Answer:
Below
Step-by-step explanation:
a = 1 b = 5 c = 5
Using these values in the Quadratic Formula given results in zeroes of
x = -5/2 ± sqrt (5) / 2
a piece of wire of length l cm is cut into two pieces. one piece, of length x cm, is made into a circle; the rest is made into a square. (a) find the value of x that makes the sum of the areas of the circle and square a minimum. find the value of x giving a maximum. (b) for the values of x found in part (a), show that the ratio of the length of wire in the square to the length of wire in the circle is equal to the ratio of the area of the square to the area of the circle.3 (c) arethevaluesofxfoundinpart(a)theonlyvalues of x for which the ratios in part (b) are equal?
As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).
(a) [tex]x = \frac{L\pi }{4+\pi }[/tex]
(b) True
(c) Yes
What is maximum and minimum?
The smallest value in the data set is the minimum. The largest value in the data set is the maximum.
(a) The circumference of the circle is xx, which means that
[tex]P_ 1= 2\pi r\\x = 2\pi r\\r = \frac{x}{2\pi }[/tex]
The area of the circle is,
[tex]A_c = \pi r^2\\A_c = \frac{x^2}{4\pi }[/tex]
The circumference of the square is L - x, which means
[tex]P_2 = 4a \\L-x=4a\\a = \frac{L-x}{4}[/tex]
The area of the square is,
[tex]A_s = a^2\\A_s=\frac{(L-x)^2}{16}[/tex]
The sum of the areas of the circle and the square is
[tex]A = A_c + A_s\\A = \frac{x^2}{4\pi } +\frac{(L-x)^2}{16} \\A = \frac{4x^2+(L-x)^2\pi \pi }{16\pi } \\A = \frac{4x^2+(L^2 -2Lx+x^2)\pi }{16\pi } \\A = \frac{(4+\pi )x^2-2Lx\pi +L^2\pi }{16\pi }[/tex]
The derivative of the function of the total area is
[tex]A = \frac{4+\pi }{8\pi }x-\frac{L}{8}[/tex]
We solve the equation A'(x) = 0
[tex]\frac{4+\pi }{8\pi }x-\frac{L}{8}=0\\ \frac{4+\pi }{\pi }x=L\\ x = \frac{L\pi }{4+\pi }[/tex]
So, [tex]x = \frac{L\pi }{4+\pi }[/tex] is a critical point A, and it is a global minimum of A since
[tex]A"(x) = \frac{4+\pi }{8\pi } > 0[/tex] for all x.
(b) The area of the circle for [tex]x = \frac{L\pi }{4+\pi }[/tex] is
[tex]A_c = \frac{(\frac{L\pi }{4+\pi } )^2}{4\pi } \\A_c = \frac{(\frac{L^2\pi ^2}{(4+\pi )^2} )}{4\pi } \\A_c= \frac{L^2\pi }{4(4+\pi )^2}[/tex]
The area of the square for [tex]x = \frac{L\pi }{4+\pi }[/tex] is
[tex]A_s = \frac{(L-\frac{L\pi }{4+\pi } )^2}{16}[/tex]
The ratio of the area is,
[tex]\frac{A_s}{A_c} = \frac{(\frac{(L-\frac{L\pi }{4+\pi })^2 }{16} )}{(\frac{L^2\pi }{4(4+\pi )^2} )}[/tex]
[tex]= \frac{(L - \frac{L\pi }{4+\pi })^2 }{16}*\frac{4(4+\pi )^2}{L^2\pi } \\ = \frac{L^2-\frac{2L^2\pi }{4+\pi }+(\frac{L\pi }{4+\pi } )^2 }{4} *\frac{(4+\pi )^2}{L^2\pi } \\= \frac{(4+\pi)^2 }{4\pi }-\frac{4+\pi }{2}+\frac{\pi }{4}\\ = \frac{4}{\pi }[/tex]
The ratio of the length of wire in the square to the length of wire in the circle for [tex]x = \frac{L\pi }{4+\pi }[/tex] is
[tex]\frac{L-x}{x} =\frac{L-\frac{L\pi }{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{\frac{4L}{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{4}{\pi }[/tex]
As we can see (1) = (2)
(c) To prove this, we solve the equation
[tex]\frac{A_s}{A_c} = \frac{L-x}{x} \\ \frac{\frac{(L-x)^2}{16} }{\frac{x^2}{4\pi } } = \frac{L-x}{x}\\ \frac{(L-x)^2}{4}*\frac{\pi }{x^2} = \frac{L-x}{x} \\ \frac{L-x}{4} *\frac{\pi }{x} =1\\L\pi -\pi x=4x\\L\pi = (4 + \pi )x\\x = \frac{L\pi }{4+x}[/tex]
As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).
