Answer:
C. (6, 5) and (3, -4)
Step-by-step explanation:
Given the equation 3x - y = 13, we need to figure out which points satisfy it. In order for an ordered pair to satisfy an equation, when we plug the x-coordinate in for x and the y-coordinate in for y, the equation should hold true.
Let's try with (6, 5):
3x - y = 13
3 * 6 - 5 =? 13
18 - 5 =? 13
13 = 13
Since this is true, we know that (6, 5) is indeed a solution.
Now let's try with (3, -4):
3x - y = 13
3 * (3) - (-4) =? 13
9 + 4 =?13
13 = 13
Again, since this is true, then (3, -4) must be a solution.
Thus, the answer is C.
~ an aesthetics lover
Answer: c
Step-by-step explanation:
lol
PLEASE HELP ME ASAP!!! Alex has 64 cubes with dimensions in feet like the one shown. (1/2 ft). He uses all the cubes to fill a box shaped like a larger rectangular prism. What is the volume, in feet, of the larger rectangular prism?
Answer: MARK AS BRAINLIST PLZ:)
A) First, find the volume of each cube:
V = s³
= (1/2)³
= 1/8 ft³
We have a total of 64 cubes, therefore the maximum volume will be:
Vmax = 64 · (1/8) = 8 ft³
B) The volume of a rectangular prism is given by:
V = w × l × h
Therefore any combination of w × l × h = Vmax = 8 will be fine.
Examples:
2 × 2 × 2
4 × 2 × 1
Step-by-step explanation:
HOPE IT HELPS BRAINLIST
Could someone help me with these? I would really appreciate.
a) William walks at a speed of 5 km/h. How long will it take him to cover the path shown on the map as a segment 36 cm long? The scale of the map is 1:40,000.
b) A farmer wants to sow a rectangular field with barley. In a plan with a scale of 1: 20,000, the dimensions of that field are 9 cm x 7 cm. How many tons of barley will the farmer need if 0.3 tons of barley are needed to sow 1 ha?
(c) A plan at a scale of 1:400 shows a circular outdoor swimming pool. Its area in plan is equal to 18.84 cm². What area does the pool occupy in reality? If the scale of the plan is 1500, this means that: 1 cm on the plan corresponds to 500 cm in reality
d) The depicted figure consists of a triangle and a semicircle (see figure).
1) Calculate the length and area of the edge of the figure
2) Draw this figure on a scale of 1 : 2 (double its smaller copy).
Calculate the edge length and area of that reduced copy.
3) Calculate the length and area of the figure twice its original size.
e) Calculate the unknown term of the proportion.
Answer:
a) To find the time it will take William to cover the path shown on the map, we need to convert the length of the path from centimeters to kilometers using the map scale. 1 cm on the map represents 40,000 cm in reality, which is equivalent to 0.4 km. So, the length of the path in kilometers is:
36 cm x 0.4 km/cm = 14.4 km
Now we can use the formula time = distance ÷ speed to find how long it will take William to cover the path:
time = distance ÷ speed = 14.4 km ÷ 5 km/h = 2.88 hours or 2 hours and 52.5 minutes (rounded to the nearest minute).
b) The area of the rectangular field can be found by multiplying its dimensions together, then converting the area from square centimeters to hectares using the scale of the map.
Area of field = 9 cm x 7 cm = 63 cm²
Area of field in hectares = 63 cm² ÷ (20,000 cm/ha)² = 0.0001575 ha
To find how many tons of barley the farmer needs, we can use the given conversion factor of 0.3 tons of barley per hectare:
Tons of barley needed = 0.0001575 ha x 0.3 tons/ha = 0.00004725 tons or 47.25 grams of barley.
c) To find the area of the pool in reality, we need to convert the area of the pool on the map from square centimeters to square meters using the map scale.
Area of pool on map = 18.84 cm²
Area of pool in reality = 18.84 cm² x (500 cm/m)² = 0.471 m²
d)
1) The length of the straight edge of the figure can be found using the Pythagorean theorem:
a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
c = √25 = 5 cm
The area of the figure can be found by adding the area of the triangle and the semicircle:
Area of triangle = 1/2 x base x height = 1/2 x 3 cm x 4 cm = 6 cm²
Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5/2)² = 19.63 cm²
Total area of figure = 6 cm² + 19.63 cm² = 25.63 cm²
2) To draw the figure on a scale of 1:2, we need to multiply all dimensions by 2. So, the straight edge of the figure would be 10 cm long, the base of the triangle would be 6 cm, and the height of the triangle would be 8 cm. The radius of the semicircle would be 5 cm.
