which of the following results in the difference of two squares?
a. (4x-5y)(4x+5y)
b. (5x+3y)(5x+3y)
c. (2x-3y)^2
d. 4x^2(3x-9)
Answers
Answer:
The answer is a.
Step-by-step explanation:
Observe the formula: \((a+b)(a-b)=a^2-b^2\)
A is the only one that has this format. Thus, it is the difference of two squares.
The results in the difference between the two squares are (4x-5y)(4x+5y). then the correct answer is option A.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Use the algebraic identity a² - b² = ( a + b ) ( a - b ).
Let a = 4x and b = 5y, two sides of the square now the difference will be calculated:-
a² - b² = ( a + b ) ( a - b ).
(4x)² - (5y)² = ( 4x + 5y ) ( 4x - 5y ).
Hence, the correct answer is option A.
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Related Questions
A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 5. The sample mean is 20.
Answers
The sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.
The formula for sample mean is given by,
Sample Mean \((X)= (x1+x2+x3+...+xn) / n\)
Where x1, x2, x3,...,xn are individual observations and n is the number of observations.
In this case, the sample mean (X) is given as 20 and the number of observations (n) is 10.
Therefore, the formula can be written as:
\(X = (x1+x2+x3+...+x10) / 10\)
Since the population standard deviation (σ) is given as 5, the standard deviation of the sample (s) can be calculated using the formula:
s = σ/√n
Where n is the number of observations.
Therefore, in this case, the standard deviation of the sample (s) is calculated as:
s = 5/√10
s = 2.23
Thus, the sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.
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Santa lost 7 cents on Monday and 12 cents on Tuesday. What was the effect on Santa's piggy bank?
Answers
Answer:
I believe it's that Santa loses 19 cents total.
Santa lost 7 cents on Monday and 12 cents on Tuesday. 7 + 12 = 19.
Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
Answers
The area of the triangle is 6 square units.
How to solveOnce you have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
Or you could use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
then find area
A=1/2bh
1/2(3*4)
6
Thus, the area of the triangle is 6 square units.
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This figure is made of rectangular prisms. What is the volume?
Answers
Answer:
1,176 cm²
Start the equation\(V = b * l * h\\V = 18 * 6 * 12\\\\= 1,296\)
Find volume of second composite figure\(V = h * l + b * a\)
Assume all sides are 10
\(V = 10 * 10 + 10 + 10\\\\= 120\)
Finally, subtract both values\(V = 1,296 - 120 = 1,176\)
Answer: 1176 cm
Step-by-step explanation:
when she chooses a password, eloise always uses exactly ten different characters: five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. how many different passwords conform to these rules?
Answers
These rules of five letters (a, b, c, d, and e) and five numbers allow for 28,800 different passwords. Additionally, she makes sure that no two letters or two numbers are ever placed back-to-back.
What is counting principle?The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. According to this statement, there are n*m methods to carry out both of these acts if there are n ways to execute one activity and m ways to conduct another action after that.
Here,
Eloise has 10 alternatives since the password's initial character can be any letter or number. She has five alternatives, and her second selection must be from the set (letter or number) that has not previously been utilized. She has four choices remaining, and Choice 3 is from the same group as Choice 1. She gets four possibilities since Choice 4 is the second item in the same set as Choice 2. The choices 5 and 6 come from separate sets, each of which has three possibilities; the choices 7 and 8 come from separate sets, each of which has two options; and the choices 9 and 10 come from separate sets, each of which has only one option left.
10 5 4 4 3 3 2 2 1 1
10 ×5 ×4 ×4 ×3 ×3 ×2 ×2 ×1 ×1 = 28,800
28,800 different passwords conform to these rules of five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive.
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Write a sine function that has a midline of 5, an amplitude of 4 and a period of 3/5
Answers
To answer this question, first, we have to recall that,
\(f(x)=\sin x,\)has an amplitude of 2, a midline
\(y=0,\)and a period of
\(2\pi\text{.}\)Now, to change the amplitude we multiply the function by a constant in the following way:
\(4\sin (x).\)For the new function to have a midline of y = 5, we have to translate the sine, 5 units up:
\(undefined\)Multiply 81.5 and 3.5
Answers
Answer:
285.25
Step-by-step explanation:
Basically we multiply them as normal numbers so,
815*35 = 28525
Then we take the amount of spots each number had to the RIGHT of the decimal point
81.5 = 1
3.5 = 1
1+1= 2
So: 28525. move to the left 2 times to get 285.25
The average annual tuition for four-year private colleges increased by 5.9 percent from last year. The average cost last year was $31,250. What is the average cost this year?
