Answer:
Step-by-step explanation:
the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
The definition of the Laplace transform of a function f(t) is given by:
L{f(t)} = F(s) = ∫_0^∞ e^(-st) f(t) dt
where s is a complex number.
If f(x) = 0, then we have:
L{f(x)} = L{0} = ∫_0^∞ e^(-st) 0 dt = 0
Therefore, the Laplace transform of the zero function is zero.
If f(x) = 1, then we have:
L{f(x)} = L{1} = ∫_0^∞ e^(-st) dt
Using integration by parts, we get:
L{1} = ∫_0^∞ e^(-st) dt = [-e^(-st)/s]_0^∞ = [0 - (-1/s)] = 1/s
Therefore, the Laplace transform of the constant function 1 is 1/s.
If f(x) = x, then we have:
L{f(x)} = L{x} = ∫_0^∞ e^(-st) x dt
Using integration by parts again, we get:
L{x} = ∫_0^∞ e^(-st) x dt = [(-e^(-st) x)/s]_0^∞ + (1/s) ∫_0^∞ e^(-st) dt
Since e^(-st) x approaches zero as t approaches infinity, the first term evaluates to zero. We can then simplify the second term using the result from part 2:
L{x} = (1/s) ∫_0^∞ e^(-st) dt = 1/s * (1/s) = 1/s^2
Therefore, the Laplace transform of the function f(x) = x is 1/s^2.
If f(x) = e^(ax), then we have:
L{f(x)} = L{e^(ax)} = ∫_0^∞ e^(-st) e^(ax) dt
Simplifying the integrand, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt
We can evaluate this integral using the formula:
∫_0^∞ e^(-bx) dx = 1/b
Setting b = a - s, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt = 1/(a-s)
Therefore, the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
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Apple needs 12 ounces of a stir fry mix that is made up of rice and dehydrated veggies. The rice cost $1.73 per ounce and the veggies costs $3.38 per ounce. Apple has $28 to spend and plans to spend it all.
Let x = the amount of rice
Let y = the amount of veggies
Part 1: Create a system of equations to represent the scenario. (2 points)
Part 2: Solve your system using any method. Write your answer as an ordered Pair. (1 point)
Part 3: Interpret what your answer means (how much rice and how much veggies Apple buys) (1 point)
The system of equations to represent the scenario is 1.73x + 3.38y ≤ 28,
and the ordered pair is (8,4).
What is the Linear equation?
A linear equation is an algebraic equation that represents a straight line on a coordinate plane. A linear equation has 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 point where the line intersects the y-axis).
What is a system of equations?
A system of equations is a set of two or more equations that involve the same variables. In a system of equations, the solution is a set of values for the variables that satisfy all the equations in the system simultaneously. For example, the system of equations:
2x + 3y = 7
x - 2y = 5
has two equations with two variables x and y. The solution to the system is the set of values for x and y that satisfy both equations simultaneously.
According to the given information:
Part 1:
We are given that Apple needs 12 ounces of the stir fry mix, which is made up of rice and dehydrated veggies. Let x be the amount of rice in ounces and y be the amount of dehydrated veggies in ounces.
The total amount of stir fry mix needed is 12 ounces, so we have:
x + y = 12
The cost of the rice is $1.73 per ounce and the cost of the dehydrated veggies is $3.38 per ounce. Apple has $28 to spend and plans to spend it all, so the cost of the stir fry mix must be less than or equal to $28:
1.73x + 3.38y ≤ 28
Part 2:
To solve the system of equations, we can use substitution or elimination. Here, we will use substitution to solve for one variable in terms of the other:
x + y = 12 --> y = 12 - x
Substituting y = 12 - x into the second equation, we get:
1.73x + 3.38(12 - x) ≤ 28
Simplifying and solving for x, we get:
1.73x + 40.56 - 3.38x ≤ 28
-1.65x ≤ -12.56
x ≥ 7.616
We round up to the nearest whole number since we cannot buy a fraction of an ounce of rice. Thus, x = 8 ounces.
Substituting x = 8 into the equation y = 12 - x, we get:
y = 12 - 8
y = 4 ounces
Therefore, Apple buys 8 ounces of rice and 4 ounces of dehydrated veggies. The ordered pair is (8,4).
