Answer:
x = 5 mph
the rate of the boat in still water is 5 mph.
Step-by-step explanation:
Let x represent the speed of the boat in still water;
Given that the rate of the current is 3 mph.
When it is traveling against current, its relative speed is;
v1 = x - 3
When it is traveling with current, its relative speed is;
v1 = x + 3
Given;
A boat can travel 10 miles against a current in the same time that it can travel 40 miles with the current.
d1 = 10 miles
d2 = 40 miles
Distance = speed × time
time = distance/speed
The time taken for both cases are the same t;
t = d1/v1 = d2/v2
d1/v1 = d2/v2
Substituting the values;
10/(x-3) = 40/(x+3)
Cross multiply;
10(x+3)= 40(x-3)
10x + 30 = 40x - 120
Collecting the like terms;
40x -10x = 120+30
30x = 150
x = 150/30
x = 5 mph
the rate of the boat in still water is 5 mph.
Dan spends 1/5 of his wages on rent and 2/3 on food. If he makes £495 per week how much money does he have left
Answer:
£66
Step-by-step explanation:
1/5 times £495
2/3 times £495
Rent =£99
Food =£330
99+330=429
495-429=£66
I hope that help you and you learned how to do it for next time.
Answer:
£66 Left
Step-by-step explanation:
Total Money = £495
Rent:
=> [tex]\frac{1}{5} * 495[/tex]
=> £99
Food:
=>[tex]\frac{2}{3} * 495[/tex]
=> 2 * 165
=> £330
Left:
=> £495-£99-£330 = £66
y is directly proportional to x.
y= 30
x= 6
a) work out an equation connecting y and x
b) work out the value of y when x=12
Answer:
a) y = 5x
b) y = 60
Step-by-step explanation:
y ∝ x
So, y = kx -----(1)
Where k is the constant of proportionality
Now, y = 30, x = 6
Putting in (1)
30 = k(6)
Dividing both sides by 6, we get
k = 5
Now, Putting k=5 in (1)
So,
a) The equation connecting x and y is :
y = 5x
b) x = 12, Putting in (1)
y = (5)(12)
y = 60
Answer:
a)y=5x
b)60
Step-by-step explanation:
it just is
There is a line that includes the point (6,–10) and has a slope of –9. What is its equation in point-slope form?
Answer:
A slope of zero means a horizontal line (parallel to the x axis). So the line is y=-6, which is the y intercept. There is no x term because y=-6 for all x.
Step-by-step explanation:
Answer: y + 10 = -9(x - 6)
Step-by-step explanation:
Use this formula to solve for point-slope form: y - y1 = m(x - x1)
m would be the slope and the given slope is -9
y1 refers to the given y coordinate and x1 refers to the given x coordinate.
y + 10 = -9(x - 6)
a line is perpendicular to y = 3/7x - 2 and intersects the point (3,3). What is the equation of this perpendicular line?
Answer:
y = -7/3x + 10
Step-by-step explanation:
Step 1: Find the slope of the perpendicular line
Do this by taking the negative inverse of the first line
m = -7/3
Step 2: Find b
y = mx + b
y = -7/3x + b
3 = -7/3(3) + b
3 = -7 + b
b = 10
You should get y = -7/3x + 10 as your final answer.
IM STUCK ON THIS QUESTION! PLEASE HELP FAST
Answer:
The function has point discontinuity (a hole in fancy terms)
Step-by-step explanation:
If you factor out the top, you will get x(x + 2)(x + 5). You can right away cross out the (x + 5)'s. When you do so, you will create a hole in the graph, because x ≠ 5. Therefore, your answer is the 1st option.
The graph and table show the ratio of pencils to erasers in various school supply sets. If Eva buys a set that contains 10 erasers, how many pencils are expected to be in her set? 2 5 40 50
Answer:
it is 50 :)
Step-by-step explanation:
im taking the review on edg and i got it right
Answer:
The answer is 50. Edge 2022
Step-by-step explanation:
If you trace the way the points move you can find out it is 50.
