It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:
$8000 = $5400e^(0.07t)
Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:
ln(8000/5400) = 0.07t
Simplifying the left side of the equation, we get:
ln(4/3) = 0.07t
Solving for t, we get:
t = ln(4/3)/0.07 ≈ 7.62 years
Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
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A cable hangs between two poles 12 yards apart. The cable forms a catenary that can be modeled
by the equation y = 12 cosh(x/12) - 5 between x =- 6 and x = 6. Find the area under the
12 catenary.
Round your answer to four decimal places.
The area under the catenary between the two poles is approximately 51.3224 square yards.
To find the area under the catenary between two poles 12 yards apart, with the equation y = 12cosh(x/12) - 5 between x = -6 and x = 6.
We can find the area by using integration.
The equation for the catenary.
y = 12cosh(x/12) - 5
Set up the integral to find the area under the curve between x = -6 and x = 6.
Area = ∫ (-6 to 6)[12cosh(x/12) - 5]dx
Integrate the function with respect to x.
Since we are dealing with the hyperbolic cosine function, we know that the integral of cosh(x/12) is 12sinh(x/12).
Therefore, the integral becomes:
Area = [12 (12sinh(x/12)) - 5x] evaluated from -6 to 6
Evaluate the integral at the bounds.
At x = 6: 12 (12sinh(6/12)) - 5(6) = 12 (12sinh(0.5)) - 30
At x = -6: 12 (12sinh(-6/12)) - 5(-6) = 12 (12sinh(-0.5)) + 30
Subtract the lower bound result from the upper bound result.
Area = [12(12sinh(0.5)) - 30] - [12(12sinh(-0.5)) + 30]
Calculate the numerical values and round to four decimal places.
Area = 51.3224
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Pls help me with this! Will give points!
Answer:
Subtract 1 from both sides.
Answer:
subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16
Sketch the region enclosed by x + y² = 2 and x + y = 0. Decide whether to integrate with respect to x or y, and then find the area of the region. The area is ...
The area of the region enclosed by x + y² = 2 and x + y = 0 is 4/3 + 4√2/3 square units.
How to find limits of integration?To find the limits of integration, we need to solve for the intersection points of the two curves.
x + y² = 2x + y = 0Substituting x = -y from the second equation into the first equation, we get:
(-y) + y² = 2y² - y + 2 = 0Using the quadratic formula, we get:
y = [1 ± √(1 - 8)]/2y = [1 ± i√7]/2Since we're dealing with a real-valued area, we can discard the complex solution. The two intersection points are:
(-1 - √2, 1 + √2)(-1 + √2, 1 - √2)We can see from the graph below that the region we're interested in is the one enclosed by the curves, which lies to the left of the y-axis.
The limits of integration for the area are y = 0 (the x-axis) and y = 1 + √2.
Since the curves intersect at right angles, we can integrate with respect to either x or y. However, since the region is easier to express in terms of y, we'll integrate with respect to y.
The equation for the curve x + y² = 2 can be rearranged as:
x = 2 - y²The area of the region is given by:
A = ∫[0, 1+√2] (2 - y²) dyA = 2y - (1/3)y³ |[0, 1+√2]A = 2(1+√2) - (1/3)(1+√2)³ - 0A = 2(1+√2) - (1/3)(3+2√2)A = 4/3 + 4√2/3Learn more about Limits of integration
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Kevin has three classes in a row. Eight classes two hours long. Kevin’s first class is at seven. When will Karen’s last class and?
Karen's last class will end at three in the afternoon.
At what time will Karen’s final class conclude?Given that Kevin has three classes in a row, each lasting two hours, we can calculate the total duration of his classes. Three classes, each two hours long, amount to a total of 6 hours.
Since Kevin's first class starts at seven in the morning, we add 6 hours to that time, resulting in the conclusion of Karen's last class at three in the afternoon.
Understanding schedules and timetables is essential for effective time management. In academic settings, students often have multiple classes with varying durations throughout the day.
Calculating the end time of a class or event based on its start time and duration helps individuals plan their activities and allocate their time efficiently.
