Enter the answer in the space provided.
Consider the figure.
142
68
N
Enter the measure of anglez, in degrees, in the space provided.
Answers
Step-by-step explanation:
as simple as it sounds, we need to do a few steps to actually get the result.
first the outer angle 142° and the corresponding inner angle in the triangle are a linear pair of angles, and together they have 180°.
so, the inner angle is 180 - 142 = 38°.
then, remember, the sum of all angles in a triangle is always 180°.
so, the third inner angle is 180 - 38 - 68 = 74°
now, this third inner angle is with z (the corresponding outer angle) again a linear pair (sum 180°).
so,
z = 180 - 74 = 106°
Related Questions
how do i find the distance between -6 and 3 in a number line
Answers
Find the absolute value in the difference of the coordinates.
5-13 Question Help opping Two friends shop for fresh fruit. Elena buys a watermelon for $6.55 and 3 pounds of cherries niy buys a pineapple for $4.35 and 2 pounds of cherries. Use the variable p to represent the price, in lars, per pound of cherries. Write and simplify an expression to represent how much more Elena sper e expression represents how much more Elena spent than Taniy. mplify your answer. Use integers or decimals for any numbers in the expression.) nter your answer in the answer box and then click Check Answer. Clear All Check Ans I parts showing Review progress Question 6 of 12 Back Next →
Answers
Answer:
The expression;
[tex]2.2+p[/tex]represents how much more Elena spent than Taniy
Explanation:
Let the variable p to represent the price per pound of cherries.
Given that Elena buys a watermelon for $6.55 and 3 pounds of cherries.
The total cost Elena spent is;
[tex]6.55+3p[/tex]Taniy buys a pineapple for $4.35 and 2 pounds of cherries.
The total cost Taniy spent is;
[tex]4.35+2p[/tex]The amount Elena spent more than Taniy is;
[tex]\begin{gathered} =(6.55+3p)-(4.35+2p) \\ =6.55-4.35+3p-2p \\ =2.2+p \end{gathered}[/tex]Therefore, The expression;
[tex]2.2+p[/tex]represents how much more Elena spent than Taniy
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4.
31.4n + 8.4 = 24
–8.4n + 31.4 = 24
24 = 31.4n + (–8.4)
24 – 31.4 = –8.4n
Answers
what is another way to write the following expression?(8x+24)+(9y+81)A) 8(x+3)+9(y+9)B) 17(x+3)+(y+9)C) 8(x+16)+9(y+72)D) 17xy+105
Answers
The given expression is
[tex](8x+24)+(9y+81)[/tex]The greatest common factor of the first expression is 8, and the greatest common factor is 9. Let's factor out it
[tex]8(x+3)+9(y+9)[/tex]Hence, the answer is A.A line includes the points (0, 3) and (1, 7). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
The equation of a line in slope - intercept form of a line includes the points (0, 3) and (1, 7)is y - 4x - 3 = 0.
A line includes the points (0, 3) and (1, 7).
We need to write its equation in slope-intercept form
The formula is
y - y₁ = ((y₂ - y₁)/(x₂ - x₁)) (x - x₁)
y - 3 = ((7 - 3)/1 - 0) (x - 0)
y - 3 = (4) x
y - 3 = 4x
y - 4x - 3 = 0
Therefore, the equation of a line in slope - intercept form of a line includes the points (0, 3) and (1, 7)is y - 4x - 3 = 0.
To learn more about equation of a line refer here
https://brainly.com/question/13763238
#SPJ1
solve 0.9x+5.1x-7=2(2.5x-3)how many solutions does the equation have
Answers
We want to solve the following equation for x:
[tex]0.9x+5.1x+7=2(2.5x-3)[/tex]First, let's expand the parenthesis on the right side of the equation using the distributive property
[tex]\begin{gathered} 0.9x+5.1x+7=2(2.5x-3) \\ 0.9x+5.1x+7=2\cdot2.5x-2\cdot3 \\ 0.9x+5.1x+7=5x-6 \end{gathered}[/tex]To add the terms with x, we just need to add their coefficients.
