(B) –9 < x – 4 < 9 inequality is equivalent to Ix-4I <9.
What is inequality?Inequality is a statement of an order relationship between two numbers or algebraic expressions (greater than, greater than, or equal to, less than, or less than or equal to). Inequality is defined as a difference in size, amount, quality, social position, or another factor. Inequality occurs when you have ten of something and someone else has none. (mathematics) A statement stating that one quantity is less than (greater than) another.So, Ix-4I <9:
|x-4|<9 ⇒ -9 < x-4 < 9-5 < x < 13Therefore, (B) –9 < x – 4 < 9 inequality is equivalent.
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The complete question is given below:
Which inequality is equivalent to I x-4 I <9?
A –9 > x – 4 < 9
B –9 < x – 4 < 9
C x – 4 < –9 or x – 4 < 9
D x – 4 > –9 or x – 4 < 9
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 then one square vertically, or two squares vertically and one square horizontally. The bishop, which begins in square f 8 , can only move diagonally.
b. After two moves, the rook is in square d3. Describe a possible translation to describe the two moves.
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.
Compare the two numbers. Use > or < .
√5, √7
Square root is a factor that, when multiplied by itself, equals the original value.
The values of √5 = 2.236 and √7 = 2.645 then √5 < √7.
What is a square root?In mathematics, a square root is a factor that, when multiplied by itself, equals the original value. Any time the idea of an object's square is mentioned, square roots can be considered more widely. These include square matrices and function spaces, among other mathematical structures.Even though it is only one of the two square roots of a positive number, the term "square root" is occasionally used to describe the major square root of a positive number.Let the values of √5 = 2.236 and √7 = 2.645
then √5 < √7.
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A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 6400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 40-kilogram crates that can be loaded into the shipping container.
If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
Inequalityx is the integer
First step is to formulate the inequality
40x≤ 25,500-6,400
Now let determine the x by using the inequality
40x≤ 25,500-6,400
40x≤19,100
x=≤19,100/40
x=≤ 477.5
Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
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ABCD is a rectangle. Find angles a and b, giving reasons with each step.
Answer:
a = 45°b = 23°Step-by-step explanation:
If I name the centre (intersection of diagonals) as O, Angle AOD will be equal to 68°
[Opposite angles are equal]
The diagonals bisect the 4 corner angles of a rectangle in equal halves. So, a = 45°
Also, Angle ADO = 90° - b
[Each of the four angles in a rectangle = 90°]
And In [tex]\triangle[/tex] AOD,
=> Angle AOD + Angle ADO + Angle OAD = 180°
=> 68° + 90° - b + 45° = 180°
=> 203° - b = 180°
=> b = 23°
I WILL MARK
Spot the mistake for all of these (if you can!)
The following procedure mistakes are listed below:
A mistake was made in the first step. (Misuse of distributive property). A mistake was made in the first step. (Misuse of distributive property). A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication). A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication). A mistake was made in the first step (Misuse of existence of multiplicative inverse and distributive property). A mistake was made in the first step (Misuse of compatibility with addition).How to spot a mistake in the procedure of resolution of equations with fractions
In this question we find six cases of equations with fractions, whose intended procedures are shown, of which we must determine in what step a mistake is done:
Case 1
x / 2 + 3 = 9 Given
x + 6 = 18 Compatibility with multiplication / Distributive property / Definition of multiplication
x = 12 Compatability with addition / Existence of additive inverse / Modulative property
A mistake was made in the first step. (Misuse of distributive property)
Case 2
(2 · x - 1) / 3 + x = 3 Given
2 · x - 1 + 3 · x = 3 Compatibility with addition / Distributive property
5 · x - 1 = 3 Commutative, associative and distributive properties / Definition of addition
5 · x = 2 Compatibility with addition / Commutative, associative and modulative properties / Existence of additive inverse
x = 2 / 5 Compatibility with multiplication / Existence of multiplicative inverse / Associative and modulative properties / Result
A mistake was made in the first step. (Misuse of distributive property).
Case 3
(5 · x + 5) / 10 + (2 · x + 6) / 10 = 6 Given
5 · x + 5 + 2 · x + 6 = 60 Compatibility with multiplication / Existence of multiplicative inverse / Commutative, associative and distributive properties
7 · x + 13 = 60 Associative, commutative and distributive properties
7 · x = 47 Compatibility with addition / Existence of additive inverse / Commutative, associative and distributive properties
x = 47 / 7 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result
A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication).
Case 4
3 - 5 / (x + 1) = 1 Given
3 · (x + 1) - 5 = x + 1 Compatibility with multiplication / Distributive, associative and commutative properties
3 · x - 2 = x + 1 Distributive property / Definition of subtraction
2 · x = 3 Compatibility with addition / Existence of additive inverse / Commutative, associative and distributive properties
x = 3 / 2 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result
A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication).
