A boat travels 40 miles downstream (with the current) in the same time it takes the boat to travel 30 miles upstream (against the current). If the boat travels at 46 miles per hour, write an equation to solve for the speed of the current, x in miles per hour.
Answers
Answer:
40/46+x=30/46-x
Step-by-step explanation:
Speed=distance/time
s=d/t
x=speed of the boat
Downstream speed=x+46
Upstream speed=x-46
Downstream
s=d/t
x+46=40/t
t=40/(x+46)
Upstream
s=d/t
x-46=30/t
t=30/(x-46)
Equate upstream and downstream
30/x-46=40/x+46
30(x+46)=40(x-46)
30x+1380=40x-1840
30x+1380-40x+1840=0
-10x+3220=0
-10x=-3220
Divide both sides by -10
x=322
x=322 miles/hour
Related Questions
In △EKL, m∠K = 90º, m∠E = 25º, EK = 3 cm, KH - altitude. Find EH.
Answers
Answer:
EH = 3.31
Step-by-step explanation:
We have been given a right angle triangle EKL. As KH has been given as the altitude (perpendicular) of the right angled triangle, and K is the right angle, we can say that EK is tthe base of the triangle and EH is the only side lleft, which is the hypotenuse of the triangle.
Where,
EK = Base = 3
KH = perpendicular altitude
EH = Hypotenuse
m<K = 90
m<E = 25
We know that
cosθ = Base/ Hypotenuse
cos 25 = 3/ EH
EH = 3/cos25
EH = 3.31
Perpendicular alitutude can also be calculated by using the formula for tanθ.
Answer ASAP In the given diagram, ∠4 = 45°, ∠5 = 135° and ∠10 = ∠11 Part A: Solve for the values of the remaining angles. Show all of your work. Part B: Use complete sentences to describe the angle relationship between the following angle pairs: 1. ∠4 and ∠1 2. ∠7 and ∠5 3. ∠9 and ∠10
Answers
Answer:
A) ∠9 = ∠10 = ∠11 = ∠12 = 90°
∠2 = ∠3 = ∠5 = ∠8 = 135°
∠1 = ∠4 = ∠6 = ∠7 = 45°
B) 1. ∠4 and ∠1 -> vertical angles
2. ∠7 and ∠5 -> supplementary
3. ∠9 and ∠10 -> supplementary
Step-by-step explanation:
Data
∠4 = 45°∠5 = 135°∠10 = ∠11The following are vertical angles, so they are congruent:
∠1 ≅ ∠4
∠3 ≅ ∠2
∠11 ≅ ∠9
∠10 ≅ ∠12
∠7 ≅ ∠6
∠5 ≅ ∠8
From here and data, it is deduced that
∠11 ≅ ∠9 ≅ ∠10 ≅ ∠12
From the picture, the addition of them is equal to 360°, then:
∠11 + ∠9 + ∠10 + ∠12 = 360°
4*∠11 = 360°
∠11 = 360°/4
∠11 = 90° = ∠10 = ∠9 = ∠12
∠2 and ∠4 are supplementary, then:
∠2 + ∠4 = 180°
∠2 = 180° - 45°
∠2 = 135°
∠7 and ∠5 are supplementary, then:
∠7 + ∠5 = 180°
∠7 = 180° - 135°
∠7 = 45°
Answer:
Started learning this today and this made a lot easier
On two investments totaling $13,500, Peter lost 3% on one and earned 5 % on the other. If his net annual receipts were $319, how much was each investment?
Answers
y = amount of 5% gain investment
x + y = 13,500 {the two investments total $13,500}
-0.03x + 0.05y = 319 {3% loss on one and 5% gain on other, receipt is $319}
x = -y + 13,500 {subtracted y from each side of first equation}
-0.03(-y + 13,500) + 0.05y = 319 {substituted (-y + 13,500), in for x, into second equation}
0.03y - 405 + 0.05 = 319 {used distributive property}
0.08y - 405 = 319 {combined like terms}
0.08y = 724 {added 405 to each side}
y = 9050 {divided by 0.08}
x = -y + 13,500 {from equation above}
x = -9050 + 13,500 {substituted 9050 in for y}
x = 4450 {added}
The 3% loss investment was $4450
The 5% gain investment was $9050
A t-shirt increased in price by 1/7. After the increase it was priced at £56. What was the original price of the t-shirt?
