The pounds of apples that he get if he goes to David’s orchard is 20 pounds.
How to calculate the pounds of apples?Let the assumed amount with him be $40.
It should be noted that for David's orchard, the first ten pounds are $2 per round and each additional round is $1 per pound.
Therefore, the expression to illustrate this will be:
($2 × 10) + ($1 × r)
where r = additional pounds
Therefore,
($2 × 10) + ($1 × r) = $40
20 + r = 40
r = 40 - 20
r = 20
He will get 20 pounds.
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PLEASE HELP 50 POINTS
Write an equation of the line that is parallel to -x + y = 5 and passes through the point (2, -5).
Responses
y = x - 3
y = x - 3, EndFragment
y = x - 7
y = x - 7, EndFragment
y = x - 5
y = x - 5
y = - x + 7
Answer: y = x -7
Step-by-step explanation: -x + y = 5
y = x + 5
y = x + a
-5 = 2 + a
a = -7
y = x - 7
Solve 7x 8 = 3x
x = …
please
Work out 1 1/4 + 4 2/3 Give your answer as a mixed number where appropriate.
The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given sum of the mixed number,
1 1/4 + 4 2/3
⇒ 1 + 1/4 + 4 + 2/3
⇒ 1 + 4 + 1/4 + 2/3
⇒ 5 + 1/4 + 2/3
Take LCM of 1/4 and 2/3 as 12.
⇒ 5 + (3 + 8)/12
⇒ 5 + 11/12 = 5 11/12
Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".
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There are two more quarters than dimes and as many nickels as dimes and quarters together. The total amount of money is 3. 75 dollars how many nickels dimes and quarters are there each
There are two more quarters than dimes and as many nickels as dimes and quarters together. The total amount of money is 3. 75 dollars, then nickels dimes and quarters are there each, D =7 dimes , Q = 9 quarters, and N = 16 nickels
tart by defining the variables for this problem :
Q : number of quarters
D : number of dimes
N : number of nickels
There are two more quarters than dimes so the equation :
Q = D+2
And as many nickels, as quarters and dimes together so the equation :
N = Q+ D
The total amount of money is $3.75 so the equation :
0.25Q + 0.10D + 0.05N =3.75
Solve the following system :
Q = D + 2 (I)
N = Q + D (II)
0.25Q + 0.10D + 0.05N =3.75(III)
In the equation (II) find Q in terms of N and D :
N = Q + D (II)
Q = N - D (IV)
If use (I) in (IV) :
Q = N - D
D + 2 = N - D
2D = N - 2
N = 2D + 2 (V)
If use (I) and (V) in (III)
0.25Q + 0.10D + 0.05N =3.75
(0.25) . (D + 2) + 0.10D + (0.05) . (2D + 2) = 3.75
0.25D +0.50 + 0.10D + 0.1D + 0.1 = 3.75
0.45D = 3.75
D = 3.75/ 0.45
D = 7
if D = 7 -----------replacing in (I)
Q = D + 2
Q = 7 + 2
Q = 9
If replace this values in (II)
N = Q + D
N = 9 + 7
N = 16
there are D =7 dimes,
Q = 9 quarters
N = 16 nickels
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9. Put the following equation of a line into slope-intercept
form, simplifying all fractions.
2x + 3y = 15
Step-by-step explanation:
slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
we have
2x + 3y = 15
3y = 15 - 2x
y = (-2/3)×x + 5
Write the equation for g(x).
Answer: [tex]-\frac{x^2}{4}[/tex]
Step-by-step explanation:
The graph of g(x) is the graph of f(x) reflected over the x-axis and horizontally stretched by a factor of 2.