Case 5
x / 3 + x = 2 Given
5 · x / 3 = 2 Modulative property / Existence of multiplicative inverse / Definition of division
5 · x = 6 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Definition of division
x = 6 / 5 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Definition of division / Result
A mistake was made in the first step (Misuse of existence of multiplicative inverse and distributive property).
Case 6
(2 · x + 5) / 5 + 2 = 7 Given
2 · x + 7 = 7 Compatibility with multiplication / Distributive, associative and commutative properties
2 · x = 0 Compatibility with addition / Existence of additive inverse / Commutative and associative properties
x = 0 Compatibility with multiplication / Existence of multiplicative inverse / Commutative and associative properties / Cancelative property / Result
A mistake was made in the first step (Misuse of compatibility with addition).
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The midpoint of AB is M (5, 1). If the coordinates of A are (3, 6), what are the
coordinates of B?
Point B's coordinates are (7, -4).
What are the coordinates of the line segment AB's midpoint?As the name implies, a midpoint is a point in the middle of something. A line segment's midpoint is a point that is located in the middle of the given line segment.Assume we have two line segment endpoints:
B and A(p,q) (m,n)Then, on that line segment, let M(x,y) be the midpoint.The coordinates are as follows:
x = (p+m)/2 and y = (q+n)/2So, M is AB's midpoint, and its coordinates are as follows:
Point B's x-coordinate:
[tex]x_m=\frac{\left(x_A+x_B\right)}{2}[/tex][tex]5=\frac{\left(3+x_B\right)}{2}[/tex]10 = 3 + xx = 10 - 3x = 7Point B's y-coordinate:
[tex]y_m=\frac{\left(y_A+y_B\right)}{2}[/tex] [tex]1=\frac{\left(6+y_B\right)}{2}[/tex]2 = 6 + yy = 2 - 6y = -4Therefore, point B's coordinates are (7, -4).
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Bonjour, j’ai un devoir pour demain et je n’y arrive pas. Merci d’avance.
33 On donne la fonction f : x +-> 5x - 7.
• Écrire un programme de calcul traduisant le calcul de l'image de x par la fonction f.
Answer:
secret hukgjkkkkouugvgv uukkoygjo
Are the lines perpendicular?
no, because the slopes of the lines are equal
no, because the slopes of the lines are not opposite reciprocals
yes, because the slopes of the lines are equal
yes, because the slopes of the lines are opposite reciprocals
The lines are not perpendicular because: B. the slopes of the lines are not opposite reciprocals
What are Slopes of Perpendicular Lines?If two line are perpendicular to each other, they will have slope values that are the opposite reciprocals of each other.
Slope of the red line = change in y / change in x = (-9 - 11)/(0 -(-8))
Slope of the red line = -20/8 = -5/2
Slope of the blue line = (8 - 2)/(8 -(-8))
Slope of the blue line = 6/16 = 3/8
3/8 is not the opposite reciprocal of -5/2. Therefore, the lines are not perpendicular because: B. the slopes of the lines are not opposite reciprocals
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Liz and Sucely were texting. The number of texts that Sucely sent was three times the difference of the number of texts liz send and the number 5.If Sucely sent 21 texts, how many texts did Liz send?
Answer:
12
Step-by-step explanation:
We'll give Sucely the variable s and Liz l.
s = 3(l - 5)
21 = 3(l - 5) distribute the 3
21 = 3l - 15 add 15 to each side
36 = 3l divide each side by 3
12 = l
So, Liz sent 12 texts
Evaluate 51x³-21 + 7 when x = -2
Answer: Substitute the value of the variable into the equation and simplify.
−
408
v
a
2
l
u
t
e
2
−
14
Step-by-step explanation:
factorize -b^2+48c^2+8bc
Answer:
(4c + b)(12c - b)
Step-by-step explanation:
- b² + 48c² + 8bc ← rearrange
48c² + 8bc - b² ( split the middle term )
= 48c² + 12bc - 4bc - b² ( factor first/second and third/fourth terms )
= 12c(4c + b) - b(4c + b) ← factor out (4c + b) from each term
= (4c + b)(12c - b)
Find the least common multiple of each pair of polynomials.
x² - 1 and x² + 2x + 1
The least common multiple of each pair of polynomials x² - 1 and
x² + 2x +1 is equal to (x-1)(x+1)².
As given in the question,
Given pair of polynomial are x² - 1 and x² + 2x +1
Simplify each pair of polynomial by factorizing them
Apply a² -b² =(a-b)(a +b)
x² -1 =(x-1)(x+1)
Apply (a +b)² =a² +2ab +b²
x² + 2x + 1 =(x+1)²
Least common multiple of (x-1)(x +1) an (x+1)² =(x-1)(x+1)²
Therefore, the least common multiple of each pair of polynomials x² - 1 and x² + 2x + 1 is equal to (x-1)(x+1)².