if z (3,-1) is the midpoint of line segment of coordinate x (5,2) and y (a,b) then find the value of a and b. I need it fast if u tell fast I'll mark ur Brainliest. It's a deal
Answer:
the coordinates of y are (1,-4)
Step-by-step explanation:
by using midpoint formula
z(x,y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
putting the values of coordinates
(3,-1)=[tex]\frac{5+a}{2}[/tex],[tex]\frac{2+b}{2}[/tex]
separating the coordinates
3=[tex]\frac{5+a}{2}[/tex] and -1=[tex]\frac{2+b}{2}[/tex]
3×2=5+a and -1×2=2+b
6=5+a and -2=2+b
6-5=a and -2-2=b
1=a and -4=b
so the actual coordinates of y are (1,-4)
i hope it will help you
Write the equation of the function y=6/x translated 5 units to the left and 4 units up
Answer:
f(x)= (6/x+5)+4
Step-by-step explanation:
y/x translated 5 units
y/x+5 then 4 units up y/(x+5) +4
IS ANYONE HERE GOOD AT CALCULUS?? IF SO, PLEASEEEE HELP ME!!!! An object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) = A) 2 cos t. B) –2 cos t. C) 2 cos t – 2. D) –2 cos t + 2.
Answer: C
Step-by-step explanation:
Since we are given velocity, which is the first derivative, we have to fidn the antiderivative of velocity to get position.
∫-2sint dt
s(t)=2cos(t)+C
Since we are given s(0)=0, we can plug in the values to find C, constant.
0=2cos(0)+C
0=2(1)+C
0=2+C
C=-2
Now that we know our constant, we can find out position.
s(t)=2cos(t)-2
Answer:
Sorry this is not an answer but it wouldn't let me comment go you friend me or something so we can work on calculus together
Step-by-step explanation:
Which expression is equivalent to 9 x squared minus 2 y + 3 x squared minus 3 y? 6 x squared minus y + 6 x squared minus 5 y 6 x squared minus y + 3 x squared minus 4 y 10 x squared minus 4 y + 2 x squared minus y 11 x squared + 2 y + x squared minus 3 y
Answer:
10 x squared minus 4 y + 2 x squared minus y
Step-by-step explanation:
9x^2-2y+3x^2-3y
Collect like terms
9x^2+3x^2-2y-3y
=12x^2-5y
10 x squared minus 4 y + 2 x squared minus y
10x^2-4y+2x^2-y
Collect like terms
10x^2+2x^2-4y-y
=12x^2-5y
9x^2-2y+3x^2-3y is equivalent to
10x^2-4y+2x^2-y
Check all the options
6 x squared minus y + 6 x squared minus 5 y
6x^2-y+6x2-5y
12x^2-6y
6 x squared minus y + 3 x squared minus 4 y
6x^2-y+3x^2-4y
9x^2-5y
10 x squared minus 4 y + 2 x squared minus y
10x^2-4y+2x^2-y
12x^2-5y
11 x squared + 2 y + x squared minus 3 y
11x^2+2y+x^2-3y
12x^2-y
Answer:
C.) 12x squared- 2y- 3y
Step-by-step explanation:
i'm not 100 percent on this but it is the only logical answer, i will comment if i am right or not :) good luck luvs
the interior angles of a Pentagon are (y+13°),(y+15°),(y+23°),(y+29°), and(y+40°) a.Find the value of y b. Find the value of each interior angles
Answer:
y=84
first : 84+13=97
second : 84+15=99
third : 84+23=107
fourth: 84+29=113
fifth : 84+40 =124
97+99+107+113+124 = 540
Step-by-step explanation:
sum of interior angles of a pentagon=540 degreas
y+13+y+15+y+23+y+29+y+40=540
5y=540-(13+15+23+29+40)
y=84
first : 84+13=97
second : 84+15=99
third : 84+23=107
fourth: 84+29=113
fifth : 84+40 =124
97+99+107+113+124 = 540
What is a system of equations for the following situation? A group of 14 people went to see a movie. The cost to go to the movie is $12 for an adult and $8 for a child. The total cost for the group was $144.
Answer:
144=12x+8y
x+y=14
Step-by-step explanation:
Answer:
12x + 8 (14 - x ) = $ 144
x + (14-x) = 14
Step-by-step explanation:
Total number of people = 14
Let the number of adults be x and the number of children be ( 14 - x)
Total cost for the group = $144
i.e., 12x + 8 ( 14-x) = 144
12x + 112 - 8x = 144
4x + 112 = 144
4x = 144-112
4x = 32
x = 32/4
x = 8
Number of adults = x = 8
Number of children = 14 - x = 14 - 8 = 6
Hope it helps : )
Answer this, please. I'm having trouble or I'm just dumb.