So, the equation is [tex]g(x)=-(x/2)^2 =-\frac{x^2}{4}[/tex]
I need help with this practice problem. *Make sure to answer (a) and (b), as they are questions included in the problem*
The answers to both the subparts using the binomial theorem are shown:
(A) Summation notations: = e⁴₀(3x⁵)⁴(-1/9y³)⁰ + e⁴₁(3x⁵)³(-1/9y³)¹ + e⁴₂(3x⁵)²(-1/9³)² + e⁴₃(3x⁵)(-1/9y³)³ + e⁴₄(3x⁵)⁰(-1/9y³)⁴(B) Simplified terms of the expansion: (3x⁵ - 1/9y³)⁴ = 81x²⁰ - 12x¹⁵y³ + 2/3x¹⁰+y⁶ -4/243x⁵y⁹ + 1/2187y¹²What is the binomial theorem?An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem. A binomial expression is an algebraic expression with two terms that are not the same.Or in simpler terms, the nth power of the sum of two numbers a and b can be represented as the sum of n + 1 terms of the form, according to the binomial theorem, which states that for any positive integer n.Probability:
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics describes the examination of events subject to probability.(A) Summation notations:
(3x⁵ - 1/9y³)⁴= e⁴₀(3x⁵)⁴(-1/9y³)⁰ + e⁴₁(3x⁵)³(-1/9y³)¹ + e⁴₂(3x⁵)²(-1/9³)² + e⁴₃(3x⁵)(-1/9y³)³ + e⁴₄(3x⁵)⁰(-1/9y³)⁴(B) Simplified terms of the expansion:
(3x⁵ - 1/9y³)⁴ = 81x²⁰ - 12x¹⁵y³ + 2/3x¹⁰+y⁶ -4/243x⁵y⁹ + 1/2187y¹²Therefore, the answers to both the subparts using the binomial theorem are shown:
(A) Summation notations: = e⁴₀(3x⁵)⁴(-1/9y³)⁰ + e⁴₁(3x⁵)³(-1/9y³)¹ + e⁴₂(3x⁵)²(-1/9³)² + e⁴₃(3x⁵)(-1/9y³)³ + e⁴₄(3x⁵)⁰(-1/9y³)⁴(B) Simplified terms of the expansion: (3x⁵ - 1/9y³)⁴ = 81x²⁰ - 12x¹⁵y³ + 2/3x¹⁰+y⁶ -4/243x⁵y⁹ + 1/2187y¹²To learn more about binomial theorem visit:
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need help 9th grade math
The slope-intercept form for this linear function is y = 8x + 47.
How to calculate the slope of a line?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
From the linear function, we have:
Points on x-axis = (-3, 2).
Points on y-axis = (23, -17).
Substituting the given points into the formula, we have;
Slope, m = (-17 - 23)/(2 + 3)
Slope, m = -40/5
Slope, m = -8
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (-3, 23), we have:
y = mx + c
23 = 8(-3) + c
23 = -24 + c
c = 23 + 24
c = 47
Therefore, the slope-intercept form is as follows:
y = mx + c
y = 8x + 47
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the Lim family are great mathematician.When asked howvold everyone are,the family replies : "our family of two adults and three childrens are 100years old altogether.The sum of father's age and son's age is 51.The father is 3 years older than mother while the twins daugthers are each 5 years younger than the brother" Can you work out everyone's age???
Answer:
Ages are as follows:
Father: 40
Mother: 37
Son: 11
Each twin daughter: 6
Step-by-step explanation:
Interesting puzzle!
Let
F denote the age of the father
M the age of the mother
S the age of the son
D the age of each of the twin daughters
Total of all ages is
F + M + S + 2D = 100 [1]
We also have
F + S = 51 ==> S = 51- F [2]
F - M = 3 ==> M = F - 3 [3]
S - D = 5 ==> D = S -5 [4]
==> D = (51-F) -5
==> D = 46 - F [5]
Substitute this in equation [1] to get
We now have everyone's age in terms of the father's age F
Substituting each of equations [2], [3] and [5] into [1] we get one equation in terms of F
F + (F-3) + (51-F) + 2(46-F) = 100
(F + F - F -2F ) + (-3 + 51 + 92) = 100
-F + 140 = 100
- F = 100 - 140
-F = -40
or
F = 40
From [3]
M = F - 3 = 40 - 3 = 37
From [2]
S = 51 - F = 51 - 40 = 11
From [4]
D = S - 5 = 11 - 5 = 6
Verify:
F + M + S + 2D = 40 + 37 + 11 + 2 x6 = 100
Step-by-step explanation:
a = father age
b = mother age
c = son age
d = daughters age
1. a + b + c + 2d = 100 (don't forget : twin-daughters)
2. a + c = 51
3. a = b + 3
4. d = c - 5
we need to transform the equations 2-4 to express 3 variables by the 4th, and then put that into the first equation and solve for that one variable.
once we have that, we can use again the equations 2-4 to solve for the other variables.
