The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).
What is meant by coordinates?A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.
To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.
Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC :
Let the equation be Distance [tex]$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex] substitute the values in the above equation, we get
[tex]$\mathrm{AC}=\sqrt{\left((2-(-2))^2+(4-1)^2\right)}$$[/tex]
simplifying the equation, we get
[tex]$A C=\sqrt{ }(4+9)=\sqrt{ }(13)$$[/tex]
We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).
Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))
Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.
The complete question is:
Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.
The coordinates are and D.
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(Look at picture) ty btw
The correct statements regarding the linear function G(t) = 10 - 2t are given as follows:
Initially, the tank has 10 gallons of gasoline.
The rate of consumption is of 2 gallons per hour.
The slope of G(t) represents the fuel consumption of the vehicle.
The t-intercept represents the time it takes for the vehicle to run out of gas.
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The linear function is defined as follows:
G(t) = 10 - 2t.
In which the variables are:
G(t) is the amount of gasoline that the car has after t hours.
t is the time in hours.
The slope and the intercept are presented as follows:
Slope of -2: 2 gallons are consumed each hour.
Intercept of 10: The initial fuel in the car is of 10 gallons.
The t-intercept is:
10 - 2t = 0
2t = 10
t = 5.
Which is the time it takes for the car to run out of fuel.
Missing Information
The options are given by the image shown at the end of the answer.
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At the 2006 Winter Olympics in Torino, Italy, US speed skater Apolo Ohno took the gold medal for the 500m sprint by completing the course in 41.935 s. What was his average speed for this event in m/s.
The average speed of Apolo Ohno, in the sprint in the Winter Olympics in 2006, given the time taken to complete the course, was 11. 92 m /s
How to find the average speed ?A body's average speed is the mean value of its speed for a certain time period. The average speed formula is necessary because a moving body's speed vary over time instead than remaining constant. Even though the speed changes, we can still use the total time and total distance numbers, and with the help of the average speed calculation, we can determine a single value that represents the entirety of the motion.
Given the distance that Apolo Ohno had to sprint and the time he completed the course in, his average speed in the event was :
= 500 m / 41. 935 s
= 11. 92 m /s
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X is the number of products. What is the minimum production cost?
Answer:
(125, -312500)
C(x) = -312500
Step-by-step explanation:
use this equation into a graphing calculator and use the minimum function
What is the equation of the line in slope-intercept form that passes through point (0, −2) and is parallel to the line y = -1/2 + 6? Show all necessary steps.
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mc + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 6 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
slope of parallel line = - [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of parallel line
2(x+2y)=2x+4y is it proportion
Nakeisha bought a concert ticket online for $32. She used a coupon code to get a 30% discount. The website also applied a 5% processing fee to the price after the discount. How much was the discount, in dollars and cents?
The amount of the discount, in dollars and cents is $14.77
How to determine discount?Total amount paid for the ticket = $32
Percentage discount = 30% of x
Percentage processing fee = 5%
Total amount paid = x - (30% of x) + 5% of x
32 = x - 0.3x + 0.05x
32 = 0.65x
divide both sides by 0.65
x = 32/0.65
x = 49.23076923076923
Approximately,
x = $49.23
Therefore,
Percentage discount = 30% of x
= 0.3 × $49.23
= $14.769
Approximately,
$14.77
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Please look at the picture and answer the question thank you
Answer: (-2, 10)
Explanation:
The left endpoint is -2. The right endpoint is 10. Both endpoints are open holes, which means we don't include them as part of the green-shaded solution region. If x is a solution, then the solution can be described as [tex]-2 < x < 10[/tex] converting to interval notation [tex](-2,10)[/tex] . The curly bracket says "do not include endpoint".
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Cuando hay una potencia de una potencia se conserva la base y los exponentes se multiplican? Verdadero o falso
Verdadero. Cuando hay una potencia de una potencia, se conserva la base y los exponentes se multiplican.
What is the statement about?Para calcular la potencia de una potencia, se puede conservar la base y multiplicar los exponentes. Esto se basa en la propiedad matemática de la potenciación que establece que (a^b)^c = a^(b*c), donde a es la base, b es el primer exponente y c es el segundo exponente.