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Molly has a rectangular piece of cardboard. If the length of the cardboard can be modeled by 3x - 1 and the width of the cardboard can be modeled by 2x + 5, which polynomial models the area of her piece of cardboard? *
The polynomial that models the area of Molly's cardboard is 6x^2 + 13x - 5.
How can the area of Molly's cardboard be modeled with a polynomial?
First, we were given that the length of the cardboard can be modeled by 3x - 1 and the width can be modeled by 2x + 5. To find the area, we use the formula:
Area = length x width
So, we substitute the expressions for the length and width:
Area = (3x - 1) x (2x + 5)
Next, we use the distributive property of multiplication to expand the expression:
Area =[tex]6x^2 + 15x - 2x - 5[/tex]
Simplifying, we get:
Area = [tex]6x^2 + 13x - 5[/tex]
Therefore, the polynomial that models the area of Molly's piece of cardboard is [tex]6x^2 + 13x - 5.[/tex]
This polynomial gives us a way to calculate the area of the cardboard for any value of x. For example, if we know that the length of the cardboard is 5 units, we can substitute x = 2 into the polynomial to find the area:
Area =[tex]6x^2 + 13x - 5[/tex]
Area =[tex]6(2)^2 + 13(2) - 5[/tex]
Area = 24 + 26 - 5
Area = 45
So, the area of the cardboard when x = 2 (and the length is 3x - 1 = 5) is 45 square units.
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What does the mapping found in part b tell you about the relationship between the two circles? explain your reasoning.
The term "mapping" refers to the process of creating a mathematical correspondence between points or objects in two different sets. In this case, the mapping found in part b tells us that there exists a one-to-one correspondence between the points in Circle A and the points in Circle B.
There is a one-to-one correspondence between the points in Circle A and the points in Circle B, and that this correspondence preserves distance.
This means that for every point in Circle A, there is exactly one corresponding point in Circle B that is the same distance away from the center of the circle as the original point.
Since the correspondence is one-to-one, it follows that the two circles have the same number of points. That is, if Circle A has n points, then Circle B also has n points.
Therefore, we can conclude that the two circles have the same size.
Furthermore, because the correspondence preserves distance, any transformation that maps one circle onto the other must be a rigid motion, meaning it preserves angles and distances.
In particular, the transformation must be an isometry.
Therefore, we have shown that the two circles are congruent. That is, they have the same size and shape, and can be transformed onto one another by a combination of translations, rotations, and reflections.
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Need help with this question
Answer:
11
Step-by-step explanation:
23-12=11
Please help... 100 points promised!
Answer:
Step-by-step explanation:
The probability of drawing 2 red cards from a standard 52-card deck can be calculated as follows:
There are 26 red cards in the deck, so the probability of drawing a red card on the first draw is 26/52.
After the first card is drawn, there are 25 red cards remaining in the deck out of 51 total cards, so the probability of drawing a red card on the second draw is 25/51.
To find the probability of both events happening together (drawing 2 red cards), we multiply the probabilities of each event:
(26/52) * (25/51) = 0.245 or approximately 24.5%
Therefore, the probability of drawing 2 red cards in a standard 52 card deck is approximately 24.5%.
The radius of a circle is 15 ft. Find its area in terms of pi
Answer:
A= 225π ft²
Step-by-step explanation:
A = π r²
A= π 15²
A= 225π ft²
Answer:
706.86
Step-by-step explanation:
1. A=πr^2 : The formula to find the area of a circle.
2. A = π15^2 : Substitute the given radius value into the equation.
3. Insert equation into calculator
706.86 (Rounded to the nearest hundredth)
Fries 420 grams = $2.77
How much if its 1kg?
Which is a solution to 2n = 16?
Answer:
3
Step-by-step explanation:
2x2=4
4x2=8
8x2=16
On Friday, Jacob planted a pinto bean in science class. When he returned to school on Monday, the bean had sprouted a stem that was 3 millimeters long. At the end of the week, Jacob's bean sprout had a stem that was 42 millimeters long. How many centimeters did Jacob's bean sprout grow during the week?
