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D: region D helppppppppp
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at maximum speed, an airplane travels 1680 miles against the wind in 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours.
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The speed of the airplane with the wind is 420 mph, and against the wind is 336 mph. The speed of the wind is 84 mph.
To find the speed of the wind, we use the following formulas:
Against the wind, the airplane travels 1680 miles in 5 hours. So, the speed against the wind is : [tex]\( S_a = 1680 \div 5 = 336 \)[/tex] mph
With the wind, the airplane travels the same distance of 1680 miles in 4 hours. So, the speed with the wind is: [tex]\( S_w = 1680 \div 4 = 420 \)[/tex]mph
Let W be the speed of the wind.
Against the wind: [tex]\( S_a = S_w - W \)[/tex]
[tex]\[ 336 = 420 - W \]\[ W = 420 - 336 = 84 \][/tex]
So, the speed of the wind is 84 mph.
a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days
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Initial mass, m₀ = 23 g
Decay constant, k = 0.13
Exponential decay obeys the equation
[tex]m(t)=m_{0} e^{-kt}[/tex]
where t = time, days
For half life, the mass is m = m₀/2.
Therefore
[tex]e^{-0.13t} = \frac{1}{2} \\ -0.13t = ln(0.5)\\t= \frac{ln(0.5)}{-0.13} =5.33[/tex]
Answer: The half life is 5.33 days
Answer:
5.3 is the right answer.
Step-by-step explanation:
Find the sum of the geometric sequence. (1 point) 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen
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1st) the common ratio is (1/4 : 1/2 ) = 1/2, so r =1/2
2nd) the sum of a GP is:
S= a(1-rⁿ)/(1-r)
S=(1/2).[1-(1/2)⁴]/(1-1/2) = 15/16
Answer:
31/16
Step-by-step explanation:
ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP
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^
whole number
if 3.xxx... < .5, round to 3.
If 3.xxx... > or = .5, round to 4.
Because .059 < .5, it is therefore rounded to 3.
Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?
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The hypotenuse of a right triangle is 3 times as long as the shorter leg. find the measure of the angle between the shorter leg and the hypotenuse
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shorter leg = x
hypotenuse = 3x
[tex]cos \alpha = \cfrac{x}{3x} = \cfrac{1}{3} \ \ \to \alpha \approx70.5^o[/tex]
The measure of the angle between the shorter leg and the hypotenuse, [tex]\theta[/tex] = 70.53 °
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Given that:
Let us consider the shorter leg be 'x'.
and, the Hypotenuse be '3x '.
Using trigonometric functions,
[tex]cos \theta= \frac{Base}{Hypotenuse}[/tex]
cos [tex]\theta[/tex] = x /3x
cos [tex]\theta[/tex] = 1/3
[tex]\theta[/tex] = [tex]cos^{-1}[/tex] (1/3)
[tex]\theta[/tex] = 70.53 °
Hence, the measure of the angle between the shorter leg and the hypotenuse 70.53 °
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A quadratic equation is shown below:
25x2 + 10x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
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hello :
help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
1/2(6x-4)=2/3x How do i solve this?
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3x-2=2/3x
Multiply all terms by 3 so we won't have to deal with fractions.
9x-6=2x
Subtract 9x from both sides
-6=-7x
Divide both sides by -7
x= 6/7
Final answer: x=6/7
If y varies directly with x and y = 10 when k = 10, what is the value of x?
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y = k *x
y=10 ; k=10
10 = 10*x
x = 10/10 = 1
x =1
Two cards are drawn at random from a standard deck of cards without replacement. What is the probability that both cards will be from the clubs suit?
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Answer:
The answer is 1/17.
Step-by-step explanation:
You will draw one club which will be 13/52. You will NOT replace it so you will draw a second card 12/51.
You will need to multiply them to find the probability.
First simplify your two fractions.
13/52 = 1/4 AND 12/51= 4/17
Multiply the two together and you will get 4/68 = 1/17
Hope this helps :)
ROUND 43.0810194943 TO THE NEAREST TEN-THOUSANDTH HELP!
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Since the hundred thousandths is a 1 which is less than a 5, you have to round down.
.help me with this please thanks
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They are not like terms because they are not all the same
Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy
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In general, if x is the number of days to eat 50 pounds of food, then x/50 is the expression representing the amount eaten per day (in pounds). Finally 365*(x/50) is the expression representing the total amount eaten over the whole year.