Hence,
(a) [tex]x = \frac{L\pi }{4+\pi }[/tex]
(b) True
(c) Yes
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What is the volume of the following triangular prism?
The required volume of the triangular prism will be 126 cubic meters.
What is the volume of a triangular prism?The triangular prism is the amount of space occupied by an object. It is determined by the number of unit cubes required to completely fill the solid.
V = 1/2 x H x W x L
The volume of the triangular prism will be
Volume of triangular prism = 1/2 x 9 x 6 x 13
Volume of triangular prism = 9 x 3 x 13
Volume of triangular prism = 27 x 13
Volume of triangular prism = 351 cubic yards
Thus, the volume of the triangular prism will be 126 cubic meters.
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where do i start with this world problem
The measure of an angle ∠TQU is 26.6° if PQ=3 and QR=4
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.
Given,
Rectangle PQRS has PQ=3 and QR=4
The points T and U are on side PS such that PT=US=1
As PQRS is rectangle so opposite sides of rectangle should be equal.
PS=QR and PQ=RS
QR=4, PS=4
But, PS=PT+TU+US
4=1+TU+1
TU=4-2
TU=2
And PU=PT+TU
1+2=3
PU=3
Consider, ΔQPU, Right angled at P.
We know that,
tan Q=PU/PQ
tan Q=3/3
tan Q=1
Q=tan⁻¹
Q=45°
∠PQU=45°
Now, let us consider ΔQPT is right angled at P
tan Q=PT/PQ
tan Q=1/3
Q= tan⁻¹(1/3)
Q=18.43°
∠PQT=18.43°
∠PQU=∠PQT+∠TQU
45°=18.43°+∠TQU
∠TQU=45°-18.43°
∠TQU=26.57°
∠TQU≈26.6°
Therefore, the measure of ∠TQU is 26.6°.
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You are given an integer n where 0 <= n <= 100, followed by another line of input which has a word w with length l where 1 <= l <= 50. Your task is to print n lines with the word w. The lines of your output should not have any trailing or leading spaces. Your output lines should not have any trailing or leading whitespaces.
The Python program prints the value of the integer n from the input string shown. (Refer to the coding below)
What is a python program?An arrangement of Python statements that have been specifically designed to accomplish a task is the simplest definition of a program.
A program is even our straightforward hello.py script.
Although it is only one line long and of limited use, it is a Python program by the strictest definition.
Functions assist in segmenting our program into manageable, modular portions.
Our program becomes more organized and controlled as it gets bigger and bigger.
It also makes the code reusable and prevents repetition.
So, we know that the program is for the given integer n:
Defining the integer variable "N" that accepts a user-supplied integer value.
The user-end string value is input using another variable "W" that is declared in the next step.
A for loop using the range method and an integer variable is declared after all input values have been entered.
This loop prints the string value.
The Python program prints the value of the supplied string.
N= int(input("Enter a value of integer N (0 <= N <= 100): "))#defining an integer variable N that inputs integer value from the user-end
W = input("Enter the word W (length of 1 <= L <= 50): ")#defining a string variable W that inputs the value fom the user-end
for n in range(N):#defining a for loop that uses the range method with integer variable and prints the string value
print(W)#printing the string value
Therefore, the Python program prints the value of the integer n from the input string shown.
