Answer: (1/3)x - 8
Step-by-step explanation:
one - third means 1/3
one - third of a number means (1/3)x
( x being the number )
Eight less means -8
Eight less than 1/3 of an number is (1/3)x - 8
Seven factory workers take part in a charity swim. Altogether they swim 179 lengths of a pool. How many lengths does each worker swim on average?
The length of each factory worker on average is 25.57 lengths
How to determine the length of each on average?From the question, we have the following parameters that can be used in our computation:
Total length of the pool = 179 lengths
Number of workers = 7
The length of each on average is calculated as
Average length = Total length of the pool/Number of workers
Substitute the known values in the above equation
So, we have the following equation
Average length = 179/7
Evaluate the quotient
Average length = 25.57
Hence, the average length is 25.57 lengths
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Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
The slope of the line is - 2 with the equation as 2 x + y - 2 = 0
We are given that:
y intercept of the line = 2
Point is (0, 2)
It is parallel to the line 2 x + y = - 5
Slope of line 2 x + y = - 5:
y' = - 2
m = - 2
Slope of parallel lines are equal
m = m'
m' = - 2
Equation of the line:
y - y₁ = m( x - x₁)
y - 2 = - 2( x - 0)
y - 2 = - 2 x
2 x + y - 2 = 0
a) standard form of the equation = 2 x + y - 2 = 0
b) slope of the line = m' = - 2
c) point-slope form = (y - 2) / (x - 0) = - 2
d) Properties of algebra used = cross multiplication and simplification.
Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0
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A movie theater sends out a coupon for 54% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation for the representation of the given situation will be
y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.
What is an equation?An equation is a statement that says that the value of two mathematical expressions is equal.
Given that, a cinema sends out a coupon for 54% off the price of a ticket.
The equation for this situation will be y = x - 0.54x,
And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.
Hence, the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be
y = x - 0.54x
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Have someone read this to you while your eyes are closed and answer the question in the end. 8 x 5 - 23 + 21 x 6 + 100 - 20 x 5 = ????
Answer:
143
Step-by-step explanation:
Anthony claims that A KLM is an isosceles triangle. Find the length of KM using the distance formula.
Answer:√53 or 7.28010988928
Step-by-step explanation:
Determine the center and radius of the circle with equation (x+3)² + (y − 2)² = 16
Answer: Center: (-3, 2). Radius: 4.
Step-by-step explanation:
The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.
The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.
The radius of the circle is the square root of the constant on the other side of the equation. So, r = [tex]\sqrt{16}[/tex] = 4.
The explanation is from the equation of a circle in a graph:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:
[tex](x+3)^2 + (y-2)^2 =16[/tex]
Which can also be written as
[tex](x-(-3))^2 + (y-(2))^2=16[/tex]
See the correlation of numbers -3 and 2 with h and k?
Notice also how the equation contains [tex]r^2[/tex], so to find the radius you do [tex]\sqrt{r^2}[/tex].
Select all the equations that have {4} as its solution set.
Responses
79−3x=12x+19
7−x=12x
x2+3=10x−21
5 + 2x = 3x + 3
SELECT ALL, THIS IS MULTIPLE CHOICE.
Answers:
A. 79 − 3x = 12x + 19
B. 7 − x = 12/x
C. x^2 + 3 = 10x − 21
Which equation is equivalent to the given equation?
x²- 10x = 14
-
(x - 10)² =-86
(x - 5)² = 39
(x - 5)²= = -11
(x-10)²= 114
use eulers method with step size 0.5 to compute the approximate y values y1 y2 y3 and y4 of the solution of the intitial value problem y'=y 2x y(3)=0
Answer:
[tex]y_1=\boxed{-3}[/tex]
[tex]y_2=\boxed{-8}[/tex]
[tex]y_3=\boxed{-16}[/tex]
[tex]y_4=\boxed{-28.5}[/tex]
Step-by-step explanation:
Given:
[tex]y'=y-2x, \;\;y(3)=0[/tex][tex]h=0.5[/tex]Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:
[tex]y'=y-2x, \;\;y(3)=0[/tex]
at x = 3.5, 4, 4.5, 5.
Therefore:
[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]
Euler's Method
[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]
[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]
[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]
please help me and please hurry. also please show working clearly!!
Answer:
The limit does not exist
Step-by-step explanation:
This is because the left hand limit is 3,we know this because as the graph approaches from the left side of the Cartesian plan the open dot is on 3
and the right hand limit is 1 because as the graph approaches the X=1 from the right hand side the open dot lands on 1
Since the left hand limit doesn't equal to right hand limit,the overall limit of x=1 doesn't exist.