Using the same calculations as before, we can find the area of the figure on the new scale:
Area of triangle = 1/2 x base x height = 1/2 x 6 cm x 8 cm = 24 cm²
Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5 cm)² = 39.27 cm²
Total area of figure = 24 cm² + 39.27 cm² = 63.27 cm²
3) To find the length and area of the figure twice its original size, we need to multiply all dimensions by 2. So, the straight edge of the figure would be 10 cm long, the base of the triangle would be 6 cm, and the height of the triangle would be 8 cm. The radius of the semicircle would be 5 cm.
Using the same calculations as before, we can find the area of the figure on the new scale:
Area of triangle = 1/2 x base x height = 1/2 x 6 cm x 8 cm = 24 cm²
Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5 cm)² = 39.27 cm²
Total area of figure = 24 cm² + 39.27 cm² = 63.27 cm²
e) Without knowing the specific proportion, it's difficult to provide a solution. Please provide more information or the specific proportion so that we can help you solve it.
i need help to solve please
Answer:
x = 8
Step-by-step explanation:
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
So,
\( \rm \longrightarrow 45 \degree + 80 \degree + (9x - 17) \degree = 180 \degree \\ \\ \rm \longrightarrow 125 + 9x - 17 = 180 \\ \\ \rm \longrightarrow 108 + 9x = 180 \\ \\ \rm \longrightarrow (108 - 108) + 9x = 180 - 108 \\ \\ \rm \longrightarrow 9x = 72 \\ \\ \rm \longrightarrow \dfrac{9}{9} x = \dfrac{72}{9} \\ \\ \rm \longrightarrow x = 8\)
write an equation for the line of fit for this data in the form y=mc+where x is latitude and y is temperature.
Solution
y= mx +b
Where y is the temperature and x the latitude
If we fit an equation line we have the following:
A= 119.24
b= -1.070
Then the equation would be:
y= -1.070 x + 119.24
10x-2x+12=2(3x+5)+2x
Answer: is this pemdas? if not there are no true solutions
Step-by-step explanation:
hope i helped
Answer:
the answer to 10x-2x+12=2(3x+5)+2x is 2
Step-by-step explanation:
step 1.
Open the brackets by multiplying the valves in the brackets by 2:
10x-2x+12=6x+10+2x
step 2.
Add or subtract the like-terms : x values.
8x+12=8x+10
step 3.
substitute by bringing like terms together:
12-10=8x-8x
2=0
ans =2
The slope of a line is -5 and its y-intercept is 8. Discuss how you will write the equation in the slope-intercept form
Step-by-step explanation:
slope-intercept form : y = mx + b
m = slope
b = y intercept
y = -5x +8
Use the mean and the standard deviation obtained from the last module and test the claim that the mean age of all books in the library is greater than 2005. Share your results with the class.
My information from last module:
The sampled dates of publication are as follows:
1967, 1968, 1969, 1975, 1979, 1983, 1984,
1984, 1985, 1989, 1990, 1990, 1991, 1991,
1991, 1991, 1992, 1992, 1992, 1997, 1999
Median = 1990
Mean = 1985.67
Variance = 84.93
SQRT of variance = 9.2 (sample standard deviation)
The confidence interval estimate of the mean age of the books is 4.33 years.
To test the claim that the mean age of all books in the library is greater than 2005, we can use a one-sample t-test. First, we need to calculate the test statistic:
t = (mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in our values, we get:
t = (1985.67 - 2005) / (9.2 / sqrt(21)) = -2.15
Using a t-table with 20 degrees of freedom (n-1), we find that the p-value is 0.0227. Since this is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the mean age of all books in the library is indeed greater than 2005.
In this question, we are asked to use the mean and standard deviation obtained from the previous module to test a claim about the mean age of books in a library. To do so, we need to use a one-sample t-test. This test allows us to compare the mean of a sample to a hypothesized mean and determine whether there is sufficient evidence to suggest that the population mean is different.
In this case, the null hypothesis is that the mean age of all books in the library is equal to 2005. The alternative hypothesis is that the mean age is greater than 2005. We plug in the relevant values into the t-formula and find the test statistic. We then use a t-table to find the p-value associated with that test statistic. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is evidence to suggest that the population mean is indeed different from the hypothesized mean.
In this case, we found a test statistic of -2.15 and a p-value of 0.0227. Since this p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the mean age of all books in the library is greater than 2005. This means that the books in the library are generally older than 2005.
