The dimension of rectangle window to admit the most light is x = 16 / ( 8 - √3) and y = 24 - 8√3 / 8 - √3
According to the question,
The perimeter of the window is 16 feet
Also, Window is surmounted by an equilateral triangle
Let x and y be the dimensions of rectangular part of window and x be side of equilateral part. If A be the total area of window, then
A = x.y + (√3/4)x² -------------(1)
Also, x + 2y + 2x = 16
=> 3x + 2y= 16
=> y = 16-3x / 2
Replacing the value of y in equation (1)
=> A = x.(16-3x / 2) + (√3/4)x²
=> A = 8x - 3x²/2 + (√3/4)x²
Differentiating A w.r.t x
=> A' = 8 - 3x + (√3/2)x
For critical value , we put A'=0
=> 8 - 3x + (√3/2)x = 0
=> x = 16 / ( 8 - √3)
Again, Differentiating A' w.r.t x ,
=> A'' = -3 + √3/2
which is Less than 0 ,
Therefore , A is maximum if x = 16 / ( 8 - √3) and y = 24 - 8√3 / 8 - √3
Hence, For admitting the most light the area should be largest , dimensions of rectangle are x = 16 / ( 8 - √3) and y = 24 - 8√3 / 8 - √3
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Which of the following is the correct boolean expression to test for:
int x is being a value between, including, 500 and 650, or int y not equal to 1000?
O ((x >= 500 && x <= 650)|| (y != 1000))
O ((x > 500 AND x < 650) OR !(y. equal(1000)))
O ((x > 500 && x < 650) || (y != 1000))
O ((x < 500 && x > 650) || !(y == 1000))
The correct boolean expression to test for int x being a value between, including, 500 and 650, or int y not equal to 1000 is:
((x >= 500 && x <= 650)|| (y != 1000))
This expression uses the "&&" operator to test for x being greater than or equal to 500 and less than or equal to 650, and the "||" operator to test for y not being equal to 1000. The expression is using the correct comparison operators and logical operators to test for the desired conditions.
A boolean expression is a statement that evaluates to either true or false. It is commonly used in programming to control the flow of a program, as the result of a boolean expression can be used to determine whether a certain block of code should be executed or not.
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What is the value of the expression:
6 - 5x when x = -2?
Answer: 16
Step-by-step: 6 - (5(-2)=-10 then the - turns into + and your answer is 6 + 10
Convert 13/50 to percent
Answer:
26%
Step-by-step explanation:
To convert a fraction to a percentage, you need to first convert the fraction to a decimal.To convert 13/50 to a decimal, you can divide 13 by 50, which gives you 0.26.To convert a decimal to a percentage, you need to move the decimal point two places to the right, which gives you 26%.So, 13/50 is equivalent to 26%.The value of number 13/50 into percentage is,
⇒ 26%
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The number is,
⇒ 13/50
Now, We get;
The value of number 13/50 into percentage is,
⇒ 13/50 x 100%
⇒ 13 x 2%
⇒ 26%
Thus, The value of number 13/50 into percentage is,
⇒ 26%
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Solve for y:
2π=2y+6x
Answer: y=pi-3
Step-by-step explanation:
2pi=2y+6
2pi-6=2y
(2pi-6)/2=y
pi-3=y
y=pi-3
hope this helped
consider the table, which reports the fruit diameter and number of offspring obtained by the researcher in the f2 generation. in the parental lines, l. cheesmanii had a fruit diameter of 8 cm and l. esculentum had a fruit diameter of 16 cm .
The total number of genes involved in fruit diameter in tomatoes is 4.
[tex]1/4^{n}[/tex] = ratio of F2 individuals expressing either extreme Phenotype
In the above equation, 'n' represents the number of genes involved.
The term 'extreme phenotype' refers to the phenotype of one of the parents from the P1 generation. In this case, it denotes the parents with fruit diameters of 8 cm and 16 cm. In the F2 generation, which consists of a total of 256 offspring, there is only 1 offspring that resembles either P1 parent.
The ratio of individuals expressing either extreme phenotype = Number of springs with either extreme phenotype / Total number of off spring.
ratio of F2 individuals expressing either extreme Phenotype = 1/256
Apply the value of 1/256 to the first equation.
