Answer:
Step-by-step explanation:
To factorise the expression, we can use the factor theorem which states that if a polynomial p(x) has a factor (x - r), then p(r) = 0.
We can use this theorem to find the factors of the polynomial expression:
(a - 2b)^3 + (2a - b)^3
We can write (a - 2b)^3 as (a - 2b)(a^2 - 4ab + 4b^2). Using the factor theorem, we see that:
(a - 2b)(a^2 - 4ab + 4b^2) = 0 when a = 2b
Similarly, we can write (2a - b)^3 as (2a - b)(4a^2 - 4ab + b^2). Using the factor theorem, we see that:
(2a - b)(4a^2 - 4ab + b^2) = 0 when a = b/2
Now we have two equations: a = 2b and a = b/2, which we can use to solve for a and b in terms of each other. We see that:
a = 2b = b/2
Multiplying both sides by 2, we get:
2a = b
We can substitute this back into the original expression:
(a - 2b)^3 + (2a - b)^3 = (a - 2(2a))^3 + (2a - (2a))^3 = (-3a)^3 + (0)^3 = -27a^3
So the factorised form of the expression is:
(a - 2b)^3 + (2a - b)^3 = -27a^3.
Work Shown:
Use the sum of cubes factoring rule
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
In this case,
x = a-2by = 2a-bSo,
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
(a-2b)^3 + (2a-b)^3 = (a-2b+2a-b)((a-2b)^2 - (a-2b)(2a-b) + (2a-b)^2)
(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-ab-4ab+2b^2) + (4a^2-4ab+b^2))
(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-5ab+2b^2) + (4a^2-4ab+b^2))
(a-2b)^3 + (2a-b)^3 = (3a-3b)(a^2-4ab+4b^2 - 2a^2+5ab-2b^2 + 4a^2-4ab+b^2)
(a-2b)^3 + (2a-b)^3 = (3a-3b)(3a^2-3ab+3b^2)
(a-2b)^3 + (2a-b)^3 = 3*3(a-b)(a^2-ab+b^2)
(a-2b)^3 + (2a-b)^3 = 9(a-b)(a^2-ab+b^2)
The answer has been fully confirmed with WolframAlpha.
Cory is a bird-watcher. He estimates that 30% of the birds he sees are
American robins, 20% are dark-eyed juncos, and 20% are song sparrows. He
designs a simulation.
Let 0, 1, and 2 represent American robins.
Let 3 and 4 represent dark-eyed juncos.
Let 5 and 6 represent song sparrows.
Let 7, 8, and 9 represent other birds.
The table shows the simulation results.
05716
16803
96568
32177
33855
76635
92290
88864
72794
14333
79019
05943
77510
74051
87238
97895
86481
94036
12749
24005
According to this simulation, what is the probability that at least one of the
next five birds he sees is a song sparrow?
The probability that at least one of the next five birds he sees is a song sparrow is 0.65
How to determine the probability from the simulationFrom the question, we have the following parameters that can be used in our computation:
05716 16803 96568 32177 33855
76635 92290 88864 72794 14333
79019 05943 77510 74051 87238
97895 86481 94036 12749 24005
Also, we have:
Let 0, 1, and 2 represent American robins.Let 3 and 4 represent dark-eyed juncos.Let 5 and 6 represent song sparrows.Let 7, 8, and 9 represent other birds.Using the above as a guide, we have the following individual representations of at least one sparrow bird
Yes Yes Yes No Yes
Yes No Yes No No
No Yes Yes Yes No
Yes Yes Yes No Yes
So, we have
At least one sparrow bird = 13
Total = 20
So, the probability is
P = 13/20
Evaluate
P = 0.65
Hence, the probability is 0.65
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Brainliest if correct!!! Please help! Geometry 5th grade
Hi there, here's your answer:
The question asked here is, "Which of the following is a line segment in the drawing?"
Let's review all the options first.
a) HD
H and D being two points of a line AK form a line segment.
b) HA
H being a point on the line AK and A being an end point of a line make HA a ray.
c) GH
Again, H being a point on line GJ and G being an end point of a line make GH a ray.
d) DI
DI are two distinct points and do not join, thus they don't form a line segment.
