The solution of the assumed equation is
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
Assuming the equation is
csc^2(θ) = 2cot(θ) + 4
and not
Assuming the equation to be:
csc^2(θ) = cot^2(θ) + 1
Solving these equations usually begins with algebra and/or trigonometry. ID for transforming equations to have one or more equations of the form:
trigfunction(expression) = number
It is not always easy to understand how to perform the desired transformation. If it's not obvious, first use the trigonometric identity to reduce the number of different arguments or functions in the equation. In this expression, all arguments are θ. Therefore, there is no need to reduce the number of arguments. But he has two different functions, csc and cot.
csc^2(θ) = cot^2(θ) + 1
Substituting the right side of this equation into the left side of the equation, we get: :
cot^2 (θ) + 1 = 2 cot(θ) + 4
Now that we have only one function cot and one argument θ, we are ready to find the form we need. Subtracting the entire right-hand side from both sides gives:
cot^2(θ) - 2cot(θ) - 3 = 0
The left-hand side factorizes:
(cot(θ)-3)(cot (θ) ) + 1 ) = 0
Using the properties of the zero product,
cot(θ) = 3 or cot(θ) = -1
These two equations are now in the desired form.
The next step is to write the general solution for each equation. The general solution represents all solutions of the equation.
cot(θ) = 3
Note that 3 is not a specific angle value for cot. That's why you need a calculator. Your computer probably doesn't have the crib button, so you'll need to switch it to tan
Since tan is the reciprocal of cot, if cot = 3...
tan(θ) = 1/3
Inverse tan tan^-1(1/3) can be used to find the reference angle. You should get a reference angle of 18.43494882 degrees. Using this reference angle and cot (and tan) being positive in the 1st and 3rd quadrants, we get the general solutions
θ = 18.43494882 + 360k
and
θ = 180 + 18.43494882 + 360k
.
θ = 198.43494882 + 360k
where
cot(θ) = -1
-1 should be recognized as a special angle value for cot. So you don't need a calculator. This reference angle is 45 degrees. Using this reference angle, cot is negative in the 2nd and 4th quadrants, so
θ = 180 - 45 + 360k
and
θ = -45 + 360k (or 360 - 45 + 360k) the general solution for
must get. to:
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
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If ₹405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
I will mark the first answerer as Brainliest.
Answer:
A = 20%
B = 33.33%
C = 46.67%
Step-by-step explanation:
Ok we need to add up 3, 5, and 7
3+5+7 = 15
405/15 = 27.
27*3 = A
27*5 = B
27*7 = C
A = 81 / 20%
B = 135 / 33.33%
C = 189 / 46.67%
The long division below shows the first term of the quotient. which polynomial should be subtracted from the dividend first? x 2 startlongdivisionsymbol x cubed 3 x squared x endlongdivisionsymbol to get a quotient of x squared
The polynomial that should be subtracted from the dividend first is; x³ + 2x²
How to carry out polynomial long division?
The long division we are given is;
__________
x + 2 ) x³ + 3x² + x
Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².
Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;
(x + 2) * (x²) = x³ + 2x²
Thus, the polynomial to be subtracted is x³ + 2x²
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HELP ASAP!!! 40 POINTS
Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x2 + 5x − 12 belongs to the interval (-1, 1).
Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:
(-15,-10).
What is the slope of the tangent line to a function f(x) at point x = x0?It is given by the derivative at x = x0, that is:
[tex]m = f^{\prime}(x_0)[/tex].
In this problem, the function is:
[tex]f(x) = 0.2x^2 + 5x - 12[/tex]
Hence the derivative is:
[tex]f^{\prime}(x) = 0.4x + 5[/tex]
For a slope of -1, we have that:
0.4x + 5 = -1
0.4x = -6
x = -15.
For a slope of 1, we have that:
0.4x + 5 = 1.
0.4x = -4
x = -10
Hence the interval is:
(-15,-10).
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What is the value of the expression when n = 3?
StartFraction 6 (n squared plus 2) Over n EndFraction
16
22
30
66
Answer:
B) 22
Step-by-step explanation:
The expression is:
[tex]\cfrac{6(n^2+2)}{n}[/tex]Find its value when n = 3, substitute n with 3 in the expression:
[tex]\cfrac{6(3^2+2)}{3} =\cfrac{6(9+2)}{3} =\cfrac{6(11)}{3}=2(11) = 22[/tex]The matching answer choice is B.
