divide 3456 by 2, we get no remainder, so it is divisible by 2.
Similarly, if we divide 3456 by 3, 4, 6, or 8, we get no remainder in each case, so it is also divisible by these numbers.
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What is the median of 6, 7, 10, 12, 15?
Answer:
10
Step-by-step explanation:
An equation of a line perpendicular to the line represented by the equation y=-1/2x-5 and passing through (6,-4)
Answer:
y = 2x - 16
Step-by-step explanation:
Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes]:
-½ → 2
-4 = 2[6] + b
-16 = b
y = 2x - 16 >> Perpendicular Line in Slope-Intercept Form
I am joyous to assist you anytime.
The equation of the line that is perpendicular to y = -1/2x - 5 and passes through the point (6, -4) is y = 2x - 16. This is found using the concept of negative reciprocals and the point-slope form of the line equation.
Explanation:The equation of the original line given is y = -1/2x - 5. The slope of this line is -1/2. Since a line perpendicular to this line will have a slope which is the negative reciprocal of -1/2, the slope of the line we're seeking is 2 (because -1 divided by -1/2 is 2).
We also know from the question that the line we're seeking passes through the point (6, -4). Using the slope-intercept form of the equation of a line (y = mx + b), where m is the slope and b is the y-intercept, we substitute the slope and the coordinates of the point into the equation to solve for 'b': -4 = 2*6 + b. Solving this equation gives us b = -16.
Therefore, the equation of the line that is perpendicular to y = -1/2x -5 and passing through the point (6, -4) is y = 2x - 16.
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Write to show how you make a ten. Then add. What is 7+8?
Answer:14
Step-by-step explanation:
Answer:
it's 15
Step-by-step explanation:
Which expressions have products of -0.64? If they do not have a product of -0.64, explain a way to make them have that product.
A.(0.32)(-2)
B.1.6(-4)
C.0.64(-1)
D.(1.28)(-0.5)
E.(-4)(-0.16)
Answer:
A, C, and D are correct
Step-by-step explanation:
A. (0.32)(-2)
(0.32)(-2) = -0.64
Correct.
B. 1.6(-4)
1.6(-4) = -6.4
Wrong.
Divide by 10.
[tex]\dfrac{-6.4}{10} = \mathbf{-0.64}[/tex]
C. 0.64(-1)
0.64(-1) = -0.64
Correct.
D. (1.28)(-0.5)
(1.28)(-0.5) = 0.64
Correct.
E. (-4)(-0.16)
(-4)(-0.16) = 0.64
Wrong.
Multiply by -1.
(0.64)(-1)= -0.64
7/5 rational or irrational
Answer:rational
Step-by-step explanation:
Answer:
Step-by-step explanation:
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.