To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side and the equation become x + 3y = 9.
What is Equation?
An equation is a mathematical statement that shows the equality of two expressions or values. It typically contains one or more variables and an equal sign, which indicates that the expressions on either side of the equal sign have the same value. Equations can be used to represent various relationships between different mathematical objects and are used extensively in many fields of mathematics, science, engineering, and other disciplines. Equations can be solved to find the values of the variables that make the equation true, which is often the goal of many mathematical problems.
To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side.
Starting with:
y = (1/3)x + 3
We can multiply both sides by 3 to eliminate the fraction:
3y = x + 9
Now we can rearrange to get the x and y terms on the left side:
-x + 3y = 9
So the equation in Ax + By = C form is:
x + 3y = 9
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A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?
PE=mgh
67,456 J
330,534.4 J
1,159.8 J
661,068.8 J
Answer:
661,068.8j
Step-by-step explanation:
The car has 661068.8 J of potential energy at a height of 62 m having a mass of 1088 grams.
What is potential energy?Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.
We know, The gravitational constant is 9.8 m/s².
From the given information, m = 1088 grams, h = 62 meters.
Therefore, The amount of potential energy the car has is,
PE = mgh.
PE = 1088×9.8×62 J.
PE = 661068.8 J.
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100 POINTSSS WILL VOTE MOST BRAINLIEST
The table lists several points on a polar graph.
θ 0 pi over 6 pi over 3 pi over 2 2 pi over 3 5 pi over 6 π
r 4 2 −2 −4 −2 2 4
Which of the following graphs is represented by the table?
Answer:
r = 4 cos(2θ)
See the attached image for a graph.
Step-by-step explanation:
The points given by the table are in the graph of a cosine rose with 4 petals whose amplitudes are 4.
For the equation r = a cos(nθ), a is the amplitude of the petals (4), and n is half the number of petals, as there are an even number of petals (4/2 = 2).
Hence,
r = 4 cos(2θ)
High Tech Chip Company is expected to have EPS in the coming year of $2.50. The expected ROE is 12.5%. An appropriate required return on the stock is 11%. If the firm has a plowback ratio of 70%, the growth rate of dividends should be
On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.
The second telephone pole is 72 feet tall. Since the ratio of the height of the first telephone pole to the length of its shadow is 24/6 = 4.
We can use this ratio to find the height of the second telephone pole.
If the second telephone pole casts a shadow of 18 feet at the same time of day, we can set up the following proportion:
height of second pole / length of shadow of second pole = height of first pole / length of shadow of first pole
Letting x be the height of the second pole, we can plug in the values we know and solve for x:
x / 18 = 24 / 6
Multiplying both sides by 18, we get:
x = 72
Therefore, the second telephone pole is 72 feet tall.
The answer is (e) 72.
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Complete question:
On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.
a. 6
b. 12
c. 24
d. 36
e. 72
The area of a rectangular wall of a barn is 110 square feet. Its length is 12 feet longer than twice its width. Find the length and width of the wall of the barn.
width= =feet
The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.
What is the length and width of the wall of the barn?Area of the rectangular wall of a barn = 110 square feet
Width of the barn = w
Length of the barn= 2w + 12
Area of a rectangle = length × width
110 = (2w + 12) × w
110 = 2w² + 12w
equate to 0
2w² + 12w - 110 = 0
w² + 6w - 55 = 0
using factorization method of solving quadratic equation
w² + 11w - 5w - 55 = 0
w(w + 11) - 5(w + 11) = 0
(w - 5) (w + 11) = 0
w = 5 or w = -11
The width of the rectangular barn cannot be negative
Therefore,
Width of the barn = w
= 5 feet
Length of the barn= 2w + 12
= 2(5) + 12
= 10 + 12
= 22 feet
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ning Page
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
14 cm
?
8 cm
16 cm
11 cm
6 cm
The missing side length from the given figure is 6 ft.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the figure,
Missing side = x
Now,
The expression we can make from the figure.
= 16 - 10
= 6 ft
Thus,
The missing side length is 6 ft.
