In the current year, Bonnie sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers total a) $55,000.
Shares, also known as stocks, are securities that represent partial ownership of the issuing company. A unit of stock is called a "share" and allows the holder to receive a portion of the company's assets and profits equal to the number of shares held.
shares are traded primarily on stock exchanges and form the basis of many individual investor portfolios. Stock trading must comply with government regulations designed to protect investors from fraud.
Taxable Gifts:
Gifts valued at $75 or more are taxable.
Non-cash gifts of small value (less than $75 annually) to employees. Holiday turkeys are tax exempt.
tax-free value is capped at $1,600 for all her awards for one year.
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ASAP The vertices of a rectangle are plotted in the image shown.
A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 4, 4, then 3, 4, then negative 4, negative 3, and at 3, negative 3.
What is the perimeter of the rectangle created by the points?
49 units
56 units
14 units
28 units
The perimeter of the rectangle created by the given points (-4, 4), (3, 4), (-4, -3), and (3, -3) is 28 units. The length of each side is calculated, and the sum of all four sides gives the perimeter. Option D.
To find the perimeter of the rectangle created by the given points, we need to calculate the sum of the lengths of all four sides.
Let's calculate the length of each side:
Side 1: The distance between (-4, 4) and (3, 4) along the x-axis is 3 - (-4) = 7 units.
Side 2: The distance between (-4, 4) and (-4, -3) along the y-axis is 4 - (-3) = 7 units.
Side 3: The distance between (-4, -3) and (3, -3) along the x-axis is 3 - (-4) = 7 units.
Side 4: The distance between (3, -3) and (3, 4) along the y-axis is 4 - (-3) = 7 units.
Now, let's sum up the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Perimeter = 7 + 7 + 7 + 7
Perimeter = 28 units
Therefore, the perimeter of the rectangle created by the given points is 28 units. Option D is correct.
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Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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36÷(x-3)=4
PLEASE HELP!!!!!!!!!!!!!!!!!!!
Answer:
12
Step-by-step explanation:
12 - 3 = 9
and
36 divided by 9 = 4
Answer:
36 ÷ ( 12 - 3 ) = 4
Step-by-step explanation:
36 ÷ 4 = 9
9 + 3 = 12
36 ÷ 9 = 4
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q22
Explanation
Step 1
Domain:
The domain of a function is the complete set of possible values of the independent variable,
so, we need to check the values that make the function undefined
\(R\lparen x)=\frac{x}{x^2-100}\)this function is undefined when the denominator equals zero, so
\(\begin{gathered} x^2-100=0 \\ x^2=100 \\ x=\pm10 \end{gathered}\)therefore, the domain is all real numbers excep 10 and -10, in set notation it is
\(\begin{gathered} \lbrace x\left|x\ne10\text{ and x}\ne-10\rbrace\right? \\ \end{gathered}\)so, the answer is B
\(B)\lbrace x\lvert\rvert x10\text{andx}-10\rbrace\)Step 2
(b) vertical asymptote
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.
so, the vertical asymptetes are
\(\begin{gathered} x=-10 \\ x=10 \end{gathered}\)so, the answer is
\(x=-10,10\)Step 3
c) horizontal asymptote
A horizontal asymptote is a y-value on a graph which a function approaches but does not actually reach.
to check the H.A.
we can use the expression
\(R\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}\)\(y=\frac{Leading\text{ coefficient of P\lparen x})}{Leading\text{ coefficient of Q\lparen x})}\)\(\begin{gathered} if\text{ degree of P\lparen x})\text{ is}<\text{ degree of q\lparen x}) \\ the\text{ asymptote is y}=0 \end{gathered}\)so, the horizontal asymptote is
\(y=0\)Step 4
therefore, the answer is B
I hope this helps you
Los dueños de un restaurante exitoso quieren un préstamo de $50,000 para renovar la cocina y ampliar el comedor. Esperan que las mesas extra agreguen entre $2,000 y $5,000 a los ingresos mensuales del restaurante. El banco está dispuesto a permitir que la empresa tenga un préstamo a plazo intermedio de $50 000 durante cinco años a una tasa de interés del 6,5 por ciento. Calcule el pago mensual y explique si tomar este préstamo es una decisión comercial inteligente.
The monthly Payment for the loan is approximately $271.24.
To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
Given:
Loan Amount = $50,000
Interest Rate = 6.5% per year
Number of Years = 5
First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:
Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667
Plugging in the values into the formula, we get:
Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))
= $271.24
Therefore, the monthly payment for the loan is approximately $271.24.
The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.
If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.
On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.
Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.
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polygon h is a scaled factor of polygon g using a scale factor of 1/4
The fraction of the area of polygon H of polygon G's area would be: 1/16.
What are Similar Polygons?When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.
What is a Scale Factor?The scale factor = new dimension/original dimension
Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:
Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation
Area of polygon H/Area of polygon G = 1²/4² = 1/16
This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².
Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.
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Mrs. O'Dell has 8 different
vegetables to plant in her
garden. She wants to divide
her garden into 8 squares. Each
square should be the same size.
Help Mrs. O'Dell divide her
garden into 8 squares. What is
the measurement of each side
of the squares?
The measurement of each of the squares will guarantee Mrs. O'Dell has 8 different squares and they are all the same size are 75 centimeters by 100 centimeters.
How to divide the total area into 8 squares which are the same size?To begin, let's identify the best way to divide the total area. For this, there are 2 options:
Create two rows each with 4 squares = 4 x 2 = 8Create four rows each with 2 squares = 2 x 4 8=Let's use the first pattern:
Length: 3 meters / 4 = 0.75meters or 75 centimetersWidth= 2 meters / 2 = 1 meter or 100 centimetersBased on this, the dimensions for each section should be 75 centimeters by 100 centimeters.
Note: This question is incomplete; here is the missing section:
Dimensions of the garden: 3 meters x 2 meters
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Solve for x and show steps . Is the solution extraneous ? Check your work to show how you determined if the solution is extraneous or not
Square 4x-3=5
The solution of the equation 4x - 3 = 5 is not extraneous .
How to solve an equation?Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.
Therefore, let's solve the equation to know whether it is extraneous solution.
Hence,
4x - 3 = 5
add 3 to both sides of the equation
4x - 3 + 3 = 5 + 3
4x = 8
divide both sides of the equation by 4
4x / 4 = 8 / 4
x = 2
Therefore, it is not extraneous solution.
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Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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35%of students wear glasses.There are 14 students who wear glasses.How many pupils are there in the class?
Answer: 40 pupils
Step-by-step explanation:
35 14
------- = --------
100 ?
find the denominator.
multiply 14 and 100:
14 x 100 = 1400
divide 1400 by 35
1400/35 = 40
Therefore there are 40 students
3. A species of orchids have a gene encoding either a dominant pink (P) or recessive white (p) flower color trait. If a heterozygous pink and white flower were crossed, what is the probability that the offspring have white flowers?
The correct probability is indeed 0.25 or 25%.
When heterozygous pink (Pp) and white (pp) flowers are crossed, the Punnett square can be used to determine the probability of offspring having white flowers:
| P p
---------------
P | PP Pp
---------------
p | Pp pp
From the Punnett square, we can see that there are four possible combinations of alleles for the offspring: PP, Pp, Pp, and pp.
Out of these four possibilities, only one combination (pp) corresponds to the white flower trait.
Therefore, the probability of an offspring having white flowers is 1 out of 4.
In terms of probability, this can be expressed as:
Probability of white flowers = Number of favorable outcomes / Total number of possible outcomes.
= 1 / 4
= 0.25
So, the correct probability is indeed 0.25 or 25%.
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1/8 of the pupils at jake's school walked to school. 3/8 came by bus. waht fraction either walked or came by bus
By adding the two given fractions we will see that 1/2 of the students either walked or came by bus
What fraction either walked or came by bus?Let's say that there are N students in total. We know that a fraction of 1/8 of these N students walk to school.
And a fraction of 3/8 of the students go by bus to the school.
Then the fraction that either walks or came by bus to school is given by the addition between the two fractions above, then we just need to solve.
f = 3/8 + 1/8
We can see that we have the same denominator in both fractions, so we can directly add the numerators:
f = (3 + 1)/8 = 4/8
Now we can simplify the fraction to get:
f = 1/2
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What is the amount of interest to be paid if u got a reducing balance loan of $2700 and you will repay it over 5 years by quarterly installments of $1899.75 at interest rate 14% p.a. (compounded quarterly)
The total interest to be paid over the 5-year period is $403.22.
What is reducing balance loan?In a loan with a declining balance, interest is added to the outstanding balance at the start of each period, such as each month or each quarter. The outstanding balance, which decreases as the borrower makes repayments, is used to determine the interest rate. As a result, the borrower gradually pays less interest and more of each payment is used to lowering the main balance due. The lowering balance approach is frequently applied to mortgages, personal loans, and auto loans.
Given that, the quarterly installments are $1899.75.
For the entire year for a total of 5 years the total amount is:
Total amount = 4 * 5 * $1899.75 = $37995
For reducing balance loan the interest is calculated as:
For the first quarter, the interest to be paid is:
interest = (total amount - 0) * (0.14 / 4)
interest = (37995 - 0) * (0.14 / 4) = $94.50
Similarly for the remaining quarters we have:
Second quarter = $87.95
Third quarter: $81.05
Fourth quarter: $73.76
Fifth quarter: $65.96
The total interest to be paid over the 5-year period is:
$94.50 + $87.95 + $81.05 + $73.76 + $65.96 = $403.22
Hence, the total interest to be paid over the 5-year period is $403.22.