[tex]\begin{gathered} 0.9x+5.1x+7=5x-6 \\ (0.9+5.1)x+7=5x-6 \\ 6x+7=5x-6 \end{gathered}[/tex]Subtracting 5x from both sides of the equation:
[tex]\begin{gathered} 6x+7-5x=5x-6-5x \\ (6-5)x+7=(5-5)x-6 \\ x+7=0\cdot x-6 \\ x+7=-6 \end{gathered}[/tex]Now, if we subtract 7 from both sides, we have
[tex]\begin{gathered} x+7-7=-6-7 \\ x=-13 \end{gathered}[/tex]Since this is a first degree polynomial, it has only one solution and this solution is x = - 13.
A line passes through point A(2,5) and B(-8,-4). Find the slope of the line.
Answers
We are going to use the formula for the slope of the line with points A(2,5) and B(-8,-4). x1= 2, x2=-8, y1=5 and y2=-4
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-4-5}{-8-2}=\frac{-9}{-10}=\frac{9}{10}[/tex]The slope of the line is 9/10
Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If thesystem has one solution, find th e solution3x + 3y = -212x + y = - 15
Answers
Isolating the variable y in the second equation, we have:
[tex]\begin{gathered} 2x+y=-15 \\ y=-15-2x \end{gathered}[/tex]Now, using this value of y in the first equation, we have:
[tex]\begin{gathered} 3x+3y=-21 \\ 3x+3(-15-2x)=-21 \\ 3x-45-6x=-21 \\ -3x=-21+45 \\ -3x=24 \\ x=\frac{24}{-3}=-8 \\ \\ y=-15-2\cdot(-8)=-15+16=1 \end{gathered}[/tex]The solution of the system is x = -8 and y = 1.
use the digagramagram to
Answers
Answer:
To what?
Step-by-step explanation:
what is 2+2?
I just cant figure it out.
Answers
Answer:4
Step-by-step explanation
If you have 2 fishes in an aquarium and add 2 more fishes to the aquarium you have 4 fishes! :D
Answer:
4
Step-by-step explanation:
Find the equation of a line passing through the point (0,1) and parallel to the line 2x – 3y = 6.
Answers
The given equation of the line is
[tex]\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=\frac{2}{3}x-2 \end{gathered}[/tex]Hence slope of the line is
[tex]\frac{2}{3}[/tex]Since the line passing through (0,1) parallel to the given line then slope is same for both of them
Since (0,1) is a point so the intercept is c=1
So the equation is
[tex]\begin{gathered} y=mx+c \\ y=\frac{2}{3}x+1 \end{gathered}[/tex]According to the statements provided, name the lines that are parallel to each other. If there is notenough information to conclude parallel, write "not enough info" and explain why.
Answers
For the given figure:
According to the statements provided, we will name the lines that are parallel to each other:
1) ∠1 ≅ ∠3; The parallel lines are (c, d)
2) ∠6 ≅ ∠9; the parallel lines are (a, b)
3) ∠6 is supplementary to ∠10; the parallel lines are (a, b)
4) ∠1 ≅ ∠11: Not enough info
5) ∠5 is supplementary to ∠8; the parallel lines are (c, d)
6) ∠3 ≅ ∠11; The parallel lines are (a, b)
7) ∠1 ≅ ∠6; Not enough info
8) ∠1 ≅ ∠14: the parallel lines are (a, b)
9) ∠15 is supplementary to ∠16; Not enough info
10) ∠13 ≅ ∠15; the parallel lines are (c, d)
can you help me on this problem
Answers
Answer/Step-by-step explanation:
h - 4
---------- = k
j
h - 4
---------- = k( j )
j( j )
h - 4 = jk
÷k ÷k
--------------------
h - 4 h 4
------- = j or j = ---- - ----
k k k
I hope this helps!
HELPPP!!!!!! MEEEEEEE!!!!!!!!! There are 2 parts to this! TY
Module 01: Project Option 1
Instructions
Scientific notation is a tool that is used frequently in science, including astronomy, chemistry, biology, and more. In this activity, imagine that you are a student intern at NASA and are researching information about travel within our solar system. You will complete a series of tasks using what you know about scientific notation and what you discover about our solar system to calculate distances that astronauts may use for their next trip to space.