Part 3:
Our solution (8, 4) means that Apple needs to buy 8 ounces of rice and 4 ounces of dehydrated veggies to make 12 ounces of stir fry mix. The cost of the stir fry mix can be calculated by substituting these values into the cost equation:
1.73(8) + 3.38(4) = $21.48
Since this is less than or equal to the $28 that Apple has to spend, they can afford to buy the necessary ingredients to make the stir fry mix.
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find f(x) for the given function.
f(x) = 1/1-x
To find f(x) for the given function f(x) = 1/1-x, we simply replace the "x" in the equation with whatever input value we want to evaluate the function at.
For example, if we want to find f(2), we would replace x with 2 and get:
f(2) = 1/1-2
f(2) = -1
Similarly, if we want to find f(a), we would replace x with a and get:
f(a) = 1/1-a
Therefore, f(x) = 1/1-x, where x is any input value.
To find f(x) for the given function, simply rewrite the function as it is:
f(x) = 1 / (1 - x)
Here, f(x) represents the function value for any input x, and the expression on the right side indicates how to calculate it.
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You spin the spinner, flip a coin, then spin the spinner again. Find the probability of not spinning a 5. Flipping tails, then spinning a 5. Write your answer as a traction in simplest form
The probability of not spinning 5 is 81/200.
What is the probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: You spin the spinner, flip a coin, then spin the spinner again.
We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.
P(not spinning a 5) = 9/10
P(heads)= 1/2 because there is an equal chance to get heads or tails
P(not spinning a 5)= same as before, 9/10 (independent events).
= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]
= [tex]\frac{81}{200}[/tex]
Hence, the probability of not spinning 5 is 81/200.
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Which system of equations is represented by the graph?
Answer:
Absoblute value Reflection
Step-by-step explanation:
You can tell it's absolbute value because of the parbolas, and it's reflected acroos the two points. Give brainliest please!
If the smith children are served randomly how likely is it that the two oldest smith children are served before the others ?
The probability of the two oldest Smith children being served first is 2/4 or 50%.
How likely is it for the two oldest Smith children to be served first?Assuming that all the children have an equal chance of being served first, there are a total of 4 possibilities for the order in which the two oldest Smith children can be served:
Oldest served first, followed by second oldestSecond oldest served first, followed by oldestOldest served first, followed by one of the younger children, then second oldestSecond oldest served first, followed by one of the younger children, then oldestOut of these 4 possibilities, only the first 2 would satisfy the condition that the two oldest Smith children are served before the others. So the probability that the two oldest Smith children are served first is 2/4 or 50%.
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Si 12kg de papas y seis kg de arroz cuentan 102. 00 mientras que 9 kg de papas y 13 kilogramos de arroz cuestan 153. 00¿cuanto cuesta cada producto?
Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.
Para resolver este problema, necesitamos plantear un sistema de ecuaciones lineales con dos incógnitas: el precio por kilogramo de papas y el precio por kilogramo de arroz. Podemos escribir:
12p + 6r = 102
9p + 13r = 153
Donde p es el precio por kilogramo de papas y r es el precio por kilogramo de arroz. Podemos resolver este sistema de ecuaciones usando el método de eliminación. Multiplicando la primera ecuación por 13 y la segunda ecuación por -6, obtenemos:
156p + 78r = 1326
-54p - 78r = -918
Sumando estas ecuaciones, obtenemos: 102p = 408
Dividiendo ambos lados por 102, encontramos que p = 4. Por lo tanto, el precio por kilogramo de papas es de 4 pesos.
Para encontrar el precio por kilogramo de arroz, podemos sustituir p = 4 en una de las ecuaciones originales y resolver para r. Por ejemplo, usando la primera ecuación:
12(4) + 6r = 102
48 + 6r = 102
6r = 54
r = 9
Por lo tanto, el precio por kilogramo de arroz es de 9 pesos.
Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.
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Para el periódico mural, los alumnos decidieron representar un pino por medio de un triángulo que tiene una superficie de 1. 5m si la base mide 1. 5 m ¿cuanto mide la altura? 
La fórmula para calcular el área de un triángulo es:
área = base * altura / 2
Podemos despejar la altura de esta fórmula y sustituir los valores que conocemos:
área * 2 / base = altura
1.5 * 2 / 1.5 = 2
Por lo tanto, la altura del triángulo es de 2 metros.
subtract -10x+3 from -7x^2 +5x +10
Answer:
-7x^2 + 15x +7
Step-by-step explanation:
-7x^2 + 5x + 10 - (-10x + 3)
-7x^2 + 5x + 10 + 10x -3.......when u distribute it multiple by -1
-7x^2 + 15x +7 ...... simplify by collecting like term.
