If x represents time in seconds and y represents distance in meters then the system of equations to represent the above situation are
20x - y = 0 and 22x - y = 15
Let x represent time in seconds and y represents distance in meters.
Let u be the speed of Elena and v be the speed of Jada.
So, according to question,
u = 20[tex]ms^{-1}[/tex] and v = 22[tex]ms^{-1}[/tex]
We know, Speed = [tex]\frac{Distance}{Time}[/tex]
So, 20 = [tex]\frac{y}{x}[/tex]
which implies 20x = y
20x - y = 0 ......................(1)
Similarly,
22 = [tex]\frac{y + 15}{x}[/tex]
Which implies 22x = y + 15
22x - 15 = y.....................(2)
Substituting the value of y from equation (2) in (1)
20x - (22x - 15) = 0
20x - 22x + 15 = 0
15 - 2x = 0
2x = 15
x = 7.5
Substituting the value of x in equation (1)
20 x - y = 0
20 × 7.5 = y
y = 150
The values of x and y satisfies the stated conditions,
Hence, the system of equations to represent the above situation are
20x - y = 0 and 22x - y = 15
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10. Jada is standing 10 feet from the base of a tree and spots • nest sitting on a branch. The
angle of elevation from the ground where she is standing to the nest is 55°. Find the height of
the nest.
This is trigonometry in geometry
Answer:
Step-by-step explanation:
so the height will be h.
if given the base length, find h using tangent.
tan55 = h/10ft
h = 10tan55
h = 14.28ft
The point T( – 1,2) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, T'?
The coordinates of the resulting point, T' after the point T( – 1,2) is rotated 180° clockwise around the origin is (1, -2).
To rotate a point 180° clockwise around the origin, you can apply the following transformations:
Reflect the point across the x-axis by negating its y-coordinate.
Reflect the point across the y-axis by negating its x-coordinate.
Starting with T( – 1,2), we first reflect the point across the x-axis, which gives us T'( – 1, -2). Then, we reflect T' across the y-axis, which results in T''(1, -2).
The transformation can be represented as follows:
T' = (x, -y)
T'' = (-x, -y)
Therefore, the final coordinates of T'' are (1, -2).
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Given the equation y = 3(2)x
Regarding the exponential function y = 3(2)^x, we have that:
We know that the graph has a y-intercept at (0,3), because the a-value is of 3.We know that the graph models exponential growth, because the b-value is of 2.The numeric value of the function at x = 3 is given as follows: 24.What is the exponential function?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The function for this problem is given as follows:
y = 3(2)^x.
Hence the parameters are given as follows:
a = 3 -> y-intercept at (0,3).b = 2 > 1, hence exponential growth.At x = 3, the numeric value of the function is obtained as follows:
y = 3 x 2^3
y = 3 x 8
y = 24.
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If def ~ triangle jkl
what is m
52
58
70
16
The measures angles are 70° and 52°
Similar triangles:The triangle in which the ratio of corresponding is equal and has an equal measure of angles is known as Similar triangle.
If ABC and XYZ are two similar triangles, the corresponding angles must be equal
=> ∠A = ∠X, ∠ B = ∠Y, ∠C = ∠Z
Here we have
ΔDEF and ΔJKL are similar triangles
As we know angles of similar triangles are equal
=> ∠D = ∠J = (9x - 20)°
=> ∠E = ∠K = 52°
=> ∠F = ∠L = (7x - 12)°
As we know the sum of angles in triangles = 180°
=> ∠D + ∠E + ∠F = 180°
=> 9x - 20° + 52° + 7x - 12° = 180°
=> 16x + 20° = 180°
=> 16x = 160°
=> x = 160°/16
=> x = 10°
At x = 10° measures of angles are
=> (9x - 20)° = 9(10) - 20° = 70°
=> (7x - 12)° = 7(10) - 12° = 58°
Therefore,
The measures angles are 70° and 52°
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we will flip a balanced coin 3 times and for each toss, record whether we get a head or a tail. write all possible outcomes of this experiment to find the probability that we get exactly 0 tails.
The probability of getting exactly 0 tails is 1/8 or 0.125.
The coin flip experiment involves three independent events, each representing the outcome of one coin flip. Since each coin flip is balanced, the outcome of each event can either be heads (H) or tails (T). Therefore, for each event, there are two possible outcomes.