Answers
Answer:
£48
Step-by-step explanation:
56 ÷ 7 = £8
56 - 8 = £48
Please let me know if my answer is correct.
Answer:
48
Step-by-step explanation:
PLEASE HELP!
What is the distance from Z= (16,−15) to the x-axis?
Answers
Answer:
15 units
Step-by-step explanation:
Distance from the x-axis is measured vertically, so you would look at the second number of the coordinates, the y value. Point Z is 15 units below the x-axis.
Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.
What is the axis?
An axis in mathematics is defined as a line that is used to make or mark measurements.
Here given that,
[tex]Z= (16,-15)[/tex] which is on the x-axis.
So,
The shortest distance between the coordinate [tex](16,-15)[/tex] and [tex](16,15)[/tex].
Now, applying the distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here,
[tex](x_1,y_1)=(16,0)\\(x_2,y_2)=(16,-15)[/tex]
Substituting these values in the formula
[tex]d=\sqrt{(16-16)^2+(-15-0)^2}\\\\d=\sqrt{(0)^2+(-15)^2}\\\\d=\sqrt{0+225}\\\\d=15[/tex]
Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.
To know more about the axis
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What is the length of the y-component of the vector shown below? A. 77.3 B. 15.0 C. 20.7 D. 21.4
Answers
Answer:
[tex]y = 20.7[/tex]
Step-by-step explanation:
Given
The figure above
Required
Calculate the y component
Represent the y component with y, the resultant vector with s and the angle with [tex]\theta[/tex]
The y component of a vector (as it is, in this case) is calculated as thus;
[tex]sin\theta = \frac{y}{s}[/tex]
[tex]Where\ \theta = 15\\ s = 80[/tex]
Substituting these values in the equation
[tex]sin\theta = \frac{y}{s}[/tex] becomes
[tex]sin\ 15= \frac{y}{80}[/tex]
Multiply both sides by 80
[tex]80 * sin\ 15= \frac{y}{80} * 80[/tex]
[tex]80 * sin\ 15= y[/tex]
[tex]80 * 0.2588190451= y[/tex]
[tex]20.705523608 = y[/tex]
[tex]y = 20.705523608[/tex]
[tex]y = 20.7[/tex] (Approximated)
In how many ways can a committee of size 5 be formed from 11 people? Assume that, when people are chosen for a committee, the order of the choices does
not matter.
Answers
Answer:
462 ways
Step-by-step explanation:
plzzzzz answer this question about density mass and volume!!!!!!!!!
Answers
Answer:
13.896 kg
Step-by-step explanation:
You can find the mass of the bar by first finding the volume.
V = BH
where B = area of the base (the trapezium), and
H = height (distance trapezium between bases)
The area of a trapezium is
A = (b1 + b2)h/2
where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and
h = the altitude of the trapezium (distance between the bases of the trapezium)
V = (b1 + b2)h/2 * H
V = (12 cm + 6 cm)(5 cm)/2 * 16 cm
V = 720 cm^3
The volume of the bar is 720 cm^3.
Now we use the density and the volume to find the mass.
density = mass/volume
mass = density * volume
mass = 19.3 g/cm^3 * 720 cm^3
mass = 13,896 g
Now we convert grams into kilograms.
1 kg = 1000 g
mass = 13,896 g * (1 kg)/(1000 g)
mass = 13.896 kg
Answer: 1.3896 kg
20 poinst please help i will mark u brainlestToday when Jeremy saw Mr. Winaki, the teacher said, “The amount of money in my wallet is more than $10, but less than $20. How much do I have?” Jeremy remembers talking about inequalities in math class and thinks that the answer may have something to do with that idea. In the Math Toolbox, we helped Jeremy solve Mr. Winaki ’s riddle. Now, Jeremy needs help in writing a brainteaser to stump Mr. Winaki. Your original riddle needs to be a real world problem that has an answer of more than 19 and less than 41. 1. Brainstorm Think about possible real world situations that might have an answer of more than 19 and less than 41. List three ideas for your original riddle.. Thesaurus Select three important words from the ideas you listed above. Use a thesaurus to look up synonyms of the words. Remember, Mr. Winaki is an English teacher. He will like your use of interesting new words. Record your findings in the chart below. 3. Select an idea From your list of ideas, select one about which to write a riddle. Remember, your riddle should have an answer of more than 19 and less than 41. Use one of the synonyms you found to make your writing more exciting. 4. Provide a possible answer In the Math Toolbox section of our lesson, we chose a possible solution to Mr. Winaki’s riddle. Choose a possible number that answers your riddle. 5. Writing Inequalities a. Write an inequality comparing it to 19. b. Choose the same value as a possible solution and write an inequality comparing it to 41. c. Write an inequality that shows the relationship between all three numbers? d. Represent the inequality algebraically.