Please help -(-4)(-6)-3/5(10+5)/1/3!! I’ll give 30 points.
The solution to the expression -(-4) (-6)-3/5(10+5)/1/3 is 15.
To solve this expression, we need to follow the order of operations, which is also known as PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction):
Start with the parentheses: (-4) (-6)= 24, so we can rewrite the expression as:
24-3/5(15)/(1/3)
Now we need to simplify the expression inside the parentheses by adding 10 and 5, which equals 15. Then we need to simplify the division by multiplying the numerator by the reciprocal of the denominator, which is the same as dividing by 1/3. We can rewrite this expression as:
24-3/5*15*3
Multiply 3/5 and 15 first, then multiply that result by 3: 24-9.
Finally, subtract 9 from 24 to get the final answer: 15.
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Find the area of this triangle.
round to the nearest tenth.
7 in
133
13 in
[ ? ) in2
Area of triangle = 45.5 in square ≈ 45.5 (rounded to the nearest tenth).
How to find area of triangle?The area of a triangle given its base and height.
The formula for the area of a triangle is:
Area = (1/2) x base x height
In this formula, "base" refers to the length of the side of the triangle that is perpendicular to the height, and "height" refers to the length of the line segment that is perpendicular to the base and passes through the opposite vertex.
In the problem you provided, the base of the triangle is given as 13 inches, and the height is given as 7 inches. So we can plug these values into the formula:
Area = (1/2) x 13 in x 7 in
= 45.5 in square
The units for area are square units, so we write the answer as "inches squared" or "in square".
Finally, we are asked to round the answer to the nearest tenth. Since there is only one decimal place in the answer, the "tenth" place is the same as the "one" place. Therefore, we look at the digit in the "one" place (which is 5) and round up to the nearest whole number. This gives us:
Area of triangle ≈ 45.5 (rounded to the nearest tenth).
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6.at what interval does the car reach the the highest acceleration ?
7. what is the highest acceleration of car ?
8. what is the lowest acceleration of the car ?
9. at what time interval did the car attains the lowest acceleration ?
10. base on the given data , how do u describe the motion of the car in the whole trip?
pls answer this thanks
I'm sorry, but you have not provided any data or information about the car's motion. Without this information, I cannot answer your questions accurately. Please provide more details or context about the car's motion.
I am unable to answer these specific questions without any given data. Please provide the data related to the car's acceleration, and I will be happy to help you with the analysis.
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The owner of a company asks a manager, "How many hours does an employee work each week?" a. Is this a statistical question? Explain. The question a statistical question because there. Question 2 b. The manager records the number of hours worked each week by several employees. Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data. Hours worked 40 39 40 39 47 38 41 37 40 41 40 43 40 41 40 38 40 42 40 42 Most of the data are clustered around. There is a peak at and a gap between. Question 3 c. Use the distribution of the data to answer the question. Most employees work about hours each week
This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.
a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.
b. Here's a dot plot of the data provided:
37: •
38: ••
39: ••
40: ••••••••
41: •••
42: ••
43: •
47: •
The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.
c. Based on the distribution of the data, most employees work about 40 hours each week.
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En una imprenta, 4 impresoras tardan 3 horas en imprimir 5000 hojas, ¿cuánto tiempo tardarán en imprimir 6000? escribe el resultado en horas con decimales
Tardarán aproximadamente 3.6 horas.
How long to print 6000 sheets?Para resolver este problema, podemos establecer una relación proporcional entre el número de hojas impresas y el tiempo requerido. Si 4 impresoras tardan 3 horas en imprimir 5000 hojas, podemos establecer la proporción
4 impresoras / 3 horas = 5000 hojas / x horas
Donde x representa el tiempo que tardarán en imprimir 6000 hojas. Podemos resolver esta proporción utilizando regla de tres:
4 / 3 = 5000 / x
Multiplicando en cruz, obtenemos:
4x = 3 * 5000
4x = 15000
x = 15000 / 4
x = 3750
Por lo tanto, tardarán aproximadamente 3750 horas en imprimir 6000 hojas.
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Find the value of b. Round your answer to the nearest hundredth.
Image may not
be drawn to scale.
The value of the tangent segment b is 20.15.
What is the value of side b?The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.
It is expressed as:
( tangent segment )² = External part of the secant segment + Secant segment.
From the diagram:
Tangent segment = WX = b
External part of the secant segment = YX = 14
Secant segment = ZX = 15 + 14 = 29
Plug these values into the above formula and solve for b.