Por ejemplo, considere (2³)⁴. La base es 2 y el primer exponente es 3 y el segundo exponente es 4. El resultado sería 2^(3*4) = 2¹². Esto significa que la expresión original (2³)⁴ es igual a 2 elevado a la potencia de 12.
En general, cuando se tiene una potencia de una potencia, el resultado se obtiene conservando la base y multiplicando los exponentes. Esto permite simplificar la expresión y encontrar el resultado de manera más fácil.
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if an adult and kids went to a theater and it 3.50 perticket for each adult and it was 2.50 for children and they sold 321 tickets and made 972.21 dollars how many tickets for aduklts and children
number of tickets for adult = 170 and number of tickets for children = 151
What is equation with two variables?
The equation that has two unknown variables and express the equality between two or more expression is called equation with two variables.
How many tickets for adult and kids?
let, x denotes the number of adults went to theater.
y denotes the number of children went to theater
price of ticket for each adult = $3.50
price of tickets for each child = $2.50
if the number of total tickets = 321
x + y = 321
total cost of tickets = $3.50x + $2.50y = 972.21 dollar
we will solve the above two equations, y = 321 - x
by putting the y value in the second equation,
3.50x + 2.50 (321- x) = 972.21
3.50x + 802.5 - 2.50x = 972.21
x = 169.71
number of adults went to theater = 170
from, y = 321 -169.71
y = 321 - 169.71
y = 151.3, y= 151
number of children went to theater = 151
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Let f(x)=−|x−4|+4 and g(x)=1/2x−4. Graph the functions in the same coordinate plane. What are the solutions to f(x)=g(x)? Enter your answers in the boxes from smallest to largest.
x =
and x =
Answer:
Step-by-step explanation:
To find the solutions to f(x) = g(x), we need to find the values of x that make the two sides of the equation equal.The function f(x) = −|x−4| + 4 is a piecewise function. For x≤4, f(x) = −(x−4) + 4 = 4−x and for x>4, f(x) = (x−4) + 4 = x.The function g(x) = 1/2x − 4 is a linear function.When we graph these two functions in the same coordinate plane, we can see that they intersect at the point (4, 4) this point is the only solution where f(x) = g(x)so the solution of x = 4
x = 4
McGuire Corporation began operations in 2021. The company purchases computer equipment from manufacturers and then sells to retail stores. During 2021, the bookkeeper used a check register to record all cash receipts and cash disbursements. No other journals were used. The following is a recap of the cash receipts and disbursements made during the year.
Cash receipts:
Issue of common stock $ 50,000
Collections from customers 320,000
Borrowed from local bank on April 1, note signed requiring
principal and interest at 12% to be paid on March 31, 2022 40,000
Total cash receipts $ 410,000
Cash disbursements:
Purchase of merchandise $ 220,000
Payment of salaries 80,000
Purchase of office equipment 30,000
Payment of rent on building 14,000
Miscellaneous expense 10,000
Total cash disbursements $ 354,000
You are called in to prepare financial statements at December 31, 2021. The following additional information was provided to you:
Customers owed the company $22,000 at year-end.
At year-end, $30,000 was still due to suppliers of merchandise purchased on credit.
At year-end, merchandise inventory costing $50,000 still remained on hand.
Salaries owed to employees at year-end amounted to $5,000.
On December 1, $3,000 in rent was paid to the owner of the building used by McGuire. This represented rent for the months of December through February.
The office equipment, which has a 10-year life and no salvage value, was purchased on January 1, 2021. Straight-line depreciation is used.
What is the Balance sheet?
The balance sheet for McGuire Corporation as at December 31, 2021, is as follows:
McGuire Corporation
Balance SheetAs at December 31, 2021
AssetsCurrent Assets:
Cash $56,000
Accounts Receivable $22,000
Inventory $50,000
Rent Prepaid $2,000
Total current assets $130,000
Long-term assets:
Office Equipment $30,000
Accumulated Depreciation (3,000) $27,000
Total assets $157,000
Liabilities and EquityCurrent Liabilities:
Accounts payable $30,000
Salaries Payable $5,000
Interest Payable $3,600
Total current liabilities $38,600
Long-term liabilities:
Notes Payable $40,000
Total liabilities $78,600
Stockholders' Equity:Common Stock $50,000
Net income $28,400 $78,400
Total liabilities and Equity $157,000
What is the Balance sheet?The balance sheet is one of the financial statements where an entity or individual reports their financial position.