2. tells us that
c = 51 - a
3. tells us that
b = a - 3
4. and 2. tells us that
d = c - 5 = (51 - a) - 5 = 46 - a
with that we get in 1.
a + (a - 3) + (51 - a) + 2(46 - a) = 100
a + a - 3 + 51 - a + 92 - 2a = 100
2a - 3a + 48 + 92 = 100
-a + 140 = 100
-a = -40
a = 40
b = a - 3 = 40 - 3 = 37
c = 51 - a = 51 - 40 = 11
d = c - 5 = 11 - 5 = 6
so, the father is 40 years old
the mother is 37 years old
the son is 11 years old
both of the twin daughters are 6 years old.
Three more than a certain number is six less than four times
the same number. What is the number?
Answer:
number is 3
Step-by-step explanation:
let n be the number , then 3 more than the number is n + 3 and six less than 4 times the number is 4n - 6 , so
4n - 6 = n + 3 ( subtract n from both sides )
3n - 6 = 3 ( add 6 to both sides )
3n = 9 ( divide both sides by 3 )
n = 3
the number is 3
Reflection across x=-2
After reflection across the line x = -2, point L(-6,2), M(-6,0), K(-1,3) and J(3,0) becomes L'(1,2), M'(1,0), K'(-3,3) and J'(-1,0)
The line x = -2 will be parallel to y-axis. Let us say that there is a general point A(a,b). If this point is reflected across the line x = -2 then the y coordinates should remain same for the reflected point but x coordinate will change.
The new x coordinate will be parallelly opposite to the initial point and also at the same distance from the line as the initial point
From the Figure, we can see,
The coordinates of,
The point L is (-6,2),
The point M is (-6,0),
The point K is (-1,3) and,
The point J is (3,0).
After reflection across the line x = -2, the coordinates of,
The point L' is (1,2),
The point M' is (1,0),
The point K' is (-3,3),
The point J' is (-1,0)
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Solve -95- 62 -25. Then find 4t.
4x =
1 point
It took me 120 minutes to answer 25 questions. How long did each question take? type your answer...
Previous
minutes
It took me 120 minutes to answer 25 questions. How long did each question take?
120/25 = 4.8 minutes per question
im so bad at things like this pls help
Answer:
Part A: C. 3c - 2 = c + 22
Part B: The cat weighs 12 pounds, and the dog weighs 34 pounds.
Step-by-step explanation:
Create a system of equations:
d = 3c - 2, d = 22 + c
And substitute to get the answer to part A:
22 + c = 3c - 2
If you solve the system, you get d = 34 and c = 12 as the answer to part B.
The cat weighs 12 pounds, and the dog weighs 34 pounds.
Answer: The weight of the dog is 34 pounds and The weight of the cat is 12 pounds The answer should be B I think that's the answer
Step-by-step explanation:
9.31x5.8 it seems like it needs factors and decimals and a explanation
Answer:
53.998x
Step-by-step explanation:
9.31x · 5.8
9.31 · 5.8x
=53.999x
Please help i’ve been stuck on this question for a too long!!
Graph the function with the given description.
A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable
decreases. The value of the function at 0 is 3.
The linear function equation exists the slope-intercept form. A linear equation exists represented as: h(x) = mx + b then [tex]$\mathbf{h}(\mathrm{x})=-\frac{1}{5} \mathrm{x}+3$\\[/tex].
What is meant by linear function?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Let the independent variable be x.
The value of the function at 0 is 3.
If h(0) = 3
When the independent variable decreases by 5, the independent variable increases by 1.
So, the slope (m) exists -1/5.
Where, m = -1/5 the slope
b = 3 - the y-intercept
A linear equation exists represented as: h(x) = mx + b then [tex]$\mathbf{h}(\mathrm{x})=-\frac{1}{5} \mathrm{x}+3$\\[/tex].
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How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions
A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
What is meant by variables?
Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable. Independent, dependent, and controlled variables are typically found in experiments. A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
The ladder's position would serve as an illustration.
Both 4x-2y=12 and -4x-9=54 are supplied to you. You are required to determine the ladder's order. But you didn't say which variable stands in for the ladder. I'll simply solve for both variables. I'll use the substitute strategy.
Let equations one and two be equivalent to 4x-2y=12 and -4x-9=54, respectively.
4x-2y=12
4x=12+2y
x=3+1/2y
Put this x in place of it in equation 2.
-4x-9y=54
-4(3+1/2y )-9y=54
Y=-6
X=3+1/2y = 3+1/2(-6) = 3+(-3) = 0 \s.
