The values of b that makes the lines parallel are given as follows:
b = ± 3/2.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the initial value of the linear function.When two lines are parallel, they have the same slope.
Given two points, the slope is given as the change in y divided by the change in x.
This means that the slopes for each line are given as follows:
Origin to (3,4b): 4b/3.Origin to (b, 3): 3/b.As they are parallel, the value of b is obtained as follows:
4b/3 = 3/b.
4b² = 9
b² = 9/4
[tex]b = \pm \sqrt{\frac{9}{4}}[/tex]
b = ± 3/2.
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What is a formula for the nth term of the
given sequence?
an = 125(³)¯n
an = 125(³)n-1
125 (-/-)¹-1
An
=
75, 45, 27...
An =
125 (5) n
Answer:
Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula. Step 2: Now, to find the fifth term, substitute n = 5 into the equation for the nth term.
what is the difference between using the unit rate to find how many feet are in a given number of inches and using the unit rate to find how many inches are in a given number of feet
For feet we will divide the given no. of inches by 12 and for inches we will multiply the given number of feet by 12.
What is feet and inches?Since 1 foot is equal to 12 inches, the given value (in feet) is converted to inches by multiplying by 12. To compare lengths given in different units or to perform arithmetic operations on them, it is crucial to learn how to convert feet to inches (ft to in).
We know that 1 feet = 12 inches.
And to find how many feet are in a given number of inches
We will divide the given no. of inches by 12.
And
To find how many inches are given in a number of feet
We will multiply the given number of feet by 12.
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a newly constructed fish pond contains 2000 liters of water. unfortunately the pond has been contaminated with 5 kg of a toxic chemical during the construction process. the pond's filtering system removes water from the pond at a rate of 200 liters/minute, removes 50% of the chemical, and returns the same volume of (the now somewhat less contaminated) water to the pond. write a differential equation for the time (measured in minutes) evolution of:
The differential equation for the time evolution of the toxic chemical in the pond is dy/dt = -200y + (100/2000)x
where y represents the amount (in kg) of the contaminant in the pond and x represents the amount of contaminant added to the pond per minute (5 kg/minute in this case). The negative sign in the equation indicates that the amount of contaminant is decreasing in the pond, while the positive term (100/2000)x indicates that the contaminant is being added to the pond at the rate of 5 kg/minute.
To solve for y, we can integrate the equation with respect to time. We start by multiplying both sides by dt, giving us the integral form of the equation: dy = -200y dt + (100/2000)x dt. Integrating both sides gives us the solution y = -200y(t) + (100/2000)x(t) + C, where C is an integration constant. Since we know the initial amount of contaminant in the pond is 5 kg, we can set y(0) = 5 and solve for C, giving us C = 5. Therefore, the solution to the differential equation is y(t) = -200y(t) + (100/2000)x(t) + 5.
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4,1234-123 =. ??????
Answer:41,111
Step-by-step explanation:4-3=1 3-2=1 2-1=1 bring the 1 down and bring the 4down to and you got your answer
a conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. if water flows into the tank at a rate of 20 ft3/min, how fast is the depth of the water increasing when the water is 16 ft de
The rate of increase of the depth of the water is 6.67 ft/min.
First, calculate the volume of the water tank:
Volume = (1/3) πr²h
Volume = (1/3) × 3.14 × 10² × 24
Volume = 7,040 ft³
Now calculate the rate of increase of the depth of the water:
Rate of increase of the depth = (Flow rate of water into tank / Volume of tank)
Rate of increase of the depth = (20 ft³/min / 7,040 ft³)
Rate of increase of the depth = 0.0028 ft/min
Finally, calculate the rate of increase of the depth of the water when the water is 16 ft deep:
Rate of increase of the depth = (Flow rate of water into tank / Volume of water)
Rate of increase of the depth = (20 ft³/min / 4,096 ft³)
Rate of increase of the depth = 0.0049 ft/min
Therefore, the rate of increase of the depth of the water when the water is 16 ft deep is 0.0049 ft/min, which is equivalent to 6.67 ft/min.
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consider the following binomial experiment: a company owns 5 copiers. the probability that on a given day any one copier will break down is 0.66. what is the probability that at least 3 copiers will break down on a given day?
The probability that at least 3 copiers will break down on a given day is 0.0909.