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Divide.
Write your answer in simplest form.
−
5
7
÷
1
5
=
?
−
7
5
÷
5
1
=
In simplest form:-5/7 ÷ 1/5 = -25/7 and -7/5 ÷ 5/1 = -7/25
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Let's calculate each division:
Division: -5/7 ÷ 1/5
To divide fractions, we multiply the first fraction (-5/7) by the reciprocal of the second fraction (5/1).
(-5/7) ÷ (1/5) = (-5/7) * (5/1)
Now, we can multiply the numerators and denominators:
= (-5 * 5) / (7 * 1)= (-25) / 7
Therefore, -5/7 ÷ 1/5 simplifies to -25/7.
Division: -7/5 ÷ 5/1
Again, we'll multiply the first fraction (-7/5) by the reciprocal of the second fraction (1/5).
(-7/5) ÷ (5/1) = (-7/5) * (1/5)
Multiplying the numerators and denominators gives us:
= (-7 * 1) / (5 * 5)
= (-7) / 25
Therefore, -7/5 ÷ 5/1 simplifies to -7/25.
In simplest form:
-5/7 ÷ 1/5 = -25/7
-7/5 ÷ 5/1 = -7/25
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Which of the following characteristics of a house would be considered a qualitative variable? Size in Square Feet Mailing Address Number of Bathrooms Estimated Market Value
The characteristic of "Mailing Address" would be considered a qualitative variable.
A qualitative variable is a type of variable that is used to assign information that can't be measured by numbers. Qualitative data is used to label the attributes of the individuals, objects, or other items in the study.Types of Qualitative DataThere are many types of qualitative data, for instance:Nominal Data is data that can't be ranked and the measurements have no specific order or sequence.Ordinal Data is data that can be ranked and that has a definite order or sequence.Below are the options given and among them which is qualitative.Size in Square FeetMailing AddressNumber of BathroomsEstimated Market ValueAmong the given options, Mailing Address is considered a qualitative variable. Therefore, the answer is "Mailing Address".
Quantitative data are generally numerical and can be counted or measured, while qualitative data are descriptive and non-numerical. Qualitative data provide a descriptive view of the information that can be used to form ideas or summarize patterns. Qualitative data are frequently used in qualitative studies, but they can also be used in quantitative studies. However, the characteristics of a house that are qualitative variables can be any type of descriptive data that cannot be measured with a numerical value.Mailing Address is a qualitative variable. Because it is a type of data that cannot be counted or measured, it is a qualitative data type. Qualitative data are often used to describe something or to provide more information than can be given by numbers alone. Therefore, the characteristic of "Mailing Address" would be considered a qualitative variable.
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PLS HELP with this from khan academy. I’m struggling, and it’s due today.
Answer:
8
Step-by-step explanation:
You can think as vertices as the corners of the shape
Answer:
the shape have 8 vertices.
45 popcorn kernels pop in the microwave in 3 seconds, how long will it take for a bag of 220 kernels to pop completely?
Answer:
14.4 Seconds
Step-by-step explanation:
220 divided by 4 is 4.8
4.8 times 3 is 14.4
what does 7/12 + 5/6 equal
\(\dfrac 7{12} + \dfrac 56\\\\\\=\dfrac 7{12} + \dfrac{10}{12}\\\\\\=\dfrac{7+10}{12}\\\\\\=\dfrac{17}{12}\)
what does \( \frac{7}{12} + \frac{5}{6} \) equal
▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
Solution:-= \(\frac{7}{12} + \frac{5}{6}\)LCM of 12 and 6 = 12
= \( \frac{7 + 10}{12} \)= \( \frac{17}{12} \)= \(1 \frac{5}{12} \)Q1-) Consider a manufacturing system with two machines. Suppose that when both ma- chines are available, one is in use and the other is on standby. The probability that a machine in use fails during a day is p. When it fails its repair may start only the next day if the single repair facility is available. It takes two days to repair a failed machine. We can use a Markov Chain model to describe the evolution of this system. Let Xn = (i, j), n ≥ 0 denote the states of the Markov chain, where i is the number of machines in working condition and j is the number of elapsed repair days of a machine at the repair facility at the beginning of the n'th day. The corresponding transition probability matrix is (2,0) (1,0) (1,1) (0,1) (2,0) [1-p P 0 0 (1,0) 0 0 1-p Р P= (1,1) 1-p 0 0 P (0,1) 0 1 0 0 For parts (a)-(c) do not assume a specific value for p, leave your answer in terms of p. (a) Given Xo = (1, 1), what is the probability that only one machine is in working condition after two days? (b) Find the expected number of days until both machines are down, given that currently both machines are operational. (c) Find the steady state probabilities. (d) Suppose the revenue of the manufacturing system is R TL per day if any one of the machines is in operating condition and currently p = 0.3. What will be the percentage change in the long run average benefit per day if a major technological improvement is achieved that changes p from 0.3 to 0.2?
