35 pounds of $0.20 coffee beans and 85 pounds of $0.68 coffee beans create a 120-pound mixture valued at $0.54 per pound when mixed. Solving the system of linear equations confirms these amounts as reasonable and correct.
To solve the problem of determining how much of each type of coffee bean is used in a mixture, we can use a system of equations to model the scenario. Let's define x as the number of pounds of the $0.20 coffee beans and y as the number of pounds of the $0.68 coffee beans. Given the total weight of the mixture is 120 pounds, we can formulate our first equation:
x + y = 120
The total value of the coffee mixture is $0.54 per pound, hence the second equation representing the total value of the mixture is:
0.20x + 0.68y = 0.54(120)
By solving this system of equations, we can find the precise quantities of each type of bean used in the mixture.
Step 1: Multiply the second equation by 100 to clear the decimals for easier calculation:
20x + 68y = 54 times 120
Step 2: Solve for one of the variables, let's say x:
x = 120 - y
Step 3: Substitute x in the second equation:
20(120 - y) + 68y = 54 times 120
This simplifies to:
2400 - 20y + 68y = 6480
48y = 4080
Step 4: Solve for y:
y = 4080 / 48
y = 85
Step 5: Substitute y back into the first equation to find x:
x = 120 - 85
x = 35
If 35 pounds of the $0.20 beans and 85 pounds of the $0.68 beans are mixed together, we achieve the desired mixture weighing 120 pounds valued at $0.54 per pound. This solution is reasonable because the sum of the weights equals the total weight of the mixture, and the calculated total value per pound matches the desired value.
Complex numbers are often used when dealing with alternating current (AC) circuits. In the equation V = IZ, V is voltage, I is current, and Z is a value known as impedance. If V = 1+i and Z=2-i, find I. Please do this quickly!!
Final answer:
The current I in the AC circuit equation V = IZ is found by complex division and is equal to 1/5 + 3/5i when V = 1+i and Z=2-i.
Explanation:
To find the current I in the equation V = IZ where V = 1+i and Z=2-i, we need to solve for I using complex division. This process involves conjugating the denominator and then performing standard multiplication of complex numbers.
Step-by-step solution:
Write down the given values in the equation: V = 1+i, Z = 2-i.Use the formula I = V / Z.Conjugate the denominator Z, which gives 2+i.Multiply the numerator and denominator by the conjugate of the denominator:So, I = (1+i) * (2+i) / ((2-i) * (2+i)).Simplify both numerator and denominator: numerator becomes 2 + 3i + i^2, and the denominator becomes 4 - i^2.Substitute i^2 with -1 and simplify: numerator becomes 2+3i-1, and the denominator becomes 4+1.The final result is I = (1+3i) / 5.Divide both the real and imaginary parts by 5: I = 1/5 + 3/5i.Therefore, the current I is 1/5 + 3/5i.
3 (4g + 6) = 2 (6g + 9)
The width of a rectangle is 3 inches less than twice the length. If the length of the rectangle is represented by L, write an algebraic expression to represent the width
The width of the rectangle is 3 inches less than twice the length, which is represented by L. The algebraic expression for the width is W = 2L - 3.
The width of a rectangle is described in the problem as being 3 inches less than twice the length of the rectangle. If the length of the rectangle is denoted by L, the algebraic expression to represent the width (W) can be written as:
W = 2L - 3
To clarify, this expression means that whatever the length L is, you would double it (that's the 2L part), and then subtract 3 inches to find the width of the rectangle.
(sinx-1)(sinx+cos^2x) multiply and simplify
solve the following formula for x
y=2mx+9b
To solve the equation y = 2mx + 9b for x, subtract 9b from both sides, and then divide by 2m. The result is x = (y - 9b) / (2m). This manipulation is emblematic of solving linear equations which are foundational in algebra.
The student is asking to solve the linear equation y = 2mx + 9b for the variable x. This type of problem involves algebraic manipulation to isolate the variable of interest. Here are the steps to solve for x:
Subtract 9b from both sides of the equation: y - 9b = 2mx.Divide both sides by 2m to solve for x: x = (y - 9b) / (2m).In this case, y is the dependent variable, m is the slope of the line, and b would be the y-intercept if this equation were graphed on a coordinate plane. To better understand this concept, let's take the specific equation y = 9 + 3x as an example which is a linear equation with b set to 9 and m set to 3.
To visualize this equation, one can construct a table of values by selecting various x values and calculating the corresponding y values. Then, these points are plotted on a graph to show the linear relationship. This process is depicted in Table A1 and Figure A1, with the equation illustrated in a graph.
