Solve the following word problems by creating and solving systems of equations.1) A plane traveled 1290 miles with the wind (downwind) for 3 hours. Then it traveled 1576 miles against thewind (upwind) for 4 hours. Find the speed of the plane in still air and the speed of the wind.
Answers
Answer:
The speed of the plane = 412 miles per hour
The speed of the wind = 18 miles per hour.
Explanation:
Let's call x the speed of the plane and y the speed of the wind.
Then, the distance that a plane traveled can be calculated as:
\(d=v\cdot t\)Where v is the sum of the speed of the plane and the speed of the wind and t is the number of hours.
Now, if the plane traveled 1290 miles with the wind (downwind) for 3 hours, we can write the following equation:
\(1290=(x+y)\cdot3^{}\)In the same way, if the plane traveled 1576 miles against the wind (upwind) for 4 hours, we get:
\(1576=(x-y)\cdot4\)So, the systems of equations is equal to:
1290 = 3(x + y)
1576 = 4(x - y)
Solving for x in the first equation, we get:
\(\begin{gathered} \frac{1290}{3}=\frac{3(x+y)}{3} \\ 430=x+y \\ 430-y=x+y-y \\ 430-y=x \end{gathered}\)Now, we can substitute x = 430 - y on the second equation and solve for y:
\(\begin{gathered} 1576=4((430-y)-y_{}) \\ 1576=4(430-2y) \\ \frac{1576}{4}=\frac{4(430-2y)}{4} \\ 394=430-2y \\ 394-430=430-2y-430 \\ -36=-2y \\ \frac{-36}{-2}=\frac{-2y}{-2} \\ 18=y \end{gathered}\)Finally, we can calculate the value of x:
\(\begin{gathered} x=430-y \\ x=430-18 \\ x=412 \end{gathered}\)Therefore, the speed of the plane is 412 miles per hour and the speed of the wind is 18 miles per hour.
Related Questions
helllllppppp pleaseeeeee
Answers
Answer:
2nd choice
Step-by-step explanation:
The slope is 2/3 (rise/run) and the y-intercept is -2
When you put those values into f(x) = mx + b, you get f(x) = 2/3x - 2
What is the solution to the systems of equations shown
above? JUSTIFY your solution ("justify" is a vocabulary
word you just learned).
Answers
Answer:
(3,-2)
Step-by-step explanation:
When looking at a graph, the way to find the solution to the system of equations is to look at the points where the two systems intersect. Where if you put in an x-value, you will get the same y-value.
One number is 19 more than twelve times another. Their sum is 149. Find the numbers.
Answers
Answer:
The numbers are 10 and 139.
Step-by-step explanation:
Assuming you have two numbers you need to search for, let's label them as x and y.
x is 19 more than 12 times y. We can rearrange this to be x = 19 + 12y. This will be our first equation. It is then stated that their sums, or x + y, is equal to 149. We have two equations now:
x = 19 + 12yx + y = 149Because x is already separated, we can plug equation (1) into equation (2).
(19 + 12y) + y = 149
Because there is nothing in the parentheses that we can combine, we can remove them and begin combining like terms.
19 + 12y + y = 149
19 + 13y = 149
We subtract 19 from both sides to begin to isolate the variable y.
13y = 130
y = 10
Because we have obtained y, we can plug it back into equation (2) to obtain x.
x + y = 149
x + (10) = 149
x = 139
A van traveled 242 km at a speed of 55 km/h. How long did it travel?
Answers
Answer:
Your answer would be 4 hrs and 24 minutes for how long the van traveled
Step-by-step explanation:
ab=r+d
Solve for a
Please include work
Answers
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\(ab = r + d\)
Divide sides b
\( \frac{ab}{b} = \frac{r + d}{b} \\ \)
\(a = \frac{r + d}{b} \\ \)
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The function f(x) = 9x + 27 represents the distance in miles a drone flew. The function g(x) = x + 3 represents the time the drone flew in hours. Part A: Find f(4) and g(4). Show your work. (2 points) Part B: Find f divided by g of 4. Show your work. (2 points) Part C: What is the domain of f divided by g of x? (2 points)
Answers
Answer: A. Part A:
f(4) = 9x + 27 = 9(4) + 27 = 36 + 27 = 63
g(4) = x + 3 = 4 + 3 = 7
B. Part B:
f(x) / g(x) = (9x + 27) / (x + 3) = 9
f(4) / g(4) = 63 / 7 = 9
C. Part C:
The domain of f(x) / g(x) is all real numbers except x = -3, because dividing by zero is undefined. The domain of f(x) / g(x) is all real numbers except x = -3.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Part A: f(4) = 63, and g(4) = 7.
My work for Part A:
Step 1: Write the first function substituting x for 3: f(4) = 9 x 4 + 27.
Step 2: Solve the function: f(4) = 9 x 4 = 36, and 36 + 27 = 63.
Step 3: Write the final answer for the first function: f(4) = 63.
