Answer:
1. 600 yd^3
2. 103,680 in^3
Step-by-step explanation:
1. To find volume we do l*w*h
(15)(8)(5)
120(5)
600 yards^3
2. We also find the volume for this
(36)(60)(48)
2160(48)
103680 in^3
Hopes this helps
Athena Investment Company is considering the purchase of an office property. After a careful review of the market and the leases that are in place, Athena believes that next year’s cash flow will be $100,000. It also believes that the cash flow will rise in the amount of $5,400 each year for the foreseeable future. It plans to own the property for at least 10 years. Based on a review of sales of properties that are now 10 years older than the subject property, Athena has determined that cap rates are in a range of 0.10. Athena believes that it should earn an IRR (required return) of at least 11 percent.
Required:
a. What is the estimated value of this office property (assume a 0.10 terminal cap rate)?
b. What is the current, or going-in, cap rate for this property?
Cap rate (going in) = 5.6%
The estimated value of this property = 17,85,714.2 $
What is the required rate of return?The needed rate of return is the rate of return that investors are looking for on assets that are similar. The value of the property and the needed rate of return are inversely related. Property value will fall as the needed rate of return rises, and the opposite is also true.
given cash flow is $100,000 and it increases by 5400$ every year hence growth rate would be 5.4 %.
Cash flows = $1,000,00
Growth rate = 5.4%
Required rate of return = 11%
the required rate of the property = cash flow / ( Required rate of return - growth)
the required rate of the property = 100,000 / (11 -5.4 ) = 17,85,714.2 $
Cap rate (going in) = Required rate of return - a growth rate of the property
Cap rate (going in) = (11 - 5.4) %
Cap rate (going in) = 5.6%
Thus, it can be concluded that the decrease in the required rate of return is the cause of the increase in the value of the property.
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Consider the following line integral. C xy dx + x2y3 dy, c is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4).(a) evaluate the given line integral directly. 20 correct: your answer is correct. (b) evaluate the given line integral by using green's theorem.
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.
How is Green's theorem demonstrated?M(x, c) M(x, d) dx is equivalent to = b M(x, c) dx + M(x, d) dx. So, by demonstrating that the two sides of a rectangle are equal, we have established Green's Theorem. The sum of rectangles theorem. Since each region can be as nearly approximated by a sum of rectangles as desired, Green's Theorem must apply to all regions.
It looks like the integral is
[tex]\int\limits^0_c {xy} + x^{2} y^{3} \, dy[/tex]
Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}
Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem
Compute the double integral:
From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by
C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}
The line integral over C' is
[tex]\int\limits^1_0 {(256t^{5} }+1280t^{4}+ 2560t^{3} - 2564t^{2} + 1288t - 260) \, dt[/tex]
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.
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Determine whether the system of equations is consistent or inconsistent and if it is independent or dependent.
3x+y=−5
3y+15=−9x
Multiple choice question.
A)
consistent and dependent
B)
consistent and independent
C)
inconsistent
D)
inconsistent and dependent
Answer:
C) inconsistent
Step-by-step explanation:
3x+y=−5
3y+15=−9x
3x + y = -5
9x + 3y = 15
3x + y = -5
3x + y = 5
The system graphs as two parallel lines.
Answer: C) inconsistent
Find the distance between the two points.
(-4,-5)
(4,2)
√ [?]
Enter the number that
goes beneath the
radical symbol.
Enter
By using distance formula, it can be calculated that-
Distance between (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units
What is distance formula?
Distance formula is used to find the distance between two coordinates.
If the points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then distance is calculated by the formula
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
The points are (-4, -5) and (4, 2)
Distance between (-4, -5) and (4, 2) = [tex]\sqrt{(-4-4)^2+(-5-2)^2}[/tex]
= [tex]\sqrt{64 + 49}\\\sqrt{113}[/tex]units
Distance between (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units
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Use linear approximation to estimate the amount of paint in cubic centimetres needed to apply a coat of paint 0.070000cm thick to a hemispherical dome with a diameter of 40.000 meters.
Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.
Given that,
We have to find applying a coat of paint 0.07cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated volume of paint in cubic centimeters, which may be calculated using a linear approximation.
We know that,
Volume of a sphere = 4/3 πr³
Volume of a hemisphere is
V= 2/3 πr³
dV = 2πr² dr
Here,
dr=0.07cm
r=(1/2)×40m=2000cm
Let plug in the formula
dV = 2×π×(2000²)×(0.07)
dV=1759291.886 cubic centimeters
Therefore, Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.