The general form of a linear equation is y = mx + b, where m represents the slope and b the y-intercept. In these exercises, understanding and manipulating this form helps us find relationships between variables and understand how changes in one variable affect another.
5.14 grater than 5.041
Suppose that alexi spent all 20 hours of his time on street tacos and tony spent 17 hours on cuban sandwiches and 3 hours on street tacos. combined they would produce a total of ______________ tacos and ______________ cuban sandwiches.
Answer: 1,900 street tacos and 510 Cuban sandwiches.
Explanation:
Alexi=20*80=1,600
Tony = 17*30=510 3x00 = 300 street tacos
1,600 + 300 = 1,900 street tacos and 510 Cuban sandwiches.
23,569 pennies rounded to nearest ten thousands
since the thousands place is a 3 which is lower than a 5
it would be rounded to 20,000
Answer:
Nearest ten thousands 20000,
Step-by-step explanation:
Given :23,569
To find : Rounded to the nearest ten thousands
Solution: We have given that 23,569
We can write it as 23,569
Step 1 : Identify the ten thousands digit 2 in 23,569
Step 2: Identify the next smallest place value 3 in 23,569
Step 2: We can the digit less than five, so it would be rounded down
Step 3 : The ten thousands remain same and Every digit after becomes a zero.
Step 4 : Number become 20000.
Therefore, nearest ten thousands 20000,
Which shows the first step in the solution to the equation log2x + log2(x – 6) = 4?
Answer:
The first steps in the solution to the equation [tex]\log_2 x + \log_2 (x-6) = 4[/tex] is, [tex]\log_2 x(x-6) = 4[/tex]
Step-by-step explanation:
Given the equation: [tex]\log_2 x + \log_2 (x-6) = 4[/tex]
Using logarithmic laws;
[tex]loa_b x + \log_b y = \log_b (xy)[/tex]
then;
[tex]\log_2 x(x-6) = 4[/tex]
Therefore, the first steps in the solution to the equation [tex]\log_2 x + \log_2 (x-6) = 4[/tex] is, [tex]\log_2 x(x-6) = 4[/tex]
Answer: log2(x(x-6))=4.
Step-by-step explanation:
A square kitchen floor has an area of 123 square feet estimate the length of one wall to the nearest tenth of a foot
area of a square = S^2
S^2 = 123
S = sqrt(123)
S = 11.0905
rounded to nearest tenth = 11.1 feet
Solve for a 6(a+3)=18+6a
The equation 6(a+3) = 18+6a is an identity after canceling out like terms on both sides, which implies that the solution for 'a' is all real numbers.
To solve for a in the equation 6(a+3) = 18+6a, we begin by expanding the left side of the equation:
6a + 18 = 18 + 6a
We notice that there are terms on both sides of the equation that can be cancelled out. The 6a on the left side can be subtracted from both sides, as well as the constant 18.
After cancelling out these terms, we are left with:
0 = 0
This equation suggests that the original equation is an identity, meaning that the value of a can be any real number, as the original equation holds true for all values of a.
All the digits are odd. The last two digits add to make ten. The first and last digits add to make eight. The first two digits add to make twelve. What is the number?
The number that fits all the given criteria is 3955, where all digits are odd, the last two add to 10, the first and last to 8, and the first two to 12.
To find a number where all digits are odd, the last two digits add up to make ten, the first and last digits add up to eight, and the first two digits add up to twelve, we can use a process of elimination and reasoning.
The last two digits must be 5 and 5 because these are the only odd digits that add up to 10.The first and last digit must be 3 and 5 respectively because these add up to 8.Since the first digit is 3 and we need the first two digits to add to 12, the second digit has to be 9.Therefore, the number is 3955.
Marcella divided 40.8 gallons of paint among 8 containers. How much paint is in each container
divide the total gallons by the number of containers
40.8 / 8 = 5.1 gallons each
you build four scale models of the Empire State Building. The smallest model is 3 centimeters tall. The height of each model is three times the height of the previous model.Write a power to represent the height of the tallest model.Then find the height.
The height of the tallest model is 81 cm and the model is [tex]y ( x ) = 3^x[/tex].
Given data:
Let x be the height of the tallest model.
According to the information given, the height of each model is three times the height of the previous model.
So, represent the heights of the models as and exponential model where [tex]y ( x ) = 3^x[/tex].
1st model: 3 centimeters (3 cm)
2nd model: 3 times the height of the 1st model = 3 * 3 cm = 9 centimeters (9 cm)
3rd model: 3 times the height of the 2nd model = 3 * 9 cm = 27 centimeters (27 cm)
4th model: 3 times the height of the 3rd model = 3 * 27 cm = 81 centimeters (81 cm)
So, the height of the tallest model can be represented as:
x = 81 centimeters
Hence, the height of the tallest model is 81 centimeters.