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What graph would best display the data shown in the frequency table?
A. line plot
B. vertex-edge graph
C. histogram
D. stem-and-leaf graph
Answer:
histogram
Step-by-step explanation:
Martin wants to buy a new bedroom set that cost $1590 including tax. Unfortunately he doesn’t have $1590 so he secures a 2 year loan from the furniture store at 9% interest to be repaid in 254 equal monthly installments. Find the monthly payment
The monthly Payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.
The monthly payment of a 2-year loan of $1590 with 9% interest which needs to be repaid in 254 equal monthly installments, we need to use the loan repayment formula. The formula is given as:
Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
Here,
Loan Amount = $1590
Interest Rate = 9% per annum
Time = 2 years = 24 months
number of Months = 254 (as there are 254 monthly installments)
First, we need to calculate the Monthly Interest Rate using the following formula:
Monthly Interest Rate = Annual Interest Rate / 12
The Annual Interest Rate is 9%,
so the Monthly Interest Rate is: Monthly Interest Rate = 9 / 12 = 0.75%Putting the given values into the loan repayment formula,
we get: Monthly Payment = (1590 x 0.0075) / (1 - (1 + 0.0075)^(-254))= 11.92 (approx)
Therefore, the monthly payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.
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At a real estate agency, an agent sold a house for $341,000. The commission rate is 4.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Therefore , the solution of the given problem of amount comes out to be the agent received $3,069 in commission.
What is an amount?aggregate attempting to determine the time, overall cost, or amount. The amount in front of us or on our minds is incredibly hectic. the outcome, its significance, or its applicability. The sum consists of principal, tax, and third bookkeeping. Some of the word variations are amounts, amounts, and amounting. a versatile term Its amount refers to the amount that something weighs, how often you consume it.
Here,
The real estate company has a 4.5% commission rate,
which means they get paid 4.5% of the house's sale price:
=> 4.5% of $341,000 divided by the agency's commission results in
=> $15,345 ($0.045 x $341,000).
Hence, the residence brought in $15,345 for the real estate company.
We must determine the commission received by the real estate agency in order to determine how much the agent earned. 20% of the commission paid to the real estate agency goes towards the agent's commission rate.
Since we already know that the real estate firm was paid a commission of $15,345; the agent's commission is:
=> 20% of $15,345 divided by the agent's commission
=> 0.2 times $15,345 = ($3,069).
As a result, the agent received $3,069 in commission.
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Rewrite as a piece wise function y=1/2 |x-6| +4
Answer:
y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}
Step-by-step explanation:
You want y = 1/2|x -6| +4 written as a piecewise function.
DomainsThe absolute value function changes its definition when its argument is negative:
y = |x| ⇒ y = -x for x < 0, and y = x for x ≥ 0
This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.
For x -6 < 0The argument is negated in this domain, so we have ...
y = -1/2(x -6) +4
y = -1/2x +3 +4
y = -1/2x +7
For x -6 ≥ 0The absolute value function is an identity function in this domain:
y = 1/2(x -6) +4
y = 1/2x -3 +4
y = 1/2x +1
Piecewise functionCombining these descriptions into one, we have ...
\(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)
<95141404393>
which equation represents the relationship between the X values and Y values in the graph
The equation which represents the relationship between X values and Y values can be found by deriving the equation of line using slope intercept form. The equation of line is 3x - 5y = 25.
How to find equation of line using slope intercept form?
Equation of line using slope intercept form is y = mx + b
where m is slope of the line and b is y-intercept
The slope intercept can be used to form equation of line using two points on the line.
According to the given question:
The two points which lie on the line are (x, y) = (5, -2) and (x', y') = (0, -5)
Slope of the line m = y' - y/x' - x
= (-5 +2)/(0 - 5)
= 3/5
Now y intercept b = y - mx
= -2 - (3/5. 5)
= -5
Therefore the required equation of line is y = 3/5x - 5
On simplifying further 3x - 5y = 25
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NEED THE ANSWERS FAST PLEASE
In Exercises 13 and 14, find a possible pair of integer values for a and c so that
the quadratic equation has the given number and type of solution(s). Then write
the equation.
13. ax² − 3x + c = 0; two real solutions
-
14. ax² + 10x + c = 0; two imaginary solutions
15. Determine the number and type of solutions to the equation 2x² - 8x = -15.
A. two real solutions
B. one real solution
C. two imaginary solutions
D. one imaginary solution
In Exercises 16 and 17, use the Quadratic Formula to write a quadratic equation
that has the given solutions.