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In the figure, m∠ 1=(3 x)° and m ∠2=(x+48)°
(a) Write an equation to find x. Make sure you use an = sign in your answer.
(b) Find the degree measure of each angle.
m ∠ 1=____°
m ∠ 2=____°
If m∠ 1=(3 x) degrees and m ∠2=(x+48) degrees
The equation to solve the value of x is
3x = x+48
The value of x = 33
The angle 1 = 99 degrees
The angle 2 = 81 degrees
The measure of angle 1 = 3x degrees
The measure of angle 2 = x + 48 degrees
The sum of the angles on a straight line is add up to 180 degrees. Therefore angle 1 and angle 2 are supplementary angles.
∠1 + ∠2 = 180 degrees
Substitute the values in the equation
3x + x + 48 = 180
4x + 48 = 180
4x = 180 - 48
4x = 132
x = 132/4
x = 33
Part b
Then the measure of angle 1 = 3x
= 3 × 33
= 99 degrees
The measure of angle 2 = x + 48
= 33 + 48
= 81 degrees
Therefore, the equation to solve x is 3x = x + 48 and the measure of angles 1 and 2 is 99 degrees and 81 degrees respectively
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t: w = 7:2
p:r = (4t+w) : (t +9w)
Calculate the ratio p : r.
Give your answer in its simplest form.
The ratio of p:r is 6/5
What is ratio?A ratio can be described as the comparison of two or more numbers which indicates their sizes in relation to one another.
From the information given, we have that;
t: w = 7:2
We have that;
t =7w = 2p:r = (4t+w) : (t +9w)Now, substitute the values into the formula
p = 4t + w
p = 4(7) + 2
expand the bracket
p = 28 + 2
Add the values
p = 30
r = t + 9w
r = 7 + 9(2)
expand the bracket
r = 25
The ratio, p:r
p:r = 30/25
p: r = 6/5
Hence, the value is 6/5
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Plot the GNP series, gnp, and then test for a unit root against the alternative that the process is explosive. State your conclusion.
Hint: [in R]
library(astsa)
library(tseries)
head(gnp)
print(gnp)
there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).
The United States is super power and has multiple resources to maintain itself and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.
The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.
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Create an inequality with 0-9
Answer:
The inequality form is 0≤x≤9 0 ≤ x ≤ 9 .
Determine the value of x that makes Triangle ABC congruent to Triangle XYZ
Select each expression that has a sum of 4 4/12 A 3 1/5 + 1 3/7. B 1 11/12 + 2 1/4. C 1 3/6 + 1 1/2 + 1 3/4. D 1 1/3 + 1 1/2 + 2 1/3. E 3/6 + 1 2/4 + 2 1/3
Write the equation of the line that passes through the points (9, 4) and (−6, −8).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
The desired equation is then y -4 = 12/15 (x -9)
What is equation of line?Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.where a ≠ 0 and b ≠ 0.
We need this line's equation in the point-slope form, y - k = m. (x - h).
The point (h, k) in the point-slope form shown above can be chosen at random from the two points (9, 4) and (-6, -8). In the above point slope form, the other point is thus denoted by (x, y):
Let (x, y) be and (h, k) be (9,4). (-6,-8). Consequently, y - k = m(x - h) becomes
-8-4 = m (-6-9), so that -12 = m(-15), and the slope is thus m = 12/15
The desired equation is then y -4 = 12/15 (x -9) (which is in point-slope form).
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suppose baby kittens' weights are normally distributed with a mean of 12.3 and a standard deviation of 2.2. the z-score tells you how many units above the average (if z-score is positive) or below the average (if z-score is negative) any particular baby kitten's weight is. find the baby kitten weight that corresponds to the following z-scores given below. hint: use the formula x
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X =
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X ,,a. X = 16.786 , b. X = 8.014
To find the baby kitten weight corresponding to the given z-scores, we use the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the z-score. For the first z-score of 1.98, we substitute the values and solve for X. X = 12.3 + (1.98)(2.2) = 16.786. For the second z-score of 2.87, we substitute the values and solve for X. X = 12.3 + (2.87)(2.2) = 8.014. Therefore, the baby kitten weights corresponding to the given z-scores are 16.786 and 8.014, respectively.
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A manufacturer of floor mops would like her product to last 700 hours, on the average. She hopes the mean number of hours is not a lot less than 700 (people will not continue to buy her product) or a lot more than 700 (people would seldom have to buy the product). However, the manufacturer has reason to believe the mean may have changed. A random sample of 48 items shows that sample mean = 675 and sample standard deviation = 77 hours. Use the significance level α=.05. What is the appropriate test to perform? Regarding the hypothesis testing in question 1, what is the rejection region? Regarding the hypothesis testing in question 1, what is the p-value of the test? Round your answer to four decimal places Regarding the hypothesis testing in question 1, what is your conlusion?
