Decomposition of the fraction [tex]1\frac{3}{4}[/tex] =7/4 = 17/4 - 10/4
Here, the numerator, or top number, 7, indicates how many pieces we will examine.
Please look at figure a and pay attention to the three coloured components. The bottom number, our denominator, provides the total number of components. As a result, pay close attention to figure a. There are a total of four parts, numbered 1, 2, 3, and 4. However, since we are working with 7/4, we will just examine the three shaded parts.
7/4 = 17/4 - 10/4
7/4 = 11/4 - 4/4
Unit fraction decomposition will be used. Unit fraction - what is it? What would we focus on if we just looked at one element? It is one in four, or 1/4. Because this is the first of a series that includes 1, 2, 3, and 4. The third component would also be 1/4, and the second piece would be 1/4.
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This system of equations has been placed in a matrix
y 650x+175
y=25,080-120x
Column 1 Col 2 Col 3
Row 1 : ___ -1 ___
Row 2 : 75 ___ ___
Answer: This system of equations can be represented in matrix form as
| -1 | 650 | 175 |
| 75 | -120 | -25080 |
This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.
You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.
The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.
Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.
Step-by-step explanation:
A new business borrows $320,000 at a yearly simple interest rate of 7%.
The total
amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan? Pls help Mee!!
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]
A new homeowner is purchasing a living room set for $2,975 and must decide between two financing offers.
Offer 1: $250 down payment, 24.90% interest rate, compounded monthly, for 3 years, with no payments due for 6 months and then fixed payments of $139.05 for the remainder of the loan term
Offer 2: $400 down payment, 22.90% interest rate, compounded monthly, for 3 years, with no payments due for 12 months and then fixed payments of $165.76 for the remainder of the loan term
Part A: What is the total cost of offer 1? Explain which technology you used to solve and each step of your process. (3 points)
Part B: What is the total cost of offer 2? Explain which technology you used to solve and each step of your process. (3 points)
Part C: Which financing offer should the new homeowner choose? Explain your reasoning. (4 points)
Answer:
To compare the two financing offers, we need to calculate the total cost of each offer.
Part A: What is the total cost of offer 1?
To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2490/12) * $2,975 * 36
Calculating, we find that the total interest is approximately $1,534.89.
To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.
Therefore, the total cost of offer 1 is $4,509.89.
Part B: What is the total cost of offer 2?
To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2290/12) * $2,
To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2290/12) * $2,975 * 36
Calculating, we find that the total interest is approximately $1,405.70.
To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.
Therefore, the total cost of offer 2 is $4,381.70.
Part C: Which financing offer should the new homeowner choose?
Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.
Step-by-step explanation:
7 - Select the equation that represents a true statement.
Mark all that apply.
A. 2+3 × 4 = 22 +12
B. z+zx9 = 9z O
C. -8y + 4.3y + 3.7 = 0
D. 12-1.8b+ 1.8b = 1.8b
E. m8+7(8) = m
So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
A. 2+3 × 4 = 22 +12 is not a true statement, because the order of operations is not followed, multiplication should be done before addition.
B. z+zx9 = 9z is not a true statement, because it is not clear what the operation is between z and x, and what the operation is between x and 9
C. -8y + 4.3y + 3.7 = 0 is a true statement because it is a linear equation with one variable y, it represents a straight line.
D. 12-1.8b+ 1.8b = 1.8b is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.
E. m8+7(8) = m is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.
So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0
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1.2/4=x/28 what is the value of x
Answer:
8.4
Step-by-step explanation:
You want to know the value of x that satisfies 1.2/4 = x/28.
One-step equationThe equation ...
x/28 = 1.2/4
can be solved in one step by multiplying by 28.
x = 28(1.2/4) = 8.4
The value of x is 8.4.
__
Additional comment
The fraction involving x can be cleared by multiplying by its denominator, effectively the inverse of the coefficient of x. This is the same way you solve any similar one-step equation.
Often, you are told to "cross-multiply" a proportion. Doing that gives you ...
