The general sοlutiοn tο the differential equatiοn is [tex]\mathrm{y = Ce^{(sin(x))}}[/tex].
Describe Differentiatiοn?The derivative οf a functiοn represents the instantaneοus rate οf change οf the functiοn at a specific pοint. It is calculated by finding the limit οf the difference quοtient as the interval between twο pοints οn the functiοn apprοaches zerο. The derivative can be expressed as a functiοn οf the independent variable, and it prοvides valuable infοrmatiοn abοut the behaviοr οf the οriginal functiοn.
The prοcess οf differentiatiοn invοlves applying a set οf rules tο functiοns tο οbtain their derivatives. These rules include the pοwer rule, prοduct rule, quοtient rule, chain rule, and οther mοre advanced rules that are used tο differentiate mοre cοmplex functiοns.
Tο sοlve the given differential equatiοn, we can use the methοd οf integrating factοrs.
First, we can rewrite the equatiοn as:
y'cοsx = ysinx + sin(175x)
Next, we can multiply bοth sides by the integrating factοr, which is [tex]e^{(\int(cos(x) dx))} = e^{(\sin(x) + C)}[/tex], where C is a cοnstant οf integratiοn:
[tex]\mathrm {e^{(sin(x)) }y'cosx = e^{(sin(x))} ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}[/tex]
Nοw, we can recοgnize the left-hand side as the derivative οf [tex]e^{(sin(x))}y[/tex]:
[tex](e^{(sin(x))y)}' = e^{(sin(x))} y' + cos(x) e^{(sin(x))}y[/tex]
Substituting this intο the abοve equatiοn, we get:
[tex]\mathrm{(e^{(sin(x))y)}' = e^{(sin(x)) }ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}[/tex]
[tex]cos(x) e^{(sin(x))}y = e^{(sin(x))y)}'[/tex]
Separating variables and integrating bοth sides, we get:
[tex]\int e^{sin(x) }dy/y = \int cos(x) dx[/tex]
ln|y| + C = sin(x) + C'
where C' is anοther cοnstant οf integratiοn.
Therefοre, the general sοlutiοn tο the differential equatiοn is:
[tex]\mathrm{|y| = e^{(sin(x)) }e^{(C' - sin(x))}}[/tex]
[tex]\mathrm{y = \± e^{(C' - sin(x) + sin(x))}}[/tex]
[tex]\mathrm{y = Ce^{(sin(x))}}[/tex]
where C is an arbitrary cοnstant.
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There are 24 people running in a race. 1/4 are wearing green shorts. 1/6 are wearing red shorts. The rest are wearing blue shorts. How many people are wearing blue shorts?
Use a tape diagram to help you answer the question.
Solve. Show or explain your work.
Answer:
First, let's find the fraction of people wearing green or red shorts:
1/4 + 1/6 = 3/12 + 2/12 = 5/12
This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):
1 - 5/12 = 7/12
So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:
7/12 x 24 = 14
Therefore, 14 people are wearing blue shorts.
Step-by-step explanation:
Answer:
To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.
Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:
4 parts + 6 parts + B parts = 24
Simplifying this equation, we get:
10 + B = 24
Subtracting 10 from both sides, we get:
B = 14
Therefore, 14 people are wearing blue shorts.
To double-check our answer, we can add up the number of people in each category:
4 parts out of 24 = 6 people wearing green shorts
6 parts out of 24 = 4 people wearing red shorts
B parts out of 24 = 14 people wearing blue shorts
6 + 4 + 14 = 24, which matches the total number of people in the race.
Can you please give me the answers of the following questions on the attached files
a) The 8 in the number 24.387 is in the hundredths place, its value is 8/100 or 2/25.
b) One and three quarter million can be written in figures as 1,750,000.
c) 2/10 or 1/5.
d) 0.26 < 0.62 < 2.06 < 6.2
e) 13.4 > 13.390.33 = 1/38 = 2³
What is the inequality equation?An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
a) The 8 in the number 24.387 is in the hundredths place.