The financial position consists of assets, liabilities, and equity or net worth at a specific time.
Analysis of Transactions:Cash $56,000 ($410,000 - $354,000)
Accounts Receivable $22,000
Inventory $50,000
Rent Prepaid $2,000
Office Equipment $30,000
Accumulated Depreciation on Equipment $3,000
Accounts payable $30,000
Salaries Payable $5,000
Common Stock $50,000
Notes Payable $40,000
Interest Payable $3,600
Sales Revenue $342,000 ($320,000 + $22,000)
Cost of goods sold $200,000 ($220,000 + $30,000 - $50,000)
Salaries Expense $85,000 ($80,000 + $5,000)
Rent Expense $12,000 ($14,000 - $2,000)
Miscellaneous Expense $10,000
Interest Expense $3,600 ($40,000 x 12% x 9/12)
Depreciation Expense $3,000 ($30,000/10)
Adjusted Trial BalanceAccount Titles Debit Credit
Cash $56,000
Accounts Receivable 22,000
Inventory 50,000
Rent Prepaid 2,000
Office Equipment 30,000
Accumulated Depreciation:
Office Equipment $3,000
Accounts payable 30,000
Salaries Payable 5,000
Common Stock 50,000
Notes Payable 40,000
Interest Payable 3,600
Sales Revenue 342,000
Cost of goods sold 200,000
Salaries Expense 85,000
Rent Expense 12,000
Miscellaneous Exp. 10,000
Interest Expense 3,600
Depreciation Expense 3,000
Totals $473,600 $473,600
Income StatementSales Revenue $342,000
Cost of goods sold $200,000
Salaries Expense $85,000
Rent Expense $12,000
Miscellaneous Expense $10,000
Depreciation Expense $3,000
Interest Expense $3,600 $313,600
Net income $28,400
Thus, before the balance sheet can be prepared, the general ledger must be summarized into an adjusted trial balance and an income statement that shows the net income.
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ANYONE GOOD AT MATH!? PLEASE HELP!!
The values of g(g(4)) = 0 and f(f(3)) = - 3.
Equation of Parabola:A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the iconic figure. The parabola is likewise a quadratic connection, much like the circle, however, unlike the circle, either 'A' or 'B' will be squared, but never both.
Here we have
Equation of parabola f(x) = x² - 2x - 3 and line g(x) = x - 2
Here we need to find g(g(4)) and f(f(3))
To find g(g(4)) take x = 4
g(4) = 4 - 2 = 2
=> g(g(4)) = g(2) = 2 - 2 = 0
Therefore, g(g(4)) = 0
To find f(f(3)) take x = 3
f(3) = 3² - 2(3) - 3 = 9 - 9 = 0
f(f(3)) = 0² - 2(0) - 3 = - 3
Therefore,
The values of g(g(4)) = 0 and f(f(3)) = - 3.
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Help Please..
Cameron reports to work at 7:00 A.M. and leaves at 4:00 P.M. after typing from the end of page to the end of page 5 to the end of page 41. His employer pays $162.00 for his work.
The amount that Cameron is paid per hour, given the number of hours he worked, is $ 18 per hour
How to find the payment per hour ?To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.
This number of hours is:
= 4 pm - 7 am
= 1600 hrs - 0700 hours
= 9 hours
The payment per hour is therefore:
= Amount Cameron paid / Number of hours worked
= 162 / 9
= $ 18 per hour
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The rest of the question is:
How much was Cameron paid per hour worked?
Right triangle ghi, shown in the coordinate plane below, is rotated 180 degrees clockwise about the origin and then dilated by a factor of 3, centered at the origin forming a new triangle g’h’i’. What is the area of the new triangle g’h’i’?
The area of the new triangle g’h’i’ is 9.
Describe area of triangle?The area of a triangle is a measure of the size of the triangle, calculated as the amount of space enclosed by its three sides. It can be calculated using the following formula:
Area = (base x height) / 2
where base is the length of one side of the triangle, and height is the perpendicular distance from the base to the opposite vertex.