4·x = 28·1.2
Then you have to divide by 4 (multiply by the inverse of the coefficient of x) to find the value of x:
x = 28·1.2/4 . . . . same as above.
That is, there is no need to multiply by 4, and then divide by 4. You can simply multiply by 28 and be done.
Answer:
8.4
Step-by-step explanation:
[tex]\frac{1.2}{4}[/tex] = [tex]\frac{x}{28}[/tex]
cross multiply to solve for x:
(1.2)(28) = 4x
4x = 33.6
x = 33.6/4 = 8.4
A family buys a studio apartment for $140,000 They pay a down payment of $35,000
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $7,000 down payment be?
Answer:
a. Their down payment is 25% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$35,000 ÷ $140,000 = 0.25 = 25%
b. A $7,000 down payment would be 5% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$7,000 ÷ $140,000 = 0.05 = 5%
Find the missing numbers 46 62 87 123 ---- 236
Answer:
The missing numbers are 74, 105, and 178.
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed.
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
26.794 yd = _________km.
By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
What is the value of 1meter in terms of centimeter ?
1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .
Given,
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
we know that ,
1yard = 0.0009144 km
so ,
26.794 yard = 26.794*0.0009144 km
= 0.024500
Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
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The ratio of the measure of an exterior angle of a triangle to the measure of the adjacent interior angle is 1:4. Is the
triangle acute or obtuse?
Justify your answer.
A.) Acute; the measure of the interior angle must be 144º.
B.)Acute; the measure of the interior angle must be 36°.
C.)Obtuse; the measure of the interior angle must be 144º
D.)The triangle could be acute or obtuse, depending on the measures of the other two angles.
Check Understanding th
Math
Board
1 There are 46 swimmers and 7 lanes. The same number of
swimmers will go in each lane. Any remaining swimmers will
practice diving. How many swimmers will each lane have?
• Write a division equation to model the problem.
• Use the space at the right to show how you can use
repeated subtraction to solve.
Each lane will have ______
Module 6 Lesson 5
swimmers.
Answer: To model the problem with a division equation, we can write 46 ÷ 7 = x, where x represents the number of swimmers that each lane will have.
To solve the equation using repeated subtraction, we can subtract 7 from 46 several times until we reach a number that is less than 7. The number of times we subtract 7 will give us the number of swimmers each lane will have. Here's one way to do it:
46 - 7 = 39
39 - 7 = 32
32 - 7 = 25
25 - 7 = 18
18 - 7 = 11
11 - 7 = 4
As you can see, we are able to subtract 7 from 46 a total of 6 times before we get a number less than 7. This means that each lane will have 6 swimmers, and the remaining 4 swimmers will practice diving. So each lane will have 6 swimmers.
So the equation 46 ÷ 7 = 6, and also by repeated subtraction method it shows the same result of 6 swimmers each lane.
Step-by-step explanation:
Denise and Gabe met for dinner in downtown Belmont. Denise did flat-rate valet parking for $20. Gabe went to another valet and paid $4 up front and $4 for every hour, including the first hour. Ultimately, the friends ended up paying the same amount. How long did they stay? How much did each one pay?
What is the greatest common factor of 20 and 65
Answer:
5
Step-by-step explanation:
Answer:I believe it would be 5
Step-by-step explanation:
because if you do it on a table chart you reach five first as the same number
Identify and write down the keywords in the word problem. (1.) Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3. Evaluate the expression 2g + 3a when g = 4 and a = 8 to find the cost of buying 4 cartons of grape juice and 8 cartons of apple juice. What is the difference in price Missy and Jared paid? Show your work.
The cost of the 4 cartons of grape juice and 8 cartons of apple juice will be $32 and the difference is $12.
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.
Given that Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3.