Therefore, its value is 8/100 or 2/25.
b) One and three quarter million can be written in figures as 1,750,000.
c) The 2 in the number 48.52 is in the tenths place.
Therefore, its value is 2/10 or 1/5.
d) Ordering the numbers from smallest to largest:
0.26 < 0.62 < 2.06 < 6.2
e) Completing the statements using the symbols <, > or = :
13.4 > 13.390.33 = 1/38 = 2³
Hence, The answers to each question are:
a) 8/100 or 2/25.
b) 1,750,000.
c) 2/10 or 1/5.
d) 0.26 < 0.62 < 2.06 < 6.2
e) 13.4 > 13.390.33 = 1/38 = 2³
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What is the constant of proportionality between y yy and x xx in the graph? 2 2 4 4 6 6 8 8 2 2 4 4 6 6 8 8 y y x x Constant of proportionality = =equals Stuck?Review related articles/videos or use a hint. Report a problem Start over 3 of 4 Check
The answer of the given question based on the constant of proportionality the answer is constant of proportionality equal to 1.
What is Slope?Slope is measure of steepness of a line. It describes how much vertical coordinate (y) changes for given change in horizontal coordinate (x). In other words, it is rate at which line rises or falls as you move horizontally along it
To find the constant of proportionality between y and x, we need to calculate the slope of this line.
We can choose any two points on the line and use them to calculate the slope. Let's choose the points (2, 2) and (8, 8), which are the first and last points on the line. The slope of the line passing through these points is:
slope = (change in y)/(change in x) = (8 - 2)/(8 - 2) = 1
This means that for every increase of 1 in the x-coordinate, there is a corresponding increase of 1 in the y-coordinate. Therefore, the constant of proportionality between y and x is 1. We can write this as:
y = x
This means that y is directly proportional to x with a constant of proportionality equal to 1.
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Delia hiked 7/10 mile one day and 67/100 the next she wanted to know how far she hiked in all her work is shown below
Delia hikes [tex]\tfrac{137}{100}[/tex] in all her wοrk, we get this answer by adding his first day hike and next day hike.
What is wοrk?Wοrk can be defined as tο achieve the purpοse, gοal οr result we use οur physical οr mental effοrt during the activity.
Their are mainly twο types οf wοrk οne is physical wοrk and οther is mental wοrk. Physical wοrk is sοmetime alsο refer as labοur wοrk and mental wοrk is usually denοtes as οffice wοrk.
Wοrk (W) = F * s
W = Wοrk, F = Fοrce And s = Displacement
Tοtal wοrk dοne by him = 7/10 + 67/100
[tex]\tfrac{137}{100}[/tex]
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Adrian and Bryan both worked a total of 88 hours in a week. Bryan worked 8 hours more than Adrian. Find the number of hours each man had worked. Enter the correct answers in the boxes. Adrian: h Bryan: h
Answer:
Let's assume Adrian worked for x hours. Then, Bryan worked for (x + 8) hours.
According to the problem, the total hours worked by both is 88, so we can set up the equation:
x + (x + 8) = 88
Simplifying the equation:
2x + 8 = 88
Subtracting 8 from both sides:
2x = 80
Dividing both sides by 2:
x = 40
So Adrian worked for 40 hours and Bryan worked for 48 hours (since Bryan worked 8 hours more than Adrian).
Answer:
Adrian: 40 hours
Bryan: 48 hours
Step-by-step explanation:
Jason and Piera decide to start a college savings account for their newborn son, Joseph. They want to have $40,000 available for him when he is 18, and they expect the account to have an average return of 7%. How much do they need to deposit each month to reach this goal?
Round answer to 2 decimal places.
Answer:
Step-by-step explanation:
What is correct regarding a
normal distribution?
The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.
What is Normal Distribution ?
A normal distribution is a continuous probability distribution that is often used in statistics to model a wide variety of phenomena, such as measurements of height, weight, or IQ.
The normal distribution is symmetric. This means that the distribution is mirror-image symmetric around its mean, so that the same proportion of values lie on either side of the mean.