If a triangle is rotated 180 degrees about the origin, its coordinates will change signs. If it is then dilated by a factor of 3, its coordinates will be multiplied by 3. The new triangle g'h'i' will have the following coordinates: g' (-3,0), h' (0,3), and i' (0,-3).
The height of the new triangle will be the absolute value of the difference between its y-coordinates: h = |3 - (-3)| = 6. The base of the triangle will be the absolute value of the difference between its x-coordinates: b = |-3 - 0| = 3.
Therefore, the area of the new triangle g'h'i' is: A = (1/2)bh = (1/2)(3)(6) = 9.
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if a^2 = 3a + 1, find the value of (a+1/a)^2
Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:
a^2 - 3a - 1 = 0
Now we can factor the left side:
(a-1)(a+1) = 0
This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.
Next, we can substitute these values into the expression (a+1/a)^2
For a = 1, (1+1/1)^2 = 2^2 = 4
For a = -1, (-1+1/(-1))^2 = 0^2 = 0
So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1
Step-by-step explanation:
On A riverboat traveled 10 miles upstream against the
current in 5 hours. The return trip took only half
da
the amount of time while the boat traveled with the current.
a. Write an equation for the trip upstream.
b. Write an equation for the return trip.
c. Use combination/elimination to find the speed of the boat and the speed of the current.
Answer:
a. Let x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour. Since the boat traveled upstream, the speed of the current is added to the speed of the boat. Therefore, the equation for the trip upstream is:
distance = (x + y) * time
10 = (x + y) * 5
b. For the return trip, the speed of the current is subtracted from the speed of the boat. Therefore, the equation for the return trip is:
distance = (x - y) * (time/2)
10 = (x - y) * (5/2)
c. To find the speed of the boat and the speed of the current, we can use the method of elimination. From the first equation, we have:
10 = 5x + 5y
From the second equation, we have:
10 = 2.5x - 2.5y
Now we can use the elimination method by multiplying the first equation by 2 and then subtracting the second equation from it.
20 = 10x + 10y
20 = 5x - 5y
so we have
0 = 5x + 5y - 5x + 5y
0 = 10y
The equation becomes impossible to solve as we can't divide by 0.
As we know that the speed of the boat and the speed of the current are non-zero numbers, we can't find the exact speed of the boat and the current. We can conclude that the information given is not sufficient to find the exact speed of the boat and the current.
Step-by-step explanation:
Iron dobrowski office exam he charges totaling $65. A primary insurance is an indemnity plan with 8515 coinsurance. She does not go on her deductible. What amount will be covered by the insurance plan and what amount if you will be billed to the patient
The amount that would be covered by the Insurance Plan would be and the amount that is billed to the patient is $ 9. 75
What is coinsurance ?The amount that would be covered by the insurance plan in a 85 / 15 coinsurance plan is 85 % of the bill. The amount to be covered by the insurance plan is:
= 85% x 65
= $ 55. 25
The amount billed to the patient is:
= Total bill - covered by insurance plan
= 65 - 55 .25
= $ 9. 75
In conclusion, the amount that would be covered by the insurance plan is $ 55. 25 and the amount to be billed to the patient to be paid by them is $ 9. 75.
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An electronics store has a 20% off sale. If a stereo originally costs $125
Answer:
Step-by-step explanation:
24
K
Round to the nearest given place.
1.80642 thousandths
I need help this homework please
Answer:
1.806 (to the nearest thousandth)
Step-by-step explanation:
1.806 (to the nearest thousandth)
The number 1.80642 would round down to 1.806
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We need to round 1.80642 to the nearest hundredth,
We can see that the 1.80642 is below 2 so it goes down, and it rounds down to 1.80642 instead of, 14.62 then that would round up to the decimal is higher than 1.
1.80642 rounded to the nearest thousandth is 1.806.
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Simplify the equation
Answer:
Option C
Step-by-step explanation:
Simplify the expression:Factorize 768
768 = 4 * 4 * 4 * 4 * 3
For every four times of a constant or variable, take one constant or variable outside the fourth root.