( tangent segment )² = External part of the secant segment + Secant segment.
b² = 14 × 29
b² = 406
b = √406
b = 20.15
Therefore, the value of b is 20.15.
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PLEASE URGENTLY HELP!!!!!!!!!!!
LOOK AT SCREENSHOT!!!
What is the value of x in degrees?
Please show work if you can!
Answer: 72
Step-by-step explanation:
Q is same as M = 72
N=36
L=x
All 3 angles of a triangle add to 180
72+36+x=180
x=72
3. the sketch shows three adjacent angles. please write an equation that can be
used to determine the value of y?
28
36
please help
The value of y is 116°.
Three given Adjacent angles are 28°, 36° and y°.
When two angles are adjacent, they have a common side between them and share a common vertex where the two sides meet. The angles are said to be adjacent because they are next to each other.
We know that if a ray stands on a straight line, then the sum of adjacent angles is 180°.
So, 28° + y° + 36° = 180°
y° + 64° = 180°
Subtracting 64° from both sides.
y°- 64° = 180° - 64°
y° = 116°
Hence, the value of y is 116°.
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the aspect ratio of a wide screen tv is 2.39:1. what is the length of the diagonal of a wide screen tv screen with an area of 150 in??
The length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.
Aspect ratio refers to the proportional relationship between the width and height of an image or screen. In the case of a wide screen TV, the aspect ratio is 2.39:1, which means that for every 2.39 units of width, there is 1 unit of height.
To find the length of the diagonal of a wide screen TV with an area of 150 inches, we need to use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the width and height.
First, we need to find the width and height of the TV screen. We can do this by setting up the equation:
2.39x^2 = 150
where x is the width of the screen. Solving for x, we get:
x = √(150/2.39) = 10.87 inches
Now we can find the height by dividing the width by the aspect ratio:
h = 10.87 / 2.39 = 4.55 inches
Using the Pythagorean theorem, we can find the length of the diagonal:
d^2 = 10.87^2 + 4.55^2 = 126.68
d = √126.68 = 11.25 inches
Therefore, the length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.
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Un Jardinero usa un total de 61. 5 galones de gasolina en un mes. De la cantidad total
3/5
de gasolina, se usaron en sus cortadoras de césped. ¿Cuántos galones de gasolina usa
el jardinero en sus cortadoras de césped en ese mes? Me ayudan plis
The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.
What are proportions?In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.
To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:
61.5 gallons x 3/5 = 36.9 gallons
Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.
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What is 43% , 2/5 , 3/7 , and 0. 42 remaining in ascending order ?
Answer:
2/5 < 0.42 < 43% < 3/7
Step-by-step explanation:
Let's convert them all to decimals:
43% = 0.43
2/5 = 0.4
3/7 = 0.428571...
0.42 = 0.42
Now we can arrange them in ascending order:
0.4
0.42
0.43
0.428571...
Leland wants to paint a portrait for his parents using a photograph of them that is 5 inches wide by 8 inches high. He wants the portrait to be proportional to the photograph and 42 inches high. Which proportion can Leland use to find , the width he needs to use to make the portrait proportional?
The ratio to make the portrait proportional is width/42 = 5/8
Which proportion can Leland use to find , the width he needs to useFrom the question, we have the following parameters that can be used in our computation:
Photograph that is 5 inches wide by 8 inches high.
This means that
Ratio = width/height
Substitute the known values in the above equation, so, we have the following representation
Ratio = 5/8
Given that he wants the portrait to be proportional to the photograph and 42 inches high.
Then, we have
width/42 = 5/8
Hence, the ratio to make the portrait proportional is width/42 = 5/8
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What occurs when a white dwarf in a binary star system if it gains mass beyond the chandrasekhar limit?.
If a white dwarf in a binary star system gains mass beyond the Chandrasekhar limit (approximately 1.4 solar masses), it undergoes a runaway nuclear reaction, causing it to collapse and explode in a Type Ia supernova.
A white dwarf is a dense stellar remnant that is left behind after a star has exhausted all its nuclear fuel and has shed its outer layers. In a binary star system, the white dwarf may gain mass from its companion star, either through accretion or a merger. If the mass of the white dwarf exceeds the Chandrasekhar limit, the gravitational forces become so strong that the electrons in the atoms are forced to combine with the atomic nuclei, forming neutrons. This process is called electron capture, and it releases a tremendous amount of energy.