Find her mistake and it’s due today
Answer:
Step-by-step explanation:
An orange grove manager uses two different sized buckets to load oranges into a truck. The first bucket can transport a pound of oranges, and the second bucket can transport
y pounds of oranges. The first bucket is filled up G times and the second bucket is filled up I times The total amount of oranges. I that have been loaded can be found usina
the equation T = Ga + Hy.
Solve for H.
T + Ge
O H
y
O H= y(T - Gx)
T
0 H = Gx+y
T_ Cr
O H
2
On solving for [H], we get -
H = (T - Ga)/y
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
T = Ga + Hy
We have -
T = Ga + Hy
Solving for [H], we get -
Hy = T - Ga
H = (T - Ga)/y
Therefore, On solving for [H], we get -
H = (T - Ga)/y
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If A = (6,7,8,11) and B = {(7,6,7,9), list the elements of A U B.
The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.
According to the question,
We have the following information:
A = {6,7,8,11} and B = {7,6,7,9}
Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.
(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)
So, we have the following expression:
AUB = {6,7,8,9,11}
(Now, note that numbers however repeated in sets are not repeated here.)
Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.
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Can you answer this question?
Answer: y= 3 times 2 to the power x. Second answer
Step-by-step explanation:
if you plug in 0 for x, y= 3x 1= 3
if you plug in 1 for x y= 3 x 2 = 6
Look at the x values and y values
(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.
please help me with these it is due tomm.
Answer:
1.) 10: 1, 2, 5, 10.
15: 1, 3, 5, 15,
Answer would be 5.
2.) 18: 1, 2, 3, 6, 9, 18
21: 1, 3, 7, 21
Answer would be 3.
3.) 12: 1, 2, 3, 4, 6, 12.
24: 1, 2, 3, 4, 6, 8, 12, 24.
Answer would be 12.
4.) 8: 1, 2, 4, 8.
20: 1, 2, 4, 5, 10, 20.
Answer would be 4.
5.) 14: 1, 2, 7, 14.
28: 1, 2, 4, 7, 14, 28.
Answer would be 14.
Step-by-step explanation:
Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.
consider the line y= 5/2x+5
1. find the equation of the line that is perpendicular to this line and passes through the point (-5,6)
2. find the equation of the line that is parallel to this line and passes through the point (-5,6)
Answer:
Step-by-step explanation:
1
y-6 = -2/5(x-(-5)
y - 6 = -2/5(x+5)
y -6 = -2/5 x -2
y = -2/5 x -2 + 6
y = -2/5 x + 4
2
y-6 = 5/2 (x-(-5)
y-6 = 5/2 (x+5)
y - 6 = 5/2 x + 25/2
y = 5/2 x + 25/2 + 6
y = 5/2 x + (25+12)/2
y = 5/2 x + 37/2
George invest $500 in his friend's startup company. his friend agrees to give him 8% of the original investment each year for the next 3 years. write a linear function for this situation.
The linear function for the situation is :-
Amount at the end of 3 years = Original investment + original investment*Rate*Time/100
It is given in the question that:-
Investment of George's friend in startup company = $ 500.
Interest percent = 8 %
Time period of investment = 3 years
We have to find the linear function for this situation.
As this interest is on original investment, the interest will be simple.
Hence,
The linear function for the situation will be :-
Amount at the end of 3 years= Original investment + original investment*Rate*Time/100
Amount at the end of 3 years = 500 + 500*8*3/100 = 500 + 120 = $ 620
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Factorise this expression as fully as possible
2xy^2 + 8y
2y(xy+4)
Hope this answers your question!
Answer:
2y(xy+4)
Step-by-step explanation:
First, Distribute
you get 2y(xy+4) because you have to isolate the like terms than find a gcf of the terms
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3x+=x+5
4
2
6
12
10
If you multiply by 12 you will get rid of all your fractions.
What are linear equations?In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
The given linear equation is
6 - (3/4)x + (1/3) = (1/2)x + 5
In this equation the fractions are
(3/4), (1/3) and (1/2)
Take the LCM of 4, 3, and 2
LCM(4, 3, 2) = 12
So, if we multiply the equation with the number 12 we can eliminate the fractions.
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WILL GIVE BRAINLiST, RATE IT 5 STARS, AND HEART IT FOR CREATIVE WRITING HELP. PLEASE ANSWER BOTH QUESTIONS, IF ITS ONE QUESTION I CAN DO THAT TOO!
1. What are 5 observations you made about the setting of “Avatar” after watching the trailer? (Play the first avatar movie trailer)
2. Based on the trailer, what is one central theme of the movie? How does the setting contribute to this theme? (Play the first avatar movie trailer)
when answering, answer it like 1= and 2=
Answer: Read explanation
Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.
Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.
Make any corrections if you want! Make it more comfortable to your style!
A Not secure admin248 acellus.com/StudentFunctions/interface/acell
Parallel Lines
Inear Functions and Systems
A line is parallel to y = -2x - 3 and
intersects the point (5, 4). What is
the equation of this parallel line?
Start by entering this into point-slope form.
y -4 = -2(x-[?])
Solve the equation below for x
Cx — 4 = 7
The equation for the value of x will be 11/C.
According to the question,
We have the following equation:
Cx — 4 = 7
Now, we can easily find the value of x from this equation by following the given steps.
We will first add 4 on both sides of the equation:
Cx = 7+4
Adding the two numbers on the right hand side:
Cx = 11
Dividing by C on both sides of the equation:
x = 11/C
(More to know: we can now find the value of x if the value of C is given.)
Hence, the equation for the value of x will be 11/C.
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There are 7 new books and 5 used books on a shelf.
(a) What is the ratio of new books to all books on the shelf?
0
(b) What is the ratio of used books to all books on the shelf?
0
Answer:
7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer
Answer:
a) 7:13 b) 5:13
Step-by-step explanation:
There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13
do the same thing for b) using the same steps.
Which model represents the sum of 4 + 12?
Answer: 16
Step-by-step explanation:
Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.
Find the slope of the line using rise/run formula please help
Answer:
20/5 is the slope, or 4.
Step-by-step explanation:
It went up 20 units on the y axis, and over 5 units on the x-axis. So 20/5 is the slope.
-Hope this helped
solve the following inequality
x³-5x² < 4x-20
The final solution is all the values that make (x+5) (x+2) (x−2)=0 true.
x = −5,−2,2
What is factorization?
Factorization, also known as factoring, is the process of breaking down an object (such as a number, a matrix, or a polynomial) into a product of another object, or factors, which when multiplied together yield the original object (such as the number or matrix) in question.
What is inequality?
A relationship between two expressions or values that are not equal to each other is called an inequality.
Here, we have
Factor out the greatest common factor from each group
x²(x+5) - 4(x+5) = 0
Factor the polynomial by factoring out the greatest common factor, (x+5)
(x+5)(x²-4) = 0
Rewrite 4 as 2².
(x+5)(x²-2²) = 0
(x+5)(x+2)(x-2) = 0
Now,
x+5 = 0
x-2 = 0
x+2 = 0
set x+5 =0 then we get
x = -5
set x+2 =0 then we get
x = -2
set x-2 =0 then we get
x = 2
Hence, the final solution is all the values that make (x+5) (x+2) (x−2)=0 true.
x = −5,−2,2
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Is f = 9 a solution to this equation?
4f = 36
Yes or no
in each of the following lines, underline the smallest number and put a ring round the largest number
15/3, 12/6, 27/9, 8/2, 10/10
Answer:
this is how to do it. Now find the answer
Step-by-step explanation:
find the common factor for the denominators, which is 30.
then × the numerator by however much you ×tl the denominator by to get 30
4x + 10y = 2
x - 10y = 13
Answer:
x = 3
y = -1
Step-by-step explanation:
4x + 10y = 2 Eq. 1
x - 10y = 13 Eq. 2
The result of the sum of Eq. 1 and Eq. 2 is:
4x + x = 5x
10y - 10y = 0y = 0
2 + 13 = 15
Then the result is:
5x = 15
x = 15/5
x = 3
From Eq. 2:
x - 10y = 13
3 - 10y = 13
-10y = 13 - 3
-10y = 10
y = 10/-10
y = -1
Check:
From Eq. 1:
4x + 10y = 2
4*3 + 10*-1 = 2
12 - 10 = 2
The solution of the equation is that the value of x = 3 and y = -1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The equation will be solved as,
4x + 10y = 2 Eq. 1
x - 10y = 13 Eq. 2
The result of the sum of Eq. 1 and Eq. 2 is:
4x + x = 5x
10y - 10y = 0y = 0
2 + 13 = 15
Then the result is:
5x = 15
x = 15/5
x = 3
From Eq. 2:
x - 10y = 13
3 - 10y = 13
-10y = 13 - 3
-10y = 10
y = 10/-10
y = -1
Therefore, the solution of the equation is that the value of x = 3 and y = -1.
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Write the number in standard form.
5.01 times 10 superscript negative 3 baseline
A. 5,010
B. 0.501
C. 0.0501
D. 0.00501
Answer:
The correct answer is D
Step-by-step explanation:
the negative power shows that on the exponent shows that the value is small and is being simplified.
When ever there is a negative power we increase zeros with respect to the exponent value.