Answers
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]
Related Questions
In which of the following circles are the values of the area and circumference the same? Approximate Π as 3.14.
a circle with a radius of 2 feet
a circle with a diameter of 2 feet
a circle with a radius of 4 feet
a circle with a diameter of 1 foot
Answers
[tex]A = \pi r^2[/tex]
and
[tex]C=2\pi r[/tex]
so:
[tex]A=C\\\\\pi r^2=2\pi r\qquad|:\pi\\\\r^2=2r\qquad|:r\\\\\boxed{r=2}[/tex]
It is true when radius = 2 units, so correct answer is:
A) a circle with a radius of 2 feet.
Answer:
Circle with a radius of 2 feet
Step-by-step explanation:
11. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
Answers
ABCD ~ NMPO. Note it's important to match up the corresponding angles.
For similar triangles, the ratio of corresponding sides is the same.
So the ratio of AB to NM equals the ratio of BC to MP.
AB/NM = BC/MP
(y - 1) / 6 = 5/3
Solve for y.
Use the same process to find x.
CD/PO = BC/MP
A cylindrical candle has a height of 11 cm and a diameter of 10 cm.
what is the volume of the candle, rounded to the nearest whole number?
Answers
The answer is 864 cm³
The system of equations below has no solution 2/3x+5/2y=15 4x+15y=12 which equation could represent a linear combination of the system
Answers
we have
(2/3)x+(5/2)y=15 equation (I)
4x+15y=12 equation (2)
multiplying equation (1) by 6
6(2/3)x+6(5/2)y=6(15)--------------------- > 4x+15y=90 equation (3)
Subtracting equation (3) from equation (2) gives
4x+15y=90
4x+15y=12
-----------------
0x+0y=78------------ > 0=78
Therefore, a system of linear equation that has no solution results on two unequal numbers in both sides of the equation.
the answer is the option B) 0=26
Answer:
B.)0=26
Step-by-step explanation: Keep it simple
A small plane is 20 miles due north of the airport. a jet at the same altitude as the plane is 64.5 miles west of the airport. to the nearest tenth, what is the distance between the small plane and the jet? enter your answer as a decimal in the box.
Answers
okay realize that the distance traveled by the small plane, distance traveled by jet, and the distance between them makes a right triangle. Using Pythagorean theorem and allowing x be the distance between them, x² = (20 miles)² + (64.5 miles
x = 67.53 miles the distance between the two entities in nearest tenth is approximately 67.5 miles.
Using the Pythagorean theorem, we can calculate the distance between a small plane 20 miles north of an airport and a jet 64.5 miles west of the airport as 67.5 miles to the nearest tenth.
Given that a small plane is 20 miles due north of the airport and a jet is 64.5 miles west of the airport, the scenario forms a right-angled triangle with the legs representing the distances from the airport to each aircraft. To find the distance between the small plane and the jet, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
The equation for the distance (d) between the two planes can be expressed as:
d² = north side² + west side²
d² = 202 + 64.52
d² = 400 + 4160.25
d² = 4560.25
d = √4560.25
d = 67.5 miles (rounded to the nearest tenth)
Thus, the distance between the small plane and the jet is 67.5 miles to the nearest tenth.
Two angles are ____ when they have a common vertex and a common side and don’t overlap.
Answers
Alice, Bob, Farhana, and Jamal went out for pizza. When the bill came, they decided to split the check. Alice figured out what she owed by multiplying the bill by 0.25. Bob figured his share by finding 30% of the total. Farhana figured out her amount by dividing the total by 3. To determine what he owed, Jamal found 12% of the total. Who paid the most money?
Answers
Alice paid $35
Bob paid $42
Farhana paid about $46.67
Jamal paid $16.80
Your answer is Farhana, any number that you pick as your total, you will end up with the same results, Farhana being the most.
Hope this helped!
~xox Melis
In the scenario where a pizza bill is split between Alice, Bob, Farhana, and Jamal, Farhana ends up paying the most since she covers approximately 33.33% of the total bill.
Explanation:The question asks about Alice, Bob, Farhana, and Jamal splitting a pizza bill and figuring out who paid the most. Alice paid 25% (0.25) of the total bill, Bob paid 30% (0.30), Farhana paid a third which is approximately 33.33% (1/3), and Jamal paid 12% (0.12). Given these percentages, it is clear that Farhana paid the most for the pizza because 33.33% is the largest percentage amongst all. Therefore, irrespective of the total bill amount, Farhana ended up paying the highest portion.
