Zach's response correctly shows combining the like terms, 2e's, and giving the remaining 2 as it is.
What is a simplification of an algebraic expression?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.
Zach simplifies the expression correctly because 2e + 2e + 2e = 6e with 2 left over.
The expression given "2+2+2+e+e+" is a mix of numerical constants and a variable, e. The correct simplification of this expression would be to combine like terms.
Like terms are terms that have the same variable raised to the same exponent.
In this case, 2's can be combined to give 6 and e's can be combined to give 2e. Adding 2 with 6 or 2e won't be correct as 6 and 2e are not like terms.
Hence, Zach's response correctly shows combining the like terms, 2e's, and giving the remaining 2 as it is.
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2. If force F = î+2 ĵ+k and displacement S=3 î+ĵ+5k then work done by the force is a) 0 b) 10 unit c) 50 unit d) 8 unit
The work done by a force [tex]$\overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \mathrm{N}$[/tex], to displace a body from position A to position B is 5j
What is force?A force in physics is an effect that has the power to alter an object's motion. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction. The normal force operates in the opposite direction from how surfaces interact with one another. A force called friction prevents motion on surfaces. Other non-fundamental forces include the Coriolis force, the elastic force, tension, and frame-dependent forces like centrifugal force.Now basically here we, are talking about the work done by a body in the form of displacement.
This displacement is done due to the force that acted upon the body.
To calculate the work done we use the formula as,
W = F.ds
where F is the force acted on the body and the 'ds' is the displacement vector or the factor,
thus we calculate 'ds' as
AB vector = r2 - r1
AB = (2i + 2j +3k ) - ( i+3j+k)
so we get as,
AB = i -j +2k
now substituting in the formula we get as
W = (i + 2j + 3k ) .(i - j +2k)
W = 1 -2 +6
W = 5 joules
Work done = 5 J
The complete question is,
The work done by a force [tex]$\overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \mathrm{N}$[/tex], to displace a body from position A to position B is : [The position vector of A is [tex]$\overrightarrow{r_1}=(\hat{i}+3 \hat{\jmath}+\hat{k}) \mathrm{m}$[/tex] and the position vector of B is [tex]$\left.\overrightarrow{r_2}=(2 \hat{i}+2 \hat{j}+3 \hat{\mathbf{k}}) \mathrm{m}\right]$[/tex]
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Jessie and Kayla decided to purchase books and DVDs for the youth library at their church. Jessie purchased eight books and four DVDs, and Kayla purchased five books and six DVDs. Jessie's total cost was $80 and Kayla's was $92. If all the books sold for the same amount and all the DVDs had the same price, how much was the cost per item?
The solution for the system of linear equations is (4,12)
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: Jessie purchased eight 8 books and 4 DVDs
Kayla purchased five books and six DVDs.
let the price of a book be x and price of a DVD be y.
Then we have as per question as
8x+4y=80
5x+6y=92
Thus solving for the two equations by the method of elimination we get
40x+20y=400
40x+48y=736
-___________
-28y=-336
y=12
∴ x=80-4×12 / 8
=32/8
=4
Hence, The solution for the system of linear equations is (4,12)
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The value of the 2 in 490,200 is.................. times the value of the 2 in 649,120.
Answer:
I believe the answer is 4,000
Step-by-step explanation:
200x20
What’s the correct answer answer asap for brainlist
The answer is B because that is what paraphrasing is
Write an inequality to represent the graph.
The inequality which correctly represents the graph as represented in the task content is; y ≤ ( -1/4 ) x + 2.
Which inequality correctly represents the given graph?First, to determine the inequality which represents the graph given, it is important to determine the equation of the border line as follows;
Since the slope formula is; m = (y₂ - y₁) / (x₂ - x₁).
Hence, given points; ( 0, 2 ) and ( 4, 1 ).
Slope, m = ( 1 - 2 ) / ( 4 - 0 )
m = -1 / 4 and y-intercept = 2.
Therefore, it follows from the slope-intercept form equation; y = mx + c that the equation of the boundary line in discuss is;
y = ( -1/4 ) x + 2.