Since each event is independent, the number of possible outcomes of three events is equal to the product of the number of possible outcomes of each individual event. This means that the number of possible outcomes of three coin flips is equal to 2 * 2 * 2 = 8. The possible outcomes of three coin flips can be listed as follows:
HHH
HHT
HTH
THH
THT
TTH
HTT
TTT
Out of these eight possible outcomes, only one outcome (HHH) results in getting exactly 0 tails. So the probability of getting exactly 0 tails is 1/8 or 0.125.
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F(x)=3/x+2-square rootx-3
Answer: -5/3
Step-by-step explanation:
a rectangular well is 6 feet long, 4 feet wide, and 10 feet deep. if water is running into the well at the rate of 3 ft3 /min , how fast is the water rising?
The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
To calculate this, we can use the following formula:
Rate of Water Rising = Volume of Water Added Per Minute / Total Volume of Well
Rate of Water Rising = 3 ft3/min / 240 ft3
Rate of Water Rising = 1/80 ft per minute
Therefore, The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
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Y<1/2x-7
Y>=-x-1
Point :(,)
From the inequalities y < (1/2)x - 7 and y ≥ -x - 1 graphed, a possible solution is the point (30, 2)
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Inequalities are used to show the non equal comparison of two or more numbers and variables.
Given the inequalities:
y < (1/2)x - 7 (1)
And:
y ≥ -x - 1 (2)
From the inequalities graphed, a possible solution is the point (30, 2) which is shown in the darker region
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a force of pounds is required to hold a spring stretched 0.4 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length? $1.8$incorrect2.025
The work done in stretching the spring from its natural length to 0.9 feet beyond its natural length is 3 foot-pounds.
This can be calculated using the equation W = F * d, where W is the work done, F is the force applied, and d is the distance the spring is stretched. In this case, F is 6 pounds and d is 0.5 feet (0.9 feet - 0.4 feet). Thus, W = 6 * 0.5 = 3 foot-pounds.
Force is a concept in physics that describes the influence that can change the motion of an object. Work done is the amount of energy transferred to or from an object when a force acts on it and causes it to move through a distance.
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Correct question:
A force of 6 pounds is required to hold a spring stretched 0.4 feet beyond its natural length.
How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?
please help its urgentt
At a local theater, 2/3 of the seats are located on the main floor. The remaining seats are located in the balcony. There are 600 seats on the main floor.
How many total seats are in the theater?
For an upcoming show, 4/5 of the floor seats have been sold and 1/2 of the balcony seats have been sold. What overall fraction of the seats in the whole theater have been sold?
Overall fraction of sold seats is 0.63333...
How to find the total number of seats in the theaterFirst we use the fact that 2/3 of the seats are located on the main floor and the number of seats on the main floor is 600, so the total number of seats can be calculated as follows:
Total number of seats = 600 / (2/3) = 900 seats
Next, we can find the number of seats in the balcony:
Balcony seats = Total number of seats - Main floor seats = 900 - 600 = 300 seats
Next, we can find the number of sold floor seats:
Sold floor seats = 4/5 * 600 = 480 seats
And the number of sold balcony seats:
Sold balcony seats = 1/2 * 300 = 150 seats
Finally, to find the overall fraction of sold seats in the theater, we add the number of sold floor seats and the number of sold balcony seats and divide by the total number of seats:
Overall fraction of sold seats = (480 + 150) / 900 = 0.63333... (rounded to the nearest hundredth)
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Suppose you deposited $40 per month into a savings plan for 9 years and at the end of that period your balance was $19,600.What was the amount you earned in interest?
------------------------------------------------------
A. It is impossible to compute without knowing the APR. To find the correct answer, multiply each $40 deposit by the APR, and then multiply the product by the number of months in 9 years.
B. It was $15,280. Calculate the amount deposited over 9 years and then subtract it from the balance of $19,600.
C. It is impossible to compute without knowing the APR. To find the correct answer, divide the number of payments by the APR.
D. It was $15,280. Divide the balance of $19,600 by the number of years,9.
E. It was $30,560. Multiply the balance of $19,600 by the number of years,9.
F. it was $30,560.Calculate the amount deposited over 9 years and then add it to the balance of $19,600.
Answer:
b. It was $15,280. Calculate the amount deposited over 9 years and then subtract it from the balance of $19,600.