The cost of 4 grapes and 8 apples will be,
Cost = 2g + 3a
Cost = ( 2 x 4 ) + ( 3 x 8 )
Cost = 8 + 24
Cost = $32
The difference in the price Missy and Jared paid is,
Difference = $32 - $ 20
Difference = $12
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5.7935 rounded to the nearest thousand
Answer:
5.794
Step-by-step explanation:
The seven after the decimal point is the tenth digit, the nine is the hundredth, and the 3 is the thousandth place. Therefore, we look at our neighbor (the number next to the thousandth place) and if its 5 or more we round up, but if its 4 or less we keep it the same.
Solve: S=2(lw+lw+wh) for w
Answer:
[tex]w=\frac{s-2lh}{2(h+l)}[/tex]
Step-by-step explanation:
Given the equation, [tex]S=2(lw+lh+wh)[/tex], solve for w.
[tex]S=2(lw+lh+wh)[/tex], distribute the 2.
=> [tex]S=2lw+2lh+2wh[/tex], subtract [tex]2lh[/tex] from both sides.
=> [tex]S-2lh=2lw+2wh[/tex], factor out a [tex]w[/tex] from the right-hand-side.
=> [tex]S-2lh=w(2l+2h)[/tex], now divide [tex](2l+2h)[/tex] from each side.
=>[tex]\frac{S-2lh}{2l+2h}=w[/tex]
Final answer: [tex]w=\frac{s-2lh}{2(h+l)}[/tex]
if x=1−sin a and y= 1+cos a, Express y in terms of x and a only
Answer:
Step-by-step explanation:
Given
[tex]x=1-sin(a)\\y=1+cos(a)[/tex]
Solve for [tex]a[/tex] in the second equation.
[tex]y=1+cos(a)[/tex]
[tex]y-1=cos(a)[/tex]
[tex]a=cos^{-1}( y-1)[/tex]
Insert our answer for [tex]a[/tex] into the first equation.
[tex]x=1-sin(a)[/tex]
[tex]x=1-sin(cos^{-1}( y-1))[/tex]
[tex]cos^{-1}=arccos[/tex]
[tex]x=1-sin(arccos( y-1))[/tex]
Lets simplify [tex]1-sin(arccos( y-1))[/tex]
A piece of graph paper would be helpful in my opinion.
Here is how I would go about doing so
Draw a triangle in the plane with vertices [tex](y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)[/tex] and the origin.
[tex]arccos(y-1)[/tex] is is the angle between the positive x-axis and the ray beginning at the origin and passing through [tex](y-1,\sqrt{1^2-(y-1)^2})[/tex]. Therefore [tex]sin(arccos(y-1))[/tex] is [tex]\sqrt{1-(y-1)^2}[/tex]
Now we have
[tex]x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)[/tex]
We can write [tex]1[/tex] as [tex]1^2[/tex]. Since both terms are now perfect squares, we can factor using the difference of squares formula.
[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=1[/tex] and [tex]b=y-1[/tex]
[tex]x=1-\sqrt{(1+y-1)(1-(y-1))}[/tex]
After simplifying we get
[tex]x=-\sqrt{y(-y+2)}+1[/tex]
[tex]x=-\sqrt{y(-y+2)}+1[/tex]
[tex]a=arccos(y-1)[/tex]
I think this is what your question was. If not let me know.
A savings account increased by $75 is now more than $500. What is the least amount of money that was originally put in the savings account?
The least amount of money that was originally put in the savings account is $426.
What is the least amount of money?The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.
The inequality that represents the total amount of money in the savings account is:
amount originally in the account + amount deposited > 500
x + $75 > $500
x > $500 - $75
x > $425
The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.
To check:
$75 + $426 = $501
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carmela translates f (x) = x2 to create p (x). If p 9 (x) = f (x+3) -10 sketch the graph
The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.
What are some rules of function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over the x-axis, (x, -y).
Given, A function f(x) = x².
Now, p(x) = f(x + 3).
p(x) = (x + 3)² and it is a transformed function to the parent function f(x).
Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.
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40% of an hour?
(I've tried 24 minutes...it's not the answer)
40% of an hour is 24 minutes = 2/5 hours.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given that,
there are 60 minutes in an hour,
we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour.
i.e. 60*40%= 24 minutes
Hence, 40% of an hour is 24 minutes = 2/5 hours.