Jacob's bean sprout grew 3.9 centimeters during the week.
What is measurements?
Measurements in math involve the assignment of numerical values to physical quantities, such as length, area, volume, mass, time, temperature, and so on. Measuring objects or events allows us to compare and quantify them, and is an essential part of mathematical problem-solving, as well as many other fields of study
Jacob's bean sprout grew 42 millimeters - 3 millimeters = 39 millimeters during the week.
To convert millimeters to centimeters, we need to divide by 10 since there are 10 millimeters in 1 centimeter.
So, the growth in centimeters is 39 millimeters ÷ 10 = 3.9 centimeters.
Therefore, Jacob's bean sprout grew 3.9 centimeters during the week.
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Kate surveyed 16 politicians from her state about their views on certain issues. is this sample of citizens of the state likely to be representative?
The representativeness of a sample depends on how it is selected and whether it accurately reflects the characteristics of the larger population. Without more information about the sampling method used, it is difficult to determine if the sample of 16 politicians is likely to be representative of the citizens of the state.
If the sample was selected randomly from a diverse pool of politicians that accurately represents the political landscape of the state, there is a higher likelihood that the sample would be representative. However, if the sample was obtained through convenience sampling or if it disproportionately represents certain political affiliations or demographics, it may not be representative of the entire population of citizens in the state.
To assess the representativeness of the sample, it is important to consider factors such as the sampling method, sample size, diversity of the sample, and the specific characteristics being studied.
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which function is shown in the graph below
Answer: y=log 3 x
Step-by-step explanation:
Please help me! It's due today!
Answer:
i think it would be...5^-5, 5^0, 5^4
Step-by-step explanation:
pls mark brainliest
Suppose a 4 is rolled on a number cube with sides numbered 1, 2, 3, 4, 5, and 6. The
complement of this event would be rolling a 1, 2, 3, 5, or 6. What is the probability of the
complement, written as a fraction in simplest form?
The probability of rolling any number other than 4 on a number cube with sides numbered 1, 2, 3, 4, 5, and 6 is 5/6, which can be written as a fraction in simplest form.
The complement of rolling a 4 on a number cube with sides numbered 1, 2, 3, 4, 5, and 6 is rolling any number other than 4, which includes rolling a 1, 2, 3, 5, or 6.
To find the probability of the complement, we need to add up the probabilities of rolling each of these numbers.
Since each number has an equal chance of being rolled, we can find the probability of rolling each number by dividing 1 by the total number of possible outcomes (which is 6, since there are six sides on the cube).
Then, we can add up the probabilities of rolling each of the five numbers in the complement:
P(rolling a 1, 2, 3, 5, or 6) = P(rolling a 1) + P(rolling a 2) + P(rolling a 3) + P(rolling a 5) + P(rolling a 6)
P(rolling any number other than 4) = 1 - P(rolling a 4)
P(rolling any number other than 4) = 1 - 1/6 = 5/6
Therefore, the probability of rolling any number other than 4 on a number cube with sides numbered 1, 2, 3, 4, 5, and 6 is 5/6, which can be written as a fraction in simplest form.
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The perimeter of a semicircle is 35. 98 millimeters. What is the semicircle's radius Use 3. 14 for a. Millimeters Submit explain
If the perimeter of a semicircle is 35. 98 millimeters, 7 mm is the semicircle's radius.
A semi-circle refers to half of the circle. The circle is cut along the diameter to form a semi-circle.
A diameter is a line segment that passes through the center of the circle and touches the boundary of the circle from both ends.
The perimeter of the semi-circle is the sum of the length of the diameter and the circumference of the semi-circle.
P = 2r + πr
where P is the perimeter
r is the radius
P = 35.98 mm
35.96 = 2r + 3.14r
35.96 = 5.14r
r = 7 mm.
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If there were eight equal pieces and seven of them were gone how many would there be in angle measurement
If there were eight equal pieces and seven of them were gone, there would be 45 degrees in angle measurement.