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A local restaurant advertises that the mode cost of their most popular meals is $8. If the costs of their most popular meals are $7, $8, $8, $12, $13, $15, $17, $18, and $20, which word or phrase best describes this kind of advertising?
Answers
Find the annual interest rate. I=$54, P=$900, t=18 months
Answers
[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$54\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{18}{12}\to &\frac{3}{2} \end{cases} \\\\\\ 54=(900)(r)\left( \frac{3}{2} \right)\implies \cfrac{54}{(900)\left( \frac{3}{2} \right)}=r\implies \cfrac{1}{25}=r\implies 0.04=r \\\\\\ r\%=0.04\cdot 100\implies r=\stackrel{\%}{4}[/tex]
Answer:
4%
Step-by-step explanation:
yw
Can anyone please help me with this problem? I got my answer incorrect, and I don’t understand why.
Answers
a) is asking what is the initial height, and that occurs right before the balloon is shot up, at 0 seconds, namely at x = 0.
Complete the tasks to subtract the polynomials vertically. (1.3t3 + 0.4t2 – 24t) – (0.6t2 + 8 – 18t) What is the additive inverse of the polynomial being subtracted? –0.6t2 + (–8) + (–18t) –0.6t2 + (–8) + 18t –0.6t2 + 8 – 18t 0.6t2 + (–8) + 18t
Answers
Final answer:
The additive inverse of the polynomial [tex](0.6t^2 + 8 - 18t)[/tex]being subtracted is [tex]-0.6t^2 - 8 + 18t.[/tex] This involves changing the sign of each term in the polynomial.
Explanation:
The additive inverse of a polynomial is obtained by changing the sign of each term in the polynomial. Given the polynomial to be subtracted ( [tex]0.6t^2 + 8 - 18t)[/tex], its additive inverse is found by changing the sign of each term, resulting in [tex]-0.6t^2 - 8 + 18t.[/tex] This operation flips the signs, preparing the polynomial for the subtraction process without altering its magnitude but reversing its direction on the number line.
(50 points worth ) A rectangular prism fish tank a length of 5 1/2 in., a width of 7 in., and a height of 2 1/2 in. Use this to answer questions (a) and (b) below.
A) What’s the volume of this fish tank? Show all work and express your answer as a mixed number in its most simplified form!
B) Could this fish tank hold 100 in³ of water? Answer yes or no, then explain why in one or more sentences.
Answers
By definition we have that the volume of a rectangular prism is given by:
V = (w) * (l) * (h)
Where,
w: width
l: long
h: height
We then have to replace the values:
V = (7) * (5.5) * (2.5)
V = 96.25 in ^ 3
Equivalently:
V = 96 1/4 in ^ 3
B) Could this fish tank hold 100 in³ of water? Answer yes or no, then explain why in one or more sentences.
No, this fish tank could not hold 100 in³ of water.
This is because the prism volume (part A) is less than 100 in ^ 3.
In other words;
96 1/4 in ^ 3 <100 in ^ 3
A line Segment is part of a line that is bounded by two distinct end points. True or False?
Answers
The part of a line that connects two points.
It has definite end points.
Adding the word "segment" is important, because a line normally extends in both directions without end.
A diagram of line segment is attached with the solution .
Batman is 4 times robins age the sum of their ages equals to 45 how old is batman and robin
Answers
We can set up a system of equations as such with the given information:
[tex]b=4r\\b+r=45[/tex]
Using substitution, we plug-in 4r from the first equation into b in the second equation to get [tex]5r=45 \\ r=9[/tex].
Now, we plug in the value of r into the first equation to get [tex]b=4(9)=36[/tex].
Thus, Batman is 36 years old, and Robin is 9 years old... A little weird?
A group of 8 friends plan to go watch a movie but they only have 5 tickets. How many different combinations of 5 friends could possibly receive the ticket?
A)13
B)10
C)56
D)64
Answers
Explanation:
1) You have to find the number of ways how you can combine 5 friend (this is form groups of 5 people) out of a group of 8.
2) That is the 5C8
3)The formula for combinatory is: nCm = m! / [ n! (m - n)!]