1. Calculate the probability that 0 copiers will break down:
P(0) = (1-0.66)^5
= 0.0729
2. Calculate the probability that 1 copier will break down:
P(1) = 5 * 0.66 * (1-0.66)^4
= 0.2221
3. Calculate the probability that 2 copiers will break down:
P(2) = 5C2 * 0.66^2 * (1-0.66)^3
= 0.3088
4. Calculate the probability that 3 copiers will break down:
P(3) = 5C3 * 0.66^3 * (1-0.66)^2
= 0.2197
5. Calculate the probability that at least 3 copiers will break down:
P(at least 3) = 1 - (P(0) + P(1) + P(2))
= 0.0909
The probability that at least 3 copiers will break down on a given day is 0.0909. This was calculated by first calculating the probability of 0 copiers breaking down (P(0)) which is (1-0.66)^5, then the probability of 1 copier breaking down (P(1)) which is 5 * 0.66 * (1-0.66)^4, and then the probability of 2 copiers breaking down (P(2)) which is 5C2 * 0.66^2 * (1-0.66)^3. Finally, the probability that at least 3 copiers will break down (P(at least 3)) was calculated by subtracting the sum of P(0), P(1), and P(2) from 1. This gives us the final result of 0.0909.
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Is dividing by 1 2 the same as dividing in half?
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately). No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively. For example, if we have the number 10, dividing by 1/2 would give us 5 (10/2), while dividing by 1 and 2 would give us 5 and 5 (10/1 = 10 and 10/2 = 5).
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately).
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.
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y=x+6
y=2x+7
solve system by using equal values method
Answer:
(- 1, 5 )
Step-by-step explanation:
y = x + 6 → (1)
y = 2x + 7 → (2)
since both equations have y on the left side, then equate the right sides
2x + 7 = x + 6 ( subtract x from both sides )
x + 7 = 6 ( subtract 7 from both sides )
x = - 1
substitute x = - 1 into either of the 2 equations for y
substituting into (1)
y = x + 6 = - 1 + 6 = 5
solution is (- 1, 5 )
Step-by-step explanation:
We would make these two equations equal to each other since both equations are in y= form
[tex](x + 6) = (2x + 7)[/tex]
Now to get numbers on one side and X's on the other.
Let's start by subtracting 6 from both sides
[tex]x = 2x + 1[/tex]
Next we can subtract 2X
[tex] - x = 1[/tex]
Last but not least, we can divide by -1 to reverse the signs
[tex]x = - 1[/tex]
a museum room, circular in shape, has 5 equally spaced sensors on its walls. there are no dead or overlapping spots along the perimeter of the room. each sensor has the same angle of detection. what is the detection angle of each sensor?
According to the given information the detection angle is 72.
How would you define an angle?An angle is formed anytime two straight lines and rays meet at a single terminal. The intersection of two points at such an angle is known as the vertex. The word "angle" comes from the Latin word "angulus," which meaning "corner."
What is the math behind angles?Degrees are a measure representing circularity or rotation and are used to express angles. You would turn 360° in order to face back in the exact direction after completing a full revolution. As a result, a quarter-circle, or straight angle, is 90°, and a half-circle is 180°. The sum of any two or maybe more angles on the a straight line is 180°.
[tex]\begin{aligned}5\theta & =360^{\circ} \\\theta & =\frac{360^{\circ}}{6} \\& =72^{\circ}\end{aligned}[/tex]
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A rectangle has an area that can be represented by the
expression 16x4 +48x³ 82. Which of the
expressions could represent one of the dimensions of the
rectangle? Select ALL that apply.
Please Help!!
Answer: A rectangle has two dimensions: length and width. The area of a rectangle is given by the formula A = L * W, where L is the length and W is the width.
Given the area can be represented by the expression 16x^4 + 48x^3 + 82, we can see that it's a polynomial of 4 degree.
So, one of the dimensions (L or W) must be represented by a polynomial of degree 4 and the other dimension by a polynomial of degree 3.
So the expressions that could represent one of the dimensions of the rectangle are:
L = 16x^4
W = 48x^3 + 82
It's important to note that this is just one of the possible representations of the dimensions of the rectangle, depending on the values of x.
Step-by-step explanation:
Can anyone figure this out for me please?
Answer:
simple 5×-5 the answer divide by -5
In a sale, the price of a TV is reduced from £250 to £180 what is the decreased percentage?