Therefore, the correct option is (a) HD
Hope it helps! Please mark as Brainliest!
Kelsey orders several snow globes that each come in a cubic box that measures 14
foot on each side. Her order arrives in the large box shown below. The large box is completely filled with snow globes.
The number of snow globe in box is x³/ 2744.
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given:
length of one small cube = 14 foot.
Volume of small cube = l³
= 2744 ft³
let the edge of one large cube be x.
So, volume of large cube= x ft³
Thus, number of globes in larges box
= Volume of large box/ Volume of small box
= x³/ 2744
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pls help!!
In the xy-plane, the point (2,10) lies on the graph of the
function f(x) = 2x2 + bx - 8. What is the value of b?
(answer choices in the image attached)
In the xy-plane, the point (2,10) lies on the graph of the function f(x) = 2x^2 + bx - 8. The value of b is 4.
What is linear equation?
A linear equation is an equation that describes a straight line in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope of a line is the measure of how steeply the line rises or falls, and the y-intercept is the point at which the line crosses the y-axis.
In a two-dimensional coordinate system, a linear equation represents a straight line that can be graphed by plotting pairs of x and y values that satisfy the equation. The line passes through all points that satisfy the equation and no others.
We can find the value of b by using the point-slope form of a linear equation, which states that the equation of a line with slope m that passes through the point (x1, y1) is given by y - y1 = m(x - x1).
In this case, the slope of the line is equal to 4x, and the point (x1, y1) is (2, 10), so we have:
y - 10 = 4x * (x - 2)
Expanding the right-hand side, we get:
y - 10 = 4x^2 - 8x
Matching this equation with the given function f(x) = 2x^2 + bx - 8, we see that b = 4.
So the value of b is 4.
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4. The running track in this diagram consists of two parallel sections with semicircular sections at each end.
Determine the area of the running track.
The area of the running track, given the parallel sections and the semicircle sections, is https://brainly.com/question/30584763
How to find the area ?To find the area of the running track, you first need to find the area of the whole shape and then the area of just the inner section.
Area of whole shape :
= Area of both semicircles + Area of the rectangle
= ( π x 46. 41 ²) + ( 85 x ( 46. 41 x 2 ))
= 14, 659.06 m ²
Then, find the area of the inner section :
= ( π x 36. 41 ²) + ( 85 x ( 36. 41 x 2 ))
= 10, 356. 45 m ²
The area of the running track is :
= 14, 659.06 - 10, 356. 45
= 4, 302. 61 m ²
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∠X = 89°, ∠Y = 90°, ∠Z = ?
∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°
→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°
→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°
angle Y and W are supplementary angles
so
→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°
angle X and Z are supplementary angles
so
→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
Therefore, the answer is
∠Z=40°
Tony saved enough money to afford a car. He needs to determine if he can afford the car insurance. Tony earns $160 per week. Tony's yearly pay is $8,320 and his monthly pay is $693.
Tony's monthly car insurance will be 1/30 of his rounded yearly pay. Can he afford it?
Explain why or why not.
Tony can afford the car insurance, and he has enough money($426.33) left over each month to cover other expenses.
What is car insurance?Automobile, truck, motorbike, and other types of road vehicles are covered by vehicle insurance. Its main purpose is to offer financial security against property loss or personal injury brought on by auto accidents, as well as against liability that can emerge from related events.
According to the information given,
Tony's yearly pay is $8,320
and his monthly pay is $693.
If we round his yearly pay to $8,000, his monthly car insurance will be 1/30 of that amount, or $266.67.
Since Tony's monthly pay is $693, and his monthly car insurance will cost $266.67, he can afford the insurance. He will have $426.33 remaining each month after paying for the insurance.
Therefore, Tony can afford the car insurance, and he has enough money left over each month to cover other expenses. However, this calculation assumes that Tony has no other major expenses or debts, and it is always a good idea to budget carefully and consider all potential costs before making a significant purchase.