On this note, since the region shaded on the graph is the region below the boundary line and the boundary line is a solid line;
It follows that the required inequality which the graph represents is; y ≤ ( -1/4 ) x + 2.
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11 buses can carry 495 passengers how many peple can fit in 8 buses
Answer:
Step-by-step explanation:
360 people can fit in 8 buses.
First we need to find how many people fit in 1 bus, so we can divide 495, the total number of people, by 11, the number of buses.
495/11=45
Now we know 45 people can go on 1 bus, and we have 8 of them, so we multiply these 2 numbers.
45*8=360
360 people.
Answer:
8 buses can carry 360 passengers
If this help please set brainliest.
Step-by-step explanation:
To find out how many people can fit in 8 buses, you need to multiply the number of people that can fit in one bus by the number of buses. Since 11 buses can carry 495 passengers and each bus can carry the same number of passengers, one bus can carry 495/11=45 45 passengers.
Therefore, 8 buses can carry 360 passengers.
A bicycle is traveling at 18 miles per hour.
How many feet will it cover in 45 seconds?
Round your answer to the nearest tenth of a foot.
Answer:
0.225
Step-by-step explanation:
hour= 60 min
18miles/h
18miles/60 = 0.3 per minute
minute = 60 sec
0.3/60 = 0.005 per second
0.005s x 45 sec = 0.225
Please i need help-------
Answer:
Sorry I dont have enough time
I hope it helps u..
Alright Ima go teacher mode for a moment,
1.
1/3+1/5= 8/15 explanation-
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD this is basically multiplying each fraction by 1.Complete the multiplication and the equation becomes. The two fractions now have like denominators so you can add the numerators.
This fraction cant be reduced Therefore - 1/3+1/5=8/15
Alright thats the only one I will explain i'll just put the answers for the rest lol
2. 1/8+2/6= 11/24
3. 8/9+11/12= 1 29/36
4. 1/7+5/8=43/56
5. 1/4+2/4=3/4
6. 1/2+3/9=5/6
7.1/10+1/4=7/20
8.3/11+11/12= 1 25/132
9. I cant see number 9 so just tell me the bottom numbers so I can help ya out :>
10. 1/8+3/5=29/40
Hope I helped good luck on your test :> <3 Ciao mate!!!
Question 1(Multiple Choice Worth 3 points)
(01.04 LC)
Evaluate the numerical expression
25
O-25
O
1
25
0_1
25
(5+) ².
The given expression (25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] is equivalent to 217.5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is the expression as follows -
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
The given expression is -
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
Solving further, we get -
(25)2 x 100 ÷ 23 + [24 ÷ 8]
25(2) x 100 ÷ 23
25(2) x 4.35
50 x 4.35
217.5
Therefore, the given expression equivalent to 217.5.
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{
Complete question expression is -
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
}
How many ¼ pound bags of nuts can be made from a 2 1/2 pound bag of nuts?
Answer:
9 bags
Step-by-step explanation:
2 1/4 ÷ 1/4
9/4 ÷ 1/4
9/4 x 4/1 = 9
-5(1/6-8) = 40 - х + 1/6х
w/ solutions pleasee thanks
The value of x in the equation -5(1/6-8) = 40 - х + 1/6х is 1
What are algebraic equations?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants.
The algebraic equation -5(1/6-8) = 40 - х +( 1/6)х has one variable which is x.
Firstly, we open the parentheses
-5/6 +40 = 40-x+(1/6) x
multiplying through by 6
-5+240 = 240-6x +x
collecting like terms
-5+240-240 = -5x
- 5 = -5x
divide both sides by -5
x= -5/-5
x= 1
therefore the value of x is 1
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Given f(x)=-x-3, solve for x when f(x)=-2.
Answer:
x = -1
Step-by-step explanation:
Substitute f(x) = -2 in the equation:
[tex] \displaystyle{ - 2 = - x - 3 }[/tex]
Add 3 both sides:
[tex] \displaystyle{ - 2 + 3= - x - 3 + 3 } \\ \\ \displaystyle{ 1= - x } [/tex]
Divide both sides by -1:
[tex] \displaystyle{x = - 1}[/tex]
Therefors x = -1 when f(x) = -2
Which fraction is closest to zero?