Answer:
Step-by-step explanation: 80
Answer: THE ANSWER IS 28%
worked it out on the calculator in the end
Step-by-step explanation:
12. Vreni took part in a charity walk.
She walked a distance of 20 kilometres.
a) She raised money at a rate of $12.50 for each kilometre.
i. How much money did she raise by walking the 20 kilometres?
(1 mark)
ii. The money she raised in part (a)(i) was 5
52
of the total money raised.
Work out the total money raised.
(2 marks)
iii. In the previous year the total money raised was $2450.
Calculate the percentage increase on the previous year’s total.
(2 marks)
11b) Part of the 20 kilometres was on a road and the rest was on a footpath.
The ratio road distance : footpath distance was 3 : 2.
i. Work out the road distance.
(2 marks)
ii. Vreni walked along the road at 3km/h and along the footpath at 2.5km/h.
How long, in hours and minutes, did Vreni take to walk the 20 kilometres?
(2 marks)
iii. Work out Vreni’s average speed.
(1 mark)
iv. Vreni started at 08 55. At what time did she finish?
(1 mark)
12
c) On a map, the distance of 20 kilometres was represented by a length of 80 centimetres.
The scale of the map was 1 ∶ .
Calculate the value of .
12. i) By walking the 20 kilometers in the charity walk, Vreni raised $250 at a unit rate of $12.50 per kilometer.
12. ii) The total money raised by all participants in the charity walk was $3,100, using proportions.
12. iii) The percentage increase on the previous year's total is 26.53%.
Part B:
11. i) Based on a ratio of 3:2 of road and footpath distance, the road distance covered 12 kilometers.
11. ii) Using the distance, time, and speed formula, Vreni took 7 hours and 12 minutes to walk the 20 kilometers.
11. iii) Vreni's average speed is 2.78 km/h.
11. iv) Vreni finished the charity walk at 16:07.
Part C: The scale of the map to the total distance covered by Vreni was 1: 4 or a scale factor of 25%.
What is the ratio?The ratio is the quotient of a value compared to another.
Ratios are proportionate values, which are equated to each other.
The average speed and scale factor show the ratios of one value and the whole.
12) Charity Walk and Vreni:
The total distance walked = 20 kilometers
The unit rate of raising money per kilometer = $12.50
i) The total amount raised = $250 ($12.50 x 20)
Money raised in 12. 1 = 5/52 of the total money raised
ii) The total money raised in the charity walk = $3,100 ($250 ÷ 5/52)
iii) The total amount raised in the previous year = $2,450
The total amount raised in the current year = $3,100
Difference between current and previous year = $650 ($3,100 - $2,450)
Percentage increase on the previous year's total = 26.53% ($650/$2,450 x 100)
11b) Ratio of road and footpath walk = 3:2
The sum of ratios = 5
Road distance = 3/5 x 20 = 12 kilometers
Footpath distance = 2/5 x 20 = 8 kilometers
Vreni's walking speed along the road = 3 km/h
Road distance = 12 kilometers
Time to walk the road = 4 hours (12/3)
Vreni's walking speed along the footpath = 2.5 km/h
Footpath distance = 8 kilometers
Time to walk the footpath = 3.2 hours or 3 hours and 12 minutes (8/2.5) or 192 minutes (8/2.5 x 60)
Total time spent by Vreni = 7 hours and 12 minutes (4 hr + 3 hr + 12 min)
Vreni's average speed = Distance/Time
= 20 km/7.2 hrs
= 2.78 km/h
Starting time = 08:55
Total hours = 7 hours and 12 minutes
Finishing time = 16:07 (08:55 + 7 hrs + 12 min)
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What is the domain and range for this function?
find the area of the shaded triangle
Answer:
20cmStep-by-step explanation:
4x10 40 divided by 2Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adults
ticket and the price of a child's ticket.
The price of an adult ticket is $20
The price of a child's ticket is $19
How to calculate the price of an adult and child ticket ?Let x represent the price of a child ticket
Let y represent the price of an adult ticket
Three adults and four children must pay 136
3y + 4x= 136.........equation 1
Two adults and three children must pay $97
2y + 3x= 97.........equation 2
From equation13 1
3y+4x= 136
3y= 136-4x
y= 136-4x/3
Substitute 136-4x/3 for y in equation 2
2(136-4x) + 3x= 97
272-8x/3 + 3x/1= 97
272-8x+9x/3= 97
cross multiply
272-8x+9x=291
collect the like terms
-8x+9x= 291-272
x= 19
Substitute 19 for x in equation 1
3y+4x= 136
3y + 4(19)= 136
3y+ 76= 136
3y= 136-76
3y=60
y= 60/3
y= 20
Hence children tickets cost $19 and adult tickets cost $20
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The area of two similar triangles are 18cm^2 and 8cm^2. ONe of the sides of the first triangle is 4.5cm. What is the length of the corresponding side of the other triangle.