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Complete question:
You are given an integer N where 0 <= N <= 100, followed by another line of input which has a word W with length L where 1 <= L <= 50. Your task is to print N lines with the word W. The lines of your output should not have any trailing or leading spaces.
Your output lines should not have any trailing or leading whitespaces
Input
3
Hello
Output
Hello
Hello
Hello
**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Fill in the blanks to solve the system of equations. Enter only 1 term in each blank.
Answer:
1st blank = 6x
2nd blank = 12
3rd blank = 2
4th blank = 2
5th blank = 8
6th blank = 5
Ms.D bought 8 1/2 pounds of ham from Excellente Hambaked Shop. She gave 1 3/4 pounds of ham to Mr.Chavir. How many pounds of ham does she have left?
The amount of ham Ms.D has left is [tex]6\frac{3}{4}[/tex] pounds.
How to find the pounds of ham she has left?Ms.D bought [tex]8\frac{1}{2}[/tex] pounds of ham from Excellente Hambaked Shop. She gave [tex]1\frac{3}{4}[/tex] pounds of ham to Mr.Chavir. The number of pounds of ham she has left can be calculated as follows:
Hence, the amount of hams in pounds she has left is the difference between what she had and the amount of pounds of hams she gave to Mr Chavir.
Therefore,
Amount bought by Ms.D = [tex]8\frac{1}{2}[/tex] pounds
Amount given to Mr.Chavir. = [tex]1\frac{3}{4}[/tex] pounds
Therefore,
Amount of she has left = [tex]8\frac{1}{2}[/tex] - [tex]1\frac{3}{4}[/tex]
Amount of she has left = [tex]\frac{17}{2} - \frac{7}{4}[/tex]
Amount of she has left = [tex]\frac{34-7}{4}[/tex]
Amount of she has left = [tex]\frac{27}{4}[/tex]
Amount of she has left = [tex]6\frac{3}{4}[/tex] pounds
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3(12-5)+8x4 what is this problem? How do I solve it?
location is known to affect the number, of a particular item, sold by walmart. two different locations, a and b, are selected on an experimental basis. location a was observed for 18 days and location b was observed for 18 days. the number of the particular items sold per day was recorded for each location. on average, location a sold 39 of these items with a sample standard deviation of 9 and location b sold 55 of these items with a sample standard deviation of 6. select a 99% confidence interval for the difference in the true means of items sold at location a and b.
The required confidence interval for the difference of means is (-18.52, -13.48).
Explain confidence of interval.Statisticians use confidence intervals to gauge vulnerability in an example variable. For instance, a scientist chooses various examples haphazardly from a similar populace and registers a certainty span so that each example might be able to perceive how it might address the genuine worth of the populace variable. The subsequent datasets are different where a few stretches incorporate the genuine populace boundary and others don't.
According to question:[tex]n_{a}[/tex] = 18 represent the sample of A
[tex]n_{b}[/tex] = 18 represent the sample of B
μₐ = 39 represent the mean sample for A
μᵇ = represent the mean sample for B
σ = 9 represent the sample deviation for A
σ = 6 represent the sample deviation for B
α = 0.01 represent the significance level
Confidence =99% or 0.99
confidence interval for the difference of means is given by the following formula,
μₐ - μᵇ± [tex]t_{\frac{α}{2}}[/tex][tex]\sqrt{\frac{S_{a}}{n_{a}} +\frac{S_{b}}{n_{b}} }[/tex]
39 - 55 ± 2.756[tex]\sqrt{\frac{9}{18} +\frac{6}{18} }[/tex]
-16 - 2.756(0.912) = -18.52
-16 + 2.756(0.912) = -13.48
Thus, required confidence interval is (-18.52, -13.48).
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What is the value of 16/2
Answer: 8
Step-by-step explanation: 16/2 is simply 16 ÷ 2 in fraction form,
16 ÷ 2 = 8
A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that rate, how many buckets will the leaky faucet fill after 3 days?