When the circle is divided into eight equal pieces, each piece has an angle of 360°/8 = 45°. If seven of these pieces are gone, only one piece is remaining, which is equivalent to 45 degrees in angle measurement. Therefore, the answer is 45 degrees.
Alternatively, we can use the formula for finding the angle of a sector of a circle. The formula is given as Angle = (θ/360) x 2πr, where θ is the central angle in degrees, and r is the radius of the circle. In this case, the radius of the circle is not given, but we know that there were eight equal pieces initially.
Therefore, the central angle for one piece is 360°/8 = 45°. So, the angle of the remaining piece is (45/360) x 2πr = (1/8) x 2πr = π/4 radians or 45 degrees.
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MAKRING BRAINLIST ^_^
"Twisted till" and "claw curled" are example of what poetic device
1) Repetition
2) Alilteration
3) Ryhme
4) Onomatopoeia
Author repeats "hands folded in as if he wished for something" because it
1) Encourages the readers to save a creature
2) Exaggerates the praying mantis's movement
3) Compares the author to the praying mantis
4) Makes the praying mantis seem more human
"Twisted till" and "claw curled" are examples of alliteration, which is a poetic device that involves the repetition of consonant sounds at the beginning of words.
The author repeats "hands folded in as if he wished for something" to exaggerate the praying mantis's movement and make it seem more human.
This repetition is a literary technique used to emphasize the mantis's behavior and draw the reader's attention to it.
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A student takes a measured volume of 3. 00 m hcl to prepare a 50. 0 ml sample of 1. 80 m hcl. What volume of 3. 00 m hcl did the student use to make the sample?.
The student used 30.0 mL of 3.00 M HCl to make the 50.0 mL sample of 1.80 M HCl.
To find the volume of 3.00 M HCl needed to make a 50.0 mL sample of 1.80 M HCl, we can use the equation:
M₁V₁ = M₂V₂
Where M₁ is the initial concentration, V₁ is the initial volume, M₂ is the final concentration, and V₂ is the final volume.
We are given M₁ = 3.00 M, M₂ = 1.80 M, and V₂ = 50.0 mL. We can rearrange the equation to solve for V₁:
V₁ = (M₂V₂) / M₁
V₁ = (1.80 M * 50.0 mL) / 3.00 M
V₁ = 30.0 mL
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please please please please please please help me this is all due tomorrow
For the following probabilities:
7. Theoretically, blue will occur 100 times.8. Based on experiment, blue will occur 95-105 times.9. a) 1/4, b) 1/2, c) 3/4.10. a) 0.25, b) 0.5, c) 0.75.11. spade can occur 125 times theoretically.12. experimentally spade occurs 500 times.How to determine probability?7. Theoretically, if the spinner is spun 400 times, you would expect to get blue 100 times since blue has a probability of 1/4 or 25% of being selected on each spin.
8. Based on the experiment, if the spinner is spun 400 times, you would expect to get blue around 95-105 times, depending on the margin of error in the experiment. This is based on the observed experimental probability of blue being selected in the given number of spins.
9. a) P(club) = 13/52 or 1/4
b) P(red card) = 26/52 or 1/2
c) P(not a heart) = 39/52 or 3/4
10. a) P(club) = 5/30 or 1/6 in the experiment, which is close to the theoretical probability of 1/4 or 0.25.
b) P(red card) = 13/30 in the experiment, which is close to the theoretical probability of 1/2 or 0.5.
c) P(not a heart) = 27/30 in the experiment, which is close to the theoretical probability of 3/4 or 0.75.
11. Theoretically, if a card is drawn at random 500 times, you would expect to get a spade around 125 times since spades have a probability of 1/4 or 25% of being selected on each draw.
12. Based on the experiment, if a card is drawn at random 500 times, you would expect to get a spade around 110-140 times, depending on the margin of error in the experiment. This is based on the observed experimental probability of spades being selected in the given number of draws.
