The equation -(a-b) = (-1)(a-b) has used the property of real numbers is Distributive Property.
Property of Real numbers:
A real number is a value that represents a quantity along a continuous number line. Real numbers can be ordered.
The properties of real numbers are,
Commutative propertyAssociative propertyDistributive propertyIdentity propertyGiven,
The equation is
-(a-b) = (-1)(a-b)
Now we have to find the property used here.
Based on the properties of real number,
The one that exactly matches the equation is Distributive property.
Because the definition of Distributive property is explained through the following,
For three numbers m, n, and r, which are real in nature, the distributive property is represented as:
m (n + r) = mn + mr
The same will be applied in the given equation also.
Therefore, the Distributive property is used in the equation.
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y=2
How do I graph this
A horizontal line passing through A ( 0 , 2 )
Find the first five terms of each sequence. aₙ=a n₋₁ +2 n , where a₁ = 1
The first five terms of the sequence are 1,4,7,9,11.
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given,
aₙ=a n₋₁ +2 n
For a1 = 1
a2 = 1 + 2.2 = 1 + 4 = 5
a3 = 1 + 2.3 = 1 + 6 = 7
a4 = 1 + 2.4 = 1 + 8 = 9
a5 = 1 + 2.5 = 1 + 10 = 11
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Simplest radical form
(-2,3) and (6,-4).
The simplest radical form of (-2,3) and (6,-4). is √113
How to determine the simplest radical form?The points are given as:
(-2,3) and (6,-4).
The distance is calculated using
d = √(x2 - x1)^2 + (y2 - y1)^2
This gives
d = √(-2 - 6)^2 + (3 + 4)^2
Evaluate
d = √113
Hence, the simplest radical form of (-2,3) and (6,-4). is d = √113
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pls who ever answers this question correctly i will give that person brainiest
1. what must be added to 649254 to make it equal to 97485
Answer:
-551,769
Step-by-step explanation:
We could just simply use subtraction:
97,485 - 649,254 = -551,769
Hope this helps!
Which of the following equations have exactly one solution?
Choose all answers that apply:
-5x+12=5a-5
-5x+12= -12x - 12
-52125 12
or 12 Nữ 12
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The following equations have exactly option (A) and option (B) and option (C) are correct answers.
option (A) ⇒ -5x + 12 = 5x - 5 ⇒ x = 17/10 is correct equation.
option (B) ⇒ -5x+12= -12x - 12 ⇒ x = -24/7 is correct equation.
option (C) ⇒ -5x+12= 5x + 12 ⇒ x = 0 is correct equation.
Based on given equations, formulate,
(A). -5x + 12 = 5x - 5
Calculate the expression,
-5x + 12 = 5x - 5
-5x - 5x = -5 - 12
We can sum or difference the values,
-10x = -17
x = -17/-10
We can divide the product,
x = 17/10
(B). -5x+12= -12x - 12
Calculate the expression,
-5x + 12 = -12x - 12
-5x + 12x = -12 - 12
We can sum or difference the values,
7x = -24
We can divide the product,
x = -24/7
(C). -5x+12= 5x + 12
Calculate the expression,
-5x + 12 = 5x + 12
-5x - 5x = 12 - 12
We can sum or difference the values,
-10x = 0
We can divide the product,
x = -0/10
x = 0
(D). -5x+12 = -5x - 12
Calculate the expression,
-5x+12 = -5x - 12
-5x + 5x = -12 - 12
12 = -12
Therefore,
The following equations have exactly option (A) and option (B) and option (C) are correct answers.
Hence,
option (A) ⇒ -5x + 12 = 5x - 5 is correct equation.
option (B) ⇒ -5x+12= -12x - 12 is correct equation.
option (C) ⇒ -5x+12= 5x + 12 is correct equation.
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The common sparrow has a wingspan of 9 to 15 centimeters. Which inequality matches the wingspan of the common sparrow?
The inequality which matches the wingspan of the common sparrow is :
9 ≤ x ≤ 15.
What is inequality and how can we frame one?