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Nicole is selling wing plates to fundraise. She's selling the plates for $7 each. She spent $147 on the ingredients and package for the plates. Which equation represents M, her profit of money, after selling p plates of wings?
Answer:
M = 7p - 147
Step-by-step explanation:
Nicole is selling wing plates to fund raise. She's selling the plates for $7 each. She spent $147 on the ingredients and package for the plates. Which equation represents M, her profit of money, after selling p plates of wings?
profit - sales - cost of goods sold
where p = number of plates sold
M = 7p - 147
Darell and edmond are training for a marathon. darell runs 4 kilometers at a time while edmond prefers to run in blocks of 8 kilometers. at the end of a month, they realize that they have run same total number of kilometers. what is the smallest number of kilometers that each must have run?
We are trying to find the Least Common Multiple. This is a number that both 4 and 8 can be multiplied by a whole number to achieve, more specifically, the minimum of that list of numbers. This one is really simple. Since 8 is a multiple of 4 (4 x 2 = 8), the LCM is 8! (8 is also a multiple of 8 because 8 x 1 = 8).
So the answer is 8.
an electrician earns $18.per hour. how will he earn for a job that from 11:30 a.m. to 2:00 p.m.?
Answer: $63
Step-by-step explanation:
If the electrician gains $18 an hour and works for 3 and a half hours, once you add the money for the total time up you will get $63.
$9 (for the 30 minutes) + $18 x 3 (for the 12-2 full working hours).
Hope this helps^^
[7th Grader]
Fine the average rate of change for f(x) on the interval [-1,3]
For any function f(x), the average rate of change on the interval [x1,x2] is given by [f(x2) - f(x1)]/(x2-x1)
For f(-1) = 2.5 and f(3) = 40, the average rate of change on the interval [-1,3] is given by:
step 1 - (40 - 2.5)/[3-(-1)] = 37.5/4 = 9.375
step 2 - (37.5)/4
step 3 - Solving the fraction we find that the average rate of change is 9.375 (or 75/8)
Help pls ASAP
1a. When a lot of people are swimming in a pool, the water become cloudy. Explain why?
b. The water in an empty pool is very clear. is it still a mixture?
Explain why?
a. Inadequate chlorine levels cause cloudy or creamy swimming pool water.
b. Even though water represents the most ample substance on the planet, it is rarely encountered in its pure form in nature.
What is defined as the term mixture?A mixture is a compound composed of a number of chemical components that aren't chemically linked to one another. A mixture is a physical combination of two or more compounds that retain their individuality and are blended as solutions, suspensions, and colloids.Part a: Cloudy or milky pool water is ended up causing by seven major issues: insufficient chlorine, an imbalanced pH and alkalinity, extremely high calcium hardness (CH), a faulty or clogged filter, and the initial phases of algae, ammonia, as well as debris.
Methods for Cleaning Cloudy Pool Water
Balance the levels of free chlorine (FC).Remove the ammonia.Remove any young algae.pH and TA levels should be monitored and balanced.Part b: A swimming pool mixture of water as well as chlorine is made reference to as a homogenous mixture even though water and chlorine cannot be separated back to one‘s distinct materials once mixed together.
Because chlorine as well as water diffuse between each other, they cannot be kept separate into their pure forms again.
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Brandon takes 1/4 of a 24-hour period to read 1/3 of his book. At this rate, how many hours will it take Brandon to complete the book?
Answer:
Step-by-step explanation:
Brandon takes 1/4 of a 24-hour period to read 1/3 of his book. At this rate, how many hours will it take Brandon to complete the book?
1/4 of 24 hours = 0.25 × 24 = 6 hours
so:
Brandon takes 6 hours to read 1/3 of his book. To read the full book, going at the same reading rate:
6 × 3 = 18
It takes Brandon 18 hours to read the book.
find two positive integers whose product is 24,999,999 and whose positive difference is as small as possible. explain how you discovered them
Answer:
5001 and 4999
Step-by-step explanation:
25,000,000 is the square of 5,000 and 24,999,999 is one less than it. Notice that the situation resembles the expression [tex]x^2-1[/tex] in which x would be 5,000.
[tex]x^2-1[/tex] can be factored into [tex](x+1)(x-1)[/tex], and substituting x with 5000 yields: [tex](5000+1)(5000-1)[/tex]. This can also be written as [tex](5001)(4999)[/tex]. Therefore, the integers would be 5001 and 4999.
