Here we must write and solve a system of equations to find the speed of the boat and the speed of the stream. We will find that the boat's speed is 23km/h and the river's speed is 4km/h.
First, remember the relation:
Distance = Speed*Time.
Now let's define the variables we will be using:
B = boat's speedR = river's speed.When the boat travels downstream, the total speed of the boat is the speed of the boat plus the speed of the river, and we know that in that case it travels 54km in 2 hours, then:
54km = (B + R)*2h
When the boat travels upstream, we must subtract the speed of the river. In that case, we know that the boat travels 57km in 3 hours, then we have:
57km = (B - R)*3h
Then our system of equations is:
54km = (B + R)*2h
57km = (B - R)*3h
To solve this, first, we need to isolate one of the variables in one of the equations, let's isolate B in the second one:
57km = (B - R)*3h
57km/3h + R = B
19 km/h + R = B
Now we can replace that in the other equation:
54km = (B + R)*2h
54km/2h = B + R
27 km/h = B + R = (19 km/h + R) + R
Now we can solve this for R:
27 km/h = 19km/h + 2*R
27 km/h - 19km/h = 2*R
8 km/h = 2*R
(8km/h)/2 = 4km/h = R
Now that we know the value of R, we can use:
B = 19 km/h + R = 19 km/h + 4km/h = 23 km/h
So the boat's speed is 23km/h and the river's speed is 4km/h.
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What is 1 1/2 divided by 8
Answer:
3/16
Step-by-step explanation:
start by converting 1 1/2 to an improper fraction by multiplying the 1 by the denomerator and then adding the 1 from teh numerator. Then place that all over the denomantor two. so you get 3/2
then set up your equation:
3/2 x 1/8
you do the resipricol of one of the numbers so instead of 8/1 we do 1/8
3 times 1= 3
2 times 8 is 16
3/16 does not simplify so thats your answer
Answer:
3/16
Step-by-step explanation:
((1 1/2)/8)=(3/2)/8
8 times 2(demoninator)=16
numerator stays same so the answer is 3/16
James joins Club One which charges a monthly membership of $19.99. In 6 months, will he spend less than $120 in all?
Answer:
120
Step-by-step explanation:
round 19.99 to 20 and do 20 times 6
Joel can do 20 math problems in 90 seconds How many seconds would it take him to do 32 problems?
HELP ME ITS SUPER HARD
Answer:
Joel can do 20 math problems in 90 seconds
He can do 1 math problem in 90/20 = 4.5 seconds
Now, Joel can do 32 math problems in
4.5×32
= 144 seconds
= 2 minutes 24 seconds
Step-by-step explanation:
Here I used the unitary method to sovle the question
Find the slope of an equation f(x)=-3sqrt(x) at the point (9,-9)
Answer:
Slope is [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-3\sqrt{x}[/tex]
Find the derivative using the product rule:
[tex]f'(x)=\frac{d}{dx}(-3)*\sqrt{x}+-3*\frac{d}{dx}\sqrt{x}[/tex]
[tex]f'(x)=-3*\frac{1}{2\sqrt{x}}[/tex]
[tex]f'(x)=\frac{-3}{2\sqrt{x}}[/tex]
Plug in coordinates to find slope at that point:
[tex]f'(9)=\frac{-3}{2\sqrt{9}}=\frac{-3}{2(3)}=\frac{-3}{6}=-\frac{1}{2}[/tex]
Therefore, the slope of the equation at the point (9,-9) is [tex]-\frac{1}{2}[/tex].
Answer:
Step-by-step explanation:
f(x) = -3√x
f'(x) = -1.5/√x
f'(x) = -1.5/√9
f'(x) = -1.5/3
f'(x) = -0.5
The length of a man's shadow is directly proportional with his height.
At the same time of day, a man who is 1.8 meters tall casts a 25.2
meter shadow and his son casts a 21 meter shadow. What is the
height of the man's son, in meters? If necessary, round to the nearest
tenth.