The fraction 1/3 lies between 1/4 and 1/2 so it it the closest among all the other fractions.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
The fraction 3/4 is greater than 1/2 and less than 1 so it lies in between
1/2 and 1.
The fraction 1/3 is greater than 1/4 and less than 1/2 so it lies between
1/4 and 1/2.
The fraction - 3/6 is - 1/2.
The fraction - 5/8 is greater than - 1/2 and less than - 1 so it lies between
- 1 and - 1/2.
Therefore, The fraction 1/3 is closest to zero.
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Each afternoon, Sanjay looks online to find the value of a stock that shares his initials: SZT. Today, the stock rose 4 points in value.
What integer represents the change in the stock's value?
The integer representing the change in the stock's value is 4.
What is integer?An integer is a whole number that can be either positive, negative, or zero. It is not a fraction, decimal, or a percentage. Integers are the basic building blocks of mathematics and are used to represent whole numbers in equations. They are also used in computer programming languages to represent whole numbers.
This means that the stock rose by 4 points in value from the previous day. Sanjay can find out the exact value of the stock by looking up its current price online.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
20/10 --> 2/1
Step-by-step explanation:
So, the original rise is 20 and the original run is 10. You wanted it in the SIMPLEST form, so 20/10 in simple is 2/1.
Hope that's right and helps.
When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5, and 6, the probability of obtaining face F is greater than 1/6, the probability of obtaining the face opposite is less than 1/6, the probability of obtaining any one of the other four faces is 1/6, and the sum of the numbers on opposite faces is 7. When two such dice are rolled, the probability of obtaining a sum of 7 is 47/288. given that the probability of obtaining face is where and are relatively prime positive integers, find m+n?
The sum of the two numbers on the opposite faces of the die is 7. The probability of rolling a sum of 7 when two dice are rolled is 47/288. Since the probability of obtaining an individual face is , m+n must be 11.
Let m and n be the numbers on opposite faces of the die.
Since the sum of the numbers on opposite faces is 7,
m+n = 7.
Since the probability of obtaining face F is greater than 1/6, we can write .
Since the probability of obtaining the face opposite is less than 1/6, we can write .
Since the probability of obtaining any one of the other four faces is 1/6, we can write .
Solving the system of equations for m and n yields
m = 4 and n = 3.
Therefore, m + n = 4 + 3 = 11.
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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $ 60 . For one performance, 25 advance tickets and 20 same-day tickets were sold. The total amount paid for the tickets was $ 1325 . What was the price of each kind of ticket?
The price of each advanced tickets sold is; $35
The price of each same day tickets sold is; $25
How to solve a system of linear equations?Let x be the cost of each advanced tickets sold
Let y be the cost of each same day tickets sold
We are told that for one performance, 25 advance tickets and 20 same-day tickets were sold. Thus;
x + y = 60 ------(1)
The total amount paid for the tickets was $1325 and as such, we have;
20x + 25y = 1325 ------(2)
Make x the subject in eq 1 to get;
x = 60 - y
Put (45 - y) for x in eq 2 to get;
20(60 - y) + 25y = 1325
1200 - 20y + 25y = 1325
5y = 125
y = 125/5
y = $25
Thus;
x = 60 - 25
x = $35
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Which statement is sometimes false?
K
The sum of a negative and a positive
number is a negative number.
The product of a negative and
a positive number is a negative
number.
J
L The quotient of a negative and
a positive number is a negative
number.
M
N
The sum of any two negative
numbers is a negative number.
The quotient of any two negative
numbers is a positive number.
There is always a positive quotient between two negative values. It is actual. As an example, (-3)/(-1) = 3 is expression .
what is expression?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.
given
A. Negative numbers are consistently smaller than positive ones.
It is real.
For instance, - 2 + 2
B. Two negative numbers added together are always negative.
It is real.
For instance, -3 + (-3) = -6.
C. Sometimes there is a positive difference between two negative integers.
It is real.
As an illustration, (-3) - (-4) = 1
D. A negative number is always the product of two negative numbers.
It is untrue.
For illustration, (-3)(-3) = 9.