There is actually enough evidence for the manufacturer to believe that the mean number of hours and mobs will last has actually changed.
We are supposed to use Israel and
significance level α=.05 to perform hypothesis test on the statement of the manufacturer.
So Let's move into our worksheet, our population is 700, our sample size is 48.
The sample mean is 675
Sample standard deviation is 77.
So the first step is to state the null and alternative hypothesis and we have that our hate notes is based on the fact that μ is a cost of 700.
This is what the manufacturer wants, but she thinks that it might have changed probably lesser than or greater than Saddam is our alternative hypotheses, his meal is not equals to 700. So she is not sure whether it does, it's either decrease or increase but it has actually changed.
So after stating our null and alternative protesters, the next needs to state the decision rule that we will be using to either reject or accept the no like protesters.
So will be making a use of the PVA limited to make the decision. It is your roost is that if our evil is better than alpha we are supposed to accept, protesters and if our pivot is lesser than alpha, We are supposed to reject the null hypothesis is that our alpha is equals deserve .05.
So that being said it's time for us to move to draw our test statistics. Now for our test statistic is going to be AT. Test. Yes, our sample size is greater than 30. There's no issue with that. But we actually don't know the value of the population standard deviation. We are making use of the samples and activation which is 27. So that means it would be better if we use our T. Test as our test statistics. So our test statistic is a teacher has given towards us. T is a cost to extra minus meal divided by S divided by the square root of n. Our expert in this case is 6 75 minus. We have 700 divided by our s is 77 divided by the square root of 48. So let's do the math. 6 75 minus 700. We have a -25 divided by so we have 77 divided by the spirit of 48. We have this to be 11.11399. So uh -25 divided by 11.11399. We have our answer to be -2.249. So they simply implies that our test statistics is manners two points 249. So the next step is for us to get the p value attached to this test statistic scenes, we are using the p value method uh to make our decision. So we need a P value. We already have the level of significance. So to get the P value, we can decide to make itself. It it it's a distribution table but that will only give us a range of values in which the p value is located. It won't give us the actual P value. So most times we decide to use calculator to get the p value the exact p value. So our test is actually a two tailed tests were testing for a T score.
Our degree of freedom is the sample size minus one.
48-1=47
And our T score uh is minus two points 249.
So that we have a miners 2.249. And as you can see our p value here is 0.02 0.0294. T. Value is 0.029 so far. Alright, so there's our p value. So the next thing is to make our decision. So we have that as you can see their .0-9 Too far is actually lesser than 0.05 hands.
We make a decision by saying, we are going to reject the null hypothesis. So the decision is that we're going to be rejected the null hypothesis.
As a result, the manufacturer has sufficient reason to think that the average number of hours and mob duration have altered.
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What is 8 divided by 2/5 in simplest form?
Answer:
20
Step-by-step explanation:
20.
Step-by-step explanation:1. Write the expression.[tex]\frac{8}{\frac{2}{5} }[/tex]
2. Apply the fraction rules.Check the attached image below.
[tex]\frac{8}{1}* \frac{5}{2}[/tex]
3. Simplify.[tex]\frac{8}{1}*\frac{5}{2}=\\\\ \frac{8*5}{1*2} =\\\\ \frac{40}{2}=\\ \\20[/tex]
4. Conclude.[tex]\frac{8}{\frac{2}{5} }=20[/tex].
7. (01.05 LC)
If x³ = 64, what is the value of x? (5 points)
04
8
21
61
Answer:
4
Step-by-step explanation:
Solve for x over the real numbers:
x^3 = 64
Take cube roots of both sides:
Answer: x = 4
4^2 = 16
4^3 = 64
Consider the matrices
S= 4 1 and T= 0 4
-3 -2 -4 3
Show that multiplication of matrices is not commutative by determining the product matrices ST and TS. Enter your answer by filling in the boxes.
ST= ______ TS= _________
Multiplication of matrices is not commutative by determining the product matrices ST and TS .
Given :
Consider the matrices
S = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex] and T = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]
Show that multiplication of matrices is not commutative by determining the product matrices ST and TS.