Answer:
The man's son height is 1.5m
Step-by-step explanation:
[tex]\frac{x}{21} =\frac{1.8}{25.2}[/tex]
[tex]\frac{21x1.8}{25.2}[/tex]
21x1.8= 37.8
37.8 ÷ 25.2= 1.5
Hope this helps
sorry if i got it wrong
solve for Y 3y =2(4-2y)+6
Answer:
HOLA MATE HERE IS UR ANSWER:-
Step-by-step explanation:
3y=2(4-2y)+63y=8-4y+63y=14-4y3y+4y=147y=14y=14/7y=2Gabe has a savings account at the local bank. He deposits $150 in his account every 2 months. Which equation models the relationship between the months that deposits are made, x, and the amount of money deposited in the account, y?
Answer:
y=150(x/2)
Step-by-step explanation:
y = 150(x/2)
y represents the amount of money that is deposited into Gabe's account. x represents the amount of time he is adding money for.
x is divided by 2 because however long gabe has been adding money into his account, he does it every 2 months. This means that if x = 12 (time = 12 months) , then Gabe has only made (12/2) = 6 deposits of $150. If x = 4 (time = 4 months), then Gabe would have only made (4/2) = 2 deposits of $150.
With this being said, 150 is being multiplied by the number of deposits (x/2) to find the total amount of money deposited (y).
(64/8/ 4 + 7 – 2) • 5 =
Answer:
35
Step-by-step explanation:
Let me know if I got it right
If f(x) = 4x2 + 2x + 7, find the value of f(-5).
=
A. -103
B. -83
C. 97
D. 117
Find ADC triangle's perimeter, if ABE triangle's perimeter is 10 and AE:AC=2:3
Answer:
give the dimensions of the figure on the paper
Solve the following for x. Show all work. x+3/5 =2
Answer:
x+3/5=2
or,x+0.6=2
or,x=2-0.6
x=1.4
7(2+3x)+8, 12+3(8+x), and (7x+2)3+8x
Answer:
The first answer is 21x+22.
Second answer is 36+3x.
Third answer is 29x+6.
Step-by-step explanation:
I just simplified
Types of Angle Relationships
Listen
Question
If two angles are supplementary, then the sum of their measures is _[blank] degrees.
Question
ol
What number correctly fills in the blank in the previous sentence?
Question
Enter your answer as a number, like this: 42
а
Answer: The answer is 180°.
Explanation: Two angles are called supplementary when their measures add up to 180 degrees, therefore the answer is 180 degrees.
What is auto insurance?
Answer:
the second option.
a policy that pays to get your vehicle replaced or repaired incase of an accident.
Step-by-step explanation:
If 20 students have only airpods,
10 students only have beats, and 30
students have beats in total how
many students have both beats and
airpods?
Answer:
There should be 20 students that have both Beats and AirPods.
Step-by-step explanation:
There are 50 students in total.
20 students have only AirPods and 30 students have Beats. Out of the 30 who own Beats, there are 10 students that have ONLY Beats.
30 - 10 = 20.
It's a tricky question, but this is the correct answer!
Hope This Helps!
Solve
[tex]\frac{a-1}{a-3} =\frac{a+1}{a-4}[/tex]
Answer:
[tex]a=\frac{7}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a-1}{a-3}=\frac{a+1}{a-4}[/tex]
[tex](a-1)(a-4)=(a-3)(a+1)[/tex]
[tex]a^2-5a+4=a^2-2a-3[/tex]
[tex]-5a+4=-2a-3[/tex]
[tex]-3a+4=-3[/tex]
[tex]-3a=-7[/tex]
[tex]a=\frac{7}{3}[/tex]
PLEASE HELPP MEE ASAPP!!
Answer:
Step-by-step explanation:
each zero of the function will have a factor of (x - x₀)
h(x) = a(x + 3)(x + 2)(x - 1)
h(x) = a(x + 3)(x² + x - 2)
h(x) = a(x³ + 4x² + x - 6)
or the third option works if a = 1
however this equation gives us the points (0, -6) and (-1. -4), so "a" must be -2
h(x) = -2x³ - 8x² - 2x + 12
to fit ALL of the given points as it fits the three zeros and also h(0) and h(-1) so I guess that is why the given group is a partial set of solution sets
h(r) = r^2 + 11r - 26
1) What are the zeros of the function?
Write the smaller r first, and the larger r second.
smaller s =
larger r =
2) What is the vertex of the parabola?