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What is 0.738 that add up to 1
Answer:
0.262
Step-by-step explanation:
1 - 0.738 = 0.262
0, 738 + 0.262 = 1
[tex]\frac{x+8}{3} =7\\[/tex]
Answer:
The solution is 13
Step-by-step explanation:
x+8/3 = 7
x+8 = 7×3
x+8 = 21
x = 21-8
x = 13
A car purchased for $9,000 depreciates at a constant rate of 16.5%. What will be the value of the car in 6 years.
The value in 6 years is $_____.
round answer to 2 decimal places
The value in 6 years is $3050.43
What is depreciation?The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life.
Using the formula:
Value = P(1-r)^n
From the question, the original value is $9,000, the depreciation rate is 16.5% or 0.165, and the time is 6 years. Plugging in the values:
Putting the values into the formula
Value = 9000(1-0.165)^6
Value = 3050.43
Hence, the value of the car after 6 years will be $3050.43
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hilary was examining the differences between perfect squares of numbers separated by 5. She made the following conjecture the differences always have the digit 5 in the ones place. for example: 17^2 - 12^2 = 289 -144 = 145
State another example that supports hilary's cpnjecture?
The another example that supports Hilary's conjecture are, 26² - 21²
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Given that,
Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.
Another example that supports Hilary's conjecture is:
= 26² - 21²
= 676 - 441
= 235
As we can see, the difference between the perfect squares of 26 and 21 is 235,
which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.
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Some candles are in the shape of a right circular cylinder. For one such candle, the radius is 9 cm and the height is 26.5 cm. Find the volume of the candle. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
radius = 9 cm
height = 26,5 cm
as we know that
volume of cylinder = πr^2h
= 3,14x9x9x2x26,5
= 13.480 cm cubic
pls help me with math i’ll give you brainlist
Answer:
choice C. y = -4/3x + 2
Step-by-step explanation:
slope of a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the first line.
m = -4/3 (negative reciprocal of 3/4)
Now use point-slope form to find the y-intercept (b):
y-2 = -4/3(x-0)
y = -4/3x + 2
Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
f is increasing on (-infty, -4) and (2,infty) since that's where you'd be walking uphill.
f is never decreasing.
f is constant on (-4,2), since that's where it's completely flat.
100 points!!!!!
Using the information for West Coast Entertainment Inc. presented in the table below, determine the following:
1. The number of shares bought and sold on this trading day.
2. Amount of income per share paid to a stockholder in the last 12 months.
3. Percentage of change in the stock's price since the beginning of the year.
Percentage of change in the stock's price since the beginning of the year is: 12.32%
What is stock's price?The price at which a stock's share is currently trading on the market is referred to as the stock price. Every publicly listed company issues its shares at a price, which is an estimation of their value that, ideally, corresponds to the worth of the firm itself.
The market forces of supply and demand govern a company's share price once it becomes public and its shares begin trading on a stock exchange. Price increases will occur if there is a large demand for its shares. A stock's price might be reduced by sellers if the company's prospects for future growth appear uncertain.
Given that,
Closing price today = $21.20
Closing price on the previous trading day= $28.83
Difference between closing price today and closing price on the previous trading day= $21.20 - $28.83
= $7.63
Percentage of change in the stock price since the beginning of the year
= Year-to-date % change
= 12.32%
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Help me with this question….
Answer:
A. 513 cubic units
Step-by-step explanation:
trust me bro.
You want to put a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.
How is the volume determined?The volume is the product of the multiplication of the thickness, length, and width.
The thickness of the topsoil = 6 inches
12 Inches = 1 Feet
6 inches = 0.5 Feet (6/12)
The length of the garden = 28 feet
The width of the garden = 17 feet
The thickness of the soil = 0.5 feet
Volume of the topsoil = 28 x 17 x 0.5
= 238 ft³
3 Feet to 1 Yard
238 ft³ = 238/3 yards
= 79.33 cubic yards
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Rob loves to run. He set a goal to run more than 390 miles this year.
To date, he has run 127 miles. If he begins to run 18 miles per week,
how long will it take Rob to reach his goal?
Write a two-step inequality, using the values provided in the problem,
that represents this situation. Use x as the variable.
The linear inequality to represent given situation will be 127+18x≥390 where x=no. of weeks and he will take 14.6 weeks to reach his goal.
What is a linear inequality, exactly?