Step 4: Write the second function substituting x for 3: g(4) = 4 + 3.
Step 5: Solve the function: g(4) = 4 + 3 = 7.
Step 6: Write the final answer for the second function: g(4) = 7.
Part B: (f/g)(4) = 9.
My work for Part B:
Step 1: Using the numbers from Part A, simply divide f(4) by g(4) to get (f/g)(4): 63/7 = 9.
Step 2: Write the final answer of (f/g)(4): (f/g)(4) = 9.
Part C: The domain of (f/g)(x) is -3 < x ≤ ∞. So, any numbers greater than -3 and less than or equal to infinity, are possible solutions to this function. Therefore, -2, 3, 7, and many more numbers greater than -3 are possible solutions.
simplify √([2m5z6]/[ xy])
Answers
The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:
Simplify the numerator:
√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)
= √2m√5z√6
Simplify the denominator:
√(xy) = √(x) * √(y)
Combine the numerator and denominator:
√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)
Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
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A customer purchased x cups of coffee for $2.32 each. The customer gives the cashier $15.00 and gets $1.08 in return.
How many cups of coffee did the customer buy?
Answers
Answer:
6
Step-by-step explanation:
15 dollars - 1.08=13.92 which is what he spent.
13.92/2.32 to calculate how many cups he bought.
13.92/2.32=6 cups
A trapezoid has a base 1 = 6 base = 8 and a height = 3 whats the area?
Answers
Answer:
\(area = 21\)
Step-by-step explanation:
Area of trapezoid formula:
\(area = \frac{a + b}{2} h\)
Given information:
a: 6
b: 8
h: 3
Using the given information,
\(area = \frac{6 + 8}{2} 3\)
Add the numbers in the numerator
\(area = \frac{14}{2} 3\)
Reduce fraction with 2
\(area = 7 \times 3\)
Answer:
\(area = 21\)
Write the coordinates for
each given point on the
coordinate plane below.
1. Point A
2. Point B
3. Point C
4. Point D
Answers
Answer:
Point A (-3,3)
Point B about (3,-2.75)
Point C (-4,-4)
Point D (1,0)
Step-by-step explanation:
There are 500 seats on a plane flying to San Francisco. 20% of the seats are next to a window. How many of the seats are next to a window?
Answers
500 Is 100%
500 ÷ 100 = 5
5 Is 1%
5 x 20 = 100
100 Is 20%
find the area of the circle 3.6
Answers
Answer:
The formula to get the area of a circle is: A = πr²
Area = pi × radius²12. A recipe calls for 4 ounces of mustard seed. You use a half a cup. If mustard seed weighs 2/5 of an ounce per tablespoon, how much more or less in ounces of the mustard seed should you have used?
Answers
18/5 more ounces of the mustard seed should you have used
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A recipe calls for 4 ounces of mustard seed
If mustard seed weighs 2/5 of an ounce per tablespoon.
We need to find how much more or less in ounces of the mustard seed should you have used
To find this we just need to subtract 4 and 2/5
4-2/5
20-2/5
18/5
Hence 18/5 more ounces of the mustard seed should you have used
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Cairde will mark brainliest!!!!
Answers
Answer:
mMN=190°
Step-by-step explanation:
Let the centre of the circle be C
An angle at the circumference of a circle is half the angle at the centre standing on the same arc.
Therefore:
2(<MLN)=<MCN
<MCN=2(95)=190°
mMN=<MCN=190°
ssume all information in example 1 above and the following additional information: Actual data for job 201 is give is given belowActual shirts completed for job 201………………2,000 shirtsActual direct material cost used………………...$30,000Actual direct cost incurred……………………...$20,000Actual direct labor hours used…………………. 400 hoursActual machine hours…………………………. 240 hoursInstruction: compute the applied factory overhead and determine the total cost of job 201 under each of the five bases. A) Physical output as allocation baseDirect materials cost as allocation base Direct labor cost as allocation base Direct labor hours as allocation baseMachine hours as allocation base
Answers
The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.
Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.
Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.
Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.
The applied overhead cost for job 201 is $30,000*120% = $36,000.
Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.
-Direct labor cost as allocation base:
The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.
The applied overhead cost for job 201 is $20,000*120% = $24,000.
Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.
-Direct labor hours as allocation base:
The actual direct labor hours used in job 201 is 400 hours.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.
Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.
-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.
The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.
-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.
The applied overhead cost for job 201 is $24*240 hours = $5,760.
Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.
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A frog jumps across a pond. Its height, as a function of time, is modeled by y
= -16x²+
+ 10x+0.5.
Which statement best describes the function?
A. The function is nonlinear.
ООО
B. Not enough information is given to decide.
C. The function is linear at some points and nonlinear at other points.
D. The function is linear.
O
Answers
Answer:The function is nonlinear
Step-by-step explanation:
5. (7.4B) It takes Juan 1.5 hours to walk 5.25 miles
to the park. How many miles can he walk per hour?