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At the end of a party, 3/4 cup of dip is left. Jim divides 4/5 of the leftover dip equally between 2 friends. How much dip does each friend get?
To answer the question, first, multiply the total leftover dip by the portion that Jim divided. Then, divide this result by the number of friends. Therefore, each friend gets 3/10 of a cup of dip.
Explanation:The subject of this question clearly falls under the category of Mathematics, more specifically, the concept of fractions. The problem here is to find out how much dip each friend gets if 4/5 of the 3/4 cup of leftover dip is divided equally between two friends.
To solve this, we need to perform multiplication of fractions, and then division by the number of friends. Step 1: Multiply 3/4 (leftover dip) by 4/5 (portion that Jim divided). Doing this, we get (3/4) * (4/5) = 12/20, which simplifies to 3/5 cup. This is the amount of dip Jim divided.
Step 2: Divide this result by 2 (number of friends). So, (3/5) / 2 = 3/10. Hence, each friend gets 3/10 of a cup of dip.
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find the Factor of 6x 2 - 17x + 5.
Answer:
Step-by-step explanation:
[tex]6x^2-17x+5[/tex]
This can be written as
[tex]6x^2-15x-2x+5[/tex]
Because -15-2=-17 and also (-15)(-2)=30
so now we have two pairs
[tex](6x^2-15x)+(-2x+5)[/tex]
Take out GCF from each pair
[tex]3x(2x-5)-1(2x-5)[/tex]
since (2x-5) is now the common factor so final factored form
[tex](3x-1)(2x-5)[/tex]
solve q+12-2(q-22)>0
The solution to the given inequality problem is;
q < 56
We are given the equation;
q + 12 - 2(q - 22) > 0
Step 1; Using distributive property, distribute 6 to the numbers inside the bracket to get;
q + 12 - 2q + 44 > 0
Step 2; Combining similar terms on the left side and simplifying gives us;
56 - q > 0
Step 3; Using addition property of equality, add q to both sides;
56 - q + q > 0 + q
q < 56
Thus, the final solution is q < 56
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what is 3×4-14+4=? It's one of my math class questions
pls help i need this done NOW!!!
#14 and #15 a. and b.
pls show work!!
Answer:
Step-by-step explanation:
To me, it seems like 14 is just telling u something.....and 15. a)30% b)75%
hope this helps :)
How do u write 1.2 as a fraction
What is -7 5/12 written as a decimal
Does this graph show a function?
What is the remainder of 21 divided by 4
1 is the remainder of 21 divided by 4
What is Division?A division is a process of splitting a specific amount into equal parts.
The number which is getting divided here is called the dividend.
21 is the dividend.
The number which divides a given number is the divisor.
4 is the divisor
And the number which we get as a result is known as the quotient.
The divisor which does not divide a number completely produces a number, which is referred to as remainder.
21 ÷ 4 = 5 with a remainder of 1.
Hence, 1 is the remainder of 21 divided by 4
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Find the slope and y-intercept of the following line
-7x+7y=-17
To the nearest ten thousand , the population of Vermont was estimated to be about 620,000 in 2008. What might have been the exact population of Vermont in 2008?
The statement given is
The population of Vermont was estimated to be about 620,000 in 2008.
Exact population of Vermont in 2008
= 615,000 ≤ A number between ≤ 620,000
=[615000, 620000]
Jed has 25 toy cars. Kai has 32 you cars. Ken has fewer cars than either Jed or Kai. How many cars might Ken have?
The possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Jed has 25 toy cars.
Kai has 32 you cars.
Since Ken has fewer cars than either Jed or Kai, the maximum number of cars Ken could have is 24 (if both Jed and Kai give him one car each).
The minimum number of cars Ken could have is 0 (if both Jed and Kai have more cars than Ken).
So the possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.
Hence, the possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.
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Pythagoras was born about 582 BC. Isaac Newton was born in 1643
AD. How many years apart were they born.?
Convert 10 centimeter to inches
Josiah went to the local barber to get his hair cut. It cost $18 for the haircut. Josiah tipped the barber 15%. What was the total cost of the haircut including the tip
The total cost of the haircut including the tip is $20.70. 18*15%=2.70+18=20.7.
Hope this helps:)
Answer:
$20.70
Step-by-step explanation:
Turn the % to a decimal.
15%= 15/100 = 0.15
Multiply the total and decimal.
18.00 x 0.15
= 2.70
Add the total to the sum.
18.00 + 2.70
= 20.70
(hope it helped please vote and say thanks <3)
solve
P=a+b-8
what is a=