Step-by-step explanation:
19,600-4,320 gives you the interest
Answer:
B. It was $15,280.
Step-by-step explanation:
Calculate the total amount deposited:
$40 per month * 12 months per year * 9 years = $4,320
Subtract the total amount deposited from the final balance: $19,600 - $4,320 = $15,280
The result is the interest earned: $15,280.
So, the answer is B. It was $15,280.
1. Suppose a graph passes the horizontal line test: No horizontal line can be drawn that touches the graph in more than one location. Does this mean that the graph represents a function? If not, is there anything special about a graph that passes the horizontal line test? Share your ideas with a classmate.
2. Dotty and Lionel are making a graph comparing a car's age with its gas mileage. Dotty says the graph should show discrete points because the car's age is stated in whole numbers of years. Lionel says they should make a continuous line because age increases gradually, like time. Which student do you agree with and why?
3. Write two linear functions, f(x) and g(x). For example, f(x) = 3x - 7 and g(x) = -2x + 5. Then see whether f(x) - (-g(x)) is equivalent to f(x)+ g(x). Hint: To find -g(x), just change the signs of all the terms in g(x). Discuss whether you think your results would apply to every function..
A graph that passes the horizontal line test represents a function. This is because if a horizontal line can only intersect the graph at one point, it means that each input value (x) has a unique output value (y), which is the definition of a function. This is true.
How to explain the informationI agree with Lionel, the graph should show a continuous line because age increases gradually like time. Also, age is usually not a discrete variable, it's a continuous variable that can have fractional values, so a line graph is more appropriate to represent the relationship between age and gas mileage.
Let's take f(x) = 3x - 7 and g(x) = -2x + 5 as two linear functions.
f(x) - (-g(x)) = 3x - 7 - (-2x + 5) = 3x - 7 + 2x - 5 = 5x - 12
f(x) + g(x) = 3x - 7 + (-2x + 5) = x - 2
So f(x) - (-g(x)) is not equivalent to f(x) + g(x). This result would not apply to every function, as the properties of addition and subtraction of functions depend on the specific functions being used.
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Divide the following <3 answer needed asap please!!!
Answer:
Below
Step-by-step explanation:
Divide 3 into all of the coefficients
16 + 12 - 9 now divide 'w' into the variables
16 w^2 + 12 w - 9 Done.
Simplify the expression 12p-8p,4p(3-2)
Answer:
Are these two different equations? Tell me so I can help you.
help, will mark as brainliest I PROMISE YOU
Answer:
Below
Step-by-step explanation:
BAC = DAC angle bisector theorem
AC = AC
BCA=BCA given
ABC congruent to ADC ASA theorem
BA = AD triangle congruence theorem
AC = AC "
BC = DC "
what the solution to practice arithmetic sequences as linear functions?
The solution of Representing an arithmetic sequence as a linear function involves finding the equation of a line in the form of y = mx + b.
Here m represents the common difference and b represents the initial term of the sequence. To do this, choose any two terms from the arithmetic sequence and use them to solve for the slope (m) and y-intercept (b). For example, if the two terms are a_n and a_n+k, where k is a constant, you can use the formula: m = (a_n+k - a_n) / k.
Once you have the slope, use one of the two terms and the slope to solve for the y-intercept using the equation y = mx + b. This will give you the equation for the line representing the arithmetic sequence. By using this method, you can practice representing arithmetic sequences as linear functions and find the equation of a line that represents any given arithmetic sequence.
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HELP NOW Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 26 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 180 square feet of carpeting. What dimensions should the rug have? The dimensions of the rug should be 28 ft. (Use a comma to separate answers as needed)
Answer: To find the dimensions of the rug, we need to subtract the width of the floor strip from both the length and the width of the room. Let x be the width of the floor strip in feet. Then the dimensions of the rug will be 18-2x by 26-2x.