4z−5<−29or4z+3>15
8x+8≥−64and−7−8x≥−79
will mark brainliest
The solutions for the inequalities are:
z < -6 or z > 3 and -9 ≤ x ≤9
We are asked to solve the inequalities given.
For the inequality 4z−5<−29 or 4z+3>15, we have to solve for z. i.e., find the value for z.
4z−5<−29 or 4z+3>15
⇒ 4z < -29 + 5 or 4z > 15 -3
⇒ 4z < -24 or 4z > 12
⇒ z < -24/4 or z > 12/4
⇒ z < -6 or z > 3
The solution for z are the values above 3 and less than -6.
For 8x+8 ≥ −64 and −7−8x ≥ −79, we need to solve for x.
8x+8 ≥ −64 and −7−8x ≥ −79
⇒ 8x ≥ -64 -8 and -8x ≥ -79 + 7
⇒ 8x ≥ -72 and -8x ≥ -72
⇒ x ≥ -72/8 and -x ≥ -72/8
⇒ x ≥ -9 and x ≤ 9
⇒ -9 ≤ x ≤9
The solution for x are between -9 and 9.
The question is not complete. The complete question is given below:
Solve the system of inequalities.
4z−5<−29 or 4z+3>15
8x+8≥−64 and −7−8x≥−79.
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PLEASE HELP MEEEE!! ILL GIVE BRIANLIEST!!
Unit rate for the given expression 625 ft² in 2/3 hours is equal to
975ft² /hour.
As given in the question,
Given expression :
650 ft² in 2/3 hours
Unit rate for the given expression 625 ft² in 2/3 hours is equal to
In 2 /3 hours = 650 ft²
Simplify the given expression for the unit rate
1 hour = 650 / 2 / 3 ft² / hour
Multiply 650 to 3 and divide it by 2 we get,
1 hour = ( 650× 3 ) / 2 ft² / hour
⇒ 1 hour = 1950 / 2 ft² / hour
⇒ 1 hour = 975 ft²/hour
Therefore, unit rate for the given expression 625 ft² in 2/3 hours is equal to 975ft² /hour.
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Help me with this rq, I’ll mark you brainlyiest
Answer: Hi this is neither.
10. (a) Find the value of 5°
5 is in hundreds place and its place value is 500, 4 is in tens place and its place value is 40, 8 is in ones place and its place value is 8.
I hope this helps :)
Select equivalent or not equivalent for each pair of expressions
Equivalent or not equivalent result for each pair of given expressions are as follow:
a.5x-7+3x and 3x-7 +5x is equivalent.
b. 4y +9 +3y and 3y + 9 + 4y is equivalent.
c. 6z -2z +4 and 4 +2z-6z is not equivalent.
As given in the question,
Each pair of given expressions are equivalent or not equivalent :
a. 5x-7+3x and 3x-7 +5x
5x-7+3x
=(5x +3x) -7
= 8x -7
3x-7 +5x
= (3x +5x) -7
= 8x -7
This pair is equivalent.
b. 4y +9 +3y and 3y + 9 + 4y
4y +9 +3y
=(4y+3y)+9
= 7y +9
3y + 9 + 4y
=(3y +4y) +9
= 7y +9
This pair is equivalent.
c. 6z -2z +4 and 4 +2z-6z
6z -2z +4
=4z + 4
4 +2z-6z
= 4 -4z
This pair is not equivalent.
Therefore, equivalent or not equivalent result for each pair of given expressions are as follow:
a.5x-7+3x and 3x-7 +5x is equivalent.
b. 4y +9 +3y and 3y + 9 + 4y is equivalent.
c. 6z -2z +4 and 4 +2z-6z is not equivalent.
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What number does T2,580 represent WHEN T = 1?
Looking for right Answer
If T = 1, then the number T2580 represents 2580 as the right answer. This is the basic rules of linear equation.
What is linear equation?The first order of equations are linear equations. For lines in the coordinate system, linear equations are defined. It is referred to as a linear equation in one variable when the equation contains a homogeneous variable of degree 1 (i.e., only one variable).
There may be multiple variables in a linear equation. Linear equations in two variables, and so forth, are what the equation is known as if it contains two variables. 2x-3=0, 2y=8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are a few examples of linear equations.
The three forms of linear equations are
Standard FormSlope Intercept FormPoint Slope FormLearn more about linear equation
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