Answers
Answer:
Given that “The amount of money in my wallet is more than $10, but less than $20 " can be written in inequality form as
10 < w < 20 where " w" is the amount in the wallet .
1 ) Puzzle : -
Ryan is eating cookies . His mother ask how many cookies did he have .
He said number of cookies he ate is more than 19 and less than 41 .
We can write it in equality form as 19 < x < 41 where ' x ' is number of cookies Ryan have .
2) Puzzle :-
Number of steps a child take in an hour is more than 19 and less than 41 .
Write the situation in inequality form .
19 < p < 41 where " p " is the number of steps a child take in an hour .
3) Puzzle :-
Mother said to his child : " the number of coins in your piggy bank is more than 19 and less than 41 .
19 < c < 41 where " c " is number of coins in piggy bank .
Step-by-step explanation:
During the recent recession, Bob's home value dropped to only $175,000. Since then the economy has turned around and the market is improving at a rate of 4.5% annually. At this rate, how much will Bob's home be worth 12 years after the market started improving? And what equation did you use?
Answers
Answer:
Bob's home will worth $296,779.25 after 12 years.
Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]
Step-by-step explanation:
Current value of Bob's house =[tex]FV = $175,000( 1 + 4.5/100)^12\\FV = $175,000( (100+ 4.5)/100)^12\\FV = $175,000( (104.5)/100)^12\\FV = $296,779.25[/tex]
market is improving at 4.5% annually.
This, means that the value of house gets appreciated by 4.5% each year from its previous year value.
This is a problem of compound interest formula
[tex]FV = PV(1+r/100)^n[/tex]
where PV is the present value of any thing
FV is the future value
r is the annual rate of interest
t is the time in number of year for which rate is applicable.
_____________________________________
Given
PV = $175,000.
r = 4.5%
t = 12 years
Value after 12 year will be given by
[tex]FV = $175,000( 1 + 4.5/100)^(12)\\FV = $175,000( (100+ 4.5)/100)^(12)\\FV = $175,000( (104.5)/100)^(12)\\FV = $296,779.25[/tex]
Thus, Bob's home will worth $296,779.25 after 12 years.
Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]
Angelo cuts a piece of wood for a project. The first cut is shown and can be represented by the equation y - 5x-1. The second cut needs to be parallel to the first. It will pass through the point (0,6). Identify the equation that
represents Angelo's second cut.
Answers
Answer:
The correct option is A
A) y = (1/5)x + 6
Step-by-step explanation:
The equation of the first cut shown in the graph is:
y = (1/5)x - 1
We know that a general form of linear equation is given as:
y = mx + c
Comparing both equations, we get that the slope m = 1/5
As the second cut is parallel to the first cut, it will have the same slope, that is m = 1/5
Substitute it in the general linear equation
y = mx + c
y = (1/5)x + c
We know that this equation passes through the point (0,6), substitute it in the above equation>
6 = (1/5)(0) + c
c = 6
The equation for second cut be found by using m = 1/5 and c = 6
y = mx + c
y = (1/5)x + 6
A mother is 30 years older than her son. Fifteen years ago the son was 1/3 of
his mother's age. How old is each now?
Answers
Answer: The son is 30 and the mother is 60
Step-by-step explanation:
Mother's age = m
Son's age = s
m = s + 30
m-15 = 3(s - 15)
m - 15 = 3s - 45
m = 3s - 30
(Substitution)
s + 30 = 3s - 30
2s = 60
s = 30
m = 60
Hope it helps <3
Trick question---
Just kidding I think that 15 years ago his mother was 45
he was 15 and now he is 30 and she is 60.
literally sat here thinking that 30 is ruled out, and 60 would be 20 but then she'd be too old, suddenly it clicked, if you said he'd be half her age now, it'd be to easy, because half her age now would be 30 and it'd give the answer straight away.
You or your teacher has a big percentage of the brain used. I respect.
solve for x 3x+3+=12 1. 6 2. 5 3. 4 4. 3
Answers
Answer:
4.(3)
Step-by-step explanation:
3x+3 = 12
Subtract 3 to both sides.