Inequalities are the equations in which two non equal expressions are compared using the mathematical relations such as ≤(less than or equal to ), ≥ (more than or equal to ), < (less than ) , >( more than).
Given that the common sparrow has a wingspan of 9 to 15 centimeters.
Let the wingspan of sparrow be x then given that x is more than or equal to 9 which gives an inequality : x ≥ 9 ....(1)
Also it is given that wingspan, x is not more than 15 centimeters which means x is less than or equal to 15 and this gives an inequality: x ≤ 15 ....(2)
Combining (1) and (2), we get:
9≤ x ≤ 15
Therefore wingspan (x) of common sparrow is shown by the inequality : 9≤ x ≤ 15
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Dominic rented a car for the weekend. When he started driving on the highway he noticed the odometer had already logged 18,115 miles. After 45 minutes of highway driving, the odometer read 18,169 miles.
If he drove on the highway a total of four hours and traveled at a constant speed that entire time, what did the odometer read when he exited the highway?
The reading in the odometer will be 18,403 miles after travelling for 4 hours on the highway as Dominic covered a distance of 288 miles on the highway.
Distance on the odometer that was already logged = 18,115 miles.
Distance on the odometer after 45 minutes = 18,169 miles.
Distance covered in 45 mins = 18169 - 18115 = 54 miles.
Speed = 54 miles / 45 min
Speed = 6 miles / 5 minutes = 72 miles / hour
Now, he drove on the highway for 4 hours.
Time = 4 h
Distance = speed × time
D = 72 × 4 miles
D = 288 miles
Reading on the odometer when he exited the highway will be:
R = 18115 + 288 miles
R = 18403 miles.
Therefore, we get that, the reading in the odometer will be 18,403 miles after travelling for 4 hours on the highway as Dominic covered a distance of 288 miles on the highway.
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Kia deposits $2650 into an account the internet rate on the account is 6% compounded annually annually what is the balance in Kia’s account after 2 years? After 3 years
The balance in Kia’s account after 2 years is $2,977.54
The balance in Kia’s account after 3 years is $3,156.19
What is future value of the deposit?
The future value of the deposit, is the equivalent future worth of the deposit after having earned interest over the 2-year and 3-year periods using the future value formula of a single cash flow as shown below:
FV=PV*(1+r)^N
FV=balance after 2 and 3 years
PV=initial deposit=$2,650
r=interest rate=6%
N=number of years 2 and 3 years respectively
FV(2 years)=$2,650*(1+6%)^2
FV(2 years)=$2,977.54
FV(3 years)=$2,650*(1+6%)^3
FV(3 years)=$3,156.19
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7/8 add 1/2 in fractions
Answer:
so first we should find LCM of the denominator.and then find the answer
[tex] \frac{7}{8} + (\frac{1}{2} \times 4) = \: \: \: \frac{7}{8 } + \frac{4}{8 } = \frac{11}{8} or1 \frac{3}{8} [/tex]
Mr. vincent is setting up 4 obstacle courses at the brookfield middle school field day. each obstacle course has 2 jump rope stations and 2 pogo stick stations. mr. vincent needs x jump ropes at each jump rope station and y pogo sticks at each pogo stick station. pick all the expressions that represent how many jump ropes and pogo sticks mr. vincent needs in all.
Answer:
8x + 8y
Step-by-step explanation:
Each obstacle course has 2 jump rope stations and 2 pogo stick stations.
There are 4 obstacle courses
So total number of jump rope stations = 4 x 2 = 8
Each jump rope station requires x jump ropes
So total number of jump ropes needed = 8x
Each pogo stick stations. requires y pogo sticks
So total number of pogo sticks needed = 8y
Expression to represent how many jump ropes and pogo sticks Mr. Vincent needs in all is
8x + 8y
Write the equation of the line in slope-intercept form.
y-5x=16
The equation of the line in slope-intercept form is y = 5x + 16 .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is y - 5x = 16 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
y - 5x = 16
On adding 5x on both sides in above equation, we will get
y = 5x + 16 equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 5
Intercept = c = 16
The equation of the line in slope-intercept form is y = 5x + 16 .