Part 1
Using technology or other resources, research the average distance that each planet is from the Sun (in kilometers). Once you have found the distance, create a chart showing each planet's distance from the Sun. The Sun itself will not receive a label since it is your starting point. For example, Mercury is located an average of 57,909,000 km from the Sun, so on the chart, Mercury would be labeled with a distance of 57,909,000. Use the example of the chart below to help you get started:
Planet
Distance from Sun (in Km)
Distance in scientific notation
Mercury
57,909,000
5.7909 x10^7
venus
108,200,000
earth
149,600,000
mars
227,900,000
jupiter
778,300,000
saturn
1,427,000,000
uranus
2,871,000,000
neptune
4,497,100,000
Part 2
Answer the following questions using the data you have found. Show your work on all questions as indicated.
A. If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? Show your work and provide your answer in scientific notation.
B. Mercury, Venus, and Earth are the three planets closest to the Sun. Would their combined distance from the Sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer.
C. If Earth was 10 times farther away from the Sun than it is now, which planet would it be closest to? Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work.
D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary
Answers
Distance divided by speed equals time. Distance is calculated by subtracting the planets' distances.
What is meant by distance?The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.
Distance = speed × time is the formula.
Therefore,
1. Assume that the sun and both planets are in line and that they are on the same side of the sun.
from the sun: Jupiter is 778,300,000
from the sun, Venus is 108,200,000
778,300,000 - 108,200,000 = 670,100,000
It would have to travel 670,100,000/6.701*10 with 8 square kilometers.
2. The three planets that are nearest to the sun are Mercury, Venus, and Earth.
Mercury's distance from the sun is 57,909,000 km.
Venus's distance from the sun is 108,200,000 km.
Earth's distance from the sun is 149,600,000 km.
combined distance between Mercury, Venus, and Earth
57,909,000+108,200,000+149,600,000 = 315,709,000
Because 315,709,000 km is less than 4,503,443,661 km, the distance from the sun to Neptune is less than the sum of the distances from the sun.
3. Assume that every planet is on the same side of the sun and is in alignment with it.
Earth is equal to Earth at ten solar distances is 149,600,000 km *10.
New distance to Earth = 1,496,000,000km
Earth would be closest to Saturn at its distance from the sun is
1,496,000,000 - 1,296,000,000 =67,000,000
and the two would be 67,000,000 km apart.
4. Notation used in science: with a 7 square kilometer. The space shuttle moves at around 28,000 km/h.
To locate Time
Time = Distance /speed
1,200,000,000 -28,000 =40,000 hrs.
To learn more about distance refer to:
https://brainly.com/question/17273444
#SPJ1
In the triangle ABC at the right above, AB=CB, and P and Q are points on the sides CB and AB such that AC=AP=PQ=QB. Find the number of degrees in angle B.
Answers
Since QP and QB are equal the triangle PQB the angles:
[tex]\begin{gathered} \measuredangle QPB=\measuredangle QBP \\ \measuredangle QPB=x \end{gathered}[/tex]The last angle can be found by adding all the internal angles and making it equal to 180 degrees.
[tex]\begin{gathered} \measuredangle QPB+\measuredangle QBP+\measuredangle BQP=180 \\ x+x+\measuredangle BQP=180 \\ \measuredangle BQP=180-2x \end{gathered}[/tex]The angle BQP and the angle AQP are suplementary, this means that their sum is equal to 180 degrees. So we have:
[tex]\begin{gathered} \measuredangle AQP+\measuredangle BQP=180 \\ \measuredangle AQP+180-2x=180 \\ \measuredangle AQP=180-180+2x \\ \measuredangle AQP=2x \end{gathered}[/tex]Since the sides AP and PQ are equal, then the angle PAQ is equal to AQP.
[tex]\begin{gathered} \measuredangle PAQ=\measuredangle AQP \\ \measuredangle PAQ=2x \end{gathered}[/tex]To find the last angle on that triangle we can add all the internal angles and make it to 180 degrees.