Answer:
f(x)=(5+a)/(a-1)
Step-by-step explanation:
input a+2 for x
f(x)=(a+5)/(a-1)
and no ur not dumb u just need practice :D
Answer:
-4 and 1/7 is your answer.
Step-by-step explanation:
substitute 19 for x in the equation.[tex]f(x)=\frac{3}{19+2} -\sqrt{19-3}[/tex]
do the processes.[tex]f(x)=\frac{3}{21} -\sqrt{16}\\f(x)=-\frac{1}{7} -4\\f(x)= -4\frac{1}{7}[/tex]Which of the following are square roots of the number below check all that apply 144
The square root of 144 is ± 12
The correct answer choice is option C.
What is square root?Square root refers to a number which, when squared, yields another number.
For instance, the square root of 4 is ± 2
the square root of 9 is ± 3
the square root of 16 is ± 4
the square root of 25 is ± 5
Therefore, square root of 144 = ±12
that is, (12 × 12) or (-12 × -12)
Read more on square root:
https://brainly.com/question/428672
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Complete question:
Which of the following are square roots of the number below check all that apply 144 a. ±14 b. ±44 c. ±12 d. ±41
Pedro predicted that he would sell 128 novels. He actually sold 150 novels. What are the values of a and b in the table below? Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Novels 128 150 a b a = Negative StartFraction 22 over 128 EndFraction; b = negative 17.2 percent a = Negative StartFraction 22 over 150 EndFraction; b = negative 14.7 percent a = StartFraction 22 over 150 EndFraction; b = 14.7 percent a = StartFraction 22 over 128 EndFraction; b = 17.2 percent
Answer:
C)
AKA
a= 22/150; b= 14.7%
AKA
a = StartFraction 22 over 150 EndFraction; b = 14.7 percent
__________________________________________________
I am very sorry if this was wrong for you, but it was correct for me.
Brainliest would be apreaciated, but if not thats completley ok.
Sorry I dont have an explaination im not very good at those.
Sorry abt my spelling i know i suck.
And sorry I could not help earlier.
hope it helped :)
Answer: C)
AKA
a= 22/150; b= 14.7%
AKA
a = StartFraction 22 over 150 EndFraction; b = 14.7 percent
A card is drawn at random from a standard pack of playing cards. Then a fair coin is flipped. What is the probability of selecting an Ace and the coin landing on tails?
Answer:
1/26
Step-by-step explanation:
In a standard pack of cards, there are 52 total cards and 4 aces, two black aces and two red aces.
The probability of selecting an ace is therefore:
4/52 = 1/13
The probability of flipping a coin and it landing on tails is:
1/2
Therefore, the probability of selecting an Ace and the coin landing on tails is:
1/13 * 1/2 = 1/26
1/6 converted to a decimal rounded to 3 dp?
Answer:
0.83?
Step-by-step explanation:
Step-by-step explanation:
1/6 or 1÷6 =
0.1666666r
What is the length of Line segment B C? Round to the nearest tenth. Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 65 degrees. The length of hypotenuse B A is 16 centimeters and the length of B C is x. 6.8 cm 7.5 cm 14.5 cm 17.7 cm
Answer:
14.5 =x
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opposite side/ hypotenuse
sin A = BC / AB
sin 65 = x /16
Multiply each side by 16
16 sin 65 =x
14.50092459 =x
14.5 =x
Answer:
C on edge
Step-by-step explanation:
what is the nth term rule of the quadratic sequence below /-7, -4, 3, 14, 29, 48, 71
Answer:
nth term = 2n^2 - 3n - 6.
Step-by-step explanation:
n = 1 2 3 4 5 6 7
- 7 -4 3 14 29 48 71
Differences 3 7 11 15 19 23
Differences 4 4 4 4 4
So the first term in the Rule is 2n^2
Subtracting the values of 2n^2 from the original terms:
- 7 -4 3 14 29 48 71
2n^2 2 8 18 32 50 72 98
Subtrct -9 -12 -15 -18 -21 -24 -27
-3 -3 -3 -3 -3 -3
So we have -3n and the last term is -6 because -7 = 2(1)^2 -3 - 6 and the other terms fit this pattern as well.
The nth term rule of the provided quadratic sequence to find the n'th term of the sequence is 2n²-3n-6.
