The algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]
Given
The word phrase
"The quotient of the sum of 2 and a number b and 3"
Sum off 2 and a number b = 2+b
Then the quotient of the sum of 2 and a number b and 3 = [tex]\frac{2+b}{3}[/tex]
Hence ,the algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]
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Solve for x: 2/3 + 1/3=2x
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] = 2x ( combine fractions on left side )
1 = 2x ( divide both sides by 2 )
[tex]\frac{1}{2}[/tex] = x
Mila buys cookies and oranges at the store.
She pays a total of $22.39.
She pays a total of $6.58 for the cookies.
She buys 3 bags of oranges that each cost the same amount.
Write and solve an equation which can be used to determine xx, how much each bag of oranges costs.
The equation that can be used to represent the cost of oranges and cookies is; 6.58 + 3x = 22.39. Thus, the cost of each bag of orange is x = $5.27
How to Solve Algebra Word Problems?We are given;
Total Amount paid by Mila = $22.39.
Amount Mila paid for cookies = $6.58
Now, we are told that she also buys three bags of oranges. Now, if we denote the cost of each bag of orange to be x, then it means that;
Cost of 3 bags of oranges = $3x
Thus, we can write the equation to represent the cost of oranges and cookies as;
6.58 + 3x = 22.39
Subtract 6.58 from both sides to get;
3x = 22.39 - 6.58
3x = 15.81
x = 15.81/3
x = 5.27
Thus, the cost of each bag of orange is x = $5.27
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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]
Peter pays 6% interest on his $30,000 college loan and 7% interest on his $12,000 car loan.
What average interest rate does he pay on the total $42,000 he owes?
Round your answer to the nearest tenth of a percent.
Answer:
12,000 for college 7.5,000 in car whe he pays around 20k for that
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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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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State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
Combining a coin toss and a roll of a die makes a simple event.
False , Combining a coin toss and a roll of a die makes a simple event.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.False , Combining a coin toss and a roll of a die makes a simple event.
A true statement is "For data at the interval level, you CAN calculate meaningful differences between data entries."
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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
How many days does it take Company C to produce the same number of radios as Company B produces in 6 days?
Answer:
I need a picture of the diagram to answer your question.
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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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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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.
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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).
y=2
How do I graph this
A horizontal line passing through A ( 0 , 2 )
The ratio of 12.9 is equal to the ratio of 1/3 to
A. 1/4
B. 1
C. 5/4
D. 2
E. 4
The ratio of 12:9 is equal to the ratio of 1/3 to 1/4.
As given in the question,
Given ratio is equal to 12:9
Simplify the given ratio by factorizing it :
12 : 9 = 12 / 9
⇒12 : 9 = ( 4 × 3 ) / ( 3 × 3)
⇒ 12 : 9 = 4 / 3
⇒ 12 : 9 = 1 / 3 × 4 / 1
⇒ 12 : 9 = 1 /3 to 1/ 4
Therefore, the ratio of 12 : 9 is equal to the ratio of 1/3 to 1/4.
The complete question is:
The ratio of 12:9 is equal to the ratio of 1/3 to
A. 1/4
B. 1
C. 5/4
D. 2
E. 4
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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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- 7 (4 - r) = 35 what's the correct answer?
Answer:
9
Step-by-step explanation:
- 7 (4 - r) = 35
First you need to do the parentheses
-7 times 4 is -28
-7 times -r is 7r
-28+7r=35
add 28 to both sides
7r=63
r=9
Answer:
r=9
Step-by-step explanation:
-28+7r=35, rearrange to put like terms together
7r=35+28, 7r=63, divide both sides by 7 to get r
r=63/7, r=9
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find the value of x if RS bisects AB and RS = 36
Answer:
18 + 2y + 6 = 36
2y = 12
y = 6
step explanation:
Since RS bisects AB,
25 - 3x = 2y + 5
25 - 3x = 2(6) + 5 = 12 + 5 = 17
3x = 25 - 17 = 8
x = 8/3
Answer to part c please
Answer:
X=least=30
Y=greatest=40
pls help!!! what do i dooo
Answer:
Save and exit.
Step-by-step explanation:
Just save and exit
Answer: Click the links slowly read or look over the meterials and then make your file(s)
not sure if i helped -^-
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:
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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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.
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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Among a town’s registered voters, there are 34% Democrats and 25% Republicans. The rest are Independents. If there are 1517 registered Independent voters in this town, how many total registered voters are there?
The total number of registered voters is 3700.
What is the total number of registered voters?
Percentage can be described as the fraction of a number expressed as an amount out of 100. Percentage is a measure of frequency. The sign that is used to represent percentages is %.
The first step is to determine the percentage of independent voters.
Percentage of independent voters : 100 - (percent of democrats + percent of republicans)
100 - (34% + 25%)
100- 59% = 41%
Total number of voters = number of independent voters / percentage of independent voters
1517 / 41%
1517 / 0.41 = 3,700
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A- x = 4, PQ = 8, QR = 13
B- x = 5, PQ = 10, QR = 11
C- x = 4, PQ = 12, QR = 9
D- x = 4, PQ = 10, QR = 11
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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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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Write algebraic expressions for two numbers with a sum of -13. Let one of the numbers be represented by x. If one number is represented by x, how would the other number be represented?
Answer:
If a sum of 2 numbers is -7 and one is x then you can write it down as X + Y = -7, or you can write it then ... Let one of the number be represented by x.
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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