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13.a) sketch a graph of a function that has a set of integers as its domain and all integers less than 5 as its range. b) sketch a graph of a relation that is not a function and that has the set of real numbers les then or equal to 10 as its domain and all real numbers greater than -5 as its range
The required function that has a set of integers as its domain and all integers less than 5 as its range is y = -|x| + 5
Given that,
To draw a sketch of a graph of a function that has a set of integers as its domain and all integers less than 5 as its range.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
In order to draw the graph of a function that has a set of integers as its domain and all integers less than 5 as its range.
We add
y = -|x|
For the domain to be all integers
Now, adding 5
Y = -|x| + 5
Thus, the required function that has a set of integers as its domain and all integers less than 5 as its range is y = -|x| + 5.
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Determine whether the regular polygon will tessellate in the plane. Write yes or no. Explain.
16 -gon
No, he regular polygon 16 -gon will not tessellate in the plane.
What is tessellation?A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.
A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.
Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.
Regular polygons tessellate if their interior angles divide by 360° evenly or if the total of their interior angles is a factor of 360°. A tessellation is a pattern made of identical forms that fit together seamlessly.
So lets find out how pentagon won't tessellate.
First we find the measure of the interior angles of 16 -gon,
[tex]\frac{2520\°}{16} = 157.5\°[/tex]
Now divide the interior angle by 360°
[tex]\frac{360\°}{157.5\°} = 2.28[/tex]
Hence, the measure of the interior angle does not divide by 360°.
Therefore, we conclude that the regular polygon 16- gon will not tessellate in the plane.
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[ Brainliest ]
Apply it! The measure of each central angle of a regular 10-sided polygon is ____ degrees.
Work Shown:
n = number of sides
c = central angle
c = 360/n
c = 360/10
c = 36
This formula applies to regular polygons only (all sides must be the same length; all angles must be the same).
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
O(x, y)
(x + 5, y-3)
O(x, y)
(x + 5, y + 3)
O(x, y) -
(x-3, y + 5)
O(x, y)
(x + 3, y + 5)
Sep 9
According to the translation rule, The translation of the rectangle is (x, y) → (x – 3, y + 5). Thus option C is correct.
According to the statement
We have to find that the translation rule.
So, For this purpose, we know that the
Translation is refers to the movement of a shape from one point to a different, without altering its appearance.
From the given information:
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left.
With this in mind,
Once there's an upwards or downwards movement, there's a shift within the y coordinate
A move to the left or right movement, the x- coordinate is affected and moving left is negative
Hence,
y-coordinate is positive
x-coordinate is negative
Therefore, the rectangle translating 5 units up and three units to the left would be: (x, y) → (x – 3, y + 5)
So, According to the translation rule, The translation of the rectangle is (x, y) → (x – 3, y + 5). Thus option C is correct.
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help please
15 points
Answer: three and two.
If you add the digits of the number you have, for example, 36 (3+6 = 9), and the result is in the on the table of multiplication of 9; then is divisible by 9.
the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0
Step-by-step explanation:
Write each of the following functions in a piecewise format and sketch its graph. For each function, find the value(s) of x where one piece ends and another begins (There's 3 problems/ screenshots) (20 pts)
Using the definition of the absolute value function, we have that, for item b, the function and breaking points are given as follows:
y = -3x - 1, x < -0.5.y = x + 1, x ≥ -0.5.The function breaks at x = -0.5.
For item c, we have that:
y = -2x - 2, x < -3.y = 4, -3 ≤ x ≤ 0.5.y = 4x + 2, x > 0.5.The function breaks x = -3 and x = 0.5.
For item d, we have that: (problem 59)
y = -2x - 2, x < -1.y = 2x + 2, x ≥ -1.The function breaks at x = -1.