There is always a positive quotient between two negative values. It is actual. As an example, (-3)/(-1) = 3
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Maria can shovel snow from her driveway in 35 minutes. Bill can do the same job in
40 minutes. How long would it take Maria and Bill to shovel the driveway if they
worked together?
Answer:
id say givin the mean for both of them.
35.7 minets aproximatly
please give brainlest
Step-by-step explanation:
18. The Marshall Plan was an example of?
Among the four options provided, the Marshall plan is the example of the option c, i.e Foreign aid.
What is Marshall plan?The Marshall Plan, also known as the European Recovery Program (ERP), was a U.S. government initiative to rebuild the economies of Western Europe after World War II.
When was Marshall plan announced?The Marshall plan was announced by U.S. Secretary of State George Marshall in 1947 and provided economic aid to European countries to help them recover from the devastation of the war and to prevent the spread of communism.
The Marshall Plan, also known as the European Recovery Program (ERP), was a foreign aid initiative provided by the United States government to aid in the reconstruction of the economies of European nations that were severely impacted by the effects of World War II. The main objective of this program was to provide financial support to these countries in order to rebuild their infrastructure, industries, and economies, with the aim of preventing the spread of communism and fostering economic recovery and stability throughout Europe.
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Select all that apply. Which of the following shows that 5/6 = 15/18 is a proportion?
A. 5 · 18 = 6 · 15
B. 5 · 15 = 6 · 18
C. 5 · 3/6 · 3 = 15/18
D. 5 + 10/6 + 12 = 15/18
Analyze the proportion below and complete the instructions that follow.
1+3x 5
=
4 2
A. 7
5
52
Solve the proportion for x.
'B. 3
C. 5
D. 6
Please select the best answer from the choices provided
The value of x is 4/3 for equation 1+3x=5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 1+3x=5
One plus three times of x equal to five
We need to solve for x
1+3x=5
Subtract 1 from both sides
3x=5-1
3x=4
Three times of x equal to four
Divide both sides by 3
x=4/3
Hence, the value of x is 4/3 for equation 1+3x=5.
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Simplify the expression
Answer:
[tex] \frac{1}{x {}^{2} y {}^{4} }[/tex]
Step-by-step explanation:
[tex] \frac{x {}^{ - 2} }{y {}^{4} } = x {}^{ - 2} \times \frac{1}{y {}^{4} } [/tex]
[tex]x {}^{ - 2} = \frac{1}{x {}^{2} } [/tex]
[tex]therefore \: \frac{x {}^{ - 2} }{y {}^{4} } = \frac{1}{x {}^{2} } \times \frac{1}{y {}^{4} } \\ = \frac{1}{x {}^{2}y {}^{4} }[/tex]
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
Step-by-step explanation:
The volume of the cone is 37.68 centimetres cube.
9.
An engineer charges £20 plus £p per hour to repair central heating boilers.
At one house a repair takes 3 hours and costs £71.
(a)
(b)
(c)
Determine the value of p.
Write down a formula for the cost, £C, of a repair that takes x hours.
A repair costs £96.50. How long does it take?
Answer:
the value of p is £3.67.
Step-by-step explanation:
(a) To determine the value of p, we need to use the information given in the problem to set up and solve a simple equation. The cost of the repair at one house was £71, and it took 3 hours, so the cost per hour was £71 / 3 = £<<71/3=23.67>>23.67 per hour. The engineer charges £20 plus £p per hour, so £23.67 per hour is equal to £20 + £p. Subtracting £20 from both sides gives us £p = £3.67. Therefore, the value of p is £3.67.
(b) The formula for the cost, £C, of a repair that takes x hours can be written as: £C = £20 + (£p * x). This formula states that the cost of the repair is equal to the fixed cost of £20, plus the cost per hour (£p) multiplied by the number of hours (x) that the repair takes.
(c) To determine how long a repair that costs £96.50 takes, we can use the formula from part (b) and solve for x. Substituting in the known values, we get: £96.50 = £20 + (£3.67 * x). Subtracting £20 from both sides gives us: £76.50 = (£3.67 * x). Dividing both sides by £3.67 gives us: x = 20.89 hours.