The number of gallons that can be filled is 18 gallons.
What is a rate?Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, the number of hours in 3 days will be:
= 24 × 3
= 72 hours.
Since the leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. The gallon filled in 72 hours will be represented by x.
5/20 = x/72
Cross multiply
20x = 72 × 5
20x = 360
x = 360/20
x = 18
There'll be 18 gallons
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you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose?
The maximum area to enclose a rectangular pasture with one side of the pasture up against a river is equal to 500,000 square feet.
As given in the question,
Let 'x' represents the length of the rectangular pasture
And 'y' represents the width of the rectangular pasture
Condition:
One side of the pasture is up against a river
Perimeter of the rectangular pasture with one side up against river
= x + 2y
⇒ 2000 = x + 2y
⇒x= 2000 - 2y
Area of the rectangular pasture
=( 2000 - 2y )( y )
= - 2 ( y² - 1000y)
= -2( y² - 1000y + 250000 - 250000 )
= -2 (y - 500 )² + 500, 000
Maximum area is at y = 500
Maximum area is 500,000
Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.
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the dunking booth is the shape of a cube represented below x 3. write a polynomial that represents the volume of the dunking booth. write your answer in descending order. please use the palette below to enter your answer.
The dunking booth is the shape of a cube represented below (x+3). Therefore, the polynomial of volume of the dunking booth is
(x +3) (x+3)².
Lets talk about the cube prism
- It has cube faces each two opposite faces are congruent
- It has three dimensions.
- Its volume = a³
In our problem the dunking booth is a cube prism with dimensions: x + 3
Side = x +3
therefore,
V = a³ = ( x +3)³
= (x)³ + 3× (x)²× 3 + 3× x × (3)² + (3)³
= x³ + 9x² + 27x + 27
Regrouping ,
= x³+ 27+ 9x² + 27x
Rewrite 27as 33.
x³+ 3³+9x²+ 27x
Since both terms are perfect cubes, factor using the sum of cubes formula,
a³+b³ = (a + b)(a²- ab+ b²) where a=x and b=3.
(x+3)(x− x⋅3 + 32)+ 9x²+ 27x
Simplify.
(x+3)(x²− 3x + 9)+ 9x²+ 27x
⇒ (x+3)(x²− 3x + 9)+ 9x(x+3)
Now,
x+3 out of (x+3)(x²− 3x + 9)+ 9x(x+3) .
⇒ (x+3)(x²− 3x + 9 + 9x)
Add −3x and 9x.
(x+3) (x²+ 6x+ 9)
Rewrite the polynomial.
(x+3)(x²+ 2⋅x⋅3+ 3²)
Factor using the perfect square trinomial rule a²+2ab+b² = (a + b)² , where a = x and b = 3.
(x+3)(x+3)².
Therefore, the polynomial is (x+3)(x+3)².
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consider an arbitrary n × n matrix a. what is the relationship between the characteristic polynomials of a and at ? what does your answer tell you about the eigenvalues of a and at ?
When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The scaling factor for the eigenvector is the appropriate eigenvalue, frequently represented as lambda.
When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by.
Hence, characteristic polynomial of A and A^T are the same, therefore their eigenvalues are also same.
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The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:
t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2 Match the variables to their description.
------------->
The variables of the test statistic can be concluded as [tex]s_{1} ^{2}[/tex], [tex]s_{2} ^{2}[/tex] as the variance of two samples, [tex]n_{1}[/tex], [tex]n_{2}[/tex] as the respective size of the two samples, [tex]t[/tex] as the t-distribution test statistic, and [tex]x_{1}[/tex], [tex]x_{2}[/tex] as the mean of the two samples.
It is given to us that the test statistic is used for a two sample test of means where the population variances are unknown and unequal.
Pooled standard deviation estimates cannot be used when the two groups have unequal variances. Instead, we have to find out the standard error for each group separately.