The graphs are given at the end of the answer.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
In general terms, we have that:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.Then, for item b, we have that:
|2x + 1| = 2x + 1, x ≥ -0.5.|2x + 1| = -2x - 1, x < -0.5.Then:
y = -3x - 1, x < -0.5.y = x - 1, x ≥ -0.5.The function breaks at x = -0.5.
For item c, we have that:
|2x - 1| = 2x - 1, x ≥ 0.5.|2x - 1| = -2x + 1, x < 0.5.|x + 3| = x + 3, x ≥ -3.|x + 3| = -x - 3, x < -3.Then:
y = -2x - 2, x < -3.y = 4, -3 ≤ x ≤ 0.5.y = 4x + 2, x > 0.5.The function breaks x = -3 and x = 0.5.
For item d, we have that:
|x + 1| = x + 1, x ≥ -1.|x + 1| = -x - 1, x < -1.Hence:
y = -2x - 2, x < -1.y = 2x + 2, x ≥ -1.The function breaks at x = -1.
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Write an algebraic expression for the verbal phrase. The quotient of 5 times
a number and 3.
Answer:
(5x)/3
Step-by-step explanation:
5 times a number is 5x.
Quotient means to divide, so the answer is (5x)/3.
Rashid asked the genie, "How many wishes have you granted?"
Is this a statistical question?
The question asked by Rashid to genie, “ How many wishes have you granted ?” is not a statistical question.
Statistical question is a question that can be answered by collecting the data that vary and for which there will be variability in that data.
According to question, the question asked by Rashid has a direct answer for which there is no need to collect any data that is it has single data point which does not have any variability.
Thus the question asked by Rashid to genie is not a statistical question.
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Give an example of a function that represents a direct variation.
If y varies in direct proportion to x and y = 6 when x = 2, the variational constant is k = = 3. Consequently, y = 3x is the equation that describes this direct variation.
What is direct variation?Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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A die is rolled. Find the probability of the outcome. P(odd)
The probability of the outcome P(odd) is 1/2.
Probability is a measure of the likelihood of an event to occur. It can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
We know that,
All outcomes in a die are 1,2,3,4,5, and 6.
Even outcomes = 2,4, and 6
Odd outcomes = 1,3, and 5
Hence,
Total number of odd outcomes = 3
Total number of outcomes = 6
We know that,
Probability of an event = Number of possible outcomes of the event/ Total number of outcomes
Therefore, we can write:-
Probability of the odd outcomes = 3/6 = 1/2
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Solve the math problem
Answer/Step-by-step explanation:
5.)
Square = 2
Triangle = 3
Circle = 3
Star = 4
2(circle) + 2(triangle) = 12
12 ÷ 4 = 3
2(3) + 2(3) = 12
2(triangle) + 2(square) = 10
2(3) + 2(square) = 10
6 + 2(square) = 10
-6 -6
2(square) = 4
÷2 ÷2
Square = 2
(circle) + (star) + 2(square) = 11
(3) + (star) + 2(2) = 11
3 + (star) + 4 = 11
7 + (star) = 11
-7 -7
Star = 4
6.)
Circle = 3
Star = 5
Triangle = 4
4(star) = 20
÷4 ÷4
(star) = 5
(star) + 3(circle) = 14
5 + 3(circle) = 14
-5 -5
3(circle) = 9
÷3 ÷3
circle = 3
2(triangle) + (circle) + (star) = 16
2(triangle) + 3 + 5 = 16
2(triangle) + 8 = 16
-8 -8
2(triangle) = 8
÷2 ÷2
triangle = 4
I hope this helps!
Find the perimeter of the figure write your answer in simplest form
Answer:
7 1/8
Step-by-step explanation:
Convert 2 3/8 to improper fraction 19/8 and multiply by 3/1. Reduce to lowest terms.
Subtract (4x2-x+6) from (3x² + 5x - 8).
O A. 7x² + 6x - 14
O B. x² + 4x + 2
O C. 7x² + 4x - 2
O D. x² + 6x - 14
Answer:
X^2 -6x+14
Step-by-step explanation:
Helen Mountain Tubing charges $25 for tube rental and $5 an hour to float down the river. Alpine Tubing charges $30 for tube rental and $2 an hour to float down the river. Create an equation to determine at what point the cost of both tubing companies is the same.