The normal distribution is characterized by two parameters: its mean (μ) and standard deviation (σ). The mean is the center of the distribution, while the standard deviation measures the spread of the distribution.
The total area under the normal distribution curve is equal to 1. This means that the probability of any event occurring is between 0 and 1.
The empirical rule, also known as the 68-95-99.7 rule, applies to normal distributions. This rule states that approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean.
Therefore, The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.
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In a series of high jumps, Megan cleared 5'6" for 80% of her jumps. She wants to create a model for the probability of jumps cleared at 5'6". What is a
hypothesis Megan could make?
A. Megan will clear 5'6" for 100% of her jumps.
B. Megan will clear 5'4" for 100% of her jumps.
C. Megan will clear 56* on 80% or more of her jumps.
D. Megan will clear 5'8" on 80% or more of her jumps.
The best hypothesis based on the given information is Option C: Megan will clear 5'6" on 80% or more of her jumps.
What is hypothesis?A hypothesis is an educated guess or tentative explanation for a phenomenon or observation that can be tested through further investigation and experimentation. It is a proposed explanation or prediction for an event or set of events that is based on limited evidence or observations, and which serves as the starting point for scientific inquiry.
According to question:Based on the given information, Megan cleared 5'6" for 80% of her jumps. To create a hypothesis for the probability of future jumps cleared at 5'6", we need to make an educated guess based on this data.
Option A, stating that Megan will clear 5'6" for 100% of her jumps, is too optimistic and doesn't take into account the possibility of error or difficulty in jumping.
Option B, stating that Megan will clear 5'4" for 100% of her jumps, is not relevant to the given information about Megan's performance at 5'6".
Option D, stating that Megan will clear 5'8" on 80% or more of her jumps, is also not supported by the given information and is too high of a goal for Megan to realistically achieve.
Therefore, the best hypothesis based on the given information is Option C: Megan will clear 5'6" on 80% or more of her jumps. This hypothesis is supported by the fact that Megan has already achieved this level of performance in the past, and it allows for the possibility of some variability or error in future jumps.
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the distance between (3, -6) and (3, -10)
Answer:
4 units
Step-by-step explanation:
Since the x-value is the same in both ordered pairs, you can just figure out the y-step ([tex]y_{2} -y_{1}[/tex]) and get your distance. -10 - (-6) = -4, so a distance of 4 units (negative sign does not matter in this case).
If both the x-values and y-values were different, another way to solve is to figure out the y- and x-steps and plug them into the Pythagoras theorem [tex]A^2+B^2 = C^2[/tex], with A being the horizontal distance (x-step) and B being the vertical distance (y-step).
You can also find the distance between 2 points by using the distance formula, which is [tex]d = \sqrt{(x_{2}-x_{1})^{2} - (y_{2}-y_{1})^{2}[/tex]. After inserting the x- and y-coordinates of your ordered pair you get [tex]d = \sqrt{(3-3)^{2} - (-10-(-6))^{2}[/tex]
Simplifying:
[tex]d = \sqrt{- (-10-(-6))^{2}}[/tex]. [tex](3-3)^{2}[/tex] was eliminated.
Then we distribute the negative signs: [tex]d = \sqrt{- (-10+6)^{2}}[/tex] --> [tex]d = \sqrt{(10-6)^{2}}[/tex].
[tex]d = \sqrt{(4)^{2}}[/tex] --> [tex]d = \sqrt{16}[/tex] --> [tex]d = 4[/tex]
So, the distance between the points is 4 units.
Side note: The distance formula works in the same way as the Pythagoras theorem.
This scatter plot shows Marie's best 200 meter times each week after she began training. The equation represents the linear model for this data. y=−0.4x+29.8 According to the model, what will Marie's lowest time be after 14 weeks? Enter your exact answer in the box.
Answer:
So the answer is 24.2
Step-by-step explanation:
Good luck to you!
according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.
What is a linear equation?