In mathematics, an inequality is a mathematical statement that does not have equal sides. In mathematics, an inequality occurs when a connection results in a non-equal comparison of two expressions or two numbers. In the statement, any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), can be used to replace the equal sign "=". Inequalities are grouped into three forms in mathematics: polynomial inequalities, rational inequalities, and absolute value inequalities.
The symbols " <and >" represent severe disparities, whereas " ≤ and ≥ " represent slack inequalities. A linear inequality resembles a linear equation, but the formula is different.
Now,
Total miles to run=390 mile
He already ran=127 mile
Distance left to run=390-127
=263 mile
Rate of running=18 miles/ week
weeks taken to complete 263 miles=263/18
=14.6 weeks
and given situation can be represented by inequality 127+18x≥390 where x=no. of weeks.
Hence,
The linear inequality to represent given situation will be 127+18x≥390 and he will take 14.6 weeks to reach his goal.
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the instructions to mix a cool drink is to use concentrate and water in a ratio 2:9 how much water should be added to 500ml of concentrate
Answer:
2250ml
Step-by-step explanation:
The concentrate-to-water ratio is 2:9. This means 2ml of concentrate requires 9ml of water. We have 500ml of concentrate, which is 250 times more than 2ml, so to find the amount of water, we also multiply 9ml by 250:
2ml concentrate : 9ml water
(Multiply both sides by 250)
500ml concentrate : 2250ml water
The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019.
Answer: $9080.13
Step-by-step explanation:
use the equation y=b(x)^t, where b is the original profit, x is the percent remaining after one year, and t is the amount of years.
SUBSTITUTE:
y=9500(0.991)^5
Use calculator, and y=9080.126 in 2019. Round off to $9080.13
hope this helps!
MM
Which of the following complexe numbers is equal to (4 + 3i)(5 - 2i)?
20 + i
20+6i
26 + i^2
26 + 7i
Answer:
The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:
(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i
= 20 - 8i + 15i - 6i^2
= 20 + 7i - 6(-1)
= 26 + 7i
So the answer is (4) 26 + 7i.
I believe the answer is (d) 26 + 7i.
If 3250 was increased by 46%, the result would be
Answer: 4745
Step-by-step explanation:
3250 = 100%
Percent Increase = +46%
46% of 3250 = 1495
3250 (100%) + 1495 (46%) = 4745
2. Explain how to calculate 8% of 350 by first calculating 1% of 350. PLEASE HELP ASAP
Answer:
Step-by-step explanation:
To calculate 8% of 350, we can first calculate 1% of 350 and then multiply it by 8.
1% of 350 is equal to 0.01 times 350 which can be calculated as:
0.01 * 350 = 3.5
Since 1% of 350 is equal to 3.5, 8% of 350 can be calculated as follows:
8 * 3.5 = 28
So, 8% of 350 is equal to 28.
The upper arm length of males over 20 years old in the United States is approximately Normal with mean 39.1 cm and standard deviation 2.3 cm. Use the 68-95-99.7 rule.
a. What range of lengths covers the middle 99.7% of this distribution?
b. What percent of men 20 have upper arm lengths greater than 41.4cm?
A rectangular pool has an area of 640 square feet. The length is 12 feet shorter than the width. The length of the pool is response area feet and the width of the pool is response area feet.
Let's assume the width of the rectangular pool is w. According to the problem, the length of the pool is 12 feet shorter than the width, so the length can be represented as w - 12.
The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. We know that the area of the pool is 640 square feet, so we can set up the equation:
A = L x W
640 = (w - 12) x w
Simplifying the equation:
640 = [tex]w^{2}[/tex] - 12w
[tex]w^{2}[/tex] - 12w - 640 = 0
We can solve for w by using the quadratic formula:
w = [-(-12) ± [tex]\sqrt{-12}^{2}[/tex]- 4(1)(-640))] / (2 x 1)
w = [12 ± [tex]\sqrt{(12^{2}+2560)[/tex]] / 2
w = [12 ± [tex]\sqrt{2596}[/tex]] / 2
w = [12 ± 51] / 2
We can ignore the negative solution, so:
w = (12 + 51) / 2
w = 31.5
Therefore, the width of the pool is 31.5 feet. We can use this value to find the length:
L = w - 12
L = 31.5 - 12
L = 19.5
Therefore, the length of the pool is 19.5 feet.