The formula for this type of test statistic is given by -
[tex]t=\frac{x_{1} -x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1} } +\frac{s_{2} ^{2} }{n_{2} } } }[/tex] ------- (1)
Here, the variables can be defined as below -
[tex]s_{1} ^{2}[/tex], [tex]s_{2} ^{2}[/tex] = The variance of two samples
[tex]n_{1}[/tex], [tex]n_{2}[/tex] = The respective sizes of the two samples
[tex]t[/tex] = t-distribution test statistic
[tex]x_{1}[/tex], [tex]x_{2}[/tex] = Mean of the two samples
Thus, the variables of the test statistic can be concluded as [tex]s_{1} ^{2}[/tex], [tex]s_{2} ^{2}[/tex] as the variance of two samples, [tex]n_{1}[/tex], [tex]n_{2}[/tex] as the respective size of the two samples, [tex]t[/tex] as the t-distribution test statistic, and [tex]x_{1}[/tex], [tex]x_{2}[/tex] as the mean of the two samples.
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please someone help me with this! (the answer is not 6c to the power of 6 btw)
8c to the power of 18
A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in Boston was 0.581 and the proportion wearing seat belts in New York was 0.832 Due to local laws at the time the study was conducted, it was suspected that a smaller proportion of drivers wear seat belts in Boston than New York. (a) Find the test statistic for this test using Ha: p8くPN. (Use standard error-0.116.) (3 decimal places) (b) Determine the p-value (3 decimal places) (c) Based on this p-value, which of the following would you expect for a 95% confidence interval for pB-PNY? All values in the interval are negative. Some values in the interval are positive and some are negative. All values in the interval are positive (d) What is the correct conclusion? There was no significant difference between the proportion of drivers wearing seat belts in Boston and New York. The proportion of Boston drivers wearing seat belts was significantly lower than the proportion of New York drivers wearing seat belts. The proportion of Boston drivers wearing seat belts was significantly higher than the proportion of New York drivers wearing seat belts
(A.)test statistic for this test using Ha: p8くPN is Z = -2.164 (B.) p-value (3 decimal places) is 0.015. (C.) Based on this p-value, which of the following would you expect for a 95% is negative. (D.) the correct conclusion is The proportion of Boston drivers wearing seat was significantly lower than the proportion of new York drivers wearing seat belts.
A.)
According to given data find the test statistic for this test using Ha:
p1 = 0.581
p2 = 0.832
standard error = SE = 0.116
Test statistics :-Z = [tex]\frac{p1 - p2}{SE}[/tex]
Z = [tex]\frac{0.581 - 0.832}{0.116}[/tex] = -2.164
Z = -2.164
B.)
According to given Determine the p-value (3 decimal places).
p - valueit is left tailed test.
p - value for left tailed test is,
p - value = P(Z < test statistics )
p - value = P(Z < -2.164)
P - value = 0.015
C.)
Based on this p-value, which of the following would you expect for a 95%
confidence level = 95% = 0.95
significance level = α = 0.05
P -value is less than 0.05
so, reject null hypothesis at α = 0.05
That is [tex]P_{B}[/tex] < [tex]P_{NY}[/tex]
so, based on P - value , All values in the 95% confidence interval
PB - PNY is negative.
D.)
According to given data What is the correct conclusion?
Reject null hypothesis at α = 0.05
so, [tex]P_{B}[/tex] < [tex]P_{NY}[/tex]
Hence, The proportion of Boston drivers wearing seat was significantly lower than the proportion of new York drivers wearing seat belts.
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x+3(2x-4) just checking answer
[tex]\fbox{7x-12}[/tex]
Distributive property:
[tex]x+(3)(2x)+(3)(-4)[/tex]
[tex]x+6x+-12[/tex]
Combine like terms:
[tex](x+6x)+(-12)[/tex]
[tex]7x-12[/tex]
13. Grace is an egg farmer who sells eggs in two different-sized containers: a
dozen eggs for $5 or a 30-egg flat for $10.80. She is going to start selling an
18-ege carton as well and is wondering what price to charge. She wants to
set the unit price of the 18-egg carton between the unit prices for the other
two sizes. What price range can she choose from for the new size?