4) So for m = 8 and n = 5 you get:
5C8 = 8! / [5! (8 - 5)! ] = 8*7*6*5! / [ 5! * 3!] = 8*7*6 / [ 3*2*1] = 8*7 = 56
So, the answer is the option C) 56.
Maya's standard deduction on her federal income tax return is $8350. If she paid $5980 in state taxes and $2430 in mortgage interest last year, should she use her standard deduction?
Answers
Answer: b no because it is less then the deduction she would get from itemizing
3. Triangle ABC has angle measures as shown.
a) What is the value of x? Show your work.
Answers
(x -5) +(3x +30) +35 = 180
4x +60 = 180 . . . . . . . . . . . . . collect terms
4x = 120 . . . . . . . . . . . . . . . . . subtract 60
x = 30 . . . . . . . . . . . . . . . . . divide by 4
a) The value of x is 30.
[tex](x - 5) + (3x + 30) + 35 = 180[/tex]
[tex]x - 5 + 3x + 30 + 35 = 180[/tex]
Sum up x + 3x
[tex]4x - 5 + 30 + 35 = 180[/tex]
Sum up all the numbers
[tex]4x + 60 = 180[/tex]
Substract 60 from both sides
[tex]4x = 120[/tex]
And finally divide by 4 (on both sides)
[tex]x = 30[/tex]
The first team of workers received 50 kg of cement less than the second team. for every hour of work the first team was using 150 kg of cement, while the second team was using 200 kg. in three hours the first team had 1.5 times as much remaining cement as the second team. how much cement was delivered to each team of workers?
Answers
the amount of cement the first team received is termed as 'x' hereafter
the cement the second team received is termed as 'y'
the first team received 50 kg less, the 1st equation is as follows;
x = y - 50 after rearranging
1) x-y = -50
for every hour 150 kg and 200 kg were used by the two teams separately
after three hours first team used up 150*3 = 450 kg
the second team used up 200 * 3 = 600 kg
however the first team had 1.5 times as much as second team had after three hours.
After three hours;
the amount second team had leftover was y - 600
the amount first team had leftover was x - 450
the amount the second team had ,multiplied by 1.5 is equal to what the first team had
we can build the 2nd equation using this information
1.5 * (y-600) = x-450
1.5y - 900 = x - 450
rearrange the equation,
1.5y - x = -450 +900
2) 1.5y - x = 450
add 1st and 2nd equations to eliminate x
1) + 2) (x - y = -50) + (1.5y - x = 450)
1.5y - y = 450 -50
0.5y = 400
y = 400/ 0.5
y = 800 kg
substitute y = 800 in x = y - 50
x = 800 - 50
x = 750 kg
first team received 750 kg and second team received 800 kg
Identify the type of sequence shown in the table below and select the appropriate response. n f(n) 1 540 2 500 3 460 4 420 5 380 arithmetic sequence; common difference is −40 arithmetic sequence; common difference is 40 geometric sequence; common ratio is −40 geometric sequence; common ratio is 40
Answers
Answer:
arithmetic sequence; common difference is −40
Step-by-step explanation:
An arithmetic sequence is a sequence in which each term is found by adding a constant, called the common difference, to each previous term.
In this sequence, we go from 540 to 500 to 460, etc. Each time we are subtracting 40. This is the same as adding -40; this makes the sequence arithmetic.
The common difference of the arithmetic sequence will be negative 40. Then the correct option is A.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The table is given below.
n f(n)
1 540
2 500
3 460
4 420
5 380
The first term is 540 and the common difference of the arithmetic sequence is given as,
d = 500 - 540
d = - 40
The common difference of the arithmetic sequence will be negative 40. Then the correct option is A.
More about the arithmetic sequence link is given below.
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Find two consecutive whole numbers that 76 lies between
Answers
Given that lines a and b are parallel and that m∠8 = 108°, find m∠3.
Answers
Answer:
The answer would be 72
What is the value of x in the figure shown?
A quadrilateral is shown with the measurements of four angles shown. The first angle measures 65 degree sign. The second angle measures 123 degree sign. The third angle measures 87 degree sign. The fourth angle measures x degree sign.
A. x = 85 B. x = 95 C. x = 150 D. x = 208
Answers
360-(65+123+87)=360-275=85
x=85
A quadrilateral is shown with the measurements of four angles shown. The fourth angle is 85 degrees.