This is why the final answer is choice C
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13.
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a/sin A=c/sin C=d/sin D
thus the value of angle A will be:
10/sin A=13/sin 85
10/sin A=13.05
sin A=10/13.05
sin A=0.7663
A=arcsin 0.7663
A=50
thus the n=value of angle B will be:
B=180-(85+50)
=45
The triangle formed will be an acute triangle
What is the length of diagonal ac in parallelogram ABCD if the diagonal BD = 10cm which is twice the diagonal AC?
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The length of the diagonal AC in parallelogram ABCD is 5 cm.
Explanation:Given that the diagonal BD is twice the length of diagonal AC, we can represent the length of diagonal AC as x. So, the length of diagonal BD would be 2x. From the given information, we know that BD = 10 cm. Therefore, we can write the equation 2x = 10 to solve for x. Dividing both sides of the equation by 2 gives x = 5. So, the length of diagonal AC is 5 cm.
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In the given parallelogram, the length of the diagonal AC is 5 cm, given that the length of the diagonal BD is twice that of AC.
Explanation:The question pertains to the properties of a parallelogram. In this case, it has been provided that diagonal BD (10 cm) is twice the length of the other diagonal AC. This implies that the length of diagonal AC is half the length of BD. Therefore, to find the length of AC, take the length of BD and divide by 2:
AC = BD / 2 = 10 cm / 2 = 5 cm
So, the length of diagonal AC is 5 cm.
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Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m
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2/3 = y /(xz) = y/(5*12)
= y/60
so y / 60 = 2/3
y = (2*60)/3
= 40
5x - 10y = 15 if 3x + 7y = 31
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3x + 7y = 31
x - 2y = 3....multiply by -3
3x + 7y = 31
---------------
-3x + 6y = -9 (result of multiplying by -3)
3x + 7y = 31
---------------add
13y = 22
y = 22/13
x - 2y = 3
x - 2(22/13) = 3
x - 44/13 = 3
x = 3 + 44/13
x = 39/13 + 44/13
x = 83/13
solution is (83/13, 22/13) <=
15x-30y-15x-35y=45-155
-65y=-110
y=22/13, making 3x+7y=31 become
3x+154/13=31
39x+154=403
39x=249
x=83/13
So the solution to the system of equation is the point (83/13, 22/13)
Draw a model to represent the problem 6/12 divided by 1/4
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The expression 6/12 divided by 1/4 is 2 and the model is attached
Drawing a model to represent the problem
From the question, we have the following parameters that can be used in our computation:
6/12 divided by 1/4
This can be expressed as
6/12 multiplied by 4
So, we have
0.5 multiplied by 4
When the product is evaluated, we have
2
Hence. 6/12 divided by 1/4 is 2 and the model is attached
at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 when gas cost $2.20 per gallon on average
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Increasing the slope of the graph increases the steepness of the line.
Therefore, increasing the average cost of gas from $1.50 to $2.20 will increases the steepness of the line. (i.e. the line becomes closer to the vertical line).
Suppose a rectangular garden has a length of 3c + 15 feet and a width of 4c feet. write an expression for the area of the garden in square feet.
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A = 4c(3c + 15)
A = 12c^2 + 60c <==
The area of the rectangle is given by the equation A = 12c² + 60c
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the length of the rectangle L = ( 3c + 15 ) feet
Let the width of the rectangle W = 4c feet
Now , the area of the rectangle A = length of the rectangle L x width of the rectangle W
Substituting the values in the equation , we get
Area of Rectangle A = ( 3c + 15 ) ( 4c )
On simplifying the equation , we get
Area of Rectangle A = ( 3c ) ( 4c ) + 15 ( 4c )
Area of Rectangle A = 12c² + 60c
Therefore , the value of A is 12c² + 60c
Hence , the area of the rectangle is A = 12c² + 60c
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I need help with all of these
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14. "Coplanar" -> "on the same plane" -> B,C,D,E
15. Planes are name by 3 non-colinear points --> Plane ACE
18. Two points -> G &F
A line -> Line GF
19. Plane T and Plane S
Find the surface area of each figure to the nearest tenth. Show your work, please
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Lateral surface area = [tex] \frac{2p*a}{2} [/tex] where p is the base perimeter and a the apothem.
The base is a sqaure so, find the area of the square.