The zeros of the function h(r) = r² + 11r - 26 are r = -13, r = 2 and the vertex is (-11/2, -225/4).
What are the zeros and vertex of the function?Given the function in the question:
h(r) = r² + 11r - 26
To find the zeros of the function h(r) = r² + 11r - 26, we need to solve the equation h(r) = 0.
Using factoring:
r² + 11r - 26 = 0
Find two numbers whose sum is 11 and whose product is -26.
The numbers are -2 and 13.
Factor the equation:
(r - 2)(r + 13) = 0
Hence:
r - 2 = 0 and r + 13 = 0
Therefore, smaller r = -13, larger r = 2.
Next, we determine the vertex of the function:
Using the formula for the x-coordinate of the vertex, which is given -b/2a.
Here, the coefficient of r² is 1 (a = 1),
The coefficient of r is 11 (b = 11).
Substituting these values into the formula, we get:
r = -b/2a
= -11/( 2×1 )
= -11/2
The x-coordinate of the vertex is -11/2.
To find the y-coordinate, we can substitute r = -11/2 value back into the function:
h(r) = r² + 11r - 26
h(-11/2) = (-11/2)² + 11(-11/2) - 26
= 121/4 - 121/2 - 26
= 121/4 - 242/4 - 104/4
= (121 - 242 - 104)/4
= -225/4
Therefore, the vertex is (-11/2, -225/4).
Learn more about quadratic equations here:https://brainly.com/question/4038687
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Line f has a slope of -9/7. Line g is perpemdicular to f. What is thr slope of line g
A car travels at an average speed of 60 km/h for 2.1 hours.
How far did the car travel in km?
Answer:
15 km
Step-by-step explanation:
Mrs. marks has to pay if she drives 300 miles. 25 + 0.30*m=
Answer:25.3
Step-by-step explanation:
Because your adding 25 to 0 and leaving the decimal point and taking away 0 from 30
The population of New York state can be modeled by: 19.71 P(t) =
1 + 61.22e-0.03513tP is the population in millions
and t is the number of years since 1800
What was the population in 2020?
P(220) = [?] million
Round your answer to the nearest thousandth.
Answer:
19.193 million
Step-by-step explanation:
Put the given value in the formula and do the arithmetic.
P(220) = 19.71/(1 +61.22e^(-0.03513·220))
P(220) = 19.71/(1 +61.22e^-7.7286) = 19.71/(1 +0.02694046)
P(220) ≈ 19.193 . . . million
19.19293355
Nearest thousandth is 19.193
Given that y = 11 cm and θ = 34°, work out x rounded to 1 DP.
Check the picture below.
tom measured his frisbee from the center to the outside and found it to be 6 inches what is the approximate circumference of tom frisbee
Answer: 37.68 inches
A frisbee is round so its a circle. And the formula of circumference of a circle is 2πr (r = 6 inches and π = 3.14)
So, 2πr = 2 * 3.14 * 6
2πr = 37.68 inches
0.03249 in standard form to 3 significant figures is
(A) 3.24 × 10−1
(B) 3.24 × 10−2
(C) 3.25 × 10−2
(D) 3.25 × 10−3
Cylinder height of 8 inches with hemisphere withdiameter of 6 inches what the volume
Find the value of x .
K
M
(2x – 10) (2x + 40)º
-
N
Answer:
?????????????????????????
A convention center is in the shape of a rectangular pyramid with a height of 332 m. Its base measures 475 m by 571 m. Find the volume of the convention center. If necessary, round your answer to the nearest tenth
Answer:
30,015,566.7 m³ OR 3.0 x 10⁷ m³
Step-by-step explanation:
The formula for finding the volume of a rectangular pyramid is:
V = lwh/3
where l = length
w= width
h = height
(475)(571)(332)/3 = 30,015,566.7 m³ = 3.0 x 10⁷
Which table of ordered pairs represents a proportional relationship?
Answer:
C)
Step-by-step explanation:
Because Its equivalent
A restaurant bill comes to $28.35. Find the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax.
Bill was for $28.35. A 20% tip would come to $5.67. If we add this tip to the $28.35 bill, we get a total of $28.35 + $5.67 + 0.0625($28.35)
= $35.79 (total)
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