Answer:
6.48 <= x <= 7.5
Step-by-step explanation:
(5/12)×18=7.5
(10.80/30)×18=6.48
6.48 <= x <= 7.5
Which rule best red the following patterns 8,4,10,6,12,8,14
The rule with describes the expression 8,4,10,6,12,8,14 is the alternating numbers gets increased by 2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be represented as A
Now , the expression A is
A = 8,4,10,6,12,8,14
Taking out the alternate numbers from the expression A , we get
A₁ = 8 , 10 , 12 , 14
So ,the values of A₁ increases by 2
And ,Taking out the alternate numbers from the expression A , we get
A₂ = 4 , 6 , 8 , 10
So , the values of A₂ also increases by 2
Hence , the alternating numbers in the expression increases by 2
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a swimming pool open 12 3/4 hours each day. the life gurads work shifts that are 3/4 hour long . how many shifts are there each day?
Answer:
17
Step-by-step explanation:
I hope this helps!!!
3/4 3/4 3/4 3/4= 3 hours
3 hours equals 4 shifts
you do this 4 times and it equals 12 hours, and 16 . Then you have 3/4 left which equals a shift. So 16+1=17
i need some help plsssssss
Answer:
Option 3 (Parentheses, division, multiplication, subtraction)
Step-by-step explanation:
Using PEMDAS, we can know that we need to solve the parentheses first. Next, we need to solve the multiplication and division, so we can eliminate the first option and last option. However, we need to solve the operations left to right, meaning we'd solve the division first. Therefore, the answer is option 3.
Answer:
The answer is Parentheses multiplication division subtraction
Step-by-step explanation:
Always remember
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Write 0.431 as a percent.
Answer:
43.1%
Step-by-step explanation:
Hassan knows how to sing 6 vocal pieces, thanks to his choir class. Now he's about to start private lessons. His teacher says he will learn 2 new pieces each month.
Write an equation that shows the relationship between the number of months Hassan takes voice lessons, x, and the number of pieces he knows, y.
y=
Answer:
2x + 6
Step-by-step explanation:
If the number of months Hassan takes voice lessons is x, and he learns two pieces every month, you would multiply the number of months, x, together with the number of pieces he will learn each month, 2, making 2x.
Hassan already knows how to sing 6 vocal pieces, which you would add to 2x.
That makes 2x + 6.
Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54.
What is the oldest Kim could be? Show all your work.
I
Answer:
8
Step-by-step explanation:
Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54. What is the oldest Kim could be?
J + k < 54 when J = 5k + 6 so:
5k + 6 + k < 54
6k + 6 < 54
subtract 6 from both sides:
6k + 6 - 6 < 54 - 6
6k < 48
divide both sides by 6:
6k/6 < 48/6
k < 8
Kim could be 8 at maximum.
find a monic quadratic polynomial $f(x)$ such that the remainder when $f(x)$ is divided by $x-1$ is $2$ and the remainder when $f(x)$ is divided by $x-3$ is $4$.
f(x) = x + 1 is the monic quadratic polynomial used here
Given,
The monic quadratic polynomial f(x)
The remainder when f(x) divided by x - 1 is 2
The remainder when f(x) divided by x - 3 is 4
We have to find f(x).
Monic Quadratic Polynomial;-
A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.
Here,
The remainder when f(x) divided by x - 1 is 2
Assume f(x) / x - 1 = 1
Then,
f(x) = (x - 1) × 1 + 2
f(x) = x - 1 + 2
f(x) = x + 1
Next,
The remainder when f(x) divided by x - 3 is 4
Assume f(x) / x - 3 = 1
Then,
f(x) = (x - 3) × 1 + 4
f(x) = x - 3 + 4
f(x) = x + 1
That is,
The monic quadratic polynomial used here is, f(x) = x + 1
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if a 10 percent increase in the price of good x results in a 20 percent decrease in the quantity of good y demanded, which of the following is true?