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Image transcribed:
7. Theoretically, if the spinner is spun 400 times, how many times would you expect to get blue?
8. Based on the experiment, if the spinner is spun 400 times, how many times would you expect to get blue?
9. A card is drawn from a standard deck of cards. Find each probability.
a) P(club)
b) P(red card)
c) P(not a heart)
10. The table below shows the results of an experiment in which a card was drawn at random 30 times. Find each probability based on the experiment and compare to the theoretical probability.
Result | Frequency
Heart | 3
Diamond | 10
Club | 5
Spade | 12
a) P(club)
b) P(red card)
c) P(not a heart)
11. Theoretically, if a card is drawn at random 500 times, how many times would you expect to get a spade?
12. Based on the experiment, if a card is drawn at random 500 times. how many times would you expect to get a spade?
What is the given function below in vertex form
1. Given the function: f(x)=-2x+7 and g(x)=5x-16
Find the function for h(x)=f(x)+g(x)
The function h(x) can be represented by -3x-9 .
Linear Equation
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+6. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=7 and b=6.
The question gives two linear equations that represent two functions: f(x)=-2x+7 and g(x)=5x-16.
For solving this you should sum both equations. See below
h(x)=f(x)+g(x)
h(x)=-2x+7 +5x-16
h(x)=-3x-9
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A phone company set the following rate schedule for an m-minute call from any of its pay phones.what is the cost of a call that is under six minutes?
For calls that are 6 minutes less, the rate is $0.70 per minute.
To find the cost of a call that is under 6 minutes, we simply need to use the first part of the rate schedule.
Let's say the call lasts for m minutes. Since m is less than or equal to 6, we can use the first part of the rate schedule, which gives us
c(m) = $0.70 per minute
So the cost of the call is simply the rate per minute times the number of minutes
c(m) = $0.70 × m
For example, if the call lasted 4 minutes, the cost would be
c(4) = $0.70 × 4 = $2.80
Therefore, the cost of a call that is under 6 minutes is simply $0.70 per minute.
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--The given question is incomplete, the complete question is given
" A phone company set the following rate schedule for an m-minute call from any of its pay phones.
c(m)=
{0.70 when m≤6
0.70+0.24(m−6) when m>6 and m is an integer
0.70+0.24([m−6]+1) when m>6 and m is not an integer }
what is the cost of a call that is under six minutes?"--
Federico enjoys catching pokemons in university campus. One day, while trying to catch charmander, he found the best spot next to a
perfectly circular pond. He was 43 feet from the bank and 75 feet from the point of tangency. Determine the radius of the pond using the
given information. Round to the nearest integer,
The radius of the pond is 32 feet, under the condition that 43 feet from the bank and 75 feet from the point of tangency.
Let us consider that the center of the circle O, the point of tangency T, and Federico's position P.
We can utilize these two points to form a line. The point of tangency is the place where Federico is closest to the pond. The radius of the pond is considered perpendicular to this line and passes through the point of tangency.
Firstly, we have to the distance between Federico's position P and covers passes through points T and B (the bank). This distance is equivalent to the given radius of the circle. We have to apply the formula for the distance between a point and a line to find this distance.
Let us assume this distance as d.
d = (|BT x BP|) / |BT|
Here
|BT| = line segment length of BT,
|BP| = line segment length of BP,
BT x BP = vectors cross product of BT and BP.
Here we evaluate |BT| applying the Pythagorean theorem
|BT|² = 75²+ r²
Here,
r = radius concerning the circle.
Then,
|BP|² = 43² + r²
Staging these values into our formula for d:
d = (|BT x BP|) / |BT|
= (|BT| × |BP|) / |BT|
= |BP|
= √(43² + r²)
We want to solve for r, so we can square both sides:
d² = 43² + r²
r² = d² - 43²
r = √(d² - 43²)
Placing in d = 75,
r = √(75² - 43²)
≈ 32 feet
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Procter & Gamble reported that an American family of four washes an average of 1
ton (2000 pounds) of clothes each year. If the standard deviation of the distribution
is 187. 5 pounds, find the probability that the mean of a randomly selected sample of
50 families of four will be between 1980 and 1990 lbs.