The area of the rug is given by:
(18-2x)(26-2x) = 180
Expanding the right-hand side gives:
468 - 72x + 4x^2 = 180
Rearranging the equation gives:
4x^2 - 72x + 288 = 0
We can use the quadratic formula to find the solutions for x:
x = (-b ± √(b^2-4ac)) / 2a
where a = 4, b = -72, and c = 288
x = (72 ± √(72^2 - 4(4)(288))) / 2(4)
x = (72 ± √(72^2 - 4(1152))) / 8
x = (72 ± √(72^2 - 4608)) / 8
x = (72 ± √(5184)) / 8
x = (72 ± 72) / 8
x = (144 ± 72) / 8
x = 72 / 8 or 0
Since the width of the floor strip cannot be negative, x = 9 feet. So, the dimensions of the rug should be 18 - 2 * 9 = 0 ft by 26 - 2 * 9 = 8 ft.
Step-by-step explanation:
The values of x are 18 and 4
How to solve for the values of xWe have the area of a rectangle
A = L* B
The l and the b would get increased by 2x
180 = (18 - 2x) (26 - 2x)
We have to open the bracket
468 - 36x - 52x + 4x² = 180
468 - 180 - 88x + 4x² = 0
rearrange the equation
4x² - 88x + 288 = 0
Solve using the quadratic formula equation
This would give us x = 144 / 8 and 32 / 8
x = 18 and x = 4
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A is C% of B
A=X
C%=80%
B=160
What is A
The value of A is 128
Solution:-
Given,
A = (C/100)* B
C = 80
B = 160
So, A = (80/100)* 160
Therefore, The value of A from the above expression is 128
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I need help with this
Answer:
Step-by-step explanation:
y=2x-7
y=-1/2x+6
-1/2x+6 = 2x-7
x= 4
y= 2(4)-7
= 1
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Find the largest domain of f (x)=x²+1
What is the slope-intercept form of this equation: 3x + 2y=8
Answer:
y = [tex]\frac{-3}{2}[/tex] x + 4
Step-by-step explanation:
3x + 2y = 8 Subtract 3x from both sides
3x - 3x + 2y = -3x + 8
2y = -3x + 8 Divide all the way through by 2
y = [tex]\frac{-3}{2}[/tex] x + 4
solve for x and find the value of x
We can write an equation for the interior angles, and we will see that x = 13
How to find the value of x?We want to find the value of x, we can see two adjacent angles on a rectangle, then the sum of these two is equal to 180°, we can write:
3x + 78 + x + 50 = 180
4x + 128 = 180
4x = 180 - 128
4x = 52
x = 52/4 = 13
The value of x is 13.
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help pleas read the image this is worth 30 points
Let's consider what the question asks for:
--> change in total cost for each book printed
--> cost to get started
The change in total cost:
--> essentially, the slope value that is given in the equation:
[tex]y=25x+1150[/tex]
--> thus, the change in total cost per book is $25
The cost to get started before printing any books:
--> we can essentially set 'x' equal to 0 to signify no books being printed
yet
[tex]y=25x+1150=25(0)+1150=1150[/tex]
--> the total cost before printing any books is $1150
Answer:
change in total cost for each book printed: $25total cost before printing any book: $1150Answer:
1. The change in total cost for each book printed is $25
2. The cost to get started is $1,150
Step-by-step explanation:
25x + 1150 = Y
-Y/-1 = -25x/-1 - 1150/-1
Y = 25x + 1150
To get the total cost to get started let X = 0
Y = 25x + 1150
Y = 25(0) + 1150
Y = $ 1,150
Find the surface area of a cylinder with a base diameter of 4 yd and a height of 9 yd . Use the value 3.14 for π , and do not do any rounding. Be sure to include the correct unit.
The surface area of a cylinder with a base diameter of 4 yd and a height of 9 yd is 113.04 yd².
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
We know, The surface area of a cylinder is 2πrh, where 'h' is the height and 'r' is the diameter.
So, The radius is = (4/2) = 2 yd.
Therefore, The surface area of the cylinder is.
= 2π×2×9 yd².
= 36π yd².
= 113.04 yd².
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) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 5 , 7, and 58. Let b represent the number of books.
The equation that represents the number of books purchased will; be 6b - 8 = 58 and the number of books is 11.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Ashley bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.
Let 'b' be the number of books. Then the equation is given as,
6b - 8 = 58
Simplify the equation, then we have
6b - 8 = 58
6b = 66
b = 11
The equation that represents the number of books purchased will; be 6b - 8 = 58 and the number of books is 11.