16. x
10 ± √√-68
14
17. x =
-3±i√√7
8
In Exercises 18-21, solve the quadratic equation using the Quadratic Formula.
Then solve the equation using another method. Which method do you prefer?
Explain.
18. 7x² + 7 = 14x
20. x² + 2 = -x
19. x² + 20x = 8
21. 8x² - 48x + 64 = 0
22. The quadratic equation x² + x + c = 0 has two imaginary solutions. Show that
the constant c must be greater than 1.
Answer:
Step-by-step explanation:
the degree of a polynomial determines 1:1 the number of solutions.
a quadratic equation (degree 2) has 2 solutions.
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = -4
b = -4
c = -1
so,
x = (4 ± sqrt((-4)² - 4×-4×-1))/(2×-4)
when we look at the square root
16 - 16
we see that it is 0.
the square root of 0 is 0, and there is no difference between -0 and +0.
so, we get only one (real) solution : 4/-8 = -1/2
but : formally, there are still 2 solutions (as this is a quadratic equation). they are just identical.
so, I am not sure what your teacher wants to see in this case as answer.
my answer would be 2 real identical solutions. did this help?
an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
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if a coin is flipped 35 times and lands on heads 21 times what is the relative frequency of Landing on heads
Work Shown:
21/35 = (7*3)/(7*5) = 3/5
find the inverse of the function y equals x squared minus 12
Answer:
Step-by-step explanation:
y=x^2-12
The inverse is
√x+12, -√x+12
Which of these values of x is NOT a solution of the equation tanx= 1?
The tangent ratio is an illustration of the trigonometry identity
The value of x that is not a solution of tan(x) = 1 is 3\(\pi\)/4
How to determine the value that is not a solutionThe trigonometry identity is given as:
tan(x) = 1
Next, we test the x values using a calculator.
When \(x = -7\pi/4\), we have:
tan(-7\(\pi\)/4) = 1
When x = 3\(\pi\)/4, we have:
tan(3\(\pi\)/4) = -1
When x = 5\(\pi\)/4, we have:
tan(5\(\pi\)/4) = 1
When x = \(\pi\)/4, we have:
tan(\(\pi\)/4) = 1
Hence, the value of x that is not a solution of tan(x) = 1 is 3\(\pi\)/4
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Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Use Structure The area of a rectangular
playground has been extended on one side.
The total area of the playground, in square
meters, can be written as 352 +22x.
Rewrite the expression to give a possible set
of dimensions for the playground,
Answer:
The width and length of the rectangle are \(22\) and \(16+x\), for \(x > -16\), respectively.
Step-by-step explanation:
From Geometry, we remember that area of the rectangle (\(A\)) is defined by:
\(A = w\cdot l\) (1)
Where:
\(w\) - Width.
\(l\) - Length.
In addition, we know that area is described by a first-order polynomial:
\(A = 352+22\cdot x\) (2)
Meaning that is the product of another first-order polynomial and a constant. That is:
\(A = a\cdot (b+c\cdot x)\) (3)
Now we determine the Great Common Divisor of 352 and 22:
\(352 = 2\times 2\times 2 \times 2 \times 2 \times 11\)
\(22 = 2\times 11\)
The Great Common Divisor is 22.
Then, the area of the rectangle can be expressed by this expression:
\(A = 22\cdot (16+x)\) (3b)
According to this, the width and length of the rectangle are \(22\) and \(16+x\), for \(x > -16\), respectively.
What's the difference between a whole, integer, rational, and irrational number?
Help me
See the picture
I’m giving brainliest
How many 6-digit numbers are there in our system of counting numbers?
there are 900,000 6 in all
brainliest or a thank you please <33 :)
Sixty men can build a wall in 40days but though they begin the work together, 55 men quit every ten days. The Time needed to build the wall is?
It would take 370 days to build the wall with the given conditions.
If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:
60 men x 40 days = 2400 man-days
However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.
The number of man-days required for the first 10 days is:
60 men x 10 days = 600 man-days
The number of man-days required for the second 10 days is:
5 men x 10 days = 50 man-days
The total number of man-days required for the first 20 days is:
600 man-days + 50 man-days = 650 man-days
The remaining work can be completed by the 5 men in:
2400 man-days - 650 man-days = 1750 man-days
Therefore, the total time needed to build the wall is:
20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days
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Given h(x) = 3x² - 6x +4, find h( - 6).
....
h( - 6) =
Answer:
h(-6) = 3(-6)² - 6(-6) + 4
= 3(36) + 36 + 4
= 148
You basically just substitute x with -6 that's all