Base Area = 16*16 = 256 in²
Calculate the perimeter = 16*4 = 64 in
LSA = (64*17)/2 = (64*17)/2 = 1088/2 = 544 in²
TSA = 544+256 = 800 in²
Total surface of cone: LSA + Base Area
LSA = πra
Let's find the apotheme. Apply Pitagora, again the hypothenuse is the apotheme. The legs are the radius and the height.
a = √8²+3² = √64+9 = √73 ≈ 8,5 in.
Base area (area of the circle) = πr² = 3²*π = 9π in²
LSA = 3*8,5*π = 25,5π in²
TSA = 25,5π+9π = 34,5π = 34,5*3,14 = 108,3 in²
HELP!!!!
Use the following data set and a separate piece of paper to make a line plot that will help you to answer questions 2-7.
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Add a box and whisker plot to the graph. Clearly mark the ends of box by drawing vertical lines and labeling their values on the horizontal axis. What are the ends of the box and whisker plot?
A. 1 and 6
B. 4 and 7
C. 4 and 8
D. 5 and 7
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minimum = 1
Q1 = 4
Q2 (median) = 6
Q3 = 7
maximum = 10
The beginning and end of the " box " are Q1 and Q3.....4 and 7
HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5
a (3x-1)(2x+5)
b (3x-5)(2x-1)
c (3x-1)(2x-5)
d (3x-5)(2x+1)
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You have to try whatever factoring method you've been taught, but this is the answer.
The solution is: the following expression factored completely,
6x^2-13x=5 is: c (3x-1)(2x-5)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, we have,
we have,
6x² - 13x = +5
6x² - 13x - 5 = 0
6x² - 15x + 2x - 5 =0
so, we get,
(3x-1)(2x-5) = 0
The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.
When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.
The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is
... C (3x-1)(2x-5)
Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c (3x-1)(2x-5)
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A solution of phosphoric acid has a boiling point of 158 degrees Celsius. What is the boiling point of the solution in degrees Fahrenheit?
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The boiling point of a phosphoric acid solution that is 158 degrees Celsius is 316.4 degrees Fahrenheit. This is found by using the formula F = C * 9/5 + 32.
Explanation:To convert the boiling point of a solution from degrees Celsius to Fahrenheit, we use the formula F = C * 9/5 + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.
In this case, the temperature in Celsius that you want to convert is 158 degrees. So you can substitute this value in the formula as follows:
F = 158 * 9/5 + 32
When you perform the calculation, you find that the boiling point of the phosphoric acid solution is 316.4 degrees Fahrenheit.
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Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant
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(x - 2)^2 - 4 = 5
(x - 2)^2 = 9
x- 2 = +/- sqrt9 = +/- 3
x = 3 + 2 or -3 + 2
solution set is {-1 , 5}
The solution of the given equation is -1 or 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, x²-4x = 5,
we need to transform it into a perfect square,
The equation is =
x²-4x = 5
Add 4 to each side,
x²-4x+4 = 5+4
x²-4x+4 = 9
(x-2)² = 9
Solving for x,
x-2 = √9
x-2 = ±3
x = -1 or x = 5
Hence, the solution of the given equation is -1 or 5
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Find the product of (2x + 5y)2.
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The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
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The two x-intercepts are x = 5 and x = 15, which are the two values of x where f(x) = 0. The vertex is located halfway between these two points, so where x = 10. When x = 10, f(x) = 25, so the vertex of this graph is (10, 25).
Part A: The vertex is (10, 25). The vertex represents the point where the profit is a maximum. When 10 photos are printed, the profit is $25.
Part B: The two x-intercepts are x = 5 and x = 15. This shows where the profit is $0. When 5 photos or 15 photos are printed, the profit is $0.
Two pools are being filled with water. To start, the first pool contains 2200
liters of water and the second pool contains 1840
liters of water. Water is being added to the first pool at a rate of 21.25
liters per minute. Water is being added to the second pool at a rate of 32.5
liters per minute.
(PLEASE ANSWER QUICK)
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2200 + 21.25X = 1840 +32.50X
subtract 1840 from each side
360+ 21.25X= 32.50X
subtract 21.25x from each side
360=11.25X
x= 360/11.25 = 32 minutes pool will have the same amount
21.25*32 = 680+2200 = 2880 liters
32.5*32 = 1040 + 1840=2880 liters
it will take 32 minutes and they will have 2880 liters each