Answers
Answer:
3.5 miles per hour
(1.5 hrs.=5.25 miles)/3 divide by 3 to see how much is walked in 1/2 an hour
(.5 hrs=1.75 miles)*2 multiply by to to see how much is walked in a full hour
For the time 8:35, rename one hour to 60 minutes. Add those minutes to the existing minutes.
A-10:20
B-6:40
C- 2:05
D- 9:55
Answers
Answer:
here we can talk if you want
Find the volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0). Slices perpendicular to the x-axis are semicircles. Enter answer using exact values.
Answers
The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.
What is a triangle?
A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.
To start, let's graph the triangle to get a better understanding of the problem:
(0,3) *
|\
| \
| \
| \
| \
(0,0) *-----*-----> x
(5,0)
The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.
The area of a semicircle is πr²/2, so the volume of this slice is:
V(x) = π * (3/10 * x)² / 2 * dx
To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:
V = ∫₀₅ π * (3/10 * x)² / 2 dx
V = π/20 * ∫₀₅ x² dx
V = π/20 * [x³/3] from 0 to 5
V = π/20 * (5³/3)
V = π/4 * (25/3)
V = 25π/12
Therefore, the volume of the solid is 25π/12 cubic units.
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write an expression using division that could be used to find the width of the rectangle
Answers
The expression used to find the width using division is:
W = A/L
Which expression can be used to find the width?We know that for a rectangle of width W and length L, we know that the area is given by the product between these two dimensions, then:
A = L*W
We want a expression using division that can be used to find the width, so, suppose we know the values of the area and the length, the we can divide both sides by L to get:
A/L = W
This expression gives the width.
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Adedayo spent 1/5 of his money to buy a Mathematics book and 1/4 of the remainder to buy an English book. What fraction of the original money has Ade left?
Answers
If Adedayo spent 1/5 of his money to buy a Mathematics book and 1/4 of the remainder to buy an English book. The fraction of the original money Ade left will be 4/5
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that, Adedayo spent 1/5 of his money to buy a Mathematics book and 1/4 of the remainder to buy an English book.
The fraction of the original money Ade left is,
=1-(1/4+1/5)
=1-(1/5)
=4/5
Thus, if Adedayo spent 1/5 of his money to buy a Mathematics book and 1/4 of the remainder to buy an English book. The fraction of the original money Ade left will be 4/5
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The graph of the function rule that models the volume of the sphere has symmetry with respect to ____?
Answers
The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.
Explain the term symmetry along origin?About the Origin: Symmetry. If a point appears on a graph at every time, then the graph is symmetric having respect to the origin. When seen in relation to the origin, this graph is symmetric.A function having a single term which is the sum of a real number, the coefficient, as well as a variable raised to something like a fixed real number is called a power function. (A coefficient is a number which multiplies a variable by an exponent.) Think of equations like area or volume as an illustration.For the stated question.
The volume of the sphere is modeled by the power function with respect to the radius as;
V = f(r) = 4/3πr³
As, r is independent of any of the coordinate axis.
Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.
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In ΔIJK, the measure of ∠K=90°, IK = 39, JI = 89, and KJ = 80. What ratio represents the sine of ∠I?
Answers
Answer: 80/89
Step-by-step explanation:
Answer:
80/89
Step-by-step explanation:
delta math told me
In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They found that 55% of those who send 51 or more text messages per day prefer to be contacted by text message rather than by a voice call. The margin of error for this sample was 5.7%. What does this margin of error tell you about the results of the survey
Answers
Step-by-step explanation:
The margin of error is a statistical tool used to describe how a set off sample data that is being analyzed will accurately correspond with the overall data.
Basically, the margin of error explains how accurate and effective the result from the analysis or a survey is.
This means that the large the margin of error the less accurate the result will be.
An acceptable margin of error typically falls between 4% and 8% at the 95% confidence level.
The margin of error for this sample was 5.7% this means that
49.3% (= 55% – 5.7%) and
60.7% (= 55% + 5.7%)
of cell phone users will prefer to be contacted by text message
What value equivalents to 5 7/8
Answers
\((3x^{3} y^{2} z)(2xy^{5} z^{5}\)
Answers
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what is the slope of a line if it doubles. like from (2,4) to (3,8)
Answers
Answer:
4/1
Step-by-step explanation:
slope = (8-4) / (3-2)
slope = 4/1
i am confused on finding the answer i have tried a few times and i do not understand
Answers
Answer:
Volume = 7.912
Step-by-step explanation:
V = πr²h
V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )
V = 3.14 × 9/16 ×18/4
V = 3.14 × 0.56 × 4.5
V = 7.912
James earned 96$ by mowing his neighbor yard. He spent 50% of his money on a video game. He is going to save 75% of his remaining money. How much would he save
Answers
Answer:
36
Step-by-step explanation
Subtract 50% from $96.00
96.00 - 48.00 = 48.00
Find out what is 75% of 48
48.00 - 75% = 36
elect all equations that represent the number of subscribers, , in terms of months since the beginning of the year (when she had 150 subscribers).