The energy released is enough to ignite a runaway nuclear reaction, causing the white dwarf to collapse and explode in a Type Ia supernova. Type Ia supernovae are important cosmic events because they are used as standard candles to measure the distance to distant galaxies. These explosions are also believed to play a significant role in the chemical evolution of the universe, as they produce heavy elements such as iron and nickel that are scattered into the interstellar medium.
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What is the height, to the nearest tenth of a foot, of a tree that creates a 35-foot shadow when the sun is at an angle of elevation of 35⁰? (do NOT type in units, just the value)
The height of the tree is approximately 20.1 feet.
What is the height of a tree that produces a 35-foot shadow when the sun is at an angle of 35 degrees?To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.
tan(35°) = height of tree / 35 feet shadow
Rearranging this formula, we get:
height of tree = 35 feet shadow x tan(35°)
Plugging in the given values and using a calculator, we get:
height of tree = 35 x tan(35°) ≈ 20.1 feet
Therefore, the height of the tree is approximately 20.1 feet.
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A glass prism on a chandelier is 93 millimeters long. A base of the prism is an equilateral triangle with side lengths of 7 millimeters and a height of about 6. 6 millimeters. What is the approximate surface area of the prism?
The approximate surface area of the glass prism is approximately 1986.66 square millimeters.
To find the surface area of the glass prism, we need to determine the area of each of its faces and then add them together. The prism consists of two congruent equilateral triangles and three rectangular faces.
The area of an equilateral triangle with side length s and height h is given by:
A = (√(3)/4) * s²
Using this formula, we can find the area of each of the two equilateral triangles in the prism:
A = (√(3)/4) * 7² ≈ 21.22 mm²
Next, we need to find the area of each of the three rectangular faces. The length of each rectangular face is equal to the side length of the equilateral triangle (7 mm), and the height is equal to the length of the prism (93 mm). Therefore, the area of each rectangular face is:
A = length x height = 7 mm x 93 mm = 651 mm²
To find the total surface area of the prism, we add the areas of the two equilateral triangles and the three rectangular faces:
Total surface area ≈ 2 x 21.22 mm² + 3 x 651 mm² ≈ 1986.66 mm²
Therefore, the approximate surface area of the glass prism is approximately 1986.66 square millimeters.
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A system of linear inequalities is shown
below. Which of the following points are
solutions of the system?
8x + 5y > 40
-6x +2y >_-18
The points (0,10) and (-8,4) are solutions of the system of inequalities.
Define system of inequalityA system of inequalities refers to a set of two or more inequalities that are graphed together on the same coordinate plane. Each inequality in the system represents a region in the plane where the solution to that inequality lies.
To determine if a point is a solution of the system of inequalities, we need to check if it satisfies both inequalities. Let's check each point given:
(4,6):
8(4) + 5(6) = 47 > 40 (true)
-6(4) + 2(6) = -14 ≥ 18 (false)
(9,8):
8(9) + 5(8) = 97 > 40 (true)
-6(9) + 2(8) = -40 ≥ 18 (false)
(0,10):
8(0) + 5(10) = 50 > 40 (true)
-6(0) + 2(10) = 20 ≥ 18 (true)
(5,-6):
8(5) + 5(-6) = 34 > 40 (false)
-6(5) + 2(-6) = -30 ≥ 18 (false)
(-1,-8):
8(-1) + 5(-8) = -44 ≤ 40 (false)
-6(-1) + 2(-8) = 10 ≥ 18 (false)
(-8,4):
8(-8) + 5(4) = -24 ≤ 40 (true)
-6(-8) + 2(4) = 52 ≥ 18 (true)
Therefore, the points (0,10) and (-8,4) are solutions of the system of inequalities.
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WILL GIVE BRAINLIEST!!!
1.)
A composite figure is composed of a semicircle whose radius measures 4 inches added to a square whose side measures 11 inches. A point within the figure is randomly chosen.
What is the probability that the randomly selected point is in the semicircular region?
Enter your answer rounded to the nearest tenth in the box.
2.)
A circular spinner has a radius of 6 inches. The spinner is divided into three sections of unequal area. The sector labeled green has a central angle of 90°. A point on the spinner is randomly selected.
What is the probability that the randomly selected point falls in the green sector?
1/90
1/9
1/4
1/3
3.)
Question
A spinner is divided into 10 equally sized sectors. The sectors are numbered 1 to 10. A randomly selected point is chosen.