Based on the given linear model, we know that Marie's best 200 meter time (y) is a function of the number of weeks of training (x), and can be calculated using the equation:
y = -0.4x + 29.8
To find Marie's lowest time after 14 weeks, we simply need to substitute x = 14 into the equation and solve for y:
y = -0.4(14) + 29.8
y = -5.6 + 29.8
y = 24.2
Therefore, according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.
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need help with these two when somebody can do so, thanks.
Answer:
1. 92 m²
2. 184 cm²
Step-by-step explanation:
1.
Look at the left triangle.
Imagine that the 8 m segment continues to the bottom, and you have a horizontal leg there.
The hypotenuse measures 15 m.
The vertical leg is 8 m + 4 m = 12 m.
a² + b² = c²
12² + b² = 225
b = 9
The horizontal leg is 12 m.
A = 2 × 12 m × 9 m / 2 - 4 m × 4 m
A = 92 m²
2.
Bottom rectangle: length = 20 cm; width = 7 cm
Upper trapezoid: bottom base = 20 cm - 13 cm = 7 cm; height = 15 cm - 7 cm = 8 cm; upper base = 4 cm
A = 20 cm × 7 cm + (1/2)(7 cm + 4 cm)(8 cm)
A = 184 cm²
Please help. ASAP!!!!!
Answer:
½(a+b)h
½(24+32)×18
504ft²
I might be wrong
A company’s employees are 40% male and 60% female. Of the male employees, 15% of them have advanced degrees and 20% of the female employees have advanced degrees.
Part A
Let c represent the total number of employees in the company. Which expression represents the number of employees in the company who have advanced degrees?
Responses
0.15c+0.20c 0 point 1 5 c plus 0 point 2 0 c
0.40c(0.15)+0.60c(0.20) 0 point 4 0 c 0 point 1 5 plus 0 point 6 0 c 0 point 2 0
(0.40c−0.15)+(0.60c−0.20) open paren 0 point 4 0 c minus 0 point 1 5 close paren plus open paren 0 point 6 0 c minus 0 point 2 0 close paren
(0.40+0.15)c+(0.60+0.20)c open paren 0 point 4 0 plus 0 point 1 5 close paren times c plus open paren 0 point 6 0 plus 0 point 2 0 close paren times c
Question 2
Part B
What percent of the company has advanced degrees?
The company's advanced degree holders make up 18% of the workforce.
A percentage is what?A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.
Part A:
The following expression sums up the amount of company employees with advanced degrees:
0.40c(0.15) + 0.60c(0.20)
Explanation: First, we multiply the overall amount of workers (c) by the proportions of male and female employees, which are, respectively, 40% and 60%. The number of male workers (0.40c) is then multiplied by the percentage of men who have advanced degrees (15%), and the number for female employees (0.60c) is multiplied by the percentage of women who have advanced degrees (20%). In order to calculate the overall number of workers with advanced degrees, we must add these two numbers.
If we condense this phrase, we get:
0.06c + 0.12c = 0.18c
Part B:
The number of staff members with advanced degrees must be divided by the total amount of employees, and the result must be multiplied by 100% to determine the percentage of the business that holds advanced degrees:
(0.18c/c) × 100% = 18%
Therefore, 18% of the company has advanced degrees.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0 Mark this and return
Answer:
Listed below.
Step-by-step explanation:
(Let y be the length of the room and x be the width of the room.)
Because the width of the room is 5 feet less than the length of the room, we have:
x = y - 5.The area of the room can be solved by multiplying its length and width, so we have x × y or xy = 750.
Substituting x for y - 5 into this equation:
y (y - 5) = 750.If we expand the left side of the equation, we get:
[tex]y^{2}[/tex] - 5y = 750Subtracting 750 from both sides, we get:
[tex]y^{2}[/tex] - 5y - 750 = 0The equation [tex]y^{2}[/tex] - 5y - 750 = 0 can be factored into:
(y + 25) (y - 30) = 0Therefore, 3 equations you can use are:
y (y - 5) = 750[tex]y^{2}[/tex] - 5y - 750 = 0(y + 25) (y - 30) = 0IRAs. You have $500,000 in your IRA (Individual Retirement Account) by the time you retire. You choose to invest this money in two funds: Fund A pays 5.2%/year and Fund B pays 7.7%/year. How should you divide your money between Fund A and Fund B to get an annual return of $34000?