OA=
Please help asap!! Thanks so much :))
In the given diagram, the value of the dashed side of rhombus OABC is 5
Distance between two pointsFrom the question, we are to determine the length of the dashed line (OA), in rhombus OABC
In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).
Using the formula for calculating distance between two points,
d =√[(x₂-x₁)² + (y₂-y₁)²]
In the diagram,
The coordinate of the origin is (0, 0)
The coordinate of point A is (3, 4)
Thus,
x₁ = 0
x₂ = 3
y₁ = 0
y₂ = 4
Putting the parameters into the formula, we get
OA =√[(3-0)² + (4-0)²]
OA =√(3² + 4²)
OA =√(9+16)
∴ OA =√25
OA = 5
Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5
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A basketball player averages 12.5 points per game. There are 24 games in a season. At this rate, how many points would the player score in an entire season?
In the entire season, the basketball player would score
point
Answer:
300 points
Step-by-step explanation:
Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:
[tex]\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300[/tex]
Question 5(Multiple Choice Worth 2 points)
(07.01 MC)
What is the range of the function f(x) = x - 3?
Answer:
(-∞, ∞)
Step-by-step explanation:
Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."
Linear functionThe given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."
-∞ < f(x) < ∞
(-∞, ∞) . . . . . in interval notation
Build Your Math Skills 2A, Round decimals to the nearest hundredth (0.01): 42.988
Answer: 42.99
Step-by-step explanation:
42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.
A polynomlal function has x-Intercepts at -2, ;, and 2 and a relative maximum at x=-1. graph Which graph matches the description of this function?
The graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.
How to Determine the Graph of a Polynomial Function?We are given that the polynomial function has the following characteristics:
Relative maximum at x = -1, this implies that the peak point of the graph has an x-value that is equal to -1. In order words, the "mountain" is at x = -1.
Graph A has a "mountain" that is at x = -1.
We are given the x-intercepts of the polynomial function as:
-2, 1/2, and 2. This means that the graph intercepts the x-axis at -2, 1/2, and 2.
Graph A in the image attached has x-intercepts of -2, 1/2, and 2.
Therefore, we can conclude that the graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.
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A circle is circumscribed around a rectangle with sides lengths 6 and 8 what is the area of the circle?
A. 16[tex]\pi[/tex]
B. 20[tex]\pi[/tex]
C. 24[tex]\pi[/tex]
D. 25[tex]\pi[/tex]
E. 30[tex]\pi[/tex]
Answer:
D. 25pi
Step-by-step explanation:
"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)
6^2 + 8^2 = d^2
36 + 64 = d^2
100 = d^2
d = 10
This is the diameter of the circle. The radius would then be 5.
Area of a circle is:
A = pi•r^2
= pi•5^2
= 25pi
H=(,),()
F=(),()
Help please asap
Thanks so much
From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
According to the statement
we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.
So, to find the points of the rectangle
firstly the given points are:
E(2,3) And G(-2,-2) and we have to find the point H and F.
So, The point H :
For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.
So, the point H become H(-3,3)
And for point F:
For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.
So, the Point F become F(2,-2).
So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
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Find the general solution of the given system of odes. { dx/dt =2x 2y,dy/dt =x 3y}
The general solution of the given system of odes is
m=1 ; m=4 (real roots)
In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.
the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.
It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.
dx/dt = 2x+2y = x^1 = 2x+2y 1
dy/dt = x+3y = y^1 = x+ 3y 2
differentiating 1 with respect to 't'
x^11 = 2x^1+ 2y^1
y^1 = x+3y
x^11 = 2x^1= 2(x+3y)
x^11 = 2x^1+ 2x+ 6y
x^11 = 2x^1+ 2x+ 6(x^1-2x/2)
x^11 = 2x^1+ 2x+ 3x^1- 6x
x^11 = 5x^1 - 4x
x^11 -5x^1 - 4x
x^11 - 5x^1 -4x =0
Auxillary equation is m^5- 5m+4=0
m^2 - m - 4m + 4 = 0
m(m-1) -4 (m-1) =0
(m-1) (m-4) = 0
m=1 ; m=4 (real roots)
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if a(5,3),b(0,0) and c(-3,5) are the vertices of a triangle then the value of AB.BC is
The dot product associated to sides AB and BC is 0.