3x = 9
Divide the left side by 3, then divide the right side by 3
x = 3
Answer:
Hi! your answer should be D. 3
Step-by-step explanation:
1. 3x+3=12
-3 -3
2. 3x=9
÷3 ÷3
3. x= 3
[So, your answer should be D. x=3]
Hope this helps!
The functions f(x) and g(x) are shown on the graph.
Rx) = x²
What is g(x)?
Answers
Therefore f(x) = - x^2 (NOT IN PARENTHESIS that would be a reflection on the y axis)
It’s a shift 4 y values down therefore
g(x) = - x^2 - 4
What is the value of Fraction 1 over 2x3 + 3.4y when x = 2 and y = 5?
18
20
21
37
Answers
Answer:
C.21
Step-by-step explanation:
The value of 1/ (2x³ + 3.4y) is 1/33.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Fraction = 1/ (2x³ + 3.4y)
We have the value x= 2 and y=5.
So, 1/ (2x³ + 3.4y)
= 1/ (2(2)³ + 3.4(5))
= 1/ (2(8) + 17)
= 1/ (16+17)
= 1/ 33
Hence, the value is 1/33.
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state whether it represents a function
Answers
Answer:
See below.
Step-by-step explanation:
To be a function the graph must pass the vertical line test. If any of the vertical lines which can be drawn intersects the graph more than once then it's not function.
So Graph 1 is not a function because a vertical line passes through the 2 points in quadrant 1, whereas Graph 2 is a function because any vertical line you can draw only passes through the graph once.
Graph 3 - not a function.
Graph 4 - not a function.
Graph 5 - not a function.
Graph 6 is a function.
Jacob is painting the walls of his new tiny house. If 3⁄4 of a can of paint is enough to paint 1 / 8of the walls, how much paint does Jacob need to paint all of the walls?
Answers
Answer:
6 cans
Step-by-step explanation:
I used Improper Fractions to solve this question.
3/4 is enough to paint 1/8
Therefore we can multiply 3 by 8 to calculate how much paint is required for the whole wall.
3 * 8 = 24
24/4 = 6
A recent survey found that 65% of high school students were currently enrolled in a math class,43% were currently enrolled in a science class,and 13% were enrolled in both a math and a science class. Suppose a high school student who is enrolled in a math class is selected at random. What is the probability that the student is also enrolled in a science class?
Answers
Answer: 0.20
Step-by-step explanation:
As per given :
P(student enrolled in a math class ) = 65% = 0.65
P( student enrolled in a science class) = 43%= 0.43
P( student enrolled in both ) = 13% = 0.13
Formula of conditional probability :
[tex]P(A|B)=\dfrac{P(A\text{ and }B)}{P(B)}[/tex]
Using the above formula,
The probability that the student is enrolled in a science class given that he is enrolled in maths class :
[tex]P(\text{science}|\text{math})=\dfrac{P(\text{science and maths})}{P(\text{math})}\\\\=\dfrac{0.13}{0.65}\\\\=\dfrac{13}{65}\\\\=\dfrac{1}{5}=0.20[/tex]
Hence, the probability that the student is also enrolled in a science class = 0.20 .
HELP. Analyze the diagram below and complete the instructions that follow. Find the exact value of tan 0.
Answers
Answer:
Using SohCahToa we know it will be opposite over adjacent, opposite being the side across from theta and adjacent being the side next to theta, Using Toa we know it will be opposite over adjacent so the answer will be 6/2sqrt5
If they wants you to simplify more than you cant have a sqrt on the bottom so to fix this you will multiply the top and bottom by sqrt5 leaving you with 6sqrt5/ 2*5 or 6sqrt5/15
hope this helped
Answer:
C. 3^5/5
Step-by-step explanation:
Find the common difference for the sequence shown.
56, 49, 42, 35, ...
0-12
0-7
07
Answers
To find the common difference, subtract all the numbers in order.
56 - 49 = 7
49 - 42 = 7
42 - 35 = 7
Therefore, common difference is 7.
Best of Luck!
Answer:
The answer is -7
(got this answer right on the lesson)
Step-by-step explanation:
Help pleaseeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
The answer is 3 mark as brainliest
Step-by-step explanation:
3 *3-4*4+2*5
9-16+10
9-6=
3
Answer:
Hey there!
3a-4b+2c
3(3)-4(4)+2(5)
9-16+10
3
Your answer would be 3.