Using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The amount in the IRA account = $500,000
Let the amount invested in fund A be x and fund B be y.
x + y = 500,000
The amount received annually for fund A = 0.052x
The amount received annually for fund B = 0.077y
This amount is given as:
0.052x + 0.077y = 34,000
Now we have a system of equations.
x + y = 500,000
0.052x + 0.077y = 34,000
Multiply the first equation by 0.052.
0.052x + 0.052y = 26,000
0.052x + 0.077y = 34,000
Subtracting,
-0.025y = -8000
y = 320,000
Then, x = 500,000 - y = 500,000 - 320,000 = 180,000
Therefore using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.
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work out the help of the f/f data of company balabce sheet.inventary turnover -6,capitalturnover 9costof good sold)-2,fixed assets turnover (cost of good sold)-4,gross profit-20%,recievables collection period-2 month,account payble payement period-73 days, gross profit 60000 ,the closing stock was 5000 inexcess of the opening stock
A balance sheet is a financial statement that presents a company's financial position at a specific point in time. It shows the company's assets, liabilities, and equity.
What are the steps for the balance sheet?Here are the steps to compute a balance sheet:
List all the assets: Assets are what the company owns, and they can be classified as current assets or long-term assets. Current assets include cash, accounts receivable, inventory, and prepaid expenses. Long-term assets include property, plant, and equipment, investments, and intangible assets.
Calculate the total value of assets: Add up the value of all the assets listed in step 1.
List all the liabilities: Liabilities are what the company owes to others and can be classified as current liabilities or long-term liabilities. Current liabilities include accounts payable, short-term loans, and accrued expenses. Long-term liabilities include long-term loans and bonds.
Calculate the total value of liabilities: Add up the value of all the liabilities listed in step 3.
Calculate equity: Equity is the difference between the assets and liabilities. It can be calculated as Total Assets minus Total Liabilities.
List equity: Write down the equity value calculated in step 5.
Add up the total liabilities and equity: This should be equal to the total assets calculated in step 2.
The balance sheet formula is:
Assets = Liabilities + Equity
By following the above steps, you can compute a balance sheet for a company. It is important to note that the balance sheet is a snapshot of the company's financial position at a specific point in time and should be updated regularly.
P.S: An overview was given due to your incomplete information.
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A certain distance is covered in 3 hours at an average speed of 120km/h how long will it take to cover the same distance at an average speed of 90km/h
Therefore , the solution of the given problem of speed comes out to be it will take 4 hours to travel the same distance at an average speed of 90 km/h.
What is speed?We can determine something's speed by keeping a watch on it from a distance. The amount of distance an object can move in a specific amount of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most popular pace measurements are miles per hour (mile), kilometres per hour (kilometres), and metres for each second (m/s) (mph).
Here,
Applying the algorithm
Distance is determined by multiplying time and motion.
We can make the two equations equal because we know that the distance travelled in both scenarios is the same:
Distance = time + speed1
1 = time2 + speed2
where time1 is the first time (3 hours), speed1 is the first average speed (120 km/h), speed2 is the second average speed (90 km/h), and we're trying to determine time2.
Inputting the numbers provided yields:
Distance: 360 km at 120 km/h for three hours.
We can now determine the time2:
360 kilometres are equal to 90 kilometres per hour multiplied by two.
time2 = 360 km x 90 km/hr = 4 hours
Therefore, it will take 4 hours to travel the same distance at an average speed of 90 km/h.
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Solve for the value of q
Answer:
-3
Step-by-step explanation:
i hope thisis the right aswrr
GIVEN That the Matrix(2 1 )
(3 4)
the Matrix K²+k+ I where I is a 2x2 Identity matrix
Now we can add K² to k + I to get the final result: K² + k + I = (4 3) + (3 1) + (1 0) = (8 4) (8 15) (3 5).
