Part a: The possible locations for the knight after two moves are a7, a5, e7 or e5.
Part b: A rook would have to move down 5 spaces and right 3 spaces, according to one possible translation.
How to describe a chess?One of the most well-known and oldest board games, played between two opponents on a checkered board with specifically made contrasting pieces, usually white and black After White moves first, players take turns in compliance with fixed rules, each attempting to force the opponent's main piece, the King, in to the checkmate—a position in which it cannot avoid capture.
Chess is played on a 64-square board divided into eight vertical rows known as files as well as eight horizontal rows known as ranks. These squares alternate among two colors: one light (white, beige, or yellow) and one dark (black or green). The board is positioned between the two competitors so that each has a light-colored square in the upper right corner.Niw, as per the given question;
Part a: The knight's first move can be to a6 (green square 1) or c6 (red square 1). If he lands on a6, he can move on to c7 or c5. He can land on a7, a5, e7, or e5 if he lands on c6.
Part b: The rook would have to move 5 spaces down and 3 spaces right.
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The complete quesion is-
Each chess piece has a path that it can follow to move. The rook, which begins in square a8, can only move vertically or horizontally. The knight, which begins in square b8, can move two squares horizontally and the one square vertically, or two squares vertically and one square horizontally. The bishop, which begins in square f8, can only move diagonally.
a. The knight moves 2 squares vertically and 1 square horizontally on its first move, then two squares horizontally and 1 square vertically on its second move. What are the possible locations for the knight after two moves?
b. After two moves, the rook is in square d3. Describe a possible translation to describe the two moves.
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
B(√3, 2,2√2) and C(-2√3, 4,4√2)
The midpoint is at ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
In the given statement is
To find the midpoint of the line segment joining the pair of points
B(√3, 2,2√2) and C(-2√3, 4,4√2)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2} ,[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points B(√3, 2,2√2) and C(-2√3, 4,4√2)
Solving for the midpoint , we have,
m = ([tex]\frac{\sqrt{3}+(-2\sqrt{3} ) }{2}, \ \frac{2+4}{2}, \frac{2\sqrt{2} +4\sqrt{2} }{2}[/tex])
m = [tex]\frac{-2\sqrt{3} }{2} ,\frac{6}{2},\frac{6\sqrt{2} }{2}[/tex]
m = ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
Therefore, the midpoint is at( [tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])
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a. A circle contains the points (0,0),(6,8) , and (7,7) . Find its equation by solving a system of three equations.
Using system of three equations, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.
The standard form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Substituting the values of the x and y coordinates of each point to the standard form of the equation of a circle, the three system of equations are:
(x - h)^2 + (y - k)^2 = r^2
(0 , 0) : (0 - h)^2 + (0 - k)^2 = r^2
(6 , 8) : (6 - h)^2 + (8 - k)^2 = r^2
(7 , 7) : (7 - h)^2 + (7 - k)^2 = r^2
Expanding these equations,
(0 , 0) : h^2 + k^2 = r^2 (equation 1)
(6 , 8) : 36 - 12h + h^2 + 64 - 16k + k^2 = r^2 (equation 2)
(7 , 7) : 49 - 14h + h^2 + 49 - 14k + k^2 = r^2 (equation 3)
Subtracting equation 1 from equation 2 and 3.
36 - 12h + h^2 + 64 - 16k + k^2 = r^2
- (h^2 + k^2 = r^2)
36 - 12h + 64 - 16k = 0
100 - 12h - 16k = 0
12h + 16k = 100
Dividing both sides by 4,
3h + 4k = 25 (equation 4)
49 - 14h + h^2 + 49 - 14k + k^2 = r^2
- (h^2 + k^2 = r^2)
49 - 14h + 49 - 14k = 0
98 - 14h - 14k = 0
14h - 14k = 98
h + k = 4 (equation 5)
h = 7 - k
Substitute h = 7 - k to equation 4 and solve for k.
3h + 4k = 25 (equation 4)
3(7 - k) + 4k = 25
21 - 3k + 4k = 25
k = 25 - 21
k = 4
Substitute the value of k to equation 5 and solve for h.
h = 7 - k (equation 5)
h = 7 - 4
h = 3
Substitute the value of h and k to equation 1 and solve for r.
h^2 + k^2 = r^2 (equation 1)
3^2 + 4^2 = r^2
9 + 16 = r^2
r^2 = 25
r = 5
Hence, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.
