So, the LU-factorization of the given matrix is:
LU = `[1 0 0 0]` `[4 0 1 8]`
`[0.25 1 0 0]` `[0 1 -4.25 6]`
`[0 4.25 1 0]` `[0 0 1.25 -2]`
`[0 0 -1.25 1]` `[0 0 0 1]`
The LU-factorization of a matrix is a method of decomposing a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). The L matrix must have a unit diagonal, meaning that all the entries on the main diagonal are equal to 1.
To find the LU-factorization of the given matrix, we can use the following steps:
1. Begin with the given matrix:
`[4 0 1 8]`
`[1 1 -4 10]`
2. Use Gaussian elimination to transform the matrix into an upper triangular matrix (U):
`[4 0 1 8]` → `[1 1 -4 10]` → `[0 1 -4.25 6]` → U = `[0 0 1.25 -2]`
3. Now, we can use the entries from the Gaussian elimination to create the lower triangular matrix (L):
L = `[1 0 0 0]`
`[0.25 1 0 0]`
`[0 4.25 1 0]`
`[0 0 -1.25 1]`
4. Finally, we can write the LU-factorization as:
LU = `[1 0 0 0]` `[4 0 1 8]`
`[0.25 1 0 0]` `[0 1 -4.25 6]`
`[0 4.25 1 0]` `[0 0 1.25 -2]`
`[0 0 -1.25 1]` `[0 0 0 1]`
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What is the average rate of change of f(X) from x=-3 to x = 6?
f(x) = x4
4 + 4x - 15
Enter your answer in the blank.
PLEASE HELPPP
((x)/(x+1)+1)*(1+x)/(2x-1)=______for_______
The simplified expression is (x+1)^2/(2x-1).
What is the simplified form of the expression?To simplify the expression ((x)/(x+1)+1)*(1+x)/(2x-1), we can begin by multiplying the numerator and denominator of the first fraction by x+1 to eliminate the fraction in the numerator:
((x)/(x+1)+1)*(1+x)/(2x-1)
= ((x)/(x+1)*(x+1)/(x+1) + (x+1)/(x+1)) * (1+x)/(2x-1)
= (x(x+1)/(x+1) + (x+1)/(x+1)) * (1+x)/(2x-1)
= (x + 1) * (1+x)/(2x-1)
= (x^2 + 2x + 1)/(2x-1)
Now, the expression is simplified to (x^2 + 2x + 1)/(2x-1).
We can further simplify this expression by factoring the numerator as (x+1)^2:
(x^2 + 2x + 1)/(2x-1) = (x+1)^2/(2x-1)
Note that I did not solve for any variables or values, as the original expression did not provide an equation or specific values to solve for. Instead, I simplified the expression to its most simplified form.
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Which city should you live in if you want to live in a city with greater variability of temperature?
Answer: If you want to live in a city with greater variability of temperature, you should look for cities with a continental climate. Continental climates are characterized by hot summers and cold winters, with large temperature fluctuations between day and night and between seasons.
Cities located in the interior of large landmasses, far from large bodies of water, are more likely to have a continental climate. Examples of cities with a continental climate include Moscow (Russia), Calgary (Canada), and Chicago (USA). These cities experience wide temperature swings throughout the year, with hot summers and cold winters.
On the other hand, cities located near large bodies of water tend to have a more moderate climate, with smaller temperature fluctuations. Examples of such cities include San Francisco (USA), Sydney (Australia), and London (UK). These cities experience mild summers and winters, with relatively constant temperatures throughout the year.
Step-by-step explanation:
Given that tangent theta = negative 1, what is the value of secant theta, for StartFraction 3 pi Over 2 EndFraction less-than theta less-than 2 pi?
Negative StartRoot 2 EndRoot
StartRoot 2 EndRoot
0
1
The value of secant theta is √2. The solution has been obtained by using trigonometry.
What is trigonometry?Trigonometry, a subfield of mathematics, is the study of the sides, angles, and connections of the right-angle triangle.
We are given that tangent theta = -1
We know that tan θ = sin θ / cos θ
So,
⇒ -1 = sin θ / cos θ
⇒ -cos θ = sin θ
We know that angle θ lies in the 4th quadrant i.e. between 3π/2 and 2π.
In the 4th quadrant, at 7π/4, the above is true.
So, at θ = 7π/4, we get
cos (7π/4) = √2/2
We know that
sec θ = 1 / cos θ
So,
sec θ = √2
Hence, the value of secant theta is √2.
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The star-spangled banner that flew over fort mchenry during the war of 1812 had a perimeter of 144 ft. Its length measured 12 ft more than its width. Use a system of equations to find the dimensions of this flag, which is displayed in the Smithsonian Institution's Museum of America History in washington, D. C
If the length of the flag is 12 ft more than its width, then the width of the flag is 30ft and length of the flag is 42ft.
Let "w" represent the width of the flag.
We know that the length of the flag is 12 feet more than its width, which means:
⇒ Length = w + 12
We also know that the perimeter of the flag is 144 feet,
The Perimeter of flag can be expressed as:
⇒ Perimeter = 2(Length + Width),
Substituting the expression for Length from above,
We get,
⇒ 144 = 2(w+12 + w)
Simplifying the equation:
We get,
⇒ 144 = 2(2w + 12)
⇒ 72 = 2w + 12
⇒ 60 = 2w
⇒ w = 30
So, width of flag is 30 feet. and Length = w + 12,
⇒ Length = 30 + 12
⇒ Length = 42
Therefore, the dimensions of the flag are 42feet by 30feet.
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Using composition, determine if the functions are inverses: f(x)=(2)/(3)x-8 and g(x)=(3)/(2)x+12
Both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.
To determine if the functions f(x) and g(x) are inverses using composition, we need to find f(g(x)) and g(f(x)) and see if they both equal x.
First, let's find f(g(x)):
f(g(x)) = f((3)/(2)x+12)
= (2)/(3)((3)/(2)x+12)-8
= (2)/(3)(3)/(2)x + (2)/(3)(12) - 8
= x + 8 - 8
= x
Now, let's find g(f(x)):
g(f(x)) = g((2)/(3)x-8)
= (3)/(2)((2)/(3)x-8) + 12
= (3)/(2)(2)/(3)x - (3)/(2)(8) + 12
= x - 12 + 12
= x
Since both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.
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Find the distance from the point $\left(1,\ 2\right)$ to the line $y=\frac{1}{2}x-3$
. Round your answer to the nearest tenth.
The distance from the point [tex]$(1,2)$[/tex] to the line [tex]$y=\frac{1}{2}x-3$[/tex] is approximately 3.7 units.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and operators, which when evaluated, produces a value. An expression can contain constants, variables, functions, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information :To find the distance from a point to a line, we need to find the length of the perpendicular segment from the point to the line.
The line [tex]$y=\frac{1}{2}x-3$[/tex] can be rewritten in slope-intercept form as [tex]$y = \frac{1}{2}x - 3$[/tex], so its slope is [tex]\frac{1}{2}$.[/tex]
A line perpendicular to this line will have a slope that is the negative reciprocal of [tex]\frac{1}{2}$[/tex], which is [tex]-2$.[/tex]
We can then use the point-slope form of a line to find the equation of the perpendicular line that passes through the point [tex]$(1,2)$[/tex]:
[tex]$y - 2 = -2(x - 1)$[/tex]
Simplifying, we get:
[tex]$y = -2x + 4$[/tex]
Now we need to find the point where the two lines intersect, which will be the point on the line [tex]$y = \frac{1}{2}x-3$[/tex] that is closest to [tex]$(1,2)$[/tex]. We can do this by setting the equations of the two lines equal to each other and solving for [tex]$x$[/tex]:
[tex]$\frac{1}{2}x - 3 = -2x + 4$[/tex]
Solving for [tex]$x$[/tex], we get:
[tex]$x = \frac{14}{5}$[/tex]
To find the corresponding [tex]$y$[/tex] value, we can substitute this value of [tex]$x$[/tex] into either of the two line equations. Using [tex]$y = \frac{1}{2}x-3$[/tex], we get:
[tex]$y = \frac{1}{2} \cdot \frac{14}{5} - 3 = -\frac{7}{5}$[/tex]
Therefore, the point on the line [tex]$y = \frac{1}{2}x-3$[/tex] that is closest to [tex]$(1,2)$[/tex] is [tex]$\left(\frac{14}{5}, -\frac{7}{5}\right)$[/tex].
Finally, we can use the distance formula to find the distance between [tex]$(1,2)$[/tex] and [tex]$\left(\frac{14}{5}, -\frac{7}{5}\right)$[/tex]:
[tex]$\sqrt{\left(\frac{14}{5} - 1\right)^2 + \left(-\frac{7}{5} - 2\right)^2} \approx 3.7$[/tex]
Rounding to the nearest tenth, the distance from the point [tex]$(1,2)$[/tex] to the line [tex]$y=\frac{1}{2}x-3$[/tex] is approximately 3.7 units.
Therefore, the distance from the point [tex]$(1,2)$[/tex] to the line [tex]$y=\frac{1}{2}x-3$[/tex] is approximately 3.7 units.
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As khan and jorman practice for college entrance tests, their scores increase. Khan's current score is 750 and is rising 8 points per week.Jormans current score is 650 but is growing by 30 points each week. write and solve a system of equations uising the equal values method to determine when their scores will be the same and what that score will be
Khan and Jorman's scores will be the same in 4.545 weeks, and their score at that time will be 786.36 using the equal values.
What exactly is the equal values approach?With the equal values approach, two expressions are made equal, and the variable that makes them equal is then solved for. When solving systems of equations with two variables, this is often done in order to determine the values of the two variables that will simultaneously make the equations true.
Let us suppose the number of weeks = y.
Let us suppose the score = x.
Given that, Khan's current score is 750 and is rising 8 points per week.
Khan's score: y = 8x + 750
Jormans current score is 650 but is growing by 30 points each week:
Jorman's score: y = 30x + 650
Their scores will be equal at:
8x + 750 = 30x + 650
22x = 100
x = 4.545
Substitute the value of x in the equation to obtain y:
y = 8(4.545) + 750
y = 786.36
Hence, Khan and Jorman's scores will be the same in 4.545 weeks, and their score at that time will be 786.36.
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Find the equation of the line shown. 10 9 8 6 5 4 3 2 1 1 23 4 5 67 8 9 10
The equation of the line shown is y = 2x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2
Constant of proportionality, k = 2.
Therefore, the required equation is given by:
y = kx
y = 2x
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In a certain shipment, the weights of twelve books average 2. 75 pounds. If one of books is removed, the weights of the remaining books average 2. 70 pounds. What was the weight, in pounds, of the book that was removed?
Answer:
Let's call the weight of the book that was removed "x".
The total weight of the twelve books can be represented as 12 times the average weight of 2.75 pounds:
12(2.75) = 33
After the book is removed, there are only 11 books left, and their total weight can be represented as 11 times the new average weight of 2.70 pounds:
11(2.70) = 29.7
We can set up an equation using these two expressions and the weight of the book that was removed:
33 - x = 29.7
Solving for x, we get:
x = 33 - 29.7
x = 3.3
Therefore, the weight of the book that was removed was 3.3 pounds.
the options are
A- 156
B-91
C-26
D-11
The solution is, that central angle Ф is, 3.49 radians.
What is arc length?Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.
here, we have,
The arc length formula is s = rФ,
where r is the radius and Ф is the central angle.
We know s and r and need to calculate Ф.
now, we get,
From s = rФ
we get Ф = central angle = s/r
Here, that central angle Ф is,
(31.4 cm) / 9 cm
= 3.49 radians
Hence, The solution is, that central angle Ф is, 3.49 radians.
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Please type the answer by company so that i can see it clearly, thank you!
The occupational safety of workers in Country ABC piqued the curiosity of a safety officer. Country ABC was split into 18 districts by the officer. For personal interviews, five workers were chosen at random from each district. The following are some of the questions that were asked during the interview.
Question (I) – How many days did you work on November 2021 (total 30 days)?
Question (II) – Which district are you living in?
Question (III) – Do you agree that the safety standard in your working environment is high? (Totally disagree/ disagree/ neutral/ agree/ totally agree)
Question (IV) – How much is your daily salary (in HK$100)?
Questions
For each of the following variables, determine whether the variable is qualitative or quantitative. If the variable is quantitative, determine whether the variable is discrete or continuous. In addition, indicate the level of measurement.
(i) The number of days that the worker worked on November 2021
(ii) District that the worker is living in
(iii) Level of agreement on the high safety standard in the working environment of the worker
(iv) Daily salary of the worker (in HK$100)
Quantitative, discrete, ratio
(i) Quantitative, discrete, interval
(ii) Qualitative, nominal
(iii) Qualitative, ordinal
(iv) Quantitative, discrete, ratio
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What does a simple machine do when it makes your effort less?
makes work go faster
makes your power more
makes the amount of work you do less
makes resistance force greater than applied force
Answer: it can change the amount of force that you can apply on an object.
Step-by-step explanation:
Answer:
Simple machine makes work go faster
Step-by-step explanation:
If you replace human Labour with simple machine, work is completed faster. It increases output
11 1 point When dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be 5 .
when dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be -5.
The given polynomial equation is x^(4)-3x^(3)-7x^(2)-80 and we have to divide it by x-5 to find the remainder.
Set up the long division as follows:
```
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
```
Divide the first term of the dividend (x^(4)) by the first term of the divisor (x) to get the first term of the quotient (x^(3)):
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
```
Multiply the first term of the quotient (x^(3)) by the divisor (x-5) and write the result below the dividend:
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
x^(4) - 5x^(3)
```
Subtract the result from the dividend to get the new dividend:
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
x^(4) - 5x^(3)
--------------
2x^(3) - 7x^(2)
```
Repeat the process with the new dividend until the degree of the remainder is less than the degree of the divisor:
```
x^(3) + 2x^(2) + 3x + 15
______________________
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
x^(4) - 5x^(3)
--------------
2x^(3) - 7x^(2)
2x^(3) - 10x^(2)
---------------
3x^(2) + 0x
3x^(2) - 15x
------------
15x - 80
15x - 75
--------
-5
```
The remainder is -5. Therefore, when dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be -5.
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what’s the answer lol <3
Answer:
Should be the second answer.
Step-by-step explanation:
A person has rupees 210 he wants to donate it he gives rupees 1 for first day rupees 2 for second day rupees 3 for third day and so on for donation he can donate this for maximum how munch days
Answer: This is a classic problem in mathematics known as the arithmetic series or the Gauss sum.
To find out how many days the person can donate with a total of Rs. 210, we need to sum the sequence of donations until we reach the total amount of Rs. 210. The sequence of donations is:
1 + 2 + 3 + 4 + 5 + ... + n
The sum of the sequence can be expressed as:
n(n+1)/2
So we need to solve the equation:
n(n+1)/2 = 210
n(n+1) = 420
n^2 + n - 420 = 0
We can solve this quadratic equation using the quadratic formula:
n = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 1, and c = -420.
n = (-1 ± sqrt(1^2 - 4(1)(-420))) / 2(1)
n = (-1 ± sqrt(1 + 1680)) / 2
n = (-1 ± sqrt(1681)) / 2
n = (-1 ± 41) / 2
Since we are looking for a positive integer value of n, we can discard the negative solution:
n = (41 - 1) / 2
n = 40 / 2
n = 20
Therefore, the person can donate for a maximum of 20 days with a total donation of Rs. 210, starting with Rs. 1 on the first day and increasing by Rs. 1 each day.
Step-by-step explanation:
help me please with this math
1. Suppose FR" - Rand GR" - Rare linear functions. That is they each preserve vector additions in their own dimension and ca multiplications. Show that G. F is a near function de, that it respects vec
FR" - Rand GR" - Rare linear functions. That is they each preserve vector additions in their own dimension and ca multiplications. G ∘ F is a linear function.
The question is asking you to show that the composition of two linear functions, G and F, is a linear function itself.
To show that G ◦ F is a linear function, we need to show that it satisfies the two properties of linearity: preservation of vector addition and preservation of scalar multiplication.
Let's first consider preservation of vector addition:
(G ◦ F)(u + v) = G(F(u + v)) [by definition of composition]
= G(F(u) + F(v)) [since F preserves vector addition]
= G(F(u)) + G(F(v)) [since G preserves vector addition]
= (G ◦ F)(u) + (G ◦ F)(v) [by definition of composition]
Therefore, G ◦ F preserves vector addition.
Now let's consider preservation of scalar multiplication:
(G ◦ F)(ku) = G(F(ku)) [by definition of composition]
= G(kF(u)) [since F preserves scalar multiplication]
= kG(F(u)) [since G preserves scalar multiplication]
= k(G ◦ F)(u) [by definition of composition]
Therefore, G ◦ F preserves scalar multiplication.
Since G ◦ F satisfies both properties of linearity, it is a linear function that preserves vector addition and scalar multiplication.
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A 7-pack of felt-tip pens costs $4.65. What is the unit price, rounded to the nearest cent?
per pen
Answer: 0.66 cents per pen
Step-by-step explanation:
$4.65 for a pack of 7 pens. You want to divide $4.65 by 7 and you get 0.66
What is the volume of this rectangular
prism?
A. 18 3/8in.³
B. 27 in.³
C. 29 1/4in.'
D. 40 1/2in.³
Answer:29 1/4
Step-by-step explanation:
Because the formula for the volume of a rectangular prism is (w)(h)(l).
a rectangular field has side lenght that measure 9\10 mile and 1\2 mile. what is the area of the field?
The area of rectangular field is [tex]\frac{9}{20} \ \text{miles}^2[/tex].
What is area of rectangle?The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
Here the given rectangle , length= [tex]\frac{9}{10}[/tex]miles and Breadth = [tex]\frac{1}{2}[/tex]miles
Now using area of rectangle formula,
=> A = length× breadth square unit.
=> A = [tex]\frac{9}{10}\times\frac{1}{2}[/tex]
=> A = [tex]\frac{9}{20} \ \text{miles}^2[/tex]
Hence the area of rectangular field is [tex]\frac{9}{20} \ \text{miles}^2[/tex].
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For the points (−8,5) and (−6,−1), (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Part 1 of 2 (a) The exact distance between the points is Part 2 of 2 (b) The midpoint is
(a) The exact distance between the points is 2√10.
(b) The midpoint of the line segment is (-7, 2).
(a) To find the distance between the two given points, use the distance formula, which is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²].
In this case, x₁ = -8, y₁ = 5, x₂ = -6, and y₂ = -1.
Plugging these values into the formula gives us:
d = √[(-6 - (-8))² + (-1 - 5)²]
d = √[(2)² + (-6)²]
d = √[4 + 36]
d = √40
d = 2√10
(b) The midpoint of a line segment can be found using the midpoint formula, which is:
(x₁ + x₂)/2, (y₁ + y₂)/2.
In this case, x₁ = -8, y₁ = 5, x₂ = -6, and y₂ = -1.
Plugging these values into the formula gives us:
midpoint = [(-8 + -6)/2, (5 + -1)/2]
midpoint = [(-14)/2, (4)/2]
midpoint = (-7, 2)
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The original price of a pair of shorts was £28. In a sale they were reduced by of their original price. What was their sale price? Original price = £28 Sale price = £
Answer:
free
Step-by-step explanation:
28-28=0
How do I solve these two ?
Geometry
The length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:
11). x = 11√3 and y = 33
12). x = 4√7 and y = 8√7
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
recall that sin60° = √3/2 and cos60° = 1/2
For question 11:
sin 60° = y/22√3 {opposite/hypotenuse}
y = 22√3 × sin 60° {cross multiplication}
y = 22√3 × √3/2
y = 11 × 3
y = 33
cos 60° = x/22√3 {adjacent/hypotenuse}
x = 22√3 × cos 60° {cross multiplication}
x = 22√3 × 1/2
x = 11√3.
For question 12:
sin 60° = 4√21/y {opposite/hypotenuse}
y = 4√21/sin 60° {cross multiplication}
y = 4√21 ÷ √3/2
y = 4√21 × 2/√3
y = 4√7 × 2
y = 8√7
cos 60° = x/8√7 {adjacent/hypotenuse}
x = 8√7 × cos 60° {cross multiplication}
x = 8√7 × 1/2
x = 4√7
Therefore, the length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:
11). x = 11√3 and y = 33
12). x = 4√7 and y = 8√7
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To be on the safe side, three detectors were installed in a factory room to make sure that if there was a fire, at least one of them would signal a warning. The company that manufactured the smoke detectors indicated that, based on their testing, the probability that any one of the smoke detectors will work correctly is 0.75 (meaning that it works 75% of the time in the long run). This also means that there is a 25% chance that if there is smoke or a fire, the detector will not work! What is the probability that if there was smoke in the factory, none of the 3 detectors would work? Does this probability indicate a safety problem for the factory? Explain.