(a) To find the probability that only one machine is in working condition after two days, we need to determine the probability of transitioning from state (1, 1) to state (1, 0) after two days.
From the transition probability matrix, we see that to transition from (1, 1) to (1, 0) in one day, both machines need to remain operational, which has a probability of (1 - p) * (1 - p) = (1 - p)^2.
Therefore, the probability of transitioning from (1, 1) to (1, 0) after two days is ((1 - p) * (1 - p))^2 = (1 - p)^4.
(b) To find the expected number of days until both machines are down, given that currently both machines are operational, we need to consider the transition probabilities from state (2, 0) to state (0, 1).
From the transition probability matrix, we see that to transition from (2, 0) to (0, 1) in one day, both machines need to fail, which has a probability of p * p = p^2.
Therefore, the expected number of days until both machines are down, given that both machines are currently operational, is 1 / (p^2).
(c) To find the steady-state probabilities, we need to solve the equation πP = π, where π is the row vector of steady-state probabilities and P is the transition probability matrix.
Solving this equation will give us the steady-state probabilities for each state (i, j). Since the given matrix is not provided, it is not possible to calculate the exact steady-state probabilities without the specific values of the transition probabilities.
(d) To determine the percentage change in the long-run average benefit per day if p changes from 0.3 to 0.2, we would need to know how the revenue R TL is related to the probability p. Without this information, it is not possible to calculate the percentage change.
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can you please help me with number 4 please?
andy wrote the equation of a line that has a slope of and passes through the point (3, –2) in function notation. step 1: y – (–2)
The equation of the line in function notation is
\(y = mx - 3m - 2\)
Step 1: y - (-2)
To write the equation of the line in function notation, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line. In this case, the slope is given as "m," and the point (x1, y1) is (3, -2).
Substituting these values into the equation, we get:
y - (-2) = m(x - 3)
Simplifying the expression in the left-hand side, we get:
y + 2 = m(x - 3)
This is the equation of the line in point-slope form. To write it in function notation, we can solve for y:
y = mx - 3m - 2
This is the equation of the line in function notation. We can use this equation to find the y-value of the line for any given x-value. For example, if we want to find the y-value of the line when x = 5, we can substitute x = 5 into the equation and solve for y:
y = m(5) - 3m - 2 = 2m - 2
So when x = 5, the y-value of the line is 2m - 2.
Question: Andy wrote the equation of a line that has a slope of "m" and passes through the point (3, -2) in function notation. Write the equation of the line in function notation, showing the first step of your work.
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express the following limit as a definite integral: lim n→[infinity] n∑i=1 i6/n7=∫b1 f(x)dx
The given limit can be expressed as the definite integral: lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx
To express the given limit as a definite integral, we need to determine the appropriate function f(x) and the integration limits b and 1.
Let's start by rewriting the given limit:
lim (n→∞) (1/n) ∑(i=1 to n) \(i^6/n^7\)
Notice that the term i⁶/n⁷ can be written as (i/n)⁶/n.
Therefore, we can rewrite the above limit as:
lim (n→∞) (1/n) ∑(i=1 to n) (i/n)⁶/n
This can be further rearranged as:
lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶
Now, let's define the function f(x) = x⁶, and rewrite the limit using the integral notation:
lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶ = ∫[a,b] f(x) dx
To determine the integration limits a and b, we need to consider the range of values that x can take. In this case, x = i/n, and as i varies from 1 to n, x varies from 1/n to 1. Therefore, we have a = 1/n and b = 1.
Hence, the given limit can be expressed as the definite integral:
lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx
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Someone please help me this will be a lot of points and I will follow u and Mark u the brainiest
Answer:
Answer is (d) 3
You can see that :
6/2 = 12/4 = 18/6 = 24/8 = 30/10 = 3
Thua the answer is 3
Let A and B be two events such that p(A) = 0.3 and P(BA) = 0.2. Then P(BnA) = O 0.4 0.7 O 0.6 0.5
If A and B be two events such that p(A) = 0.3 and P(B/A) = 0.2 then P(BnA) is 0.2.