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can someone please help me
Answer:
It's B
Step-by-step explanation:
Step-by-step explanation:
[tex]\displaystyle\\12-15x > 22\\12-15x+15x > 22+15x\\12 > 22+15x\\12-22 > 22+15x-22\\-10 > 15x\\Divide\ both\ parts\ of \ the \ equation\ by\ 15:\\-\frac{10}{15} > x\\\\-\frac{5*2}{5*3} > x\\\\-\frac{2}{3} > x \\\\Thus,\\\\x < \frac{-2}{3}[/tex]
Answer: A
[tex]\displaystyle\\4\leq 3x+10 < 19\\\\4-10\leq 3x+10-10 < 19-10\\\\-6\leq 3x < 9\\\\Divide\ the\ inequality\ by \ 3:\\\\-2\leq x < 3\\\\Answer:\ -2\leq x < 3[/tex]
Six times the sum of a number and negative one is the same as two more than eight times the number
Answer:-5/4
Step-by-step explanation:
A craftsman wants to build this fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the area? Use your strategy to find the area of the face of
the fiddle.
Max is building a set of shelves. he buys a board that is 4 yards long. he wants to cut as many pieces of board that are 3/4 yard long as he can. how many pieces can he cut? will he have any board left over? if so how much?
If Max is building a set of shelves and he buys a board that is 4 yards long and he wants to cut as many pieces of board that are 3/4 yards long as he can, then the no of pieces he can cut is 5 and he will have 0.25 yards of board left over.
3/4 is a fraction which can be represented as,
3/4 = 0.75
The number of pieces of board that Max can cut that is 4 yards long can be determined by the division of the length of the board by the length of the cut pieces. Therefore,
number of pieces cut = length of the board ÷ length of a cut piece
number of pieces cut = 4 ÷ 0.75
number of pieces cut = 5.33, that is round off to 5
Thus he can cut 5 pieces of 3/4 yards.
As 5 × 3/4 = 3.75 yards
The remaining yards of the board can be calculated by subtraction.
Board leftover = 4 - 3.75 = 0.25 yards
Hence, Max can cut 5 pieces of 3/4 yards and will have 0.25 yards of the board left over.
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What equation/inequality represents the following scenario? Product of two consecutive odd integers is less than 76, where b is the first odd integer
a) n(n+2)> with a line under 76
b) n(n+1)>76
c) n(n+1)<76
d) n(n+2)<76
The two consecutive odd integers are less than 76 is the numbers are 37 and 39.
Any integer's reverse and sum are both equal to zero.
A positive sum results from adding two positive numbers, whereas a negative sum results from adding two negative integers.
Take the absolute value of each integer, then subtraction, to obtain the total of a positive and a negative integer.
Let two consecutive odd numbers be x and x+2
According to question
⇒ x........... equation (1)
⇒ x+2........equation (2)
by adding equation 1 and 2
⇒ x+x+2=76
⇒ 2x+2=76
⇒ 2x=76-2
⇒ 2x=74
⇒ x=74/2
⇒ x=37
We apply the value of x=37 in equation (2)
⇒ x+2
⇒ 37+2
⇒ 39
so, the numbers are 37 and 39.
Therefore, the two consecutive odd integers are less than 76 is the numbers are 37 and 39
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Write an equation of each line.slope =0 ; through (4,-2)
The equation of the line, with slope equal to 0 and passing through the point located at (4 , -2), is y = -2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 0 and (x1 , y1) = (4 , -2)
(y - -2) = 0(x - 4)
(y + 2) = 0
y = -2
In slope-intercept form, the equation of the line is:
(y + 2) = 0
y = -2
In standard form, the equation of the line is:
y = -2
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translate triangle P using the vector (2 -7)
The transformation rule for the triangle P by translating the vector (2, -7) is ( x , y ) <=> ( x + 2 , y - 7 )
Transformation rule says that, if a translation occurs then each point of the shape will be shifted in the same direction with the same distance.
The original figure and the translated figure will have the same shape and size.Also they both faces in same direction.This is called a direct geometry.According to the rule , the translation for the triangle P using the vector (2,-7) is ( x + 2 , y - 7 ).
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Find each measure if m ∠ D G F=53 and m∠ A G C=40 .
m ∠ 4
Answer:
a
Step-by-step explanation:
i ink
Use the Distance Formula to find the distance between the pair of points.
A(0,0), B(15,20)
Using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units
Given,
The points = A(0,0) and B(15,20)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
The distance = [tex]\sqrt{(15-0)^{2}-(20-0)^{2} }[/tex]
[tex]=\sqrt{15^{2}+20^{2} } \\=\sqrt{225+400}\\ =\sqrt{625}[/tex]
=25 units
Hence, using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units.
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Solve each equation. Check each solution. y/5 + y/2 = 7
The solution of the above equation y/5 + y/2 = 7 for y is 10.