ST = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]
[tex]ST_{11[/tex] = 4 * 0 + 1 * -4 = -4
[tex]ST_{12[/tex] = 4 * 4 + 1 * 3 = 19
[tex]ST_{21[/tex] = -3 * 0 + -2 * -4 = 8
[tex]ST_{22[/tex] = -3 * 4 + -2 * 3 = -18
ST = [tex]\left[\begin{array}{ccc}-4&19\\8&-18\end{array}\right][/tex]
TS = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]
[tex]TS_{11[/tex] = 0 * 4 + 4 * -3 = -12
[tex]TS_{12[/tex] = 0 * 1 + 4 * -2 = -8
[tex]TS_{21[/tex] = -4 * 4 + 3 * -3 = -25
[tex]TS_{22[/tex] = -4 * 1 + 3 * -2 = -10
TS = [tex]\left[\begin{array}{ccc}-12&-8\\-25&-10\end{array}\right][/tex]
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X-3y = 16 4x-y=9
I’m so confused
Answer:
x = 1, y = -5.
Step-by-step explanation:
X-3y = 16 Equation (1)
4x- y = 9 Equation (2)
We can solve this by the Method of Elimination.
One way is to multiply the second equation by -3, as follows:
-3(4x - y = 9)
= -12x + 3y = -27 Call this equation (3)
Now if we add equation (3) to equation (1) we eliminate the y terms:
x - 3y = 16
-12x + 3y = -27 Adding:
-11x + 0 = -11
-11x = -11
x = -11/-11 = 1
Finally, we find the value of y by substituting x = 1 into equation (2):
4(1) - y = 9
-y = 9 - 4
-y = 5
y = -5.
So, the answer is x = 1, y = -5.
or we can write it as an ordered pair (1, -5).
Hope this helps.
Answer:
x=1 and
y= -5
Help me solve it 79 points for the answer
Answer:
Step-by-step explanation:
2. Unit Rate: 1:2
3. A class has 26 kids. Johnny is trying to figure out the number of ears everyone has in total. You can use the ration 1:2. For every kid there are 2 ears. Therefore there are 52 ears total. [tex]\frac{1}{2}=\frac{26}{52}[/tex]
4. Multiplication
5. No, you can't have half an ear
Which statement proves that parallelogram KLMN is a rhombus?
d. The slope of KM is 1 and the slope of NL is -1.
The midpoint of both diagonals is (4 1/2, 5 1/2), the slope of RP is 7, and the slope of SQ is -1/7
Answer: D is the right answer .The slope of KM is 1 and the slope of NL is –1.
A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.
i.e. product of its slope should be -1.
[∵if one line is perpendicular to the other lines then product of its slope should be -1.]
Slope of KM= 1
Slope of NL= -1
Product of slope of diagonals=1×-1=-1
∴diagonals of given parallelogram perpendicularly bisect each other.
Therefore, it is a rhombus.
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Kanoi can weed a garden in 40 minutes. Ale'a can weed the same garden in 50 minutes. How long would it take for Kanoi and Ale'a to weed the same garden together? (Round to the nearest hundredth)
Kanoi and Ale'a can weed the same garden together in 22.22 minutes
How to find the time it will take to weed the garden togetherRate of work refers to amount to of work completed at a given time
Information from the question include
Kanoi can weed a garden in 40 minutes
Kanoi's rate = 1/40 per minute
Ale'a can weed the same garden in 50 minutes
Ale'a rate = 1/50 per minute
When both are working together the rate will be
1/40 per minute + 1/50 per minute
= 9/200 per minute
The time is solved
1 / 9/200
= 200/9
= 22.2222 minutes
= 22.22 minutes to the nearest hundredth
The time it will take both of them to weed is 22.22 minute
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Akin's salary is 20% less than Shola's and Shola spent 45% of his salary on accommodation leaving him with #550. How much is Akin's salary?
Answer:
$800
Step-by-step explanation:
Let's say that Shola's salary is x dollars. This means that Akin's salary is 0.8x dollars, because his salary is 20% less than Shola's salary.
Since Shola spent 45% of his salary on accommodation, he had 0.55x dollars left, or $550. This means that we can write the equation 0.55x = 550.
To solve for x, we can divide both sides of the equation by 0.55 to get x = 1000. This means that Shola's salary is $1000, and since Akin's salary is 20% less than Shola's, his salary is 0.8 * 1000 = $800. Therefore, Akin's salary is $800.
HELP PLEASE FAST!! Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
Answer:
26
Step-by-step explanation:
One leg measures 7.