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what does SSS stand for ? what does it have to do with similar triangles?
Answer:
Side, Side, Side. The short cut is SSS
Can yall help me with this
Answer:week 4
Step-by-step explanation:
If two coplanar lines are cut by _________ so that a pair of alternate interior angles are _,_____ then the two lines are parallel.
If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.
The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.
In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.
In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.
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-2/3y -3/4 =5
What does y equal
Student Council sells soft drinks at basketball games and makes $ 1.50 from each. If they pay $ 75 to rent the concession stand, how many soft drinks would they have to sell to make $ 250 profit?
F. 116
G. 117
H. 167
J. 217
Answer: 166 Soft Drinks
Step-by-step explanation:
250 ÷ 1.50 = 166
b + 12a; use a = 4, and b = 2
Answer:
50
Step-by-step explanation:
All my work shown in the screenshot provided. If you have any questions please let me know! Have a wonderful day!
Answer:
b + 12a; use a = 4, and b = 2
=2+12*4
=2+48
=50
Write an equation for each transformation of y=x .
Vertical compression by a factor of 1/4 .
Vertically Stretching and Compressing
Multiplying a function by positive constant yields a function whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done. You get vertical compression.
Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
Solution:
To write the equation of the function y = x with a vertical compression by a factor of 1/4, we will use the formula given below:
y = a · x
This equation means y = a · x, and a is the vertical compression/stretch. Since a = 1/4, we can substitute 1/4 for a.
Therefore, the answer is D, y = 1/4x.
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Cindy is shopping for a new desk chair at a store where the desk chairs are 50% off. She also has a coupon for 50% off any one item. Cindy thinks that she can now get the desk chair for free. Is this true? If not, what will be the percent off she will receive with both the sale and the coupon?
Cindy thinks that she can now get the desk chair for free which is false. Then the percent off that she will receive with both the sale and the coupon will be 75%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
Let X be the price of a new desk chair.
Cindy is shopping for a new desk chair at a store where the desk chairs are 50% off. Then the cost of a new desk chair after 50% off will be
⇒ 50% of X
⇒ 0.50X
She also has a coupon for 50% off any one item. Then the cost of a new desk chair after applying the coupon of 50% will be
Cost = 50% of 0.50X
Cost = 0.25X
Cindy thinks that she can now get the desk chair for free which is false.
Then the percent off that she will receive with both the sale and the coupon will be
Discount = [(X - 0.25X) / X ] * 100
Discount = 0.75 x 100
Discount = 75%.
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Name the circle, a radius, a chord, and a diameter of the circle.
(a). Using the concept given above, PC and AB are the circle's chords.
(b). In the given figure, OC, OP, OA and OB are the radii of the circle.
(c). A chord which is not the diameter of the circle is PC.
What is meant by Circle?A circle is a shape in which all points are the same distance from the center. Circles are named after their centers. Therefore, the right circle is called circle A because its center is at point A. Real-world examples of circles include (the surface of) wheels, dinner plates, and coins.
(a). Circle chords are two-point line segments that connect two different places on the circumference of a circle.
Using the concept given above, PC and AB are the circle's chords.
(b). Line segments formed by joining any point on the boundary on the circle with the center of the circle are known as radii of the circle.
In the given figure, OC, OP, OA and OB are the radii of the circle.
(c). A chord which passes through the center of the circle is known as diameter of the circle.
A chord which is not the diameter of the circle is PC. ( By using the definition of chord and diameter of the circle.)
The complete question is:
In figure, O is the center of the circle
(a) Name all chords of the circle
(b) Name all radii of the circle
(c) Name a chord, which is not the diameter of the circle
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Does the orientation of the vertices change or stay the same after a reflection?
The orientation of the vertices stay same after a reflection.
The orientation of the vertices is nothing but The relative arrangements of points following a transformation or after surrounding a geometric shape are known as orientation. In terms of how the points align, orientation is divided into clockwise and counterclockwise. The points are opposite the original shape when the orientation is reflected. Same orientation denotes that the points are simply a reflection of the original figure and are arranged in exactly the same manner.
The orientation of the vertices stay same after a reflection.
When you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for the vertices of the figure will alter on the coordinate plane.
Apply the same change to each point to graph a.
The variations in a reflection's coordinates can be used to identify it. The figure makes a mirror image of itself when it flips across a line in a reflection. Consider the reflection in the image.
Therefore, The orientation of the vertices stay same after a reflection.
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Evaluate the function at the given value.
If g(x) = 10x + 4 find g(x + 2) and
g(x) + g(2).