According to the given question.
We have an equation y/5 + y/2 = 7.
Since, we have to solve the above equation y/5 + y/2 = 7 for y.
Therefore, the solution of the above equation for the above equation y/5 + y/2 = 7 is given by
y/5 + y/2 = 7
⇒ (2y + 5y)/10 = 7
⇒ 7y /10 = 7
⇒ 7y = 70
⇒ y = 70/7
⇒ y = 10
Hence, the solution of the above equation y/5 + y/2 = 7 for y is 10.
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Evaluate the function for f(x) = x + 3 and g(x) = x2 − 2. (f + g)(−8) (f + g)(−8) =
The value of the function (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.
We are given the functions:
f(x) = x + 3
g(x) = x² − 2
Now,
(f + g) (−8) × (f + g)(−8)
= [ (f + g) (−8) ]²
Substituting the values of the functions, we get that:
=(x + 3 + x² - 2)² , where x = -8
= ( -8 + 3 + 64 - 2 )²
= ( -5 + 62)²
= (57) ²
= 3249
So, the value of the function (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.
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What is the property of 10+(-10)=0
Find the measures of the sides of ΔX Y Z and classify
triangle by its sides.
X(-4,-2), Y(-3,7), Z(4,-2)
The measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ = 8. and the triangle XYZ must be an acute triangle
In this questions we have been given the the coordinates of the triangle XYZ.
X(-4, -2), Y(-3, 7), Z(4, -2)
We need to find the measures of the sides of ΔXYZ .
We find the the measures of the sides using distance formula.
XY = √[(7 + 2)² + (-3 + 4)²]
XY = √[9² + 1²]
XY = √(81 + 1)
XY = √(82)
XY = 9.1
Now side YZ
YZ = √[(-2 - 7)² + (4 + 3)²]
YZ = √[(-9)² + (7)²]
YZ = √81 + 49
YZ = √130
YZ = 11.4
And the length of side XZ would be,
XZ = √[(-2 + 2)² + (4 + 4)²]
XZ = √0 + 8²
XZ = 8
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 8² + 9.1²
= 64 + 82.81
= 146.81
= 12.12²
And 11.4² = 129.96
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, the measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ = 8. and the triangle XYZ must be an acute triangle
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The graph of function f is shown.
Function g is represented by the equation.
g(x) = 9(1/3)^x - 4
Which statement correctly compares the two functions?
OA. They have the same y-intercept but different end behavior.
OB. They have different y-intercepts but the same end behavior.
OC. They have different y-intercepts and different end behavior.
OD. They have the same y-intercept and the same end behavior.
Answer:
Step-by-step explanation:
B) is correct
Determine whether the sequence converges or diverges. if it converges, find the limit. if it diverges write none. a_n = (9 3 n**2)/(n 8 n**2)
According to the question, determine whether the given sequence converges or diverges.
The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]
Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]
Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].
Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].
What converges and diverges in limits?
When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.
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Question 9 of 10
How many dimensions does a point have?
OA. Zero
B. Two
C. Three
D. One
SUB
Answer: A
Step-by-step explanation: took the quiz got it right
MATH HELP
PART 2 since the first one was to blurry
Using a system of equations, it is found that there were a total of 825,000 Arabic speakers, and the diagram is completed as follows:
Larger part: 639,000.Smaller part: 825,000 - 639,000 = 186,000.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable f: number of French Creole speakers.Variable a: number of Arabic speakers.There were 639,000 French Creole speakers, hence:
f = 639,000.
There were 186,000 more Arabic speakers than French Creole speakers, hence:
a = 186,000 + f = 186,000 + 639,000 = 825,000.
There were a total of 825,000 Arabic speakers, and the diagram is completed as follows:
Larger part: 639,000.Smaller part: 825,000 - 639,000 = 186,000.More can be learned about a system of equations at https://brainly.com/question/24342899
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Five of seven kittens in a litter had black markings. Write a simplified ratio for each of the following:
Kittens without black markings to kittens with black markings: 2 to 5
s: 2 to 7
2 t
Kittens without black markings to total kittens:
Kittens with black markings to total kittens: 5 to 7
Kittens without black markings to kittens with black markings: 2:5
Kittens without black markings to total kittens: 2:7
Kittens with black markings to total kittens: 5:7
Put the numbers in order from smallest to largest.