What is the dot product generated by two sides of a triangle?
In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:
Side BA
BA = (5, 3) - (0, 0)
BA = (5, 3)
Side BC
BC = (- 3, 5) - (0, 0)
BC = (- 3, 5)
By definition of dot product, the result associated to the two sides of the triangle is:
BA • BC = (5, 3) • (- 3, 5)
BA • BC = (5) · (- 3) + (3) · (5)
BA • BC = - 15 + 15
BA • BC = 0
The dot product associated to sides AB and BC is 0.
Remark
The statement is poorly formatted, the correct form is shown below:
If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:
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The face of a clock is divided into 12 equal parts. the radius of the clock face is 10 inches. assume the hands of the clock will form a central angle. the face of a clock is divided into 12 equal parts. which statements about the clock are accurate? select three options.
The options C and E is a correct options which are
C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.
E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.
According to the statement
we have given that the radius of the clock face is 10 inches and the face of a clock is divided into 12 equal parts.
And we have to choose the three statements which are correct from the given options.
So,
Check the all given options to find the correct options.
So, OPTION A :
360/12=30 degrees between each number
3-1 = 2 2*30 = 60 degrees so A is FALSE
Now, OPTION B:
C=2 x π x r
r=10
using 3.14 for PI = 10*3.14 =31.4 x 2 = 62.8 so B is TRUE
Now OPTION C:
30 x 4 = 120 degrees = TRUE
Now, OPTION D:
10-3 = 7
7/12 x 62.8 = 0.5833*62.8 = 36.63 inches = FALSE
Now, OPTION E:
1/12=0.0833 x 62.8 = 5.23 rounded to 5.2 = TRUE
So, The options C and E is a correct options which are
C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.
E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.
Disclaimer: This question was incomplete. Please find the full content below.
Questions:
The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.
Which statements about the clock are accurate? Check all that apply.
A. The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.
B. The circumference of the clock is approximately 62.8 inches.
C.The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.
D. The length of the major arc between 3 and 10 is approximately 31.4 inches.
E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.
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Li Juan solves the equation below by first squaring both sides of the equation. [tex]\sqrt{3-2w}=w+6[/tex]
What extraneous solution does Li Juan obtain?
Answer:
w = -11
Step-by-step explanation:
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex](\sqrt{3 - 2w})^2 = (w + 6)^2[/tex]
[tex] 3 - 2w = w^2 + 12w + 36 [/tex]
[tex] w^2 + 14w + 33 = 0 [/tex]
[tex] (w + 11)(w + 3) = 0 [/tex]
[tex] w + 11 = 0 [/tex] or [tex] w + 3 = 0 [/tex]
[tex] w = -11 [/tex] or [tex] w = -3 [/tex]
When you square both sides of an equation, you must check all solutions for extraneous solutions.
Check w = -11.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-11)} = -11 + 6 [/tex]
[tex] \sqrt{3 + 22} = -5 [/tex]
[tex] \sqrt{25} = -5 [/tex]
[tex] 5 = -5 [/tex]
This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.
Check w = -3.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-3)} = -3 + 6 [/tex]
[tex] \sqrt{3 + 6} = 3 [/tex]
[tex] \sqrt{9} = 3 [/tex]
[tex] 3 = 3 [/tex]
This is a true statement, so the solution w = -3 is valid.
Answer: w = -11
Which equation could represent a linear combination of the system?
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Complete question
The system of equations below has no solution.
2/3x + 5/2y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0, and x y≤6
For function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
For given question,
We have been given a function k(x, y) = -x² - y² + 4x + 4y
We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
First we find the partial derivative of function k(x, y) with respect to x.
⇒ [tex]k_x=-2x+4[/tex]
Now, we find the partial derivative of function k(x, y) with respect to y.