One leg measures 8.
a² + b² = c²
7² + 8² = c²
c² = √113 = 10.630 = 11
perimeter = 7 + 8 + 11
perimeter = 26
in the air, it had an average speed of 161616 \text{m/s}m/sstart text, m, slash, s, end text. in the water, it had an average speed of 333 \text{m/s}m/sstart text, m, slash, s, end text before hitting the seabed. the total distance from the top of the cliff to the seabed is 127127127 meters, and the stone's entire fall took 121212 seconds.
The time it takes for the stone to fall in the air is 7 seconds, and it takes 5 seconds for the stone to fall in the water in the seabed.
The average speed of the stone in air is shown here as 16 m/s.
The average speed of the stone in water is 3 meters per second.
The total distance from the top of the cliff to the seabed is 127 meters.
Total fall time = 12 seconds
Therefore
Let t1 represent the time spent by the stone in the air and
t2 = time spent by the stone in water
Now using the equations of motion we get :
Therefore, t₁ + t₂ = 12 s........(1)
16·t₁ + 3·t₂ = 127............(2)
From (1) t₁ = 12 - t₂
16×(12 - t₂) + 3×t₂ = 127
13t2 = 65 is the result.
and t2 equals 5 seconds
t1 = 12 - t2 = 12 - 5 = 7 sec
The time it takes for the stone to fall in the air is t1 = 7 seconds.
The time it takes for the stone to fall into the water is t2 = 5 seconds.
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give an example of a function that is discontinous at one and only one point in its domain but is continous at every other point
An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.
This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.
The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.
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f(x)=7-2x
g(x)=x+3
find (fog^-1)(5)
3 is the value of (fog⁻¹)(5) for functions f(x)=7-2x and g(x)=x+3.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that the functions are f(x)=7-2x and g(x)=x+3.
We need to find the value of (fog⁻¹)(5)
g⁻¹(x)=x-3.
By composite functions
f(g⁻¹)(x)=7-2(x-3)
f(g⁻¹)(x)=7-2x+6
Now plug in the value of x as 5
f(g⁻¹)(5)=7-2(5)+6
=7-10+6
=-3+6
=3
Hence, the value of (fog⁻¹)(5) is 3.
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19. The ___ is the amount or part that results from the base multiplied by the rate.
A. increase
B. percent
C. rate
D. portion
Answer: B, Percent
Step-by-step explanation: The formula to find a whole after a percent is:
Worth = Part percent * Wole number / 100
This is the same as the definition says, "the amount or part that results from the base multiplied by the rate."
Solve for 2 sin A sin B =
2 sin A sin B with two angles A and B, 2 sin A sin B = cos (A-B) - cos (A + B). The 2sinasinb formula is equivalent to the difference between the angle sum and the angle difference of the cosine functions. The formula for two sins is two sins A and two sins B: cos (A-B) - cos (A + B).
What is 2SinASinB Identity?
2SinASinB identity is a trigonometric formula and it is used for the simplification of trigonometric expressions. It is also used for evaluating integrals involving trigonometric functions for easy calculation. We can derive the formula for 2SinASinB using the angle sum and angle difference formulas of the cosine function. Using the 2SinASinB formula, we can derive another trigonometric formula for SinA SinB given by, sinA sinB = (1/2)[cos(A - B) - cos(A + B)].
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Question 3 of 5
A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.
Let x represent the canoe's speed with no water current (in still water) and y represent the speed of the water current, in miles per hour. Then the situation can be represented by this system of equations:
x+y=7
x-y=1
Choose the two correct options.
A. The speed of the canoe in still water is 3 miles per hour.
B. The speed of the water current is 4 miles per hour.
C. The speed of the canoe in still water is 4 miles per hour.
D. The speed of the water current is 3 miles per hour.
Two correct options are option (C) The speed of the canoe in still water is 4 miles per hour and option (D) The speed of the water current is 3 miles per hour.
A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.
x is the Canoe's speed with no water current in miles per hour
y is the speed of the water current, in miles per hour
The equations are
x + y = 7
x - y = 1
Here we have to use the elimination method
Add both the equation
2x = 7 + 1
2x = 8
x = 8/2
x = 4
Then substitute the value of x in the first equation
4 + y = 7
y = 7 -4
y = 3
Therefore, the correct options are option (C) and option (D)
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Use Elimination for the answer on both :)
The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
-5x - 10y = 30 and - 3x + 3y = 27
Solve by using the elimination method,
Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,
(- 3x + 3y) / 3 = 27 / 3 and (-5x - 10y) / 5 = 30 / 5
-x + y = 9 and -x - 2y = 6
Subtract equation
-x + y = 9 - (-x - 2y = 6)
-x + y - 9 = x - 2y - 6
y = 3
and - x + 3 = 9, x = -6
Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
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