What is quadratic sequence?The quadratic sequence is the series of the numbers in which the rule for the n'th term included an n squared term (n²). The quadratic equation for n can be given as,
[tex]an^2+bn+c[/tex]
Here, (2a) is equal to the second difference, (3a+b) is equal to the first difference and (a+b+c) is equal to the first term.
The sequence given in the problem is
[tex]-7, -4, 3, 14, 29, 48, 71[/tex]
Thus, (a+b+c) is,
[tex]a+b+c=-7[/tex] ......1
The first difference between the sequence is,
[tex]3,7,11,15,19,23[/tex]
Thus, the value of (3a+b) is,
[tex]3a+b=3\\b=3-3a[/tex] ......2
The second difference between the sequence is,
[tex]4,4,4,4,4[/tex]
Thus, the value of 2a is,
[tex]2a=4\\a=\dfrac{4}{2}=2[/tex]
Put this value in equation 2 as,
[tex]b=3-3\times2\\b=-3[/tex]
Put the value of a and b in equation 1 as,
[tex]2-3+c=-7\\c=-7+1\\c=-6[/tex]
Put these values in the above formula as,
[tex]2n^2-3n-6[/tex]
The nth term rule of the provided quadratic sequence to find the n'th term of the sequence is,
[tex]2n^2-3n-6[/tex]
Learn more about the quadratic sequence here;
https://brainly.com/question/26373760
What is the answer in these boxes
Answer:
I found that the answer is (5,1)
Step-by-step explanation:
4 times x(5) is 20
3 times y(1) is 3
20 + 3 = 23
bottom equation:
x(5) -- 5y(1) = 0
I will mark you brainliest! The value of a car decreases by 1/6 every year. What type or function represents this pattern?
Answer:
C
Step-by-step explanation:
When the value of something decreases by a certain factor every unit of time, instead of by a set constant, then this is called exponential decay. When the rate is constant, this is called linear decay. Hope this helps!
how big is New York city
Answer:Land area: 302.6 mi²
Population: 8.399 million
Step-by-step explanation:
New York City can be described as very big and it has actually been ranked as the 24th biggest city in the United States in terms of land area it ...
Answer:
Land area: 783.8 km²
Population: 8.399 million
Step-by-step explanation:
which equation has no solution?
Answer:
Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution.
Step-by-step explanation:
We are looking at two lines.
4(x + 3) + 2x = 6(x +2)
4x + 12 + 2x = 6x + 12
6x + 12 = 6x + 12
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3x + 3
4x + 11 = 4x + 3
Both lines have the same gradient but have a different incline with the y axis. By definition, they are parallel to each other and there fore have zero solutions. Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution, which is the answer we are looking for.
5(x + 3) + x = 4(x +3) + 3
5x + 15 + x = 4x + 12 + 3
6x + 15 = 4x + 15
These are two different lines with exactly one solution.
4 + 6(2 + x) = 2(3x + 8)
4 + 12 + 6x = 6x + 16
6x + 16 = 6x + 16
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
Help me compleate the sentance
Answer:half
Step-by-step explanations:
Please check photo below
Answer:
Half :D
Step-by-step explanation:
Also hello brother
Identify the recursive formula for the following sequence. 8, 16, 32, 64, ...
Answer:
The recursive formula for the given sequence
[tex]t_{n}= (2)^{n+2}[/tex]
Step-by-step explanation:
Explanation:-
Given sequence is 8 , 16, 32, 64 ,.....
First term is a = 8
common ratio [tex]r = \frac{16}{8} =2[/tex]
[tex]r = \frac{32}{16} =2[/tex]
[tex]r = \frac{64}{32} =2[/tex] and so on..
Given sequence of the common ratio 'r' is equal
The [tex]n^{th}[/tex] term of the sequence
[tex]t_{n} = a r^{n-1}[/tex]
[tex]t_{n}= 8 (2)^{n-1}[/tex]
[tex]t_{n}= (2)^{(3+n-1)}[/tex]
[tex]t_{n}= (2)^{n+2}[/tex]
This is recursive formula for the given sequence
[tex]t_{n}= (2)^{n+2}[/tex]
Verification:-
[tex]t_{n}= (2)^{n+2}[/tex]
put n=1 ⇒ t₁ = 8
put n=2 ⇒ t₂ = 16
put n=3 ⇒ t₃ = 32
put n=4 ⇒ t₄= 64
and so on..