[tex]\Rightarrow k_y=-2y+4[/tex]
To find the critical point:
consider [tex]k_x=0[/tex] and [tex]k_y=0[/tex]
⇒ -2x + 4 = 0 and -2y + 4 = 0
⇒ x = 2 and y = 2
This means, the critical point of function is (2, 2)
We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
Consider k(0, 0)
⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)
⇒ k(0, 0) = 0
Consider k(3, 3)
⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)
⇒ k(3, 3) = -9 - 9 + 12 + 12
⇒ k(3, 3) = -18 + 24
⇒ k(3, 3) = 6
Therefore, for function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
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What number has to fill in the blank to make this a perfect square trinomial: 9x^2 + ___+ 144
The number that has to fill the blank to make the trinomial a perfect square is 72x
Perfect square trinomialFrom the question, we are to determine the number that makes the given trinomial a perfect square
The given trinomial is
9x² + ___+ 144
For any given trinomial ax² + bx + c, the trinomial is a perfect square if
b² = 4ac
In given trinomial,
a = 9, c = 144, b = ?
Now, we will determine the value of b
Putting the values into the equation,
b² = 4ac
b² = 4×9×144
b² = 5184
b = √5184
b = 72
Thus,
The trinomial will become 9x² + 72x+ 144
Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x
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he table shows the mean number of basketball goals made by four random samples of players from the school team during this year’s season. Sample # Sample Mean Number of Goals 1 7 2 4 3 5 4 8 Is a valid prediction for the mean of the population possible using these samples? No, there are not enough samples. Yes, the sample means are all less than 10. Yes, the variation of the sample means is small. No, the variation of the sample means is too great.
The valid prediction for the mean of the population possible using these samples is C. Yes, the variation of the sample means is small
What is a sample mean?It should be noted that a sample mean is an average of a set of data . Also, the sample mean can be used to calculate the standard deviation, central tendency, and the variance of a data set.
The sample mean can be applied to a variety of uses, including calculating population averages.
Here, the sample variance is a measure of the degree to which the numbers in a list are spread out. Here, the numbers given are close to each other.
If the numbers in a list are all close to the expected values, the variance will be small and if they are far away, the variance will be large.
Therefore, the correct option is C.
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Answer:
C: Yes, the variation of the sample means is small.
Step-by-step explanation:
Correct answer on edge
A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. what is the name of the polygon?octagonhexagonheptagonquadrilateral
The name of the polygon is (B) hexagon.
What is a hexagon?A hexagon is a six-sided polygon or 6-gon in geometry. The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.To find the name of the polygon:
Let the number of sides in a polygon be n.Triangles are formed by drawing diagonals from one vertex to each of the others.Because there is no overlapping of the triangles, no diagonal will be drawn back to itself, and the diagonals to each adjacent vertex will lie on top of the adjacent sides, so the number of diagonals from a single vertex is three less than the number of sides or n - 3, and the number of triangles is one more, or n - 2. Number of triangles = number of sides in polygon - 2 Number of triangles = n - 2 n = 4 + 2 n = 6The polygon containing 6 sides is called a hexagon.Therefore, the name of the polygon is (B) hexagon.
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The complete question is given below:
A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?
A) Octagon
B) Hexagon
C) Heptagon
D) Quadrilateral
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 634" by 412" on the drawing, how large is the bedroom?
For a bedroom measuring 6 3/4" by 4 1/2" on the drawing, the dimensions of the bedroom are 18 ft. by 27 ft.
Option (C) is correct.
In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
According to the question,
The scale of an architectural sketch is 1/4" = 1'. If, according to the drawing, a bedroom has the dimensions 6 3/4 by 4 1/2 inches.
Then, the dimensions of the bedroom in feets are calculated as follows:
As 1/4" = 1'
6 3/4" = 27'= 27 ft.
Similarly,
4 1/2" = 18' =18 ft.
Thus, the dimensions of the bedroom are: 18 ft. by 27 ft.
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What is the las digit of the product of all the numbers between 11 and 29?
The last digit of the product of all the numbers between 11 and 29 is 0.
A product is something that has undergone one or more multiplications.
Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.
Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28
Now take note of the 20 that is present.
Any number multiplied by 20 will result in a zero, so:
Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)
Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.
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Hurry A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $510?
Answer:
Step-by-step explanation:
We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:
[tex]5x+10x=510[/tex]
Solve for x
[tex]15x=510\\x=34[/tex]
Now multiply x by the corresponding percentages to find how much was invested into each percentage.