Elastic demand for a good is defined as when the price of a good rises by 10% while the quantity required falls by 20%.
What is Elastic demand?When a product's price changes, consumer demand is said to be elastic. Consumers will purchase significantly more if the price drops just a little. They won't buy as much if prices increase somewhat instead opting to wait for them to level out.
If all other variables remain constant, the ratio of a product's percent change in demand to its percent change in price determines whether a product's demand is elastic or inelastic.
It is neither elastic nor inelastic for an item's price to alter in proportion to its change in demand. In other words, a product has elastic demand if demand fluctuates more than price does.
Hence, Elastic demand for a good is defined as when the price of a good rises by 10% while the quantity required falls by 20%.
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Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1). Is this trapezoid an isosceles trapezoid? select from the drop-down menu to correctly complete the statement.
Yes, if Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) , ABCD is an isosceles trapezoid.
Since, If in a trapezoid two opposite nonparallel sides are equal then it is called isosceles trapezoid.
In trapezoid ABCD sides are AB, BC, CD and DA.
According to the question, A≡(2,4) B≡(5,4) C≡(7,1) and D≡(0,1)
After making the diagram of ABCD, we found that DA and BC are nonparallel sides.
And, by the distance formula BC = √((7 - 5)² + (1 - 4)²) =
⇒ BC =√(4 + 9)
⇒BC = √13 unit.
Similarly, DA = √((0 - 2)² + (1 - 4)²)
DA = √(4 + 9)
⇒ DA = √13 unit.
Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.
Therefore, trapezoid ABCD is a isosceles trapezoid.
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Ameekah is working with consecutive integers. if she uses x to represent her first number, what should she use to represent her second number? x x 1 x 2 2x
The second number used by Ameekah to represent the consecutive integers is (x + 1).
Explain the term consecutive integers?Integers that follow one another in a predictable counting pattern are referred to as consecutive integers. There are no numbers missed while showing consecutive integers in either a sequence, so the range between them is absolutely fixed. The consecutive integers in increasing order are referred to as consecutive integers.Let 'x' be the first number written by Ameekah.
Then, the second number will be obtained by adding one to first number.
= x + 1
Thus, the second number used by Ameekah to represent the consecutive integers is (x + 1).
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Answer:
"B" is correct, "x + 1"
Step-by-step explanation:
Have a Jocular Day
Ffgggggggggggggggggggggggggggggggggggg
Answer:
Step-by-step explanation:
Cosine is adjacent over hypotenuse.
So for Angle Z, the adjacent leg is 12 and the hypotenuse leg is 20.
The Cosine ratio is 12/20.
16 is not used and would be the opposite leg to Angle Z
How many times smaller is 2.9 × 10^3 than 3.654 × 10^5?
126
79
1.26
0.79
The number 2.9 × 10^3 is 126 times smaller than 3.654 × 10^5. Because its ratio is 126. It can be calculed by the concept of ratio.
What is ratio?
It is the way of representation of a quantity relative to the other quantity. Its symbol is :. For example size of 2 relative to 5 is represented by 2:5 or 2/5.
To find how many times 2.9 × 10^3 is smaller than 3.654 × 10^5, take ratio of 3.654 × 10^5 and 2.9 × 10^3 as follows:
[tex]=\frac{3.654\times 10^5}{2.9 \times10^3}\\[/tex]
Now, subtract the indices as follows:
[tex]=\frac{3.654\times 10^2}{2.9}\\[/tex]
Now, divide the number as follows:
[tex]=1.26\times 10^{2}\\[/tex]
Now, write in simplest form as follows:
[tex]=126[/tex]
Hence, 2.9 × 10^3 is 126 times smaller than 3.654 × 10^5. It can be calculed by the concept of ratio.
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Answer:
126 times smaller
Step-by-step explanation: