By solving a linear equation we will see that the polygon has 19 sides.
How to find the number of sides of the polygon?Remember that for a polygon of n sides, the sum of the interior angles is equal to:
(n - 2)*180°
Here we also know that 3 angles are:
136°, 138°, and 146°
And the rest of the angles (n - 3) angles are of 165° each.
Then the sum of the interior angles gives:
136° + 138° + 146° + (n - 3)*165°
And that must be equal to the expression above, so we can write the linear equation:
136° + 138° + 146° + (n - 3)*165° = (n - 2)*180°
420° + n*165° - 495° = n*180° - 360°
n*165° - 75° = n*180° - 360°
360° - 75° = n*180 - n*165
285° = n*15°
285°/15° = n
19 = n
That is the solution.
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If f(x)=4x^4-3x^2+4f(x)=4x
4
−3x
2
+4, then what is the remainder when f(x)f(x) is divided by x+3x+3?
Answer:
synthetic division method use it
Yen is planning for her retirement. She is 30 years old today and would like to have RM800,000 when she turns 55. She estimates that she will be able to earn a 9% rate of return on her retirement investment over time; she wants to set aside a constant amount of money every year (at the end of the year) to help achieve her objective. How much money must she invest at the end of each of the next 25 years to realize her goal of RM800,000 at the end of that time?
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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what's th y intercept of y=6(x-1/2)(x+3)
to get the y-intercept of any equation we can simply set x = 0 and solve for "y", so let's do so
[tex]y=6\left( x-\cfrac{1}{2} \right)(x+3)\implies \stackrel{\textit{setting x = 0}}{y=6\left( 0-\cfrac{1}{2} \right)(0+3)}\implies y=6\left( -\cfrac{1}{2} \right)(3) \\\\\\ y=(-3)(3)\implies y=-9\hspace{12em} {\Large \begin{array}{llll} \stackrel{y-intercept}{(0~~,~~-9)} \end{array}}[/tex]
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.
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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What is the nth term rule of the quadratic sequence below?
−
5
,
−
3
,
3
,
13
,
27
,
45
,
67
,
.
.
.
Answer:
Step-by-step explanation:
y=ax²+bx+c
x=1,y=-5
-5=a+b+c ...(1)
x=2,y=-3
-3=4a+2b+c ...(2)
x=3,y=3
3=9a+3b+c ...(3)
(2)-(1) gives
2=3a+b ...(4)
(3)-(2) gives
6=5a+b ...(5)
(5)-(4) gives
4=2a
a=4/2=2
from (4)
6=5(2)+b
b=6-10=-4
from (1)
-5=2+(-4)+c
-5=-2+c
c=-3
y=2x²-4x-3
Rationalize the denominator and simplify the following expression:
fraction numerator 4 plus square root of 2 over denominator 2 space minus square root of 2 end fraction
5 plus 3 square root of 2
10 plus 6 square root of 2
2 plus 6 square root of 2
2 plus 3 square root of 2
Answer:
[tex]\textsf{A)} \quad 5+3\sqrt{2}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{4+\sqrt{2}}{2 -\sqrt{2}}[/tex]
To rationalise the denominator, multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of an expression is where we change the sign in the middle of the two terms. Therefore, the conjugate of the denominator of the given expression is:
[tex]2 + \sqrt{2}[/tex]Multiply the numerator and denominator by the conjugate of the denominator:
[tex]\implies \dfrac{4+\sqrt{2}}{2 -\sqrt{2}} \cdot \dfrac{2 +\sqrt{2}}{2 +\sqrt{2}}[/tex]
Simplify:
[tex]\implies \dfrac{(4+\sqrt{2})(2 +\sqrt{2})}{(2 -\sqrt{2})(2 +\sqrt{2})}[/tex]
[tex]\implies \dfrac{8+4\sqrt{2}+2\sqrt{2}+\sqrt{2}\sqrt{2}}{4+2\sqrt{2}-2\sqrt{2}-\sqrt{2}\sqrt{2}}[/tex]
[tex]\implies \dfrac{8+6\sqrt{2}+2}{4-2}[/tex]
[tex]\implies \dfrac{10+6\sqrt{2}}{2}[/tex]
Reduce to its simplest form by dividing the numerator and the denominator by 2:
[tex]\implies 5+3\sqrt{2}[/tex]
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
What’s Ln(d)=n in exponential form?
Answer:
ln(d) = n can be rewritten in exponential form as d = e^n.