[tex]34*5=170[/tex]
[tex]34*10=340[/tex]
Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.
We can of course check our answer by adding 170+340 which equals our original investment of 510.
$1800 is invested at 5% and the remainder, $4200, is invested at 10%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let us consider the amount invested at 5% x.
The amount invested at 10% is then the remainder, which is:
$6000 - x
Now we can set up an equation for the total interest earned:
0.05x + 0.10($6000 - x) = $510
Simplifying and solving for x:
0.05x + $600 - 0.10x = $510
-0.05x + $600 = $510
-0.05x = -$90
Divide both sides by 0.05
x = $1800
Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.
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What are the solutions to the system of equations? {−x+y=4y+12=x2+x
Answer: (-4, 0) and (4, 8)
Step-by-step explanation:
Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)
PLLLLLEASE I NEEED HELP
Answer:
-3/(b-6) = 3/(-b+6) = 3/(6-b)
Step-by-step explanation:
7/(b-6) + 10/(6-b)
= 7/(b-6) + 10/(-b+6)
= 7-10/(b-6)
= -3/(b-6) = 3/(-b+6) = 3/(6-b)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{6 - b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{ - (b - 6)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{7}{b - 6} - \cfrac{10}{ b - 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ - 3}{ b - 6}\:\:\: or \:\:\: \dfrac{3}{6-b} [/tex]
find the solution of the given simultaneous equations
y = 2x - 3
3x - 2y = 4
Answer:
Step-by-step explanation:
x+3y=1
The value of x from the set {1, 3, 5, 7} that holds true for the equation is?
The value of x from the given set of values is 5
Area and perimeter of a rectangleA rectangle is a 2 dimensional shape with 4 sides and angle. The formula for calculating the area and perimeter is given as:
Area = length * width
Perimeter = 2(length + width)
If the length of a rectangle is 2 inches more than its width and the perimeter of the rectangle is 24 inches, the resulting equation will be:
2x + 2(x + 2) = 24,
Expand and determine the value of "x"
2x+ 2x + 4 = 24
4x + 4 = 24
Subtract 4 from both sides
4x = 24 - 4
4x = 20
Divide both sides by 4
4x/4 = 20/4
x = 5
Hence the value of x from the given set of values is 5
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Complete question
The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches.
5 1/2 divided by 1 3/8
Answer:
4
Step-by-step explanation:
1. Convert from mixed number to fraction
[tex]5\frac{1}{2} =\frac{5(2)+1}{2} =\frac{11}{2}[/tex]
[tex]1\frac{3}{8}=\frac{(1)(8)+3}{8} =\frac{11}{8}[/tex]
2. Divide fractions
[tex]\frac{\frac{11}{2} }{\frac{11}{8} } =\frac{(11)(8)}{(11)(2)} =\frac{8}{2} =4[/tex]
Hope this helps
A three-digit number has one more ten than it has hundreds, and it also has one more than twice as many units as tens. The sum of the number and that number reversed is 31 less than 10 cubed. Find the reverse number.
15 pts
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
Read more about digits at:
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Please explain to me how to do this
Answer:
see explanation
Step-by-step explanation:
basically Gauss' method simplifies to
Sum = (number of terms) ÷ 2 × (1st term + last term)
43
S₂₀₀ = 200 ÷ 2 × (1 + 200) = 100 × 201 = 20,100
44
S₄₀₀ = 400 ÷ 2 × (1 + 400) = 200 × 401 = 80,200
45
S₈₀₀ = 800 ÷ 2 × (1 + 800 ) = 400 × 801 = 320,400
46
S₂₀₀₀ = 2000 ÷ 2 × (1 + 2000) = 1000 × 2001 = 2,001,000
Answer:
Sum = (number of terms) = 2 x (1st term + last term) 43
43. S200 = 200 = 2 × (1+200) = 100 201 = X 20,100
44 400 400 = 2 × (1+400) = 200 × 401 = 80,200
45 S800 = 800 = 2 × (1+800) = 400 × 801 = 320,400
46 S2000 = 2000 2 × (1+ 2000) = 1000 × 2001 = 2,001,000