What is the angle sum property?The angle sum property of a quadrilateral states that the sum of the interior angles of a triangle is 360 degrees.
A quadrilateral is shown with the measurements of four angles shown. The first angle measures 65 degree sign.
The second angle measures 123 degree sign.
The third angle measures 87 degree sign. The fourth angle measures x degree sign.
The total amount of angles in a quadrilateral is 360:
x + 65 + 123 + 87 = 360
x = 360-(65+123+87)
x =360-275
x=85
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Jason's insurance company pays 80% of the cost of an ambulance ride, after he pays a $200 deductible. The ambulance ride costs $1200. How much would Jason pay for an ambulance ride?
A. $200B. $240C. $400D. $440
Answers
That's 1200 - 200 = 1000.
The insurance pays 80% of 1000. Percent means "out of 100" (per means "for every" and "cent" means 100 --> think CENTury...100 years). So 80% means 80 out of 100. That is, [tex] \frac{80}{100} [/tex]. To find 80% of 1000 we multiply: [tex] (\frac{80}{100})( 1000) = \frac{80000}{100}=800 [/tex]
If decimals are more your thing then represent 80% as .80 and multiply (1000)(.80) = 800.
Now, that's what the insurance pays. So out of that $1,000 the insurance pays $800 leaving Jason with a bill of $200 plus the deductible (another $200). That means Jason pays $400.
Answer:
400
Step-by-step explanation:
Classify the polynomial according to its degree and number of terms.
7b^3 + 3b^2 − 7b
A. linear monomial
B. quartic monomial
C. linear trinomial
D. cubic trinomial
HELP ASAP!!
Answers
The degree of this polynomial is 3 and the number of terms is 3 which makes it a cubic trinomial.
The equation given to us here is
[tex]7b^3+3b^2-7b[/tex]
Data Given;
[tex]7b^3+3b^2-7b[/tex]From this equation above, we have to know the degree of the polynomial. This will enable us to know what type of polynomial is this.
Degree of PolynomialThe degree of the polynomial is the highest value of the power in any of the variable.
In this question, the highest degree of polynomial here is 3 and this makes it a cubic polynomial.
However, it have only three variables also which makes it a trinomial. Put together it becomes cubic trinomial.
Generally, the degree of polynomials and their names are,
2 degree = quadratic3 degree = cubic4 degree = quarticLearn more on polynomials here;
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20 POINTS,, PLEASE HELP!!!
Given points K'(1, -2) and L'(1, -4), what are the coordinates of the point J' that produces a triangle J'K'L' congruent to JKL resulting from a rotation of 90 degrees clockwise around the point (1, -6)?
J' ______, _______
Answers
where is point J' that produces a triangle J'K'L' congruent to JKL resulting from a rotation of 90 degrees clockwise around the point (1, -6)
J' (5, 0)
Find the area of each figure.
Answers
141.3ft^2 second
Simplify the expression 75/153 completely.
Answers
GCD of 75 and 153 is 3
Divide both the numerator and denominator by the GCD
75 ÷ 3
153 ÷ 3
Reduced fraction:
25/51
So,its 25/51 hope this helps
75 / 3 = 25
---- ---
153 / 3 51
if you want to check it then simply multiply both the numerator and denominator 25/51 by 3 to get 75/153
A spider ate 25%, percent more bugs this month than last month. The spider ate 8 bugs last month. How many bugs did the spider eat this month?
Answers
it ate 10 bugs this month
simplify the expression 5+4•(8-6)^2
Please show steps.
Answers
( 8 - 6 ) = 2
E- exponents
2^2 = 2 × 2 = 4
M- multiplication / division
4 × 4 = 16
D- division
N/A
A- addition / subtraction
5 + 16 = 21
S- subtraction
N/A
~~
Answer : 21
If p is true and q is false, then p ∧ ~q is true.
true
false
Answers
Justification
1) ∧ is the and operator
2) ~ is the symbol for negation (which is the same that making false)
3) p ∧ ~q means p and not q.
4) The and operator means that the two joined premises, this is p and ~q, have to be true for the whole statement ve true.
5) It is given that p is true and q is false, then p and ~ q is true.
Answer: true.
Answer:
true
Step-by-step explanation: