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.
If you want to learn more, you can read:
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State the postulate or theorem you would use to prove each pair of triangles congruent.
a) SSS
b) SAS
c) ASA
d) AAS
e) HL
f) Not possible
Answer:
f) Not possible
Step-by-step explanation:
The triangles can be shown to be similar by SAS, but the corresponding sides are not marked as congruent. With the given information, it is not possible to show the triangles are congruent.
A rock is launched from a cannon. Its height, h(x), can be represented by a
quadratic function in terms of time, x, in
seconds.
After 1 second, the rock is 94 feet in the
air; after 2 seconds, it is 176 feet in the
air.
Complete the height function, h(x), for this situation
h(x) =
Answer:
The height, in feet, of the rock after 5 seconds = 875 feet
Step-by-step explanation:
You use substitution to solve a system of equations and, after simplifying, end with a statement that says 7 7. Describe what this statement means about the number of solutions and about the graph of the system.
Answer:
Sample Response: Since the statement is true, there are an infinite number of solutions to the system. This statement also indicates that the lines are equivalent.
can someone help me please
Answer:
1)B 4 x 4 x 4 x 4
2)B 8292
Step-by-step explanation:
if lateral surface area of cube is double then the ratio of volume of new cube to original cube
Answer:
2√2
Step-by-step explanation:
The area ratio is the square of the side length ratio, so the ratio of side lengths is √2.
The volume ratio is the cube of the side length ratio, so the new cube has a volume that is (√2)³ times that of the original.
The volume ratio is 2√2.
Evaluate the following expression.
53
Enter the answer
Answer:
125
Step-by-step explanation:
5^3 = 5 ✕ 5 ✕ 5, and 5 ✕ 5 ✕ 5 = 125
Hope this helps :)
Answer:
125
Step-by-step explanation:
all you have to do is 5*5*5. so multiply the number that many times it tells you on the exponent.
Two increased by five times a number is twenty two
What is the equation
Answer:
2 + 5 x a = 22
Step-by-step explanation:
What is the value of 25
Answer:
5 po its my volt
Step-by-step explanation:
yan hooo
Solve for the value of x
Answer:
x=9
Step-by-step explanation:
To solve for x, you can set up a proportion between the 2 triangles we see.
The small triangle can be written as [tex]\frac{16}{20}[/tex], and the large triangle can be written as [tex]\frac{16+12}{20+2x-3} = \frac{28}{2x+17}[/tex].
Set both proportions equal to each other.
[tex]\frac{16}{20}=\frac{28}{2x+17}[/tex]
Cross multiply and solve for x.
[tex]16(2x+17)=(28)(20)[/tex]
32x+272=560
32x=288
x=9
What is 6.995 to a decimal, fraction, and percent?
Answer:
1399/200 699.5%
Step-by-step explanation:
1. 6.995 is already a decimal.
2. As a fraction it is [tex]\frac{1399}{200}[/tex] and as an improper fraction it would be 6 [tex]\frac{199}{200}[/tex].
3. As a percent it would be 669.5%.
help me please I'm stuck on this question!!!!
Answer:
1: 2.8
Step-by-step explanation:
15:42
Divide each side by 15
15/15 : 42/15
1: 2.8
ABC has vertices A(-3,2). B(3,2), and C(0, – 3). Is ABC scalene, isosceles, or equilateral?
Is ABC scalene, isosceles, or equilateral?
Answer:
isoselses!
Step-by-step explanation:
i hope that helps
1/3(6-9j)
PLEASE HELP!!!
Answer:
2-3j
Step-by-step explanation:
Distribute 1/3 to the rest of the equation and you'll get 2-3j
I hope this helps!
Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles by SSS or SAS, write "not enough information". Explain your answer.
Write a congruence statement and give a reason why the triangles are congruent. Select the correct choice below and, if necessary, write the vertices of the second triangle in the correct order.
Answer:
option B is correct answer. ∆SVZ~=∆YVX, SSS
Step-by-step explanation:
reasons,
VY=VS, S
YX=SZ, S
VX=VZ, S
therefore, ∆SVZ~=∆YVX.
hope this helps you.
The two triangles are congruent by side angle side property. The correct option is A.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
Given that there are three triangles and these three triangles are connected to each other at the centres' A, B, and C.
The diameter of the three circles is HF, DF, and DH. The three diameters are similar in shape and are also equal to each other.
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What is the x-value of the vertex of f(x) = -x2 + 9x - 11 ?
Answer:
7
Step-by-step explanation:
7
Identify If the gas pressure in a ball is low,
how will it affect the physical properties of
the ball?
HELP PLS!!
Answer: i hope it was helpful
Step-by-step explanation:
The ball will appear normal or fully blown up with air. It will bounce like a normal ball that is inflated well. The ball will appear deformed and deflated.
The polygons are similar. Find the value of each variable.
Answer:
z = 2Step-by-step explanation:
Similar figures have equal ratios of corresponding sides:
z / (z + 4) = 3/ 99z = 3(z + 4)9z = 3z + 129z - 3z = 126z = 12z = 22 procedimientos por favor
Answer:
184.8
Step-by-step explanation:
385/25×12
385÷25=15.4
15.4×12=184.8
The two legs of right triangle measures 6 and 8 inches respectively. What is the area of the circle that contains all 3 verticals of the triangle
Answer:
See image.
Step-by-step explanation:
Remember if you have a right angle inside of a circle, the hypotenuse is going to land exactly on the diameter. Also, Area of a circle = (pi)r^2 Lastly, remember pythagorean triples such as 3,4,5 or at least, the Pythagorean theorem a^2 + b^2 = c^2
The ordered pair (-3,9) is in the _______ Quadrant
Answer:
It would be located in the second quadrant
Step-by-step explanation:
The reason for this is because the x is a negative and the y is positive.
Which ordered pair is in the solution set of 3x − 2y ≥ -1?
F.(-2, -2.5)
G.(-1, 1)
H.(2, 4)
J.(1, 2.5)
Answer:
G
Step-by-step explanation:
Therefore, the option [tex]G(-1,1)[/tex] is correct.
What is the inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Here given inequality equation
[tex]3x- 2y \geq -1[/tex]
When the points [tex](-1,1)[/tex] so it would be
[tex]3(-1)-2(1)\geq -1\\\\-3-2\geq -1\\\\-5\geq -1[/tex]
Hence, the option [tex]G(-1,1)[/tex] is correct.
To know more about the inequality
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plz help verbal expression
Answer:
3(9+r) = 27 + 3r
Sum = addition
Distributive property
In 2020 researchers took random samples to compare the proportion of adult females to the proportion of adult males who use 2 or more credit/debit cards. The adults were aged 21 and older and they lived in all areas of the U.S. Based on the data collected, the researchers computed a 96 percent confidence interval for the true difference between the proportions of adult females minus the proportion of adult males who use 2 or more credit/debit cards. The confidence interval is: (0.013, 0.049). Assume all checks have been verified.
Question:
Choose the best answer below concerning the confidence interval for the difference between the true proportions of adult females minus the true proportion of adult males who use 2 or more credit/debit cards.
Using the z-distribution, it is found that the correct option is:
[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
A confidence interval is given by:
[tex]p \pm zs[/tex]
In which:
p is the estimate of the proportion.z is the critical value.s is the standard error.In this problem, the proportions are:
A proportion [tex]p_1[/tex] in a sample of size [tex]n_1[/tex].[tex]p_2[/tex] in a sample of size [tex]n_2[/tex].Hence, the standard errors are:
[tex]s_1 = \sqrt{\frac{p_1(1 - p_1)}{n_1}}, s_2 = \sqrt{\frac{p_2(1 - p_2)}{n_2}}[/tex]
When two proportions are subtracted, the estimate is the subtraction of proportions, while the standard error of the subtraction is the square root of the sum of each standard error squared, hence:
[tex]p = p_1 - p_2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Thus, the interval is:
[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
A similar problem is given at https://brainly.com/question/12517818
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students were surveyed ?
Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:
375 x 2 = 750
Is the point (-2, 5) a solution to the equation 2x + 5y = 0?
Answer:
No
Step-by-step explanation:
substitute -2 for 'x' and 5 for 'y'
2(-2) + 5(5) = 0?
-4 + 25 = 21, not 0
Please solve i need help :,) tyy
Answer:
6. 47
7. –25
8. 15
9. –33
10. –9
Step-by-step explanation:
Substitute.
6. x=-7
y = -8x - 9
= -8(-7)-9
= 56-9
y=47
7. x=2
y= -8x-9
= -8(2)-9
= -16-9
y= -25
8. x=-3
y= -8x-9
= -8(-3)-9
=24-9
y= 15
9. x=3
y= -8x-9
= -8(3)-9
= -24-9
y= -33
10. x=0
y= -8x-9
= -8(0)-9
= 0-9
y= -9
what is an equation of the line that passes through the points 0,-2and 0,-5
Answer:
Any equation with a slope of 3 will work. You can use any y-intercept. This equation will work: y = 3x+1
Step-by-step-explanation:
3x says that the slope is 3, and on a coordinate plane, 2 is 3 places above 5, and since the slope is 3, it will go 3 spots up, and run into (0,2)
Juana is making a triangular hat for a puppet. If two of the three angles of the hat both measure 30°
, what is the measure of the third angle?
Enter the correct answer in the box.
30+30=60 180-60=120
So the answer is 120
Mrs. terrance has a large bin of 236 crayons. She divides them equally among four containers.
GEOMETRY The perimeter of a square is four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. Write an equation in point-slope form to find the perimeter y of a square with side length x.
Answer:
y-4=4(x-1)
Step-by-step explanation:
The perimeter of a square is 4 times the length of one side, so we can write the equation like this.
y=4x
To find the equation in point-slope form, we know that when x=1, y=4. This gives us the point, (1,4). We also know that the slope of the equation is 4.
Plug the coordinate point into the point slope formula.
y-y1=m(x-x1)
y-4=4(x-1)