Answer:
If two triangles are similar, the ratio of their corresponding side lengths is the same as the ratio of their areas.
We know that the area of the first triangle is 18 cm^2, and the area of the second triangle is 8 cm^2. So, the ratio of their areas is 18/8 = 9/4
We also know that one of the sides of the first triangle is 4.5 cm.
So the ratio of the corresponding side of the second triangle to the first triangle is:
(length of corresponding side of second triangle) / 4.5 = 9/4
We can cross-multiply and solve for the length of the corresponding side of the second triangle:
4.5 * (9/4) = 9 * (9/4) / 4 = 9 * 2.25 / 4 = 20.25 / 4 = 5.0625 cm
So, the length of the corresponding side of the second triangle is 5.0625 cm.
Help :
(1 + 2 + 3 .... + 5) - 4 = ?
(1 + 2 + 3 .... + 4) - 1 = ?
(1 + 2 + 3) - 2 = ?
Interpret the answer with some logic
Answer:
whats ..... representating
is it a continuous series?
a plane can fly 3750 km in 3 hours with the wind. the plane takes 5 hours to travel the same distance aganist the same wind speed. find the rate of the plane in still air. find the speed of the wind
The rate of the plane in still air is 1,000 kph and the speed of the wind is 250 kph. The result is obtained by using elimination and substituting method.
Elimination and Substitution MethodTo eliminate equations, we can either add or subtract the equations. Substitution is substituting the value of one variable in the other equation.
A plane can travel:
3750 km in 3 hours with the wind.The same distance in the first trip against the same wind speed in 5 hours.Find the rate of the plane in still air and the speed of the wind!
Let's say
v = the rate/speed of the plane in still airw = the speed of the windThe speed of the plane with the wind is
v + w = 3750 km/3 h
v + w = 1250 kph ... (equation 1)
The speed of the plane against the wind is
v - w = 3750 km/5 h
v - w = 750 kph ... (equation 2)
Eliminate the equation 1 and 2!
v + w = 1250
v - w = 750 +
2v = 2000
v = 1000 m/s
Substitute the value of v in equation 1!
v + w = 1250
1000 + w = 1250
w = 1250 - 1000
w = 250 m/s
Hence, the speed of the plane when there is no wind and the speed of the wind respectively are 1000 m/s and 250 m/s.
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Now you're going to imagine that you invested $1,000 in a company one year ago, and you want to see how well your investment would be doing today.
To begin, choose a company that you're familiar with and that seems as if it might be a good investment - that is, a company that you think will have rising stock prices. Think about companies that you use or know are popular Remember, not all companies are public companies. You'll need to check the New York Stock Exchange to find out if you can actually buy shares in this company Once you've settled on a company, find its stock price from one year ago and for today Write a journal entry about your imagined investment Answer the following questions as you write
1.) What stock did you buy?
2.) Why did you think buying this stock would be a good idea?
3.) How much would you have made or lost on an investment of $1,000?
(Hint First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today Compare that to your initial investment of $1,000)
4.) Could you have made more money by selling sooner?
Answer:
Step-by-step explanation:
1. What stock did you buy?
Apple Inc.
2. Why did you think buying this stock would be a good idea?
Apple products are becoming more and more popular every day. The company is always introducing new and exciting devices. I knew it would be a safe choice to invest in.
3. How much would you have made or lost on an investment of $1,000?
I would have made $105.
Hint: First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph. Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today. Compare that to your initial investment of $1,000.
4. Could you have made more money by selling sooner?
Yes, on October 3, 2018 it was at its peak for the year.
your investment would be doing great today. you would make $115 from the given investment.
What are Stocks?A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.