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The complete question is given below.
Ashley bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6. How many books did she buy?
Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 58, 8, and 6. Let b represent the number of books. and then solve the equation.
Solve for h.
Z =
M
g (h-f)
h = 0
X
믐
Ś
PLEASEEEEE WILL MARK!
On solving the provided question, we can say that value of the equation , h = [tex]\frac{M}{Zg} + f[/tex]
Which equation is this?Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.
here,
the equation
[tex]Z=\frac{M}{g(h-f)}[/tex]
[tex]for, h , \\h - f = \frac{M}{(Zg)}\\h = \frac{M}{Zg} + f[/tex]
value of the h will be [tex]\frac{M}{Zg} + f[/tex]
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let the continuous random variable x denote the current measured in a thin copper wire in milliamperes. assume that the range of x is [0, 20 ma], and assume that the probability density function of x is f (x) 0.05 for 0 x 20. what is the probability that a current measurement is less than 10 milliamperes?
The probability that a current measurement is less than 10 milliamperes can be found by computing the cumulative distribution function (CDF) of the random variable x at 10 milliamperes.
The CDF of a continuous random variable x is defined as the probability that x is less than or equal to a given value.
In this case, we want to find the CDF of x at 10 milliamperes, which we can write as F(10), where:
F(10) = P(X <= 10) = ∫_0¹⁰ f(x) dx
Using the probability density function f(x) given in the problem, we can evaluate the integral to find the CDF:
F(10) = ∫_0¹⁰ 0.05 dx = 0.5
So the probability that a current measurement is less than 10 milliamperes is 0.5. This means that half of the possible current measurements will be less than 10 milliamperes, and half will be greater than 10 milliamperes.
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Mark needed to buy some items for a science project. The items were priced $3.25, $0.55, $2.95, and $4.25 before tax. If everything in the store was on sale for 20% off, what was the total cost of the items he bought, before tax?
Total cost of items Mark bought = $8.80
What is percentage?The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given,
Price of the items, $3.25, $0.55, $2.95, and $4.25 before tax.
Total price = $11
Discount on items = 20%
Discount = (20/100)11 = $2.20
Cost of the items = $11 - $2.20 = $8.80
Hence, $8.80 is total cost of items Mark bought.
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Find the general solution of the differential equation. (Enter your solution as an equation.)
y^3y’=6cos(pix)
Answer:
Find the general solution of the differential equation. (Enter your solution as an equation.)
y^3y’=6cos(pix
Answer:
The differential equation is a separable differential equation, so we can separate the variables and integrate both sides to find the general solution.
Separating the variables, we get:
(y^3)dy = 6cos(pix)dx
Integrating both sides with respect to their respective variables, we get:
(1/4)y^4 = -3sinx + C
Where C is an arbitrary constant of integration.
So the general solution to the differential equation is:
(1/4)y^4 = -3sinx + C
Step-by-step explanation:
Carbon-14 has a half-life of 5700 years. Scientists use this fact to determine the age of things made of organic material. Suppose the average page of a book containing approximately 0.5 mg of carbon-14 is put into a time capsule.
a. Write an exponential function where x is the number of 5700 year periods and y is the amount of carbon-14.
b. Find the amount of carbon-14 after 11,400 years.
a. an exponential function where x is the number of 5700 year periods and y is the amount of carbon-14 is: y = a (b)^(x/h)
b. the amount of carbon-14 after 11,400 years is 0.25 mg
What is half-life?The amount of time needed for a procedure to affect half of anything, such as the amount of time needed for a radioactive substance's atoms to split in half. The half-life of a radioactive sample is the amount of time needed for half of its atomic nuclei to spontaneously decay, which releases energy and particles, or, alternatively, the amount of time needed for the radioactive sample to disintegrate 60 times every second.
a.
y = a (b)^(x/h)
here, y = amount of carbon-14
a = initial amount
b = final amount
x = time elapsed
h = half life
b. we know that half of it will change into another form in 5700 years, Therefore, if start with 0.5 mg, that would be half in 5,700 years, or 0.25 mg in 11,400 years, which is another half life.
Thus, the amount of carbon-14 after 11,400 years is 0.25 mg
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