Show your work here
g(x + 2) =
g(x) + g(2)
=
Answer:
g(x + 2) = 10x + 24
g(x) + g(2) = 10x + 28
Step-by-step explanation:
1) If g(x) = 10x + 4, then g(x+2) = 10(x+2) + 4
g(x) = 10x + 20 + 4
g(x + 2) = 10x + 24
2) If g(x) = 10x + 4, then g(x) + g(2) = 10x + 4 + 10(2) + 4
g(x) + g(2) = 10x + 4 + 20 + 4
g(x) + g(2) = 10x + 28
If your brother borrows $835 at 10% interest rate for eleven years, how much interest will he pay?
For this case, your interest rate will be (. 11 x 100 = 11) 11%. Step 3: Apart from this, you can also calculate your time period involved, principal amount and interest amount paid in a specific time period if you have other inputs available with you. Calculate interest amount paid in a specific time period, I = Prt
Answer:
918.50 in interest over 11 years.
Step-by-step explanation:
Comment
You have to make an assumption here. The assumption is that this is simple interest.
So if the brother pays 10% each year, he is paying
10/100 * 835 each year in interest
10/100 * 835 = 83.50 every year.
There are 11 years, so the total interest paid is 11 * 83.50 = 918.50 dollars in total.. That's more than what he borrowed!
2 beliefs about gods nature
Answer: What are two beliefs about the nature of God?
The Psalms say, God is fair and just (Psalm 25:8). Omniscience - God knows everything. Christians believe that God knows every person's inner thoughts as well as knowing all that has happened and all that will happen in the future. Transcendence - God exists outside of our worldly constraints and physical laws.
Step-by-step explanation: hope this helps!!!
Answer:
He is good.
He is forgiving.
He is love.
He is our Shepperd.
He is our judge.
He is our Father.
He Is King.
Find the distance between A(4,6) and B (9,7) . Write your answer as a radical and as a decimal rounded to the nearest tenth.
The distance between A(4,6) and B (9,7) is√26 or 5.1.
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
Given the points A(4,6) and B (9,7)
Now,
x₁ = 4 ,x₂ = 9
y₁ = 6 , y₂ = 7
So,
Distance between them,
[tex]d = \sqrt {\left( {4 - 9 } \right)^2 + \left( {6 - 7 } \right)^2 }[/tex]
d = √26
d = 5.099 and by rounding to the nearest tenth.
5.099 → 5.1
Hence "The distance between A(4,6) and B (9,7) is√26 or 5.1".
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if g (x) = 3(4)^x, what is the value of g(2)
If function g(x)= [tex]3(4)^{x}[/tex], then the value of g(2) is 48
The function g(x) = [tex]3(4)^{x}[/tex]
Function is the expression the defines the relationship between between a set of inputs having one output each. The set of all possible input of the function is called domain and set of all possible output of the function is called range
Here the function is g(x)= [tex]3(4)^{x}[/tex]
The values of x = 2
Substitute the value of x in the function
g(x)= [tex]3(4)^{2}[/tex]
First find the value of [tex]4^{2}[/tex]
g(x)= 3×16
Multiply it
g(x)= 3×16
g(x)=48
The value of g(2) is 48
Hence, If function g(x)= [tex]3(4)^{x}[/tex], then the value of g(2) is 48
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The function y=3√-x-3 is graphed only over the domain of {x 1-8 ≤x≤ 8). What is the range of the graph?
The function y=3√-x-3 is graphed only over the domain of {x 1-8 ≤x≤ 8). is the range of the graph is b) {y : -5 < x < - 1 }
Range is set of Y values for which the function is define.
So, in order to find the range , we need to find the corresponding y values for given domain.
Put x = -8 in y = ∛-x -3 then we get,
y = ∛-x -3
y = ∛-(-8) -3
y = ∛8 -3
y = 2 -3
y = - 1
Put x = 8 in y = ∛-x -3 then we get,
y = ∛-(8) -3
y = ∛-8 -3
y = -2 -3
y = - 5
Hence the range of function y = ∛-x -3 over the domain of {x : -8 < x < 8 } is
{y : -5 < x < - 1 }
correct option is b) {y : -5 < x < - 1 }
In arithmetic, the range of a function may seek advice from either of intently associated concepts: The codomain of the feature The image of the function Given two units X and Y, a binary relation f between X and Y is a function if for each x in X there is exactly one y in Y such that f relates x to y.
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What is the prime factorization of 100 I really need help this do tommorrow
What is wrong with the following statement? If t, then r t = S.
The correct statement for the expression is that 't' should be multiplied by 's'.
Given r/s = t and explain what is wrong with the statement as r * t = s.
Given expression as r/s = t
We can write this expression as
r/s = t/1
By cross multiplication on both sides we get
r * 1 = t * s
r = t * s
This is the correct expression we get. But the given statement r * t = s is false.
We conclude this as 't' should be multiplied by 's'.
Hence, the correct option is option B is correct.
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