[tex]\sqrt[4]{768x^8y^5}=\sqrt[4]{4*4*4*4*3 * (x^2)^4 * y^4 * y}[/tex]
[tex]=4x^2y\sqrt[4]{3y}[/tex]
Let A= {a,b,c,d,e,f } and let B= {1,2,3,} determine n(AxB)
The value of n(AxB) is mathematically given as
n(A x B) = 18
What is the magnitude of the sample?Generally, It is possible to extend the formula for calculating the magnitude of a vector to any number of dimensions. For instance, the magnitude of a four-dimensional vector denoted by
a=(a1,a2,a3,a4) may be calculated using the following formula: a=a21+a22+a23+a24.
The question "how much of a quantity" is what's meant to be answered when one asks about magnitude.
For instance, the magnitude may be used to provide an explanation for why the speeds of a vehicle and a bicycle cannot be compared directly to one another. It is also possible to use it to describe the distance traveled by an item or the quantity of an object in terms of its magnitude. Both of these applications need the usage of magnitude.
n(A x B) = |A| x |B|
= 6 x 3
n(A x B) = 18
Where
|A| is the number of elements in set A (in this case, 6) and |B| is the number of elements in set B (in this case, 3).The product of these two values is the total number of ordered pairs that can be formed from the elements of A and B, which is 18.
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Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices
W(-2,5), X(2, 5), Y(4, 0), and Z(0, 0).
The coordinates of the intersection are ( , )
Step-by-step explanation:
the intersection of the diagonals of a parallelogram is always the middle point of either of the diagonals.
so, all we need to do is identify a diagonal and find is middle point.
a diagonal is e.g. from all the way on the left and up (-2, 5) to all the way right and down (4, 0).
the middle point between 2 points is
((x1 + x2)/2, (y1 + y2)/2)
so, here
((-2 + 4)/2, (5 + 0)/2) = (1, 2.5)
the coordinates of the intersection are (1, 2.5).
The equation of line 1 is shown.
v=-3x-1
Click to show whether each line, represented by their
equations, is parallel to line I, perpendicular to line 1, or neither
(Or just look at picture) lol
x = 3y perendicular to l
y = -3x parallel to l
y = 3x + 2 neither
x -3y = -6 perpendicular to l
6y = 2x + 10 perpendicular to l
What is Slope ?A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks.
One approach for determining a line's slope from a graph is to use the formula immediately after knowing the coordinates of two points that are on the line. Let's assume that the coordinate values for the two spots are unknown. Therefore, we also have another way to determine the slope of the line. This approach entails attempting to determine the tangent of the angle formed by the line and the x-axis.
The line is
y = -3x -1
slope is -3 by slope intercept form
The line x = 3y
or y = (1/3)*x
slope is 1/3
we know for a line perpendicular to a given line slope should be -1/m so the slope will be (1/3)
so, x = 3y is perpendicular
y = -3x have slope -3 so it is parallel
y = 3x + 2 slope is 3 so neither
x - 3y = -6
or , y = (1/3)*x + 2 , so slope is (1/3) so perpendicular to line
And
6y = 2x + 10
here slope is 1/3 so perpendicular to line.
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I need help with this problem
the space between [tex]3x-2\ge -5 : $x \geq-1$[/tex] the time between
[tex]2x+5\le 17 : $x \leq 6$[/tex] . When two simple inequalities are combined, the result is a compound inequality.
What are compound inequalities in math?Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and." When a number resolves both inequalities, it also resolves the compound inequality. Compound inequality can come in two different forms. Both congruence and disjunction issues are at play.
Occasionally, these compound inequality formulas will be represented as two simple inequality formulas that have been separated by the words AND or OR. If there are multiple "and/or" compound inequalities, start by resolving each one separately. It is an inequality when two simple inequalities are combined to form it. The two expressions that make up an equation or an inequality are connected in a mathematical statement.
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The table shows the costs of playing several carnival games. You have $20 and play each game twice. How much money do you have left?