The required probability is approximately 0.1253 or 12.53%.
We can use the central limit theorem to approximate the sampling distribution of the mean of the weights of clothes washed by 50 families of four. According to the central limit theorem, the sampling distribution of the mean will be approximately normal if the sample size is large enough (n > 30), regardless of the shape of the population distribution.
The mean of the sampling distribution of the mean will be equal to the population mean, which is 2000 lbs
[tex]SEM=\frac{\sigma}{\sqrt{n} }[/tex]
σ = population standard deviation
n = sample size.
[tex]SEM=\frac{187.5}{\sqrt{50} }[/tex]
= 26.5
Now we need to find the z-scores corresponding to the two values of the mean.
[tex]z_1=\frac{1980-2000}{26.5}[/tex]
= -0.75
[tex]z_2=\frac{1990-2000}{26.5}[/tex]
= -0.38
Using a standard normal table, we can find the probability that a z-score is between -0.75 and -0.38.
P(-0.75 < Z < -0.38) = 0.1253
Therefore, the required probability is approximately 0.1253 or 12.53%.
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My office is 10 ft by 12 ft. I want to buy border for the top of my wall. I have a 3ft door on a 10 ft wall and a 3 ft window directly across from it. How much wallpaper border should I buy?
a. 24
b. 44
c. 38
You should buy 38 feet of wallpaper that cover the border for the top of the wall using the perimeter of the room. Thus, option C is correct.
Length of office = 10 feets
width of office = 12 feets
Door length = 3 feet
Wall length = 10 feet
Window length = 3 feet
To estimate the length of the wallpaper border needed, we need to calculate the perimeter of the room that needs the bordering of wallpaper. It is given that only the top of the roof needs bordering.
We need to add the lengths of all 4 sides of the walls and subtract the lengths of the door and window.
Mathematically,
The perimeter of the room =(sum of the length of sides of the room) - (length of the window) - (length of the door)
Perimeter of room = (10 + 12 + 10 + 12) - 3 - 3
Perimeter of room = 38 ft
Therefore, we can conclude that we need to buy 38 feet of the wallpaper border.
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If (x+1/x)² = 3, find x³+1/x³.
The value of the algebraic expression from the given parameters is:
x³ + 1/x³ = 0
How to solve Algebraic Expressions?The given problem is simply based on the expansion.
In expansion, what we do is that we expand the mathematical terms by first of all removing all the brackets that are in that mathematical expression.
In expanding a mathematical expression, what we have to do is that we have to make use some of the identities that can be gotten by multiplying one binomial with the another one and then this type of identities are called as Standard Identities.
For example:
(x + a)(x + b) = x² + (a + b)x + ab
Thus:
(x + 1/x)² = 3
x + 1/x = √3
(x+1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)
√3³ = x³ + 1/x³ + 3(√3)
x³ + 1/x³ = 3√3 - 3√3
x³ + 1/x³ = 0
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Please help it would be amazing if you knew this
The solution of the function (f - g)(x) is 17x + 7.
How to solve composite function?A function relates input and output. A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function as follows:
f(x) = 10x + 3
g(x) = -7x - 4
Therefore, let's find (f - g)(x)
Hence,
(f - g)(x) = f(x) - g(x)
Therefore,
f(x) - g(x) = 10x + 3 - (-7x - 4)
f(x) - g(x) = 10x + 3 + 7x + 4
f(x) - g(x) = 17x + 7
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Please help me im struggling sm
The measurements are x = 7 and ∠NJK = 51°
Given is a rectangle, we need to find the asked measurement,
So,
Since we know that the diagonals of a rectangle bisect each other,
So,
JN + JN = JL
4x+4+4x+4 = 5x+29
8x+8 = 5x+29
3x = 21
x = 7
And,
The vertex angle is 90° so,
∠NMJ + ∠NML = 90°
∠NML = 51°
Also,
∠NML = ∠NJK because they are alternate angles,
So, ∠NJK = 51°
Hence x = 7 and ∠NJK = 51°
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