What is the probability that the randomly selected point lies in a sector that is a multiple of 3?
Enter your answer in the box.
4.)
Question
Two concentric circles form a target. The radii of the two circles measure 8 cm and 4 cm. The inner circle is the bullseye of the target. A point on the target is randomly selected.
What is the probability that the randomly selected point is in the bullseye?
Enter your answer as a simplified fraction in the boxes.
Answer:
1. 17.2
2. 1/4 or 0.25
3. 3/10 or 30%
4. 15/16
I hope this helped
Step-by-step explanation:
Help a man out. Its due tomorrow need to get it done.
Answer:
A≈166.28
Step-by-step explanation:
Answer:
A≈166.28
Step-by-step explanation:
can someone please help will give brain
Answer:
y = 9
Step-by-step explanation:
• Parallel lines have equal slopes
calculate the slope m of TU using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = T(- 7, 4 ) and (x₂, y₂ ) = U(- 2, - 6 )
[tex]m_{TU}[/tex] = [tex]\frac{-6-4}{-2-(-7)}[/tex] = [tex]\frac{-10}{-2+7}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2
now calculate the slope of VW and equate to - 2
with (x₁, y₁ ) = V(8, 7 ) and (x₂, y₂ ) = W(7, y )
[tex]m_{VW}[/tex] = [tex]\frac{y-7}{7-8}[/tex] = [tex]\frac{y-7}{-1}[/tex]
now equating gives
[tex]\frac{y-7}{-1}[/tex] = - 2 ( multiply both sides by - 1 to clear the fraction )
y - 7 = 2 ( add 7 to both sides )
y = 9
Jack is making $9.50 per hour at his job re-stocking grocery shelves. His supervisor is impressed with his good work and gives him a 10% raise. How much per hour is Jack making now?
PLS HELP I WILL MARK YOU BRAINLIEST
Answer:
Jack now makes $10.45
Step-by-step explanation:
First, we need to find 10% of 9.50. To do that we must divide 9.50 by 10 or simply move the decimal one place to the left to get 0.95. 0.95 is 10% of 9.50. Now we must ADD 0.95 to 9.50 because Jack is getting a 10% raise. 0.95 + 9.50 = 10.45. Therefore Jack makes $10.45 per hour at his job.
A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point. At a certain moment, the angle between the observer's line of sight and the horizontal is π/5 , and it is changing at a rate of 0.4 rad/h. How fast is the balloon rising at this moment? (Round your answer to three decimal places.)
The balloon is rising at a rate of approximately 3.532 km/h at this moment.
We will use the tangent function in trigonometry and the concept of related rates.
Let x be the horizontal distance from the observer to the lift-off point (5 km) and y be the vertical distance from the ground to the balloon. The angle between the observer's line of sight and the horizontal is given as π/5.
We can use the tangent function:
tan(θ) = y/x
At the given moment, x = 5 km and θ = π/5, so:
tan(π/5) = y/5
Now, let's differentiate both sides with respect to time (t):
d(tan(θ))/dt = d(y)/dt / 5
We know that d(θ)/dt = 0.4 rad/h, so we can find d(tan(θ))/dt using the chain rule:
d(tan(θ))/dt = (sec^2(θ)) * d(θ)/dt
d(tan(θ))/dt = (sec^2(π/5)) * 0.4
Now, substitute this back into the first equation and solve for d(y)/dt:
(sec^2(π/5)) * 0.4 = d(y)/dt / 5
d(y)/dt = 5 * (sec^2(π/5)) * 0.4
After calculating the expression, you'll find that d(y)/dt ≈ 3.532 km/h. Thus, the balloon is rising at a rate of approximately 3.532 km/h at this moment.
To learn more about tangent function, refer below:
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Select the statement that best describes how pollination begins.
The statement that best describes how pollination begins is that it starts when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower. Pollination is an essential step in the reproduction of plants, and it allows for the exchange of genetic material between different plants.
Pollination can occur through various methods, including wind, water, and animals such as bees, butterflies, and birds. Once the pollen is transferred, it begins to grow and develop, ultimately leading to the formation of a seed and the growth of a new plant.
Pollination is vital to the continuation of plant life, and without it, many plant species would not be able to survive. It is essential for plant breeders to understand the pollination process, as they can use it to cross different plant varieties and produce new and improved plants.
In conclusion, pollination begins when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower, allowing for the exchange of genetic material and the growth and development of new plants.
To know more about statement refer here
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