Ring Toss : $1.50
Balloon Pop : $1.5
Basketball : $2.50
Answer:
$9 left
Step-by-step explanation:
1.50 x 2 = $3
1.50 x 2 = $3
2.50 x 2 = $5
5 + 3 + 3 = $11
$20 - $11 = $9
Answer:
9Step-by-step explanation:
1.50+1.50+3
1.50+1.50+3
2.50+2.50= 5
5 + 3 + 3 = 11
20 - 11 = 9
Mr. Heritage starts a new business, and to get it started he borrows $2 500 from a bank. If the loan is for two years, and the amount of interest for those two years is $175, what SIMPLE interest rate was he charged? (SIMPLE INTEREST: the principle and interest calculations dont change- they stay the same for the entire two year period!) BONUS- if he pays off the whole loan in the two years, what would his monthly bill be, (DON'T FORGET TO INCLUDE THE INTEREST CHARGE FOR HIS MONTHLY BILLS!!! YOU CAN ROUND YOUR CALCULATION TO THE NEAREST HUNDRETH- THAT IS, TO TWO DECIMAL PLACES...)
The rate of interest is given by the equation R = 3.5 %
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the rate of interest be represented as R
Now , the simple interest I = $ 175
The principal amount invested P = $ 2,500
The time period T = 2 years
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )
Substituting the values in the equation , we get
Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )
Rate of Interest R = 17500 / 5000
Rate of Interest R = 3.5 %
Hence , the interest rate is 3.5 %
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A car radiator needs a 40% antifreeze solution the radiator now holds 49% of a 30% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength
If a car radiator needs a 40% antifreeze solution the radiator now holds 49% of a 30% solution. The number of liters that should be drained and replaced with 100% antifreeze to get the desired strength is 7 liters.
How to find the number of liters to be drained?Let x represent the number of liters that should be drained
So, Let solve for x
x+.30(49-x)=.40× 49
x=14.7-.30x=19.6
.7x=19.6 - 14.7
.7x=4.9
x=4.9/.7
x = 7 liters need to be drained & filled with 100% antifreeze.
Therefore the number of liters is 7 liters.
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Which polynomial is a prime?
The prime polynomial in this problem is defined as follows:
D. 3x² + x - 6x + 3
What are prime polynomials?A prime polynomial is a polynomial that cannot be reduced, that is, the polynomial cannot be factored.
The reduced forms of each polynomial are given as follows:
x^4 + 2x² - 3.x^4 - 4x² + 3.3x² - 5x - 2.3x² - 5x + 3.The first polynomial can be factored as follows:
x^4 - x² + 3x² - 3
x²(x² - 1) + 3(x² - 1)
(x² + 3)(x² - 1).
It can be factored, hence it is not prime.
The second polynomial is factored as follows:
x^4 - 3x² - x² + 3
x^4 - x² - 3x² + 3
x²(x² - 1) - 3(x² - 1)
(x² - 3)(x² - 1).
It can be factored, hence it is not prime.
The third polynomial is factored as follows:
3x² + x - 6x - 2
3x² - 6x + x - 2
3x(x - 2) + x - 2
(x - 2)(3x + 1)
It can be factored, hence it is not prime.
The fourth polynomial cannot be factored, hence it is prime.
3x² + x - 6x + 3
3x² + 6x + x + 3
3x(x + 2) + x + 3.
x + 2 and x + 3 cannot be factored.
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Divide $940 among A,B,C in the ratio 1/3 : 1/4 : 1/5
Answer:
A = $400, B = $300, C = $240
Step-by-step explanation:
The ratio will be [tex]\frac{20}{60}:\frac{15}{60}:\frac{12}{60}[/tex], that means the total of them is (20 + 15 + 12 = 47).
Divide $940 by 47 to find the value of 1 unit [tex]\frac{940}{47}=20[/tex]
A = 20 × 20 = $400
B = 20 × 15 = $300
C = 20 × 12 = $240
Slopes of parallel/Purpendicular lines - What is the slope of a line parallel to the line whose equation is x + 2y = -14
Explanation:
First we solve for y.
x + 2y = -14
2y = -14 - x
2y = -x - 14
y = (-x - 14)/2
y = -x/2 - 14/2
y = (-1/2)x - 7
The equation is in slope intercept form y = mx+b
m = -1/2 = slopeb = -7 = y interceptParallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2
For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.