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If 3250 was increased by 46%, the result would be
Answer: 4745
Step-by-step explanation:
3250 = 100%
Percent Increase = +46%
46% of 3250 = 1495
3250 (100%) + 1495 (46%) = 4745
Andrew collects coins. He collected a total of 150 coins. If 76% of the coins he collected were foreign, how many other coins did he collect?
With percentage=76% of foreign coins of total 150 coins, Other coins collected were 36.
What is the percentage?
In mathematics, a percentage is a statistic or ratio that may be expressed as a fraction of 100. To find the percentage of a number, divide it by its total and multiply by 100. Hence, the percentage represents one part of a hundred. The phrase % stands for one hundred percent. It is represented by the symbol "%".
Here are some instances of percentages:
10% is one-tenth of a fraction.20% is one-fifth of a share.25% is divided into quarters.Now,
Given that total coins=150
Foreign coins=76% of total
then other coins are 24% of total
so other coins=150*24/100
=72/2
=36
Hence,
Other coins collected were 36.
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Find the x - and y -components of the vector d⃗ = (5.0 km , 29 ∘ left of +y -axis).
Express your answer in kilometers. Enter the x and y components of the vector separated by a comma.
The x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.
What is vector?In physics and mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are often represented by arrows, with the length of the arrow indicating the magnitude of the vector, and the direction of the arrow indicating the direction of the vector.
For example, the velocity of a moving object is a vector quantity, because it has both a magnitude (the speed of the object) and a direction (the direction in which the object is moving).
To find the x-components and y-components of the vector [tex]\mathbf{\hat d }[/tex] = (5.0 km, 29° left of +y-axis), we can use trigonometry.
The magnitude (or length) of the vector is given by the first component, which is 5.0 km.
The angle between the vector and the positive y-axis is 29° left of +y-axis, which means it forms a 61∘ angle with the negative y-axis (since 29∘ + 61° = 90°).
The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:
x-component = magnitude x cos(angle) = 5.0 km x cos(61°) ≈ -2.25 km
The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.
The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:
y-component = magnitude x sin(angle) = 5.0 km x sin(61°) ≈ 4.30 km
Therefore, the x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.
Expressed as an ordered pair, the components are (-2.25 km, 4.30 km).
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High Tech Chip Company is expected to have EPS in the coming year of $2.50. The expected ROE is 12.5%. An appropriate required return on the stock is 11%. If the firm has a plowback ratio of 70%, the growth rate of dividends should be
Given right triangle ABC with altitude
BD drawn to hypotenuse AC. If
AC 36 and DC = 9, what is the length
of BC?
=
C
9
D
36
X
A
B
Can someone please helppp
The measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles; ∆ABC with hypotenuse = 45 and adjacent = BC, the triangle ∆ADC with hypotenuse = BC and adjacent = 9 with the angle C we can solve for BC as follows:
for ∆ABC;
cosC = 9/BC {adjacent/hypotenuse}
for ∆ADC;
cosC = BC/45 {adjacent/hypotenuse}
9/BC = BC/45
BC² = 9 × 45 {cross multiplication}
BC² = 405
BC = √405 {take square root of both sides}
BC = 20.1246
Therefore, the measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
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am a 4-digit number. My thousands digit is greater than 6, but less than 8 My hundreds digits is the highest even number. and ones The sum of my tens cligit a digit is equal to my hundreds digit. My tens digit is 6. Who am I?
Answer:
From the given information, we know that:
The thousands digit is greater than 6 and less than 8, so it must be 7.
The hundreds digit is the highest even number, so it must be 8.
The tens digit is 6.
The sum of the tens and ones digit is equal to the hundreds digit, so 6 + ones digit = 8.
Solving for the ones digit, we get:
ones digit = 8 - 6 = 2
Putting the digits together, we get the number: 7862.
So, the 4-digit number that satisfies all the given conditions is 7862.
Step-by-step explanation:
Given the clues, the thousands digit is 7, the hundreds digit is 8, the tens digit is 6, and the ones digit is 2; therefore, the 4-digit number is 7862.
Explanation:Given the hints, we can infer that:
The thousands digit is greater than 6, but less than 8, so it can only be 7.The hundreds digit is the highest even number, which is 8.The tens digit was specifically said to be 6.The sum of the tens and ones digit is equal to the hundreds digit. The tens digit is 6 and the hundreds digit is 8, so the ones digit must be 2 because 6 + 2 = 8.Therefore, the 4-digit number is 7862.
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COWS
Tt
Lakayja brushed 24 cows in 2 hours. How many can she brush in 15 hours?
Answer: 180
Step-by-step explanation: Hope this helps :D
Answer:
180 Cows
Step-by-step explanation:
24 in 2 = 12/hr
12 cows x 15 hours = 180 cows
Mia bought five pounds of potatoes and sent a total of 3.65 for them
The cost of one pound of potato is 0.73 pounds.
What is Algebra ?The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Now in the given question , we have to find the cost of one pound of potato.
here we have to find the cost of one pound of potato mia bought.
she total spent $3.65 for them and bought five pounds of potatoes.
cost of one pound of potato
= [tex]\frac{total spent}{total bought} = \frac{3.65}{5} =0.73 pounds[/tex]
hence, cost of one pound of potato is 0.73 pounds.
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¿Qué volumen de solución de ácido a 60% debe mezclarse con una solución a 30% para producir
300 mililitros de solución al 50%?
Answer:
Step-by-step explanation:
To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:
(C1 * V1) + (C2 * V2) = (C3 * V3)
Where:
C1 = concentration of the acid solution at 60% (in percent)
V1 = volume of the acid solution at 60% (in ml)
C2 = concentration of the acid solution at 30% (in percent)
V2 = volume of the 30% acid solution (in ml)
C3 = concentration of the resulting 50% acid solution (in percent)
V3 = volume of the resulting 50% acid solution (in ml)
In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values into the equation:
(60 * V1) + (30 * V2) = (50 * 300)
Clearing V1:
V1 = (300 * 50 - 30 * V2) / 60
Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values into the equation:
V1 = (300 * 50 - 30 * V2) / 60
V1 = (15000 - 30 * V2) / 60
V1 = 250 - (V2 / 2)
We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:
V2 = 2 * (250 - V1)
Clearing V1:
V1 = 250 - (V2 / 2)
V1 = 250 - (2 * (250 - V1) / 2)
V1 = 250 - 250 + V1
V1 = 250
Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.
I ALSO NEED HELP WITH THIS TOO
Answer:
Step-by-step explanation:
Two angles are said to be supplementary when their sum is equal to 180°.
Given angle 1 and 50° are supplementary.So, angle1+50°= 1880°
angle1 =180°-50°
angle 1=130°
Given 50° and angle 3 are supplementary
So,50°+ angle 3=18=0°
angle 3=130°
So angle 1 equals to angle
Complete the table of inputs and outputs for the function.
Problem #1
A motorist travelling at 90 km/h applied the brakes until the car stopped. If the stopping distance was 12 m, what was the acceleration? (-26 m/s2)
The acceleration was -26.04 m/s².
What are Equations of Motion?Equations of motion are a set of equations which describes the basic motion concepts like velocity, position, time and acceleration.
There are mainly three equations of motion.
v = u + at
s = ut + [tex]\frac{1}{2}[/tex] at²
v² = u² + 2as
v is the final velocity, u is the initial velocity, a is the acceleration, t is the time and s is the displacement.
Given,
Initial velocity of the motorist, u = 90 km/h = 90 × (5/18) m/s = 25 m/s
Final velocity of the motorist, v = 0 m/s (since the bike stopped)
Stopping distance, s = 12 m
Using the third equation of motion,
v² = u² + 2as
0² = 25² + (2a × 12)
24a = -625
a = -625 / 24 = -26.04 ≈ -26 m/s²
Hence the acceleration of the motorist was -26 m/s².