[tex]\begin{gathered} \measuredangle PAQ+\measuredangle AQP+\measuredangle APQ=180 \\ 2x+2x+\measuredangle APQ=180 \\ \measuredangle APQ=180-4x \end{gathered}[/tex]The angle APC is suplementary with the sum of the angles APQ and BPQ. So we have:
[tex]\begin{gathered} \measuredangle APC+\measuredangle APQ+\measuredangle BPQ=180 \\ \measuredangle APC+180-4x+x=180 \\ \measuredangle APC=3x \end{gathered}[/tex]The sides AP and AC are equal, therefore the angles APC and ACP are also equal.
[tex]\begin{gathered} \measuredangle ACP=\measuredangle APC \\ \measuredangle ACP=3x \end{gathered}[/tex]Then we can find the last angle on that triangle.
[tex]\begin{gathered} \measuredangle CAP+\measuredangle ACP+\measuredangle APC=180 \\ \measuredangle CAP+3x+3x=180 \\ \measuredangle CAP=180-6x \end{gathered}[/tex]The angle CAB is equal to the sum of CAP and PAQ. So we have:
[tex]\begin{gathered} \measuredangle CAB=\measuredangle CAP+\measuredangle PAQ \\ \measuredangle CAB=180-6x+2x \\ \measuredangle CAB=180-4x \end{gathered}[/tex]Since the sides AB and BC are equal, then the angles ACB and CAB must also be equal. We can find the value of x with this.
[tex]\begin{gathered} \measuredangle BAC=\measuredangle ACB \\ 180-4x=3x \\ 7x=180 \\ x=\frac{180}{7} \end{gathered}[/tex]The value of x is 180/7
Can someone please help me out with this
Answers
The value of UR = 13 mm
Given:
HGJI ≅ RSTU
proportional sides:
HG = JI
GJ = ST
JI = TU
IH = UR
From the figure:
IH = 13 mm
so IH = UR = 13
UR = 13 mm.
Therefore the value of UR = 13 mm.
Learn more about the value here:
https://brainly.com/question/14316282
#SPJ1
Prism pen , Base som 3cm) bom 8cm 2cm 7 cm height=8m 7 find volume
Answers
We can put the 5-sided face downwards so that we have a pentagon-prism.
The volume of the figure will be area of base (area of pentagon) x height.
This way, the height of the figure will be 8 cm and we will find the area of the pentagon, below.
Let's find the area of the base first:
The pentagonal base can be broken down into a square (top left), a triangle (top right), and a rectangle (bottom). We find each of the areas.
• Area of Square
Side lengths are 3 cm, so the area will be:
Area = 3 x 3 = 9
• Area of Triangle
Base is 3 cm and height is 4 cm, so the area will be:
Area = (1/2) * base * height
Area = (1/2) * 3 * 4 = 6
• Area of Rectangle
Base is 7 cm and height is 2 cm, so the area will be:
Area = 7 x 2 = 14
Total Area of Pentagon = 9 + 6 + 14 = 29
Now, the Volume of the Composite Figure is:
Volume = Area of Pentagonal Base * Height
Volume = 29 * 8
Volume = 232 cubic centimeters
AnswerVolume = 232 cubic centimeters
Determine the degree
-1/4abc+2b^2
Answers
The degree of polynomial is 3.
Given polynomial:
⇒ -1/4(abc)+2[tex]b^{2}[/tex]
⇒ -abc/4 + 2[tex]b^{2}[/tex]
the polynomial has two terms,
terms = -1/4(abc), 2[tex]b^{2}[/tex].
Degree of first term is =(-1/4) [tex]a^{1} b^{1} c^{1}[/tex] = 1+1+1 =3
= 3.
Degree of second term = [tex]2b^{2}[/tex] = 2.
Here degree can be determined as highest degree which is equal to 3.
Hence the degree of polynomial is 3.