Step-by-step explanation:
The natural logarithm, denoted by ln, is the logarithm to the base e (approximately 2.718). The inverse of the natural logarithm function is the exponential function e^x. Therefore, when you take the natural logarithm of a number, you can raise e to the power of that number to get the original value.
ln(d) = n is the same as d = e^n
So, Ln(d)=n can be written as d = e^n
This is because e^n is the inverse function of Ln(d) and Ln(d)=n is the logarithm form of d = e^n
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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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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PLSSS HELPP
IMAVE ATTACHED
Answer:
38[tex]\sqrt{3}[/tex]
Step-by-step explanation:
6[tex]\sqrt{5x5x3}[/tex] + 4[tex]\sqrt{2x2x3}[/tex] We can pull out a pair of 5's and 2's
6(5) [tex]\sqrt{3}[/tex] + 4(2)[tex]\sqrt{3}[/tex]
30[tex]\sqrt{3}[/tex] + 8[tex]\sqrt{3}[/tex]
38[tex]\sqrt{3}[/tex]
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?
The graph of the function f(x) =-3x^2 - 3x + 6 is shown. Which statements describe the graph? Select three options.
1) The vertex is the maximum value.
2) The axis of symmetry is x = -1/2.
3) The domain is all real numbers.
4) The range is all real numbers.
5) The function is decreasing from (-∞, 6.75).
Answer:
1) The vertex is the maximum value.
2) The axis of symmetry is x = negative one-half.
3) The domain is all real numbers.
Step-by-step explanation:
What is the slope of the line shown below?
(1,6) (-5,-7)
A. 13/6
B. -13/6
C. -6/13
D. 6/13
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }[/tex]
help me with this question and find f8
Answer:
f(8) = - 1
Step-by-step explanation:
f(8) has x = 8 which is in the interval x > 0 , then f(x) = - 1 , so
f(8) = - 1
What is the equation?
N=4 Y=3
2y + 6n
A person standing on an escalator reaches the top in 3 minutes. How many minutes will it take the person to reach the top if he walks up the moving escalator at a speed of 25 meters per minute? The escalator is 150 meters long.
Due today, I NEED HELP!!
If he walks up the moving escalator at a speed of 25 meters per minute,
the person will reach the top in six minutes.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A person standing on an escalator reaches the top in 3 minutes.
The escalator is 150 meters long.
He walks up the moving escalator at a speed of 25 meters per minute.
So, the time taken = divide 150 by 25
The time taken = 150/25
The time taken = 6 minutes.
Therefore, he will reach the top in six minutes.
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The fourth grade is going on a field trip and taking two buses. One bus has 3 rows of seats with 9 seats in each row the other bus has four times as many seat as the first bus. How many seats are there in both buses?
The number of seats of each bus is given as follows:
First bus: 27. Second bus: 108.How to obtain the number of seats?The number of seats of each bus is obtained applying the proportions in the context of the problem.
One bus has 3 rows of seats with 9 seats in each row, hence the number of seats of the first bus is given as follows:
3 x 9 = 27.
The other bus has four times as many seat as the first bus, hence the number of seats of the second bus is given as follows:
4 x 27 = 108.
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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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What is the equation of the midline of the sinusoidal function?
Answer:
y = -3
Step-by-step explanation:
The midline of a sinusoidal function is y = a where "a" is halfway between the minimum and maximum y-values of the function.
From inspection of the given graph:
Maximum y-value = 1Minimum y-value = -7Therefore, the y-value that is halfway between the minimum and maximum points is:
[tex]\implies y=\dfrac{y_2+y_1}{2}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3[/tex]
Therefore, the equation of the midline of the given sinusoidal function is:
y = -3Let 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).
Find the domain of fg f(x) = x + 2 g(x) =1/x + 2
Answer:
x+2 domain: (-infiniy, +infinity) or -infinity<x<infinity
1/x +2 domain: (-infinity, 0) and (0, infinity) or 0<x<0
use substitution to solve the following system of equations.
4x+4y=16 AND y=x+2
( [?], [?])
The solution of the system of equations by using substitution method is x = 1 and y = 3
How to use substitution method to solve system of equations?The substitution method is a method for solving systems of equations. It involves solving for one variable in one of the equations and then substituting that value into the other equation to find the value of the other variable.
We have the equations 4x + 4y = 16 and y = x+2
Substitute y = x +2 into 4x + 4y = 16:
4x + 4y = 16
4x + 4(x +2) = 16
Clear the parenthesis:
4x + 4x + 8 = 16
8x + 8 = 16
8x = 16-8
8x = 8
x = 8/8
x = 1
put x = 1 into y = x+2:
y = x+2
y = 1 + 2
y = 3
Therefore, the solution of the system of equations is x = 1 and y = 3
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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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2(x+2y)=2x+4y is it proportion
Find the distance between the two points rounding to the nearest tenth (If necessary)
(1,-3) and (-7,2)
Answer:
Step-by-step explanation:
Distance formula is as follows.
The distance between two co-ordinates, say, (x₁ , y₁) and (x₂,y₂), is equal to
√((x₁ - x₂)² + (y₁ - y₂)²)
Just substitute the values here.
√((1 - (-7) )² + ( - 3 - 2)²)
= √((1 + 7)² + ( - 3 - 2)²)
= √(8² + -5²)
= √(65 + 25)
= √90 ≈9.5 units
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