That is, [tex]1/4^{n}[/tex] = 1/256
1[tex]1/4^{4}[/tex] = 1/256
As shown above, the value of 'n' is 4.
Therefore, the total number of genes involved in fruit diameters is 4.
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The path of the airplane the astronauts are flying
in can be modeled using the function h(x) =
10000cos(0.0001x) + 20000 in which h indicates
the height in feet. What is the approximate period
of the wave?
Answer:
The approximate period of the wave representing the airplane's path is 0.9 hours.
Step-by-step explanation:
The period of a wave is the time it takes for one complete cycle of the wave to occur. In the case of the airplane's path, this would be the time it takes for the airplane to complete one full oscillation, or "up and down" motion.
To find the period of the wave, we need to determine the value of x that corresponds to one complete cycle of the wave. In this case, the wave is defined by the function h(x) = 10000cos(0.0001x) + 20000.
To find the period, we can use the formula T = 2π/ω, where T is the period, π is the mathematical constant pi, and ω is the angular frequency of the wave. The angular frequency is related to the frequency of the wave, which is the number of cycles per second.
In this case, the angular frequency is given by the coefficient of the x term in the function, which is 0.0001. Plugging this value into the formula above, we get T = 2π/0.0001 = 200000π seconds.
Since one cycle of the wave corresponds to one complete oscillation of the airplane, the period of the wave is approximately 200000π seconds. This is a very large number, so it is usually more useful to express the period in minutes or hours. To convert to minutes, we can divide the period by 60, which gives us a value of about 3334 minutes. To convert to hours, we can divide the period by 3600, which gives us a value of about 0.9 hours.
In summary, the approximate period of the wave representing the airplane's path is 0.9 hours.
Ask me any questions you may have!
The amount of time it takes for a wave to complete one full cycle is known as the wave's period. This would be the amount of time needed for the plane to perform one full oscillation, or “up and down” motion, in the case of the flight path.
What path airplane the astronaut's period of the wave?Finding the value of x that represents the wave's full cycle is necessary to calculate the wave's period. The equation h(x) = 10000cos(0.0001x) + 20000 in this instance defines the wave.
The formula T = 2/, where T is the period, is the mathematical constant pi, and is the wave's angular frequency, can be used to determine the period. The wave's frequency, or the number of cycles per second, and the angular frequency are connected.
We may convert the period to hours by dividing it by 3600, which gives us a number of approximately 0.9 hours.
Therefore, The wave that represents the course of the airplane has an approximate period of 0.9 hours.
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An entry-level civil engineer earns an average bi-weekly net pay of $2,175.25. The engineer has created a monthly budget using the following percentages for expenses:
Percent
Housing 35%
Food/Household 10%
Savings 10%
Transportation 15%
Debt 5%
Entertainment 6%
Medical/Personal Care 5%
Giving 5%
Clothing 4%
Miscellaneous 5%
Which balance sheet correctly represents the engineer's income, expenses, and balance?
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $2,175.25
Expenses
Percent Amount
Housing 35% $761.34
Food/Household 10% $217.53
Savings 10% $217.53
Transportation 15% $326.29
Debt 5% $108.76
Entertainment 6% $130.52
Medical/Personal Care 5% $108.76
Giving 5% $108.76
Clothing 4% $87.01
Miscellaneous 5% $108.76
$2,175.25
Balance
Income $2,175.25
Expenses $2,175.25
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $3,262.88
Expenses
Percent Amount
Housing 35% $1,142.01
Food/Household 10% $326.29
Savings 10% $326.29
Transportation 15% $489.43
Debt 5% $163.14
Entertainment 6% $195.77
Medical/Personal Care 5% $163.14
Giving 5% $163.14
Clothing 4% $130.52
Miscellaneous 5% $163.14
$3,262.88
Balance
Income $3,262.88
Expenses $3,262.88
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,713.04
Expenses
Percent Amount
Housing 35% $1,649.56
Food/Household 10% $471.30
Savings 10% $471.30
Transportation 15% $706.96
Debt 5% $235.65
Entertainment 6% $282.78
Medical/Personal Care 5% $235.65
Giving 5% $235.65
Clothing 4% $188.52
Miscellaneous 5% $235.65
$4,713.04
Balance
Income $4,713.04
Expenses $4,713.04
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses
Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $-
PLEASE HELP
The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.
How tp determine percentages of income?We should know that balance sheet is a summary of assets and liabilities and income and expenses of a legal person.
We are told that the the balance sheet shows a bi-weekly net pay
This implies that a month has two bi-weeks. therefore every income and expenses is multiplied by 2 to get the following figures.
Income Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $0
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a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. a total of 28 boxes of paper were shipped weighing 1850 pounds altogether
On solving the provided question we can say that, 8 tiny boxes total were shipped and 13 huge boxes were dispatched.
What is equation?A formula is a statement that the values of two expressions are equal. The formula essentially says that two things are equal. An equals sign or '=' indicates that. 8+2=12-2 is an example equation. According to the above formula, the left side of the formula is equal to the right side. So the equation is the statement "this is equal to that".
Let x represent the quantity of tiny boxes, and y represent the quantity of large boxes.
21 cartons in all were despatched, according to the first statement.
Equation 1 is as follows:
[tex]x+y=21[/tex]
For the equation's solution, use the substitution approach.
x's value being entered into equation 2
[tex]25(21-y) +70y =1110 \\ 525-25y+70y = 1110\\ 45y = 585\\ Y=13[/tex]
x+13 = 21
X = 8
8 tiny boxes total were shipped.
13 huge boxes were despatched.
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i need help asap!!!!!
Answer:
The slope is same for both points.
Step-by-step explanation:
1st set of points: (1, 4) and (7, 2)
m = 2-4/7-1
m = -2/6
m = -1/3
2nd set of points: (7, 2) and (10, 1)
m = 1-2/10-7
m = -1/3
The slope is same for both points.
The positive integers greater than 3 are arranged in rows and columns as illustrated.
In which column is the number 5018?
A) 2
B) 4
C) 6
D) 5
E) 3
The rows and columns of the positive integers greater than three are as shown. And the number 5018 is found in the third column.
When performing a permutation test, you repeatedly rearrange one of the variables without affecting the other variable (s). From the given table, we can start with column 4. Here, each row has about 6 numbers. That is singular row has numbers from columns 1 to 6 and an even row from columns 7 to 2.
Then subtract 5018 by 3. We get 5018-3=5015.
Divide this by 6,
5015/6 = 836.
So 5018 is located in an even row from 7 to 2.
Therefore, 5018 is located in the 836th row and 3rd column.
So the required answer is E) 3.
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. Acme Burgers sells a large pop which is 14 oz and comes in a 8" high container. The small pop comes
in a 6" high container which is the same shape as the small pop container. How much does the small
container hold?
Answer:
10.5 oz
Step-by-step explanation:
The large pop and container are similar to the small pop and container.
Thus, we can use proportions to find how much the small container can hold, letting x represent the volume of the small container:
[tex]\frac{14}{8}=\frac{x}{6}\\ 8x=84\\ x=21/2=10.5[/tex]
Calculate the slope over the interval 1≤ x<3.
The slope over the interval 1 ≤ x < 3 is m = 3 / 2 .
Given :
the slope over the interval 1 ≤ x < 3
From the graph :
take two points which lies on the interval
( 1 , 0 ) and ( 3 , 3 )
slope :
Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line .
slope m = y2 - y1 / x2 - x1
= 3 - 0 / 3 - 1
= 3 / 3 - 1
= 3 / 2
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Find The length of the third side. If necessary, round to the nearest tenth. need answer ASAP
The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.
What is the Pythagoras theorem?The theorem is given by (hyp)² = (opp)² + (adj)².This theorem applies to a right-angle triangle only.Calculation:The given triangle is a right-angle triangle.
It has two lengths. They are
length of the hypotenuse = 21
length of the adjacent or base = 13
Then, the third side i.e., the opposite side length is calculated by
(hyp)² = (opp)² + (adj)²
⇒ (21)² = (opp)² + (13)²
⇒ 441 = (opp)² + 169
⇒ (opp)² = 441 - 169 = 272
⇒ opposite side length = √272 = 16.49 ≅ 16.5
Therefore, the length of the third side is 16.5.
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A roller coaster ride holds a total of 48 passengers. The ratio of males to females on the ride is 5 : 7. Let x represent the number of males on the ride. Let y represent the number of females on the ride. Which two linear equations form a system that you can use to find the number of males and the number of females on the ride?
Answer:
5x + 7y = 48 (total number of passengers on the ride)
x + y = 48 (total number of males and females on the ride)
Step-by-step explanation:
To find the number of males and the number of females on the roller coaster ride, you can use the following two linear equations to form a system:
5x + 7y = 48 (total number of passengers on the ride)
x + y = 48 (total number of males and females on the ride)
The first equation states that the total number of passengers on the ride is equal to the sum of the number of males (5x) and the number of females (7y). The second equation states that the total number of males and females on the ride is equal to the sum of the number of males (x) and the number of females (y).
To solve this system, you can use algebraic techniques to eliminate one of the variables and solve for the other. For example, you could multiply the first equation by 5 and the second equation by 7, then subtract the two equations to eliminate the y variable:
5 * 5x + 7 * 7y = 5 * 48
7 * x + 7 * y = 7 * 48
25x + 49y = 240
49x + 49y = 336
24x = 336 - 240
24x = 96
x = 4
Substituting this value for x in the first equation, we can solve for y:
5 * 4 + 7 * y = 48
20 + 7 * y = 48
7 * y = 28
y = 4
Therefore, there are 4 males and 4 females on the roller coaster ride.
What reason would you use to prove ΔFGH ≅ ΔJHK ?
Select one:
ASA
HL
SAS
cannot prove congruency
SAA
The reason that is used to prove ΔFGH ≅ ΔJHK is SAS property
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.
According to the question,
Given : (1) ∠FGH and ∠JHK are right angles
(2) H is midpoint of GK
(3) GH ≅ JK
In ΔFGH and ΔJHK
∠FGH = ∠JHK ( right angles )GH ≅ JK (given) GH = KH ( H is midpoint of GK )Therefore , ΔFGH ≅ ΔJHK using SAS property
Hence , The reason use to prove ΔFGH ≅ ΔJHK is SAS
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Secondary Mortgage Purchasing Company (SMPC) wants to buy your mortgage from the local savings and loan. The original balance of your mortgage was $153,000 and was obtained five years ago with monthly payments at 10 percent interest. The loan was to be fully amortized over 30 years.
Required:
a. What should SMPC pay if it wants an 11 percent return?
b. What is the balance of the original loan after five additional years (10 years from origination)?
SMPC should pay 136,992.36$ if it wants an 11 percent return. and the balance of the original loan after additional years 142,229.05$.
What is the monthly rate of the loan?A monthly rate is a fee for services calculated over a thirty-day period.
Given, Your mortgage will be purchased by the Secondary Mortgage Purchasing Company (SMPC) from the nearby savings and loan. Your mortgage had an initial amount of $153,000 and was obtained five years ago with regular payments at a 10% interest rate. The loan was to be completely repaid over a 30-year period.
Payment Formula = PMT (monthly rate, month, -mortgage)
Present value formula = PV( monthly rate, month left, - payment, - repayment)
Loan value formula = PV (monthly rate, month left, -payment)
a. formula = PMT( 10%/12, 30*12, -153000)
Payment = $1342.68
Formula = PV(11%/ 12, (30-5)* 12, -1342.68)
Smpc pays = $136,992.36
b. Loan balance = 139134.70$
Formlua = PV(11%12,5*12, - 1342.68, -139134.7)
Smpc pays = 142,229.05$
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the sugar sweet company delivers sugar to its customers. let be the total cost to transport the sugar (in dollars). let be the amount of sugar transported (in tons). the company can transport up to tons of sugar. suppose that gives as a function of . identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.
The domain and the range of a function are the possible input and output values of the function.
The function is given as:
C = 130S + 3500
The domain
This is the possible S values of the function.
S cannot be less than 0, because it represents a physical quantity (i.e. tons of sugar)
The value of S can be any value greater than 0
Hence, the domain of the function is [0, ∞)
The range
This is the possible C values of the function.
The function is given as:
C = 130S + 3500
When S = 0
C = 130(0) + 3500
C = 3500
The above means that:
C cannot be less than 3500
The value of C can be any value greater than 3500
Hence, the range of the function is [3500, ∞)
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Determine the whole number of standard deviations that includes all data values. The mean price of the nonfiction books on a best-sellers list is $24.18; the standard deviation is $ 3.98.
$19.95, $24.00, $21.00, $28.95, $19.00, $27.95, $19.00, $25.95, $26.00, $29.95
All of the values fall within __ standard deviation (s) of the mean.
All of the values fall within 1.45 standard deviation of the mean.
How to illustrate the standard deviation?From the information given, the mean price of the nonfiction books on a best-sellers list is $24.18 and the standard deviation is $3.98.
It should be noted that from the problem, the variable that is the farthest from the mean is $29.25.
Therefore, the z score will be illustrated as:
Z = (29.95 - Mean) / Standard deviation
Z = (29.95 - 24.18)) / 3.98
= 1.45
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Which equation is the inverse of 2(x - 2)² = 8(7+ y)?
O-2(x-2)2 = -8(7+ y)
Oy-x²-x-6
O y=-2± √√28+4x
Oy-2± √√28+4x
Answer:
[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]
Step-by-step explanation:
The inverse of [tex]2(x-2)^2=8(7+y)[/tex] is
[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]
does anyone know this
The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.
How to determine the equivalent expressionWe shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:
squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)
a² is common and can be cancel out
square root of (36a⁸/255a²) = square root of (36a⁶/255)
square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}
square root of (36a⁸/255a²) = 6a³/15
square root of (36a⁸/255a²) = 2a³ × 3/5 × 3
we divide through by the common factor 3
square root of (36a⁸/255a²) = 2a³/5
Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.
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Please explain your answer to this question! Thank you!
Answer:
B. Incorrectly applied the distributive property
Step-by-step explanation:
You want to find Maria's error in her solution of -2(3x -5) = 40.
StepsThe solution can proceed as follows:
-2(3x -5) = 40 . . . . . . . . given
-6x +10 = 40 . . . . . . . . . use the distributive property
-6x = 30 . . . . . . . . . . subtract 10
x = -5 . . . . . . . . . . divide by -6
Comparing this solution to Maria's, we find that Maria incorrectly applied the distributive property. (She multiplied (-2)(-5) and got -10 instead of +10.)
Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation in graphing form. y=(x-3)(x-11)
The vertex of the parabola is at the point (7, 0) and since the vertex of this parabola is (7, 0), the equation of the parabola in graphing form is
y = a(x - 7)^2.The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. To find the vertex of the parabola y = (x - 3)(x - 11), you can average the x-intercepts of the parabola, which are the points where the parabola crosses the x-axis. The x-intercepts of this parabola are at x = 3 and x = 11, so the average of these two points is (3 + 11) / 2 = 7.
To write the equation of the parabola in graphing form, you can use the vertex form of a parabola, which is written as
y = a(x - h)^2 + kwhere (h, k) is the vertex of the parabola and a is a coefficient that determines the direction of the parabola (whether it opens upwards or downwards). Plugging in the values for the vertex and the y-coordinate of the vertex (which is 0), we get
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What is the slope in the given line?
Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
The slope/gradient of a line is defined by this formula:
[tex]\frac{y_{1}-y_{0} }{x_{1}-x_{0} }[/tex]
Where you pick two coordinates, find the change in the [tex]y[/tex] values, and divide it by the change in the [tex]x[/tex] values.
Two coordinates that this line passes through are (3, -2) and (-3, 2).
You can take the second [tex]y[/tex]-value (2) from the first [tex]y[/tex]-value (-2) or vice versa, so long as you do it in the same order the [tex]x[/tex] values.
For this example, I will take the first [tex]y[/tex]-value (-2) from the second [tex]y[/tex]-value (2), and take the first [tex]x[/tex]-value (3) from the second [tex]x[/tex]-value (-3).
The gradient/slope is defined by [tex]m[/tex] in the following:
[tex]m=\frac{2--2}{-3-3}=\frac{4}{-6}=-\frac{4}{6}=-\frac{2}{3}[/tex]
a response variable y has correlation coefficient 0.3 with each of the predictors x1 and x2. however, these predictors are heavily correlated r x1x2
If the response variable y has a correlation coefficient of 0.3 with each of the predictors x1 and x2, it means that there is a weak linear relationship between y and both x1 and x2.
This means that as x1 and x2 increase or decrease, y is likely to change by a small amount. If x1 and x2 are heavily correlated, it means that there is a strong linear relationship between the two variables. This means that as x1 increases or decreases, x2 is likely to change by a large amount in the same direction. When two predictors are highly correlated, it can be difficult to determine the individual contribution of each predictor to the response variable y.
In this situation, it may be useful to use techniques such as multi-collinearity analysis or principal component analysis to understand the relationship between the predictors and the response variable better.
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A tree is 108 inches tall. A second tree is 120 inches tall. What is the combined height of the trees?
Answer:228
Step-by-step explanation:
All you have to do is add 108 to 120.
0+8=8, 2+0=2, 1+1=2
120
108
+_____
228
The perimeter of a triangle is 3x² + 6x - 9. If one side length is x² + 2x - 1 and the
other is x² + x - 5, what is the length of the 3rd side?
Answer:
x^2+3x-3
Step-by-step explanation:
(x^2+2x-1)+(x^2+x-5)
2x^2+3x-6
(3x^2+6x-9)-(2x^2+3x-6)
x^2+3x-3
hopes this helps
Answer:
[tex]x^2 + 3x - 3[/tex]
Step-by-step explanation:
The perimeter of a triangle, can be calculated as, the sum of the sides.
So let's first assume the third side is a polynomial, and more specifically, a quadratic in the form: [tex]ax^2+bx+c[/tex]. This assumption is denoted from the fact that the perimeter only has terms up to the degree of 2, also known as x squared. The answer is also a quadratic, so it isn't an unreasonable assumption that if we add two quadratics (the ones given), and add one more quadratic, we should still have quadratic.
So, the sum of the three sides can be expressed as: [tex](x^2 + 2x - 1) + (x^2 + x - 5) + (ax^2 + bx + c)[/tex]
We can combine like terms to get:
[tex](x^2+x^2+ax^2)+(2x+x+bx)+(-1-5+c)[/tex]
Now from here, we can combine like terms (add coefficients):
[tex](2+a)x^2 + (3+b)x + (-6+c)[/tex]
From here, we simply set this equal to the given perimeter of: [tex]3x^2 + 6x-9[/tex], which gives us the equation:
[tex](2+a)x^2 + (3+b)x+(-6+c) = 3x^2 + 6x - 9[/tex]
Now from here, the coefficients need to correspond for both quadratics to be equal to each other, so that means that the following must be true:
[tex](2+a)=3\implies a = 1\\(3 + b) = 6\implies b = 3\\(-6 +c) = -9 \implies c = -3[/tex]
We now plug this into the quadratic standard form to get:
[tex]x^2 + 3x - 3[/tex]
Which is our third side!
For 7.45 - 3.029 why do you rewrite 7.45 as 7.450
For 7.45 - 3.029 the reason why they rewrite 7.45 as 7.450 is so as to have both values in three decimal place so the calculation can be easier.
What is decimal place?It should be noted that the first digit after the decimal represents the tenths place then the next digit after the decimal could be reffered to as hundredths place however the remaining digits continue to fill in the place values until there are no digits left.
It should be noted that Decimal place value can be described as the place values of all the digits in a given decimal number.
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How do you classify -15
-15 is an integer , rational and a real number
What are rational,real numbers and integers?Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.
A negative number is not a natural number.
This means that -15 is a real number because real number comprises of rational and irrational number and rational numbers include negative numbers and they are called negative integers.
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A tool set is on sale for $424.15. The original price of the tool spt was $499.00. What percent of the original price
is the sale price?
Answer:
94 percent.
Step-by-step explanation:
Since the tool set used to be worth 499, but is now worth 424.15, we divide the two prices.
Calculation.
424.15/499 = 0.944654788.
We are figuring out the percent, so we need to round.
0.94465478 is about 0.94
0.94 IS EQUALVENT to 94%, so that is our answer.
11 A fisherman wants to know how many fish there are in a lake. One day, he catches 50, marks them and puts them back. The next day he catches 80 fish. 20 of these fish have marks on them. Estimate the total number of fish in the lake.
The total number of fish in the lake would be = 60 fishes
What is total of a data set?The total of a data set is the addition of the various components that makes up a data set which gives a particular value.
On the first day the number of fish that was marked by the fisher man = 50 fishes.
On the second day the total amount of fishes that was caught = 80 fishes
The number of fishes that where among the 80 fishes that are marked= 20
Therefore the total amount of fishes in the lake = 80 - 20
= 60 fishes.
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