Answer:
3.24x10^-5, 5.48x10^-2, 1.2x10^1, 4.68x10^6, 8.34x10^6
Step-by-step explanation:
3.24 x 10^-5 = 0.0000324
5.48 x 10^-2 = 0.0548
1.2 x 10^1 = 12
4.68 x 10^6 = 4680000
8.34 x 10^6 = 8340000
let f(x)=4x^2+5 and g(x)=2x-4. find f(x)+g(x)
Answer:
[tex]4x^2+2x+1[/tex]
Step-by-step explanation:
[tex]f(x)=4x^2+5\\g(x)=2x-4\\\\f(x)+g(x)=(4x^2+5)+(2x-4)\\\\4x^2+5+2x-4\\\\4x^2+2x+1[/tex]
Determine whether each relation is a function. (3,9),(11,21),(121,34),(34,1),(23,45)
Domain - { 3, 11, 121, 34 , 23 , } is domain of each relation is a function.
What is domain and range ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.How are the domain and range determined?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).Domain - { 3, 11, 121, 34 , 23 , }
Range - { 9, 21 , 34 , 1 , 45 }
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Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four pack of markers costs $5.49, including tax. Write and solve an inequality to solve for the number of packs of markers Mr. Sowers can purchase
The number of packs of markers Mr. Sowers can purchase is 6.4 packs.
The number of packs of markers Mr. Sowers can purchaseAccording to the task content, it is required that an inequality should be written and solved for the number of packs of markers Mr. Sowers can purchase.
Mr sower's budget = $35Cost of four pack of markers including tax = $5.49Number of packs of markers = x5.49x ≤ 35
divide both sides by 5.49x ≤ 35 / 5.49
x ≤ 6.375227686703096
Approximately
x ≤ 6.4
Therefore, the number of packs of markers Mr. Sowers can purchase is 6.4 packs
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Three bands are going to play in a concert. In how many different orders can the bands play
Answer:
6
Step-by-step explanation:
Let's call the bands by numbers :
So we have Band 1,2 and 3
The orders can be :
1,2,3
2,3,1
3,1,2
1,3,2
3,2,1
2,1,3
so there must be 6 different orders
Another method of doing this is to called product rule of counting :
3 × 2 × 1 = 6
Hope this helped and have a good day
a 12 pound can of lemonade cost 1.32 how much would a 16 ounce can of lemonade cost? please tell me the answer I need to get this right thx xo
Answer:
1.76.
Step-by-step explanation:
1.32 ÷ 12 = 0.11
16 x 0.11 = 1.76.
Hope this helped! ..・ヾ(。＞＜)シ xx
Pre Algebra 1/10+x=1/5 view attachment for more
Answer:Your answer would be x=1/10
Step-by-step explanation:
Use square roots to solve the equation x2 = –100 over the complex numbers. Select any solutions that apply.
The solution using the square root property for given complex numbers would be x = 10i where i is an imaginary number.
What is a complex number?A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,
where a, and b are real numbers and i is an imaginary number.
We have been given the equation of complex numbers x² = -100
Using the square roots property to solve the above equation
⇒ x² = -100
⇒ x = √-100
⇒ x = √(-1×10×10)
∵ i² = - 1 or i = √-1
Here i is an imaginary number.
⇒ x = 10(√-1)
⇒ x = 10i
Therefore, the solution of given complex numbers would be x = 10i where i is an imaginary number.
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Sam figures that he also earns about $2.50 in tips for each person he serves.
Sam works 4 hours on a particular day.
If n represents the number of people Sam serves that day, which of the
following functions could Sam use to figure E, his total earnings for the day?
An+ 10
Option c is the correct answer. Sam's total earning for the day is equal to
E(n) = 2.5n + 24
Given data
Sam earning per hour = $6
Sam earning on tips per person = $2.5
Sam's total hour per day =4
How to find the function for Sam's total earningsSam's daily earning excluding tips = Sam earning per hour * Sam's total hour per day
= $6 * 4 hours = $24
If n represents the number of people Sam serves that day, then Sam's earnings on tips in a day = $2.5 * n = $2.5n
The function for Sam's total earning is given by E(n)
E(n) = Sam's daily earning excluding tips + Sam's earnings on tips in a day
E(n) = $24 + $2.5n
this is re arranged as
E(n) = 2.5n + 24
Therefore we can say that Sam's total earning for the day is equal to
E(n) = 2.5n + 24
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Complete question
Sam is a waiter at a local restaurant where he earns wages of $6 per hour. Sam figures that he also earns about $2.50 in tips for each person he serves. Sam works 4 hours on a particular day. If n represents the number of people Sam serves that day, which of the following functions could Sam use to figure E, his total earnings for the day?
A. E(n) = 2.5n
B. E(n) = 4n + 10
C. E(n) = 2.5n + 24
For a fundraiser, a school club is selling raffle tickets for $2 each and healthy snacks for $1.50 each. What is the cost of: 7 tickets and 5 snacks?