Given:
P(A) = 0.3
P(B|A) = P(B ∩ A) / P(A)
The notation P(B|A) represents the conditional probability of event B occurring given that event A has already occurred.
In other words, it's the probability of the intersection of events B and A divided by the probability of event A.
P(B|A) = 0.2 / 0.3
= 0.6667
Therefore, P(B ∩ A) = P(A) × P(B|A)
= 0.3 × 0.6667
= 0.2.
Therefore, P(B ∩ A) is equal to 0.2.
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Class work help Algebra 2
Answer:Algebra 2 is the third math course in high school and will guide you through among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.
twelve is what percent of 42
Answer:
28.57 percent
hope that helped
Answer:3.5 percent of 42 gives you 12
Step-by-step explanation:
Solve the inital value problem dy/dt= ey-t sec(y)(1+t2) y(0)=0. Solve the inital value problem.
The solution of the initial value problem is \(\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}\).
What is initial value problem?Initial value issues are a specific kind of calculus issue. Calculus initial value issues include differential equations with a known beginning condition that identifies the function's value at a certain point. Finding the function that best describes the system is the goal of these puzzles, and this can be accomplished by integrating the differential equation.
There is always an unknown constant present when doing an integration with an indeterminate integral or without initial conditions. The constant of integration is what is commonly indicated by the letter C.
Given that the initial value problem is:
dy/dt= e^(y-t) sec(y)(1+t2)
This can be re written as follows:
dy/ dt = e^(y-t) (1 + t^2) / sec (y)
Separate the derivative in terms of y and t and take integration:
\(\int{e^{-y}cos(y)} \, dy = \int {e^{-t}(1 + t^2)} \, dt\)
Integrate the following:
\(\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + c\\\)
The initial conditions given are y(0) = 0, substitute the value of the variables as 0:
\(\frac{e^{0}}{2} [sin0 - cos0] = -e^{0} [0^2 + 2(0) + 3] + c\\\\\\\frac{1}{2} [-1] = 3 + c\)
c = 5/2
Hence, the solution of the initial value problem is:
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#SPJ4\(\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}\)
What is the missing side length in this right triangle? Round the answer to the nearest tenth.
A: 4.7 units
B: 6.6 units
C: 15.6 units
Answer:
The answer is B. i.e. 6.6units.
When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive?
(–∞, 0)
(0, 2)
(2, ∞)
(∞, ∞)
Considering their graphs, the interval in which both functions are positive is:
(0, 2)
When are the functions positive?A function is positive when it's graph is positioned above the x-axis.
Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:
(0, 2)
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sam got a new job with a $7.00 per hour raise. he worked for 5 hours and got paid $85.00. how much did he make before the raise?
Which statement best describes the function?
Answer:
i dont have an answere but i would suggest the app desmos for the graphing part
Order of Operations: Write an equation that means "Multiply 6 by the sum of 3 and 2."
Write tan 41π/36 in terms of the tangent of a positive acute angle.
tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))
To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.
First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):
41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π
Now, we can rewrite the angle as:
tan(41π/36) = tan((10/9)π + (1/36)π)
Next, we'll use the tangent addition formula, which states that:
tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
In this case, A = (10/9)π and B = (1/36)π.
tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))
Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.
For (10/9)π, we can subtract π to get an equivalent angle within the range:
(10/9)π - π = (1/9)π
Similarly, for (1/36)π, we can add π to get an equivalent angle:
(1/36)π + π = (37/36)π
Now, we can rewrite the expression as:
tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))
Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:
tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))
Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.
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the difference between 75% of a number and 20% of the same number is 378.9 what is 40% of that number?
Thus, the 40% of the number is
\(688.909\cdot0.4=275.563\)Please need help 100 points
Answer:
(29/37)-(48/37i)
Step-by-step explanation:
Use complex arithmetic rule:
a+bi/c+di = [(c-di)(a+bi)/(c-di)(c+di)] =[(ac+bd)+(bc-ad)i]/c^2+d^2
To get: (29-48i)/37
Then rewrite it in standard complex form to get your answer.
Hope that helps!
the length of a rectangular field is 60 cm the breadth is half of its length.find the area of the field
Answer:
the answer is 1800cm²
Step-by-step explanation:
1. L=60cm
2. B=L/2=60/2=30cm
area of rectangular field=L×B
=60×30=1800cm²