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15 x 109 is how many times greater than 5 x 103?
Enter the answer using scientific notation
The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Given that, 15×10⁹ and 5×10³.
Number of times 5×10³ greater than 15×10⁹ is
Now, 15×10⁹/5×10³
= 3×10⁶
Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.
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Devin purchased a container of sport drink that contains 300 calories. The label says that 80% of the calories are from carbohydrates. How many calories are from carbohydrates?
Answer: 240 Calories are from Carbohydrates
Step-by-step explanation:
First, we will convert 80% into the decimal 0.8, then we will multiply this by the amount of total calories in the drink to create the following equation:
300 * 0.8 = 240 Calories.
Find, rounded to the nearest hundredth, the diagonal of a rectangle whose sides are 6 and 11.
WHAT IS THE ANSWER. I NEED IT ASAP
Answer:
The length of the diagonal is 12.53
Step-by-step explanation:
Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.
a^2 + b^2 = c^2
We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.
See image.
Graph the function n(x) = |x6|.
+Move Ray
-6
-4
-2
104
9
4
2
0
-2
Undo
2
4
Redo
6
x Reset
8
10
Answer:
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Tessa bought stock in a restaurant for $208.00. Her stock is now worth $284.96. What is the percentage increase of the value of Tessa's stock?
Answer:
37.04%
Step-by-step explanation:
To find the percentage increase in the value of Tessa's stock, we need to calculate the difference between the original price and the current price, and then divide that difference by the original price, and multiply by 100 to express the result as a percentage.
Here is the calculation:
percentage increase = ((284.96 - 208.00) / 208.00) * 100
= (76.96 / 208.00) * 100
= 37.04 * 100
= 37.04%
So Tessa's stock has increased in value by 37.04%.
Answer:
37 % increase
Step-by-step explanation:
To find the percentage increase, take the new amount and subtract the original amount
284.96 -208 =76.96
Divide this by the original amount
76.96/208=.37
Change the decimal form to a percent
.37 * 100% = 37 %
find angle D thank you so much need help. geomtry
The angle m∠D of the triangle is 78 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The ΔKDT and ΔKPQ are isosceles triangle.
Isosceles triangle is a triangle that has two sides and angles equal to each other.
Therefore,
∠D + ∠T + ∠k = 180
∠D = 6x + 6
∠T = 6x + 6
∠K = 2x
Therefore,
6x + 6 + 6x + 6 + 2x = 180
14x + 12 = 180
14x = 180 - 12
14x = 168
divide both side by 14
x = 168 / 14
x = 12
Therefore,
m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.
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please help me with this thank you.
how to solve this equation for x x/3+7-5
the answer is right there
38) Your bank account has$82in it when you write checks for$54,$35, and$15. You then deposit $35and $42. How much is in the account? Are you overdrawn
the answer is 55 can you show me how to get that answer.
If you have $82 in your bank account and you write checks for $54, $35, and $15, then the total amount you have written in checks is $54 + $35 + $15 = $104.
So the remaining balance is $82 - $104 = -$22, which means you are now overdrawn.
After you deposit $35 and $42, the new balance will be $82 - $22 + $35 + $42 = $155
So after the deposit, the account balance is $155
It is important to keep track of your bank account balance, if you do not have enough funds in the account and the check you wrote is cashed the bank will bounce the check and incur additional fees.
Which of these systems of equations has infinitely many solutions? Explain your choice(s).
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
b. 7x + 2y = -14
-7x + 2y = -14
c. x + 6y = -18
x - 6y = 18
d. (3/4)x - 9y = 12
(-3/4)x + 9y = 12
Distribution of toys : Is this different or just the division with remainder
Answer:
Step-by-step explanation:
20)63(3
-60
-------
3
so every children gets 3 toys but 3 toys are left which can be distributed among 3 children.
so 3 children get 1 toy more.
Hence 3 children get 3+1=4 toys (each)