Hope this helps :)
20 points brainlist thanks
What is the distance from (−2, 4) to (0, −6)? Round your answer to the nearest hundredth.
9.23
10.20
10.98
11.34
please explain how you got the awnser im having a hard time
Answers
Answer:
The answer Is 10.20
Step-by-step explanation:
d = \/(0-(-2))² + (-6-4)²
d = \/(0+2)² + (-10)²
d = \/(2² + 100)
d = \/(4+100)
d = \/104
d ~ 10,20
Step-by-step explanation:
by using distance formula it is easily calculated
HELP NEEDED PLS HELP! THANK YOU Use the fundamental theorem of algebra to state all the possible roots of the function f(x)=2x^3+3x^2-4x-12 Can someone please show me how to do it
Answers
Answer:
x=2 (−∞,∞)
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x
Hope this helps (sorry if it's confusing)
Answer:
x = 1.71282
Step-by-step explanation:
2x^3+3x^2-4x-12
2 x³ + 3 x² - 4x - 12 = 0
x = 1.71282
see attachment.
What is the surface area of a sphere with a radius of 11 units?
A. 13317 units2
B. 3637 units2
C. 7267 units2
D. 48470 units2
Answers
Answer:
Step-by-step explanation:
The surface area of a sphere with radius r is given by
S = 4 pi r^2
for a radius of 11 units,
S = 4 pi 11^2 = 484 pi = 1520.5 sq. units
This does not correspond to any of the answers.
Please check question.
Answer:
484[tex]\pi[/tex]
Step-by-step explanation:
Surface Area of Sphere Formula: 4[tex]\pi[/tex]r[tex]r^{2}[/tex]
When you plug it in it is 4[tex]\pi[/tex][tex]11^2[/tex]
Then you would get 484[tex]\pi[/tex]
witch expression is equivalent to 10-8
Answers
Answer:
2
Step-by-step explanation:
=> 10-8
=> 2 (Equivalent Expression)
Dan must choose a shirt, a pair of pants, and a cap for today's outfit. He has 2 shirts, 2 pairs of pants, and 3 caps to choose from. How many different outfits can he make?
Answers
Answer:
12 different outfits
Step-by-step explanation:
2 x 2 x 3 = 12 outfits.
Answer:
12
Step-by-step explanation:
He has 2 possibilities for a shirt, 2 possibilities for a pant, and 3 possibilities for a cap. You just multiply them together:
2 * 2 * 3 = 12 outfits
x^2 + 20x + 28 = 9 find the graphing/vertex form
Answers
Answer: [tex](x+10)^2+119=0[/tex]
Step-by-step explanation:
For a quadratic equation, the vertex form is given by : [tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.
The given quadratic equation: [tex]x^2 + 20x + 28 = 9[/tex]
Subtract 9 from both sides
[tex]=x^2+20x+19=0[/tex]
compare this to [tex]x^2+bx=c[/tex], and add [tex](\frac{b}{2})^2[/tex] both sides
b= 20
[tex]x^2+20+100+19=-100[/tex] [(b/2)²=20/2=10]
[tex]\Rightarrow\ x^2+2(x)(10)+10^2+119=0[/tex]
[tex]\Rightarrow\ (x+10)^2+119=0\ \ \ [\because\ (a+b)^2=a^2+b^2+2ab][/tex]
So, the vertex form : [tex](x+10)^2+119=0[/tex]
A parachutist's rate during a free fall reaches 198 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answers
Answer:
300 feet
Step-by-step explanation:
If we were using feet the expression would be 198x, where x is feet per second
Since they are asking in meters we need to convert feet to meters
When you do that you get 60
Now the expression is 60x
When you plug 5 into the equation it is 300
A hobbyist is making a toy sailboat. For the triangular sail, she wants the height h (in inches)
to be twice the length of the base b (in inches). Can the area of the sail be 10 inº?

Answers
Answer:
xx
Step-by-step explanation:
give your answer as a mixed number
4 3/7 - 2 5/7
get brainliest urgent plz help
Answers
Answer:
[tex]1\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]4\frac{3}{7} -2\frac{5}{7}[/tex]
Step 1. Simplify left side 4*7+3 , Right Side 2*7+5
[tex]=\frac{31}{7} -\frac{19}{7} = \frac{12}{7}[/tex]
Step 2. Re-write 12/7 as mixed number
[tex]\frac{12}{7} = 1\frac{5}{7}[/tex]