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If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a (normal, uniform, skewed, or bimodal) distribution?
If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a (normal, uniform, skewed, or bimodal) distribution?
Answer:
Step-by-step explanation:
If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a normal distribution.
If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a normal distribution. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution.
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that, as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution. This means that even if the original population distribution is skewed, bimodal, or any other shape, the distribution of the sample means will tend towards a normal distribution as the sample size increases.
The reason for this is that the sample means are essentially an average of a number of independent random variables, and the normal distribution is the result of the combination of many independent random variables. When the sample size is large, the distribution of the sample means becomes very close to a normal distribution, even if the underlying population is far from normal.
In the case of a bimodal distribution, the sample means will still approach a normal distribution as the sample size increases, but the distribution may have a different mean and standard deviation than the original population.
In the case of a very skewed distribution, the sample means will also approach a normal distribution as the sample size increases, but the distribution may still be skewed, just less so than the original population.
In conclusion, the Central Limit Theorem states that the distribution of the sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.
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5-D rocess The perimeter of a rectangle is 60 meters. The length of the rectangle is 3 more than twice the width. What is the length and width of the rectangle?
Answer:
Width: [tex]9[/tex] Length: [tex]21.[/tex]
Step-by-step explanation:
Let's say [tex]l[/tex] is the length, and [tex]w[/tex] is the width. We can rewrite [tex]l[/tex] as [tex]2w + 3.[/tex] So [tex]2(2w + 3) + 2w = 60,\\4w + 6 + 2w = 60,\\6w + 6 = 60,\\6w = 54,\\w = 9.\\[/tex]So the length of the rectangle is [tex]2 \cdot 9 + 3 = 21[/tex] and the width is [tex]9.[/tex]
Hope that helps!
Given JK LM LM L IS THE MIDPOINT OF JN PROBE JKLNLNM
The required proof has been below that ΔJKL ≅ ΔLMN due to the SAS postulate.
What are Similar Triangles?Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
The triangles are given in the question, as shown.
As per the given figure, we have
JK = LM
∠LJK ≅ ∠NLM (same side inner angles)
Since L is the midpoint of JN. (Definition of midpoint)
Then JL ≅ LN
Now, for triangles ΔJKL and ΔLMN
JK ≅ LM (sides)
∠LJK ≅ ∠NLM (angle)
JL ≅ LN (sides)
By SAS postulate, ΔJKL ≅ ΔLMN.
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Identify the y- intercept of the graph below
b= -4
b=6
b=4
b= -10
Alex jogs for 15 minutes at an average speed of 4 mph. He then walks at an average speed of 2.4 mph
for minutes. The total distance traveled is 1.4 miles.
(a) Convert 15 minutes and r minutes to hours.
(b) Form an equation in terms of t and solve it.
(c) Hence, calculate Alex's average speed for the whole journey.
(a) Conversion of 15 minutes and r minutes into hours, 0.25 hours & r/60 hours.
(b) An equation in terms of t and solution of it, S = 0.04r miles and r = 10
(c) Alex's average speed for the whole journey is, 3.33 mph
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
(a) 15 minutes is equal to 0.25 hours (15/60) and r minutes is equal to r/60 hours.
(b) Let's use the formula:
distance = speed x time for both jogging and walking.
Distance traveled while jogging = 4 mph x 0.25 hours
= 1 mile
Distance traveled while walking = 2.4 mph x (r/60) hours
= 0.04r miles
Total distance traveled = 1 mile + 0.04r miles
= 1.4 miles
Solving for r, we get:
0.04r = 0.4
r = 10
So, Alex walked for 10 minutes.
(c) Total time taken = 15 minutes + 10 minutes
= 25 minutes
= 0.42 hours
Total distance traveled = 1.4 miles
Average speed = Total distance / Total time
= 1.4 miles / 0.42 hours
= 3.33 mph (rounded to two decimal places).
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Choose the answer that is equal to the expression below.
5^2.5^0
Answer:
5
Step-by-step explanation:
The expression 5^2.5^0 is equal to 5^(2.5^0), which can be simplified as follows:
2.5^0 = 1 (because any number raised to the power of 0 is equal to 1)
So, 5^2.5^0 = 5^1 = 5
Therefore, the answer is 5.