25x - 5 = 30x - 2
25x + 5 = 30x + 2
25 + 5x = 30 + 2x
25 - 5x = 30 + 2x
hi
As rental charges is contant and then price vary with time of location, then it's answer C
25 + 5x = 30 + 2x
Solve for the value of w
Answer:
[tex]w=9[/tex]
Step-by-step explanation:
[tex](4w-7)+(7w-2) = 90\\11w-9=90\\11w=99\\w=9[/tex]
Work out the next three terms in the sequence shown below. Give your
answers as simply as possible, without any brackets.
2.x
The term-to-term rule is
multiply by 2 then add x + 2 each time
→5x+2 →
D
7
The next three terms are 11x+6 , 23x+14 , 47x+30
The term-to-term rule is multiply by 2 then add x + 2 each time
First term is 2x
second term is 5x +2
next terms we can find by multiply by 2 then add x + 2 each time
third term 2(5x+2)+x+2
= 10x+4+x+2
= 11x+6
fourth term 2(11x+6)+x+2
= 22x+12+x+2
= 23x+14
fifth term = 2(23x+14)+x+2
= 46x+28+x+2
= 47x+30
The phrase equation and its cognates in other languages can also have subtly extraordinary meanings; as an example, in French an équation is described as containing one or more terms , even as in English, any well-shaped components together with two expressions related with an equals sign is an equation.
There are two kinds of equations: identities and conditional equations. An identity is authentic for all values of the variables. A conditional equation is simplest genuine for particular values of the variables
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Give an example of a sequence that is not an arithmetic sequence.
The sequence 2, 3, 5, 6..is example of the sequence which is not in arithmetic sequence AP.
What is the AP sequence (arithmetic progression)?In Arithmetic Progression (AP), the distinction between two arithmetical orders is a constant. It is also known as Arithmetic Sequence.
Then we'd run into some important words in AP, such as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be described using common distinctions, as shown below.
The following is the way to determine an AP's n-th term: an = a + (n − 1) × dThe formula for arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' is d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as per the question;
Consider any sequence. Let's say 2, 3, 5, 6..
Let's consider the first term is'a₁' = 2.
Let's consider 'a₂' = 3 is the second term.
Let's consider the third term is 'a₃' = 5.
Let's consider the fourth term be 'a₄' = 6
d₁ = a₂ - a₁
Substitute the values;
d₁ = 3 - 2 = 1 ........(equation 1)
Now take the other set;
d₂ = a₃ - a₂
d₂ = 5 - 3 = 2 .......(equation 2)
From the two equations 1 and 2. it is clear that the value of both common difference d₁ is not equal to d₂. Thus, the sequence considered is not in AP.
Therefore, the considered sequence 2, 3, 5, 6.. is not in AP.
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WILL CHOOSE BRAINLIEST!!!!
ALGEBRA Simplify 4(3 x-2)(2 x+4)+3x² + 5x-6
F 9x² + 3x - 14
H 27x² + 37x - 38
G 9x² + 13x - 14
J 27x² + 27x - 26
The simplified form of the given equation 4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6 is [tex]27x^{2} + 37x - 38[/tex].
The branch of mathematics that deal with the study of mathematical symbols and the rules for manipulating those symbols is known as Algebra. Elementary Algebra, Abstract Algebra, Advanced Algebra, Linear Algebra, and Commutative Algebra are sub-branches of Algebra.
Algebra forms the basis for advanced studies in many fields, including science, mathematics, medicine, engineering, and economics.
The given equation is 4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6. The step wise simplification of this algebraic equation is as follows :
4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6
= (12x - 8)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6
= [tex]24x^{2} - 16x + 48x - 32 + 3x^{2} + 5x -6[/tex]
= [tex]27x^{2} + 37x -38[/tex]
The simplified form of the given equation 4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6 is [tex]27x^{2} + 37x - 38[/tex].
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