What is matrix?A matrix is a rectangular array of numbers or other mathematical objects, such as symbols or expressions, arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent and manipulate data.
Given by the question.
To find the matrix K²+k+I, we need to first find the matrix K.
The matrix K is the given matrix:
K = (2 1)
(3 4)
To find K², we can simply multiply K by itself:
K² = K × K = (2 1) × (2 1) = (4 3)
(3 4) (8 15)
To find k + I, we need to add the identity matrix I to K:
k + I = K + I = (2 1) + (1 0) = (3 1)
(3 4) (0 1) (3 5)
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A woman wants to measure the height of a nearby tower. She places a 7 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by
the shadow of the tower. The total length of the tower's shadow is 188 ft, and the pole casts a shadow that is 3.75 ft long. How tall is the tower? Round your
answer to the nearest foot. (The figure is not drawn to scale.)
Sun
Tower
Pole
Shadow of pole"
Shadow of tower
Ú
ft
X
The height of the tower obtained from the 188 ft long tower's shadow, the 3.75 ft long pole's shadow, the 7 ft height of the pole, and the equivalent ratio of the corresponding sides of similar triangles is about 351 feet
What are similar triangles?Similar triangles are triangles that have the same shape but may have different sizes.
Height of the pole = 7 ft
Length of the shadow cast by the tower = 188 ft
Length of the shadow cast by the pole = 3.75 ft
The triangle formed by the length of the shadows of the tower and the pole the tower and the pole and the line of sight from the tip of the shadow to the top of the tower and the pole are similar triangles, therefore, the ratio of the corresponding sides are the same, which indicates;
[tex]\frac{3.75}{188} = \frac{7}{Height \ of \ the \ tower}[/tex]
Height of the tower × 3.75 = 7 × 188
The height of the tower = 7 × 188/3.75 ≈ 351
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 4
4
6
12
17
Car sales, y (in hundreds)
2
5
8
9
The linear regression equation for the data given in the table is presented as follows:
y = 0.51x + 1.07.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.
The points for the data-set in this problem are given as follows:
(4,2), (6, 5), (12, 8), (17,9).
Inserting these four points into a linear regression calculator, the linear regression equation for the data given in the table is presented as follows:
y = 0.51x + 1.07.
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can you help me?3 2/5+ _____= 4?
Answer: 0.6
Step-by-step explanation:
3 2/5 + 0.6 = 4
this side lengths of a tringal are 6,8.10. is this a right triangle
Answer:
yes
Step-by-step explanation:
It is a Pythagorean triangle 3-4-5
Hope this helps.
Antonio is wrapping a birthday gift for his brother. He starts with 2 meters of ribbon. Then, he cuts off 27 centimeters to decorate the gift. How many centimeters of ribbon does he have left now?
Answer: 173 centimeters of ribbon left
Step-by-step explanation:
Antonio starts with 2 meters of ribbon, which is equal to 200 centimeters (since 1 meter = 100 centimeters). He cuts off 27 centimeters to decorate the gift, so he is left with:
200 - 27 = 173 centimeters
Therefore, Antonio has 173 centimeters of ribbon left.
Quadralateral ABCD is a rectangle. BE = 2x+1 and AC 6x -12. What is BE
Answer:
BE=15
Step-by-step explanation:
Since E is the center, BE=2x+1
And AC is 6x-12 with E being a midpoint.
Since AC is 2 segments and BE is only 1 then you multiply 2x+1 by 2 so that
you can find x. You multiply 2x+12 by 2 because E is the midpoint so that means ED is the same value as BE
6x-12=4x+2
BD=AC
6x-4x-12=2
2x=2+12
2x=14
x=7
BE= 2x+1
2(7)=14+1=15
8y³+10y²-63y÷2y+7
give me ans quickly
Step-by-step explanation:
you can simply solve this question by simple division
For the functions f(x)=2x−2 and g(x)=6x2−3, find (g∘f)(x).