Learn more about the degree and polynomial here:
https://brainly.com/question/2284746
#SPJ1
Which of the h values are solutions to the following equations? h^2=0.36
Answers
to solve this, you need to isolate x,
Step 1
square root in both sides
[tex]\begin{gathered} h^2=0.36 \\ \sqrt{h^2}=\sqrt{0.36} \\ \text{the }\sqrt{\square}\text{ eliminates the square} \\ h=\pm\sqrt{0.36} \end{gathered}[/tex]so, there are two values for h that fit this equation
[tex]\begin{gathered} +\sqrt{0.36\text{ }}=0.6 \\ \text{and} \\ -\sqrt{0.36}=-0.6 \end{gathered}[/tex]so, the answers are A and B
An official lady's basketball has a circumference of 28.5 inches. How much volume is inside this basketball? Use 3.14 for Pi and round your final answer to the nearest whole cubic inch. A. 1,175B. 392C. 86D. None of the aboveI need help with problem I would appreciate the help.
Answers
If four pounds of jelly beans costs $6.82, how much would 2 Ibs cost?
Answers
Four pounds of jelly beans: $6.82
First, calculate the cost of 1 lb by dividing the price by the number of pounds:
6.82 / 4 = $1.705 per pound
Now, multiply by 2:
1.705 x 2 = $3.41
A rectangle has a length of 26 inches and a width of 14 inches. If 1 inch = 2.54 centimeters, find the area of the rectangle in centimeters. Round the answer to the nearest tenth.
560.4 cm2
56.4 cm2
2,348.4 cm2
924.6 cm2
PLS hurry and thank you
Answers
The area of the rectangle will be 2,348.3824 cm² as "A rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm".
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Here,
Length in inches=26
Width in inches=14
area in inches=26*14
=364 inch²
Now,
1 inch=2.54 cm
area in cm,
=364*2.54*2.54
=2,348.3824 cm²
Since "a rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm," the area of the rectangle will be 2,348.3824 cm².
To know more about area,
https://brainly.com/question/13194650?referrer=searchResults
#SPJ1
Question 5(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify √5 (10-4√2).
A 14
B 15√2
C 5√2-4√10
D 10√5-4√10
Answers
Answer:
I think the answer is D. sorry if I'm wrong
How many angles can you make with the angles 120, 60,40
Answers
All types of triangles must have a total angle of 220 degrees. Otherwise, it is not a triangle.
A triangle has three sides three corners and three vertices. The sum of all interior angles of a triangle is always 180°. This is called the sum property of the triangle angles. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A triangle is a three-sided polygon with three corners.
The three sides are joined end to end at points forming the corners of the triangle. The sum of the three angles of a triangle is 180 degrees. A true triangle is a shape with three sides and three angles. The sum of the two side lengths must be greater than the third side and the sum of the three angles must be 180°.
Learn more about The angles here:-https://brainly.com/question/25716982
#SPJ1
Which of the followings have infinitely many solutions. Select all that
apply.
2x = 3x - X
3x = 3(2 + x)
4×=×+4
-2x = -X-2
×=1=2×-(×+1)
Answers
Option C and Option D has infinite number of solutions
C. 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4D. 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4) What is defined as the solution of the equation?Given that we must find equations with an infinite number of solutionsWe have infinite solutions if we end up using the same term on the both sides of a equal sign, including such 4 = 4 or 4x = 4x.There are no solutions if we end up with distinct numbers along both side of the equal sign as in 4 = 5.Option A: -2(x - 2) + 3x = x - 4
Simplify the equation;
-2x + 4 + 3x = x - 4
x + 4 = x - 4
LHS ≠ RHS
Thus, equation does not have infinite solutions.
Option B: 2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
Simplify the equation;
2x + 4x - 4 = 6x + 3 - 2x + 2
6x - 4 = 4x + 5
6x - 4x = 5 + 4
2x = 9
Obtained equation has only one solution.
Thus, equation does not have infinite solutions.
Option C: 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
Simplify the equation;
3x + 2x - 4 + 6 = 4x + 6 + x - 4
5x + 2 = 5x + 2
LHS =RHS
Thus, this equation has infinite solutions.