PLEASE HELP MEEEE!!
The probability that none of the 3 detectors would work if there was smoke in the factory is 0.25³, or 0.015625 (1.56%).
What is Probability?Probability is a branch of mathematics that deals with the likelihood of certain outcomes or events occurring. Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event that is certain to occur has a probability of 1, while an event that is impossible to occur has a probability of 0. The probability of an event occurring can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.
This probability indicates that the factory does have a safety problem, as there is a 1.56% chance that none of the smoke detectors would sound an alarm if there was smoke present. This presents a significant risk to the factory, as it could lead to an undetected fire that may cause damage to the facility or put employees in danger.
The company should look into ways to reduce the risk of the smoke detectors not working. One way to do this would be to increase the number of smoke detectors in the factory room, as the more detectors there are, the lower the probability that none of them will work. The company could also consider using more reliable smoke detectors that have a higher probability of working correctly when needed. Ultimately, the company should seek to reduce the risk of none of the detectors working by taking steps to increase the probability that at least one of them will sound an alarm in the event of smoke or a fire.
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Consider the expression.
17 (5) (9 + 14y)
Select all statements about the expression that are true.
There are exactly 4 terms.
One term of the expression is 23
The expression has exactly 3 factors.
The constant in the factor 9 + 14y is 9.
The factors in the expression are 17.5.9, and 14y.
Answer: None of the statements are true.
The expression has only two terms: 17 and (5)(9 + 14y).
No term in the expression equals 23.
The expression has three factors: 17, 5, and (9 + 14y).
The constant in the factor 9 + 14y is 9.
The factors in the expression are 17, 5, 9, and (9 + 14y).
Step-by-step explanation:
Si el dividendo es 872 y el cociente es 62 y residuo es 4 cual es el divisor
If the dividend is 872 and the quotient is 62 and remainder is 4, the divisor is equal to 14.
What is a quotient?In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.
How to calculate the dividend?In Mathematics, dividend can be calculated by using this mathematical expression:
Dividend = divisor × quotient + residual
Substituting the given data points into the dividend formula, we have the following;
Dividend = divisor × quotient + residual
872 = divisor × 62 + 4
Divisor = (872 - 4)/62
Divisor = 868/62
Divisor = 14
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Complete Question;
If the dividend is 872 and the quotient is 62 and remainder is 4. What is the divisor?
(1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) The restrictions on the variable in the rational equation are x!= and x!
The restrictions on the variable in the rational equation (1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) are x != 4 and x != -5.
The restrictions on the variable in the rational equation are x != 4 and x != -5. This is because the denominators of the rational expressions (x-4) and (x+5) cannot equal zero, as division by zero is undefined.
To find the restrictions, we can set each denominator equal to zero and solve for x:
x - 4 = 0 => x = 4
x + 5 = 0 => x = -5
So, the restrictions are x != 4 and x != -5.
In summary, the restrictions on the variable in the rational equation (1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) are x != 4 and x != -5.
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find the value of x,
de=5
The solution is, the value of x is, x=10.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
from the given figure, we get,
the two triangles are similar
and, DE is the bisector of other two sides,
so, we know from the property of triangles, that,
DE = 1/2 * AB
we have,
DE = 5
and. AB =x
so, we get,
5 = x/2
or, x = 10
Hence, The solution is, the value of x is, x=10.
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I need help this is due today
The measurements are shown in the solution
What are Trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Given are right triangles, we need to find the value of x in each,
We will use Trigonometric ratios to find the same,
The sine is the ratio between the length of the opposite leg and the length of the hypotenuse.
The cosine is the ratio between the length of the adjacent leg and the length of the hypotenuse.
The tangent is the ratio between the length of the opposite leg divided by the length of the adjacent leg.
1) sin 21° = 11/x
x = 30.7
2) cos 34° = x/28
x = 23.21
3) tan 49° = 33/x
x = 28.68
4) T = cos⁻¹ (11/23)
= 61.42°
5) T = sin⁻¹(21/44)
= 28.50°
6) T = tan⁻¹(8/12)
= 33.7°
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