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When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality
True
False
"When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality" statement becomes: true
What is an inequality?A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers. The equals sign in the equation-like phrase 7x 4 > 2x + 5 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 7x 4, is larger than the right part, 2x + 5, in the equation. Finding the values of x for which the inequality holds true will be of importance to us.
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Teresa needs to make a total of 95 deliveries this week. So far she has completed 76 of them. What percentage of her total deliveries has Teresa completed?
Answer:
Step-by-step explanation:
its Reduced to 2 / 5, which is 40 percent. Maria has 40 percent of her work completed
What are the zeros of this function?
A. -1, 3
B. 3, 1
C. 0, 1.5
D. 1, 2
Answer:
B
Step-by-step explanation:
the zeros are the values of x on the x- axis where the graph crosses
the graph crosses the x- axis at 1 and 3
then the zeros are x = 1 , x = 3
Can anyone help me solve this? Thank you!
Your friend sings every Saturday night at your favorite bar in San Diego. During his show, people show up at the rate of 1 person every minute.
a) What is the probability that on a random minute, at least 3 people show up?
b) What is the probability that he will have to wait at least 3 minutes for the next person to show up?
c) If he has already waited for 1 minute for the next person to show up, what is the probability that he will have to wait at least 3 more minutes for the next person to show up?
Answer:
Step-by-step explanation:
a) The number of people showing up at the bar during any given minute is a Poisson process with an average rate of 1 person per minute. Let X be the number of people who show up during a random minute. Then X follows a Poisson distribution with parameter λ = 1. The probability of at least 3 people showing up in a random minute is:
P(X >= 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:
P(X = k) = (e^-λ) * (λ^k) / k!
Plugging in λ = 1, we get:
P(X = 0) = e^-1 / 0! = 1/e
P(X = 1) = e^-1 * 1^1 / 1! = 1/e
P(X = 2) = e^-1 * 1^2 / 2! = 1/2e
So, the probability of at least 3 people showing up in a random minute is:
P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)) = 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e) = 1 - (5/2e)
b) The probability of having to wait at least 3 minutes for the next person to show up is equal to the probability of having 0, 1, or 2 people show up during the first three minutes. Using the same calculation as above, we find:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = (1/e) + (1/e) + (1/2e) = (2/e + 1/2e) = (5/2e)
So, the probability of having to wait at least 3 minutes for the next person to show up is 1 - (5/2e) = 1 - P(X <= 2).
c) If he has already waited for 1 minute, the probability of having to wait at least 3 more minutes for the next person to show up is equal to the probability of having 0 or 1 people show up during the next 2 minutes. Using the same calculation as above, we find:
P(X <= 1) = P(X = 0) + P(X = 1) = (1/e) + (1/e) = 2/e
So, the probability of having to wait at least 3 more minutes for the next person to show up is 1 - (2/e) = 1 - P(X <= 1).
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A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $10.40 per pound should be mixed with 10 pound of trail mix costing $4.30 per pound to create a mixture worth $7.96. (round to the nearest pound)
Answer: 15 pounds
Step-by-step explanation:
10.4(x)+4.3(10)=7.96(x+10)
10.4x+43=7.96x+79.6
2.44x=36.6
x=15 pounds
(check my work. I may have done something wrong, but the equation should be correct.)
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
Somebody help, I don't get this!
The statements are (a) False, (b) True and (c) False
What are Right Angles?Right angles are angles whose measure is 90 degrees.
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
(a) ∠AHB and ∠AHG are vertical angles.
Vertical angles are angles which are formed on the opposite sides of two intersecting lines.
∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.
So the statement is false.
(b) ∠EHF and ∠DHE are adjacent angles.
∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.
So the statement is true.
(c) The measure of ∠FHG is equal to the measure ∠DHF.
We know that DG is a straight line.
∠FHG and ∠DHF are linear pair of angles.
So, ∠FHG + ∠DHF = 180°
Given that ∠FHG is right angle.
90° + ∠DHF = 180°
∠DHF = 180° - 90°
∠DHF = 90°
So the statement is true.
Hence the statements (a), (b) and (c) are false, true and true respectively.
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Your question is incomplete. The complete question with the figure is given below.
Write the simplest polynomial function with the given zeros: -2 , 2 , 3
Step-by-step explanation:
Zeros is another term for X intercepts.
We'd right the simplest form as (x-/+a), a being the zero
Just remember when you do that, change the signs. It shows -2, +2, +3. That becomes +2, -2, -3
Following that simple form, we get
[tex](x + 2)(x - 2)(x - 3)[/tex]
Pls help me with this math space question
The required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching to infinity.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
Given expression,
= 3ˣ
put x = 4
= 3⁴ = 81
Now put x = -4
= 3⁻⁴
= 1/3⁴
= 1/81
Since x gets larger as x = 0, 1, 2, 3, and so on 3ˣ get 1, 9, 27, 81 and so on approaching to infinity.
Thus, the required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching infinity.
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A plane traveled 3900 miles with the wind in 6.5 hours and 3120 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
Answer:
the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.
Step-by-step explanation:
Step 1: Define the variables
Let's call the speed of the plane in still air "V". Let's call the speed of the wind "W".
Step 2: Write an equation for the distance traveled with the wind
The distance traveled by the plane with the wind in 6.5 hours can be represented by the equation:
D1 = (V + W) * t
where D1 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.
Substitute the known values into the equation:
3900 = (V + W) * 6.5
Step 3: Write an equation for the distance traveled against the wind
The distance traveled by the plane against the wind in 6.5 hours can be represented by the equation:
D2 = (V - W) * t
where D2 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.
Substitute the known values into the equation:
3120 = (V - W) * 6.5
Step 4: Solve for the speed of the wind
We can now use the two equations from Steps 2 and 3 to solve for the speed of the wind.
First, let's rearrange the equation from Step 2 to isolate "W":
W = (3900 / 6.5) - V
Next, substitute this expression for "W" into the equation from Step 3:
3120 = (V - ((3900 / 6.5) - V)) * 6.5
Expand the right side of the equation:
3120 = (V - 3900 / 6.5 + V) * 6.5
Simplify the equation:
3120 = 2V * 6.5 - 3900
Divide both sides of the equation by 2:
1560 = V * 6.5 - 1950
Multiply both sides of the equation by 2:
3120 = V * 13 - 3900
Add 3900 to both sides of the equation:
7020 = V * 13
Divide both sides of the equation by 13:
V = 540
Step 5: Solve for the speed of the wind
Now that we know the speed of the plane in still air, we can use the equation from Step 2 to find the speed of the wind:
W = (3900 / 6.5) - V
Substitute the value of "V" that we found in Step 4 into the equation:
W = (3900 / 6.5) - 540
Simplify the equation:
W = 280
Step 6: Conclusion
Therefore, the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.
This net will be folded to form a prism.
A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C.
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
B and F
B and E
B and C
E and F
A and F
Answer:
i think the answer is A and C, B and E
Answer:
D and F
A and C
B and E
Step-by-step explanation:
NEED HELP ASAP PLEASE! What is the equation of the function shown in the table?
Input x: -2 -1 0 1 2
Output y: -3 -1 1 3 5
A: y = -2 x + 1
B: y = 2 x + 1
C: y = 2 x - 2
D: y = - 1/2x - 1
With the data points (-2,-3) and (-1,-1), the linear equation is obtained as Option B: y = 2x + 1.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The data points are given for the equation.
Consider the first two points (-2,-3) and (-1,-1).
The slope intercept form of the linear equation is -
y = mx + b
Here m is the slope.
For calculation of slope the formula is -
m = (y2 - y1) / (x2 - x1)
Substitute the values in the equation -
m = [(-1) - (-3)] / [(-1) - (-2)]
m = (-1 + 3) / (-1 + 2)
m = 2/1 = 2
The equation becomes y = 2x + b.
Substitute the point (-2,-3) to get the value of b.
y = 2x + b
-3 = 2(-2) + b
-3 = -4 + b
b = -3 + 4
b = 1
Therefore, the linear equation is y = 2x + 1.
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