Option D: 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
Simplify the equation;
4x + 8 + x + 1 = 2x - 3 + 3x + 12
5x + 9 = 5x + 9
LHS =RHS
Thus, this equation has infinite solutions.
To know more about the solution of the equation, here
https://brainly.com/question/17145398
#SPJ1
The correct question is-
Which equations have an infinite number of solutions?
Select all that apply.
A -2(x - 2) + 3x = x - 4
B 2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
C 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
D 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
Use a calculator to estimate the value of the following. Round to the nearest ten-thousandth.sin 84.1°
Answers
Given
[tex]\sin 84.1^o[/tex]Calculating,
[tex]\sin 84.1^o=0.9947[/tex]Rounding off to ten-thousands place,
[tex]\sin 84.1^o=0.995[/tex]The answer is 0.995
Please help! I need explanation on why the answer is what it is.
Answers
The y-intercept of the given equation is (B) -2.
What is the y-intercept?When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0. A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.So, the y-intercept will be:
Equation: 3x + 4y = -8Plot the equation on the graph as follows:
We can clearly see that the line intersecting on the y-axis is (0, -2).So, the y-intercept will be -2.Therefore, the y-intercept of the given equation is (B) -2.
Know more about y-intercept here:
https://brainly.com/question/25722412
#SPJ1
i need to answer this question then find the matching graph
Answers
we have
[tex]\begin{gathered} 5a-2\ge8 \\ \text{solve for a} \\ 5a\ge8+2 \\ 5a\ge10 \\ a\ge2 \end{gathered}[/tex]the solution is the interval {2, infinite)
In a number line the solution is the shaded area at right of a=2 (close circle)
therefore
the answer is
First option
If y=x+2 we’re changed to y=x-1 how would the graph of a new function compare with the first one
A it would be shifted down
B it would be shifted left
C it would be less steep
D it would be shifted up
Answers
The graph of the new function compares with the first one by A it would be shifted down
What is a graph?A graph is a pictorial representation of a function.
What is a function?A function is a mathematical expression that shows the relationship between two variables.
How to determine how would the graph of a new function compare with the first one?Since we are given the functions y = x + 2 and If y = x + 2 we’re changed to y = x - 1. We want to determine how the graph of the new function would change compared with the first one.
We proceed with the transformation as follows.
Let
y₁ = x + 2 and y₂ = x - 1So, we can see that
y₂ = x - 1
= x - 1 + 2 - 2
= x + 2 - 1 - 2
= x + 2 - 3
= y₁ - 3
Since y₂ = y₁ - 3, we see that the second graph is shifted down by 3 units from the first one.
So, the graph compares with the first one by A it would be shifted down
Learn more about graph transformation here:
https://brainly.com/question/19967824
#SPJ1
A motorboat takes 5 hours to travel 200 miles going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Rate of the boat still in water=Rate of the current=
Answers
Given,
Time taken by motorboat to going 200 miles upstream is 5 hours.
Time taken by motorboat to going 200 miles downstream is 4 hours.
At upstream,
The speed of boat is offosed by the speed of current.
At downstream,
The speed of boat is incraesed by the speed of current.
Consider,
The speed of boat is b.
The speed of current is c.
The speed is calculated as,
[tex]\begin{gathered} \text{Speed=}\frac{dis\tan ce}{time} \\ b-c=\frac{200}{5} \\ b-c=40 \\ b=c+40\ldots\text{.}\mathrm{}(1) \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \text{Speed=}\frac{dis\tan ce}{time} \\ b+c=\frac{200}{4} \\ b+c=50 \\ b=50-c\ldots\text{.}(2) \end{gathered}[/tex]Substituting the value of b from equation (2) then,
[tex]\begin{gathered} c+40=50-c \\ 2c=10 \\ c=5\text{ mile per hour} \end{gathered}[/tex]Substituting the value of c in equation (1) then,
[tex]\begin{gathered} b=5+40 \\ b=45\text{ mile per hour} \end{gathered}[/tex]Hence, the speed of boat is 45 mile per hour and speed of current is 5 mile per hour.