Answer: To find (g∘f)(x), we need to first find the composite function g(f(x)):
g(f(x)) = g(2x - 2)
We can now substitute the expression for f(x) into g(x):
g(f(x)) = g(2x - 2) = 6(2x - 2)^2 - 3
Expanding the squared term, we get:
g(f(x)) = 6(4x^2 - 8x + 4) - 3
Simplifying and combining like terms, we get:
g(f(x)) = 24x^2 - 48x + 21
Therefore, (g∘f)(x) = 24x^2 - 48x + 21.
Step-by-step explanation:
calculate the following using the column method to 3045 - 2572
The subtraction of 3045 and 2572 by the column method has the result given as follows:
473.
How to obtain the subtraction using the column method?When we subtract two amounts by the column method, we subtract digit by digit separately, hence:
3045
-2572
5 > 2, hence:
5 - 2 = 3.
4 is less than 7, and 0 is also less than 5, hence we must borrow from the last column, where 2 - 2 will be of zero, hence:
14 - 7 = 7.9 - 5 = 4. -> one was borrowed to the 4 - 7 subtraction.Hence the result of the subtraction is given as follows:
3045 - 2572 = 473.
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What is 14 1/3- 6 5/8
Answer: To subtract mixed numbers with different denominators, we need to convert them into like fractions first.
14 1/3 can be converted to an improper fraction as follows:
14 1/3 = (14 x 3 + 1) / 3 = 43/3
6 5/8 can be converted to an improper fraction as follows:
6 5/8 = (6 x 8 + 5) / 8 = 53/8
Now we can subtract the fractions:
43/3 - 53/8
To get a common denominator, we can multiply the denominators together: 3 x 8 = 24
43/3 x 8/8 = 344/24
53/8 x 3/3 = 159/24
Now we can subtract the numerators:
344/24 - 159/24 = 185/24
Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 13/24 as a mixed number in simplest form.
Step-by-step explanation:
The simplified value of 14 1/3- 6 5/8 is 7 17/24.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
To subtract 6 5/8 from 14 1/3, we need to have the same denominator.
Converting the mixed numbers to improper fractions, we get:
14 1/3 = 43/3
6 5/8 = 53/8
Now, we need to find a common denominator, which is 24.
Multiplying the numerator and denominator of 43/3 by 8 and 53/8 by 3, we get:
43/3 * 8/8 = 344/24
53/8 * 3/3 = 159/24
Now, we can subtract:
43/3 - 53/8 = (344/24) - (159/24) = 185/24
Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 17/24 as a mixed number.
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pls help i am having a panic attack
The value of cos(2x+y) is -12/65.
Describe cosine ?Cosine, commonly denoted as cos, is a mathematical function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In other words, it is the ratio of the length of the adjacent side of an angle to the hypotenuse of the right triangle containing that angle. Cosine is one of the basic trigonometric functions, along with sine and tangent, and is widely used in mathematics, physics, and engineering to model various phenomena.
Cosine is periodic with a period of 2π, and its values range from -1 to 1. When the angle is 0°, the cosine is equal to 1, indicating that the adjacent side of the triangle is equal to the hypotenuse.
We can use the trigonometric identities for cosine to find cos(2x+y), using the values of x and y given:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
To find cos(2x), we can use the double angle identity for cosine:
cos(2x) = cos²(x) - sin²(x)
To find cos(x) and sin(x), we can use the fact that x = sin⁻¹(4/5) and the Pythagorean theorem:
sin(x) = 4/5
cos(x) = √(1 - sin²(x)) = √(1 - 16/25) = 3/5
Substituting these values into the double angle identity, we get:
cos(2x) = cos²(x) - sin²(x) = (3/5)² - (4/5)² = -7/25
To find sin(2x), we can use the double angle identity for sine:
sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5) = 24/25
To find cos(y) and sin(y), we can use the fact that y = tan⁻¹(12/5) and the Pythagorean theorem:
sin(y) = 12/13
cos(y) = 5/13
Substituting these values into the expression for cos(2x+y), we get:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
= (-7/25)(5/13) - (24/25)(12/13)
= -60/325
= -12/65
Therefore, cos(2x+y) = -12/65.
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