Given, you're going to imagine that you invested $1,000 in a company one year ago
I will buy the stocks of amazon.The popularity of Amazon products is rising daily. The business frequently introduces cutting-edge technology. I was confident that it would be a secure investment.I would have made $115.Hint: To start, divide $1,000 by the stock's current price, one year ago, to see how many shares you might have purchased. It can be necessary to infer the stock price from the graph. The number of shares should be rounded up to the next whole number. Then, multiply the number of shares you purchased by the stock's current price to determine the share's current worth. Contrast that with your $1,000 original investment.on September 5, 2022, it was at its peak for the year.Therefore, Today, your investment would be flourishing. Your return on the stated investment would be $1,115.
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Why is absolute value always positive or zero?
The absolute value of a number is always positive or zero because it represents the distance of a number from zero on a number line, and the distance between two points can never be negative.
The absolute value of a number is defined as the distance of that number from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5. When we apply the absolute value function to a number, the result is always positive or zero.
Additionally, the definition of absolute value is |x| = { x if x >=0, -x if x<0 }
if x is greater or equal to 0, the absolute value of x is x, otherwise is -x, which is positive.
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Using f(x) = 3x - 3 and g(x) = -x, find g(f(0)).
0
1
3
-3
Answer: 3
Step-by-step explanation:
[tex]f(0)=3(0)-3=-3\\\\\implies g(f(0))=g(-3)=-(-3)=3[/tex]
While on vacation you visit a canyon. you shout at the far wall and the sound returns after 6.00 seconds. the speed of sound that day was 345 m (about the height of the empire state building)/s. how far was it to the far side of the canyon? the sound you made had a frequency of 600 hz. what was its wavelength? what was the period?
The distance travelled is 1035 meters, The period T is 1.67m/s and The wavelength is 0.575 meters.
What is wavelength?Because sound is a wave, we can use the proper definitions of the terms to derive the relationship between the wavelength, frequency, and speed of a wave. The wavelength is the distance travelled by the wave in one time period of its cycle, whereas the frequency is the number of cycles per second.
Formula used:
Speed = Distance/time
Frequency of wave = 1/Time period of the wave
Wavelength = Distance travelled by the wave in one time period
Given,
a)The distance travelled is 2d,
where d is the distance to the wall
Thus d = 345 × 6/2= 1035 m
b)The frequency is 600 Hz thus the period T = 1/f= 1.67ms
c)The wavelength λ = Velocity/Frequency
= 345/600
= 0.575 meters
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What are the 4 parts of a system?
It can include things like answers to equations, solutions to problems, and visualizations of data.
1. Input: The data and instructions a system receives.
2. Process: The manipulation of data and instructions to produce an output.
3. Output: The result of the system's processing of the data and instructions.
4. Feedback: Information from the output that is used to improve the system's performance.
1. Input: The first part of a system in mathematics is the input. This is the data and instructions that the system receives. It can include things like numbers, equations, formulas, and instructions for how to process the data.
2. Process: The second part of a system in mathematics is the process. This is where the data and instructions are manipulated to produce an output. This can include things like calculations, algorithms, and other mathematical operations.
3. Output: The third part of a system in mathematics is the output. This is the result of the system's processing of the data and instructions. It can include things like answers to equations, solutions to problems, and visualizations of data.
4. Feedback: The fourth part of a system in mathematics is the feedback. This is information from the output that is used to improve the system's performance. This can include things like error messages, suggested changes, and suggestions for optimization.
The four parts of a system in mathematics are input, process, output, and feedback. Input is the data and instructions a system receives. Process is the manipulation of data and instructions to produce an output. Output is the result of the system's processing of the data and instructions. Feedback is information from the output that is used to improve the system's performance.
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(03.05 MC)
A moon's elliptical orbit around a planet is modeled by the equation 225x2 +576y2 = 176,400, where distance is measured in megameters
(Mm). If the planet is the center of the orbit's path, what is the maximum distance between the planet and its moon?
As, the moon has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm.
What is an elliptical orbit?
When an object moves around another object in an oval shaped path (ellipse), it is known to be revolving in an elliptical orbit.
The standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is given by
x²/a² + y²/b² = 1
Now,
Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.
Since the equation of the path is the equation of an ellipse, we write it in standard form
As standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is
x²/a² + y²/b² = 1 (1) where
a = vertex of major axis and
b = vertex of minor axis
So, converting 225x² + 576y² = 176,400 into standard form, we have
225x² + 576y² = 176,400
225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000
x²/7840 + y²/3062.5 = 1 (2)
Comparing equation (2) with (1), we have that
a² = 7840 and b² = 3062.5
⇒ a = √7840 = 88.54 and
⇒ b = √3062.5 = 55.34
Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm
So, the maximum distance between the planet and its moon is 88.54 Mm
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Since the moon's has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm
How to find the maximum distance between the planet and its moon?
Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.Since the equation of the path is the equation of an ellipse, we write it in standard form.Equation of ellipse in standard formThe standard form of the equation of an ellipse wth center at the origin (0,0) and x - axis major axis is given byx²/a² + y²/b² = 1 (1) where
a = vertex of major axis and
b = vertex of minor axis
o, converting 225x² + 576y² = 176,400 into standard form, we have
225x² + 576y² = 176,400
225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000
x²/7840 + y²/3062.5 = 1 (2)
Comparing equation (2) with (1), we have that
a² = 7840 and b² = 3062.5
⇒ a = √7840 = 88.54 and
⇒ b = √3062.5 = 55.34
Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm
So, the maximum distance between the planet and its moon is 88.54 Mm
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What is the slope of the line that contains the points (2, -8) and (-4, 4)?
2
1/2
-1/2
-2
Option D) The slope of the line that contains the points (2, -8) and (-4, 4) is -2
What is a slope ?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
Slope is give by 2 points on a line is [tex]\frac{y\x_{2}- y\x_{1} }{x_{2}-x_{1}}[/tex]
so the slope is
[tex]\frac{4 - (-8)}{-4 - 2} = \frac{12}{-6} = -2[/tex]
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Parallelogram AB'C'D' was obtained by dilating parallelogram ABCD using the center if dilation.
A. What was the scale factor of the dilation?
B. How many congruent copies of ABCD can fit inside of AB’C’D’?
C. If the original area was 12 square units, what is the dilated area of AB’C’D’?
Answer:
A) 2, B) 4, C) 48--------------------------------
Part AThe scale factor is 2, since each side is twice the initial length.
Part BThere are 4 congruent copies, as we can see on the picture.
Part CThe dilated area is 12*4 = 48 square units, since the area is the product of two dimensions, each dimension is twice the initial value therefore the area is 2*2 = 4 times greater.
let f be the function with derivative given by f'(x)=x^2-2/x. On which of the following intervals is f decreasing ?
A. (- [infinity], -1] only
B. (- [infinity], 0)
C. [- 1,0) only D. (0, ∛2]
E. (∛2, [infinity])
Therefore, the function f is decreasing on the interval (- [infinity], -1].
A. (- [infinity], -1] only
We can use the first derivative test to determine where a function is increasing or decreasing. The first derivative test states that if the derivative of a function is positive, then the function is increasing, and if the derivative is negative, then the function is decreasing.
For this problem, the derivative of the function f is f'(x) = x^2 - 2/x.
We can see that for x < 0, the derivative is negative, so the function is decreasing on that interval. For x > 0, the derivative is positive, so the function is increasing on that interval.
Therefore, the function f is decreasing on the interval (- [infinity], -1].
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i dont know the answer to this question Mark wants to eat one last cookie from the cookie jar. In the jar there are 5 chocolate chip cookies, 6 peanut butter cookies, and 9 oatmeal cookies. He will randomly select one cookie from the jar. What is the probability that Mark will NOT pick a peanut butter cookie?
so the sample space will be simply all the cookies in the jar, namely 5 + 6 + 9 = 20.
the probability that Mark will NOT pick a Peanut Butter one hmm, that means that Mark will pick either a Chocolate Chip or an Oatmeal one, now this is an OR case so that means sum. so what are the chances Mark will pick either one? P(Chocolate) + P(Oatmeal)
[tex]\stackrel{P(Chocolate)}{\cfrac{5 }{20}}~~ + ~~\stackrel{P(Oatmeal)}{\cfrac{9}{20}}\implies \cfrac{5+9}{20}\implies \cfrac{14}{20}\implies \cfrac{7}{10}\implies 0.7~\hfill \text{\LARGE 70\%}[/tex]
Solve for X, Leave in simplest radical
The value of x using trigonometry is √6.
What is trigonometry ?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.
The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.
In the triangle base = [tex]\sqrt{2}[/tex] and height as x
The value of the angle is [tex]60\x^{o}[/tex]
so tanθ = tan[tex]60\x^{o}[/tex]
[tex]\frac{height }{base} = tan60\x^{o} \\[/tex]
⇒ x = √3 * √2
⇒ x = √6
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