The sequence 8 ,16 , 32 , 64 ....
Write a quadratic function that has an axis of symmetry of x=7
Answer:
If a function has an axis of symmetry x = a,
Step-by-step explanation:
then f (x) = f (- x + 2a). The following graph is symmetric with respect to the origin. In other words, it can be rotated 180o around the origin without altering the graph. Note that if (x, y) is a point on the graph, then (- x, - y) is also a point on the graph.The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
WILL GIVE BRAINIEST TO ONLY THE FIRST ANSWER!! Find the sum of the first 150 terms in the sequence 20, 15, 10, 5...
Answer:
-450
Step-by-step explanation:
Say the first number is x to get the idea.
The first 150 terms are 150x - 5 * 150
15x - 750
300 - 750 = -450
A proportion is an equation stating that two ratios are equivalent.
False
True
Answer:
A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions
Therfore it is true
We can multiply all values by the same amount and still have the same ratio.
The given statement is true.
We have given the statement,
A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions.
We have to determine whether the statement is true or false.
What is the proportion?Proportion is a mathematical comparison between two numbers.
A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions
Therefore it is true.
We can multiply all values by the same amount and still have the same ratio.
To learn more about the proportion of visits:
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Sophia has an ear infection. The doctor prescribes a course of antibiotics. Sophia is told to take 500 mg doses of the antibiotic regularly every 12 hours for 10 days. Sophia is curious and wants to know how much of the drug will be in her body over the course of the 10 days. She does some research online and finds out that at the end of 12 hours, about 4.5% of the drug is still in the body. What quantity of the drug is in the body right after the first dose, the second dose, the third dose, the fourth dose (10 points)? When will the total amount of the antibiotic in Sophia’s body be the highest? What is that amount (10 points)? Answer Sophia’s original question: Describe how much of the drug will be in her body at various points over the course of the 10 days (10 points).
Answer:
After 1st Dose:As Sophie has just taken the medicine, the quantity of drug present in her body is 500mg
After 2nd Dose:
Amount left from 1st dose = 4.5/100 × 500 = 22.5mg
Amount of Drug after 2nd dose = Amount left from 1st dose + 2nd dose taken.
Amount of Drug after 2nd dose = 22.5mg + 500mg
Amount of Drug after 2nd dose = 522.5mg
After 3rd Dose:
Amount left from 2nd dose = 4.5/100 × 522.5 = 23.513 mg
Amount of Drug after 3rd dose = Amount left from 2nd dose + 3rd dose taken.
Amount of Drug after 3rd dose = 23.513mg + 500mg
Amount of Drug after 3rd dose = 523.513 mg
After 4rth Dose:
Amount left from 3rd dose = 4.5/100 × 523.513 = 23.558mg
Amount of Drug after 4rth dose = Amount left from 3rd dose + 4rth dose taken.
Amount of Drug after 4rth dose = 23.558mg + 500mg
Amount of Drug after 4rth dose = 523.558 mg
Highest Amount:
The pattern formed above can be written in the form of sum of finite geometric series:
Sₙ = 500 + 500(0.045) +500(0.045)² + ........................500(0.045)ⁿ
Sₙ = 500(1 + 0.045 + 0.045² ........................0.045ⁿ)
Where
Sₙ = Sum till nth term
a = 500
r = 0.045
As Sophia takes medicines 2 times a day, she takes medicine 20 times in 10 days. So substitute n=20 in the formula for the sum of finite geometric series
[tex]S_n=a\frac{(1-r^n)}{1-r}\\S_{20}=500(\frac{1-0.045^{20}}{1-0.045})\\S_{20}=523.5602~\text{mg}[/tex]
Greatest amount of antibiotic present = 523.5602 mg
This amount is almost constant after 3rd dose, so it will occur after every dose after 3rd dose
Drug present in body at different points:
After 1st dose = 500mg
After 2nd dose = 522,5mg
After 3rd dose = 523.513 mg
After the the amount left in the body almost remains constant.
Which means that after each dose, the amount in body is maximum, at the end of the 12 hours, the amount reduces to 4.5%, which reaches almost the same maximum after taking another dose.
ims struggling with this question help???
Answer:
Option 3.
Step-by-step explanation:
Angle E and angle A are corresponding angles, therefore they are congruent angles. Corresponding angles have the same angle.