Answers
Answer:
The average cost this year = $33,093.75
Step-by-step explanation:
The computation of the average cost this year is shown below:
Given that
The average cost for the last year = $31,250
Increased percentage = 5.9%
Based on the above information, the average cost this year is
= The average cost for the last year × (1 + Increased percentage)
= $31,250 × (1 + 0.059)
= $31,250 × 1.059
= $33,093.75
6(7-5) jkwjwjnwnwnnenenenenenne
Answers
consider the curve defined by the equation y+cosy=x+1
Answers
The equation y + cos(y) = x + 1 defines a curve in the xy-plane. The curve represents the relationship between x and y values that satisfy the given equation.
The equation y + cos(y) = x + 1 is a transcendental equation, which means it does not have a simple algebraic solution. To study the curve defined by this equation, we can analyze it graphically or numerically.
By plotting points that satisfy the equation, we can observe the shape and behavior of the curve. The equation combines both algebraic terms (y and x) and trigonometric functions (cos(y)), resulting in a complex relationship between x and y values.
Therefore, the curve represents all the points (x, y) that satisfy the equation, forming a distinct pattern in the xy-plane.
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Select the correct answer.
What is the value of y in the triangle?
a 30-60-90 triangle with long leg length y and hypotenuse length 6
A.
B.
C.
D.
Answers
Answer: In a 30-60-90 triangle the side opposite the 30 degree angle is half the length of the hypotenuse. The shorter leg is the side opposite the 30 degree angle, therefore the shorter leg = 30/2 = 15
By the Pythagorean theorem
the longer leg = √(30² - 15²) = √(900-225) = √675 = 15√3 ≈ 25.98 units
Q1. Find all possible Jordan forms of a matrix with characteristics polynomial C(t) = (t – 2)^4(t – 3) [3]
Answers
1. A Jordan block of size 4 corresponding to the eigenvalue 2 and a Jordan block of size 1 corresponding to the eigenvalue 3.
2. A Jordan block of size 3 corresponding to the eigenvalue 2, a Jordan block of size 1 corresponding to the eigenvalue 2, and a Jordan block of size 1 corresponding to the eigenvalue 3.
The characteristic polynomial C(t) provides information about the eigenvalues and their multiplicities. In this case, we have two distinct eigenvalues: 2 and 3. The multiplicity of the eigenvalue 2 is 4, and the multiplicity of the eigenvalue 3 is 1.
The Jordan form represents the structure of a matrix using Jordan blocks. Each Jordan block corresponds to an eigenvalue, and its size is determined by the multiplicity of that eigenvalue.
In the first possible Jordan form, we have a Jordan block of size 4 corresponding to the eigenvalue 2, denoted as [2]. Additionally, we have a Jordan block of size 1 corresponding to the eigenvalue 3, denoted as [3].
In the second possible Jordan form, we have a Jordan block of size 3 corresponding to the eigenvalue 2, denoted as [2], a Jordan block of size 1 also corresponding to the eigenvalue 2, denoted as [2], and finally a Jordan block of size 1 corresponding to the eigenvalue 3, denoted as [3].
These two possible Jordan forms encompass all the potential arrangements of Jordan blocks for a matrix with the given characteristic polynomial.
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Triangle DEF is a scaled copy of triangle ABC. Two triangles labeled ABC and DEF. Triangle ABC has horizontal side AB with point B to the right of point A and point C is directly above side AB. Triangle DEF has horizontal side DE with point E to the right of point D and point F is directly above side DE. Angle ABC corresponds to angle [ Select ] . Angle BCA corresponds to angle [ Select ] . Segment AC corresponds to segment [ Select ] . Segment BA corresponds to segment [ Select ] .
Answers
Answer:
\(\angle ABC\) corresponds to the \(\angle D EF\)
\(\angle BCA\) corresponds to the \(\angle EFD\)
Segment AC corresponds to segment DF.
Segment BA corresponds to segment ED.
Step-by-step explanation:
As per the given statements, kindly refer to the attached figure for the diagrammatic representation of the situation.
Given two triangles: \(\triangle ABC, \triangle D EF\).
Horizontal sides are AB and DE with points B and E are on the right side of A and D respectively.
Points C and F are directly above the corresponding sides AB and DE respectively.
Kindly refer to the attached diagram for the representation as per the given situation.
Scaled version of a figure and the original figure are similar to each other.
It means that corresponding sides and angles are equal to each other.
\(\angle ABC\) corresponds to the \(\angle D EF\)
\(\angle BCA\) corresponds to the \(\angle EFD\)
Segment AC corresponds to segment DF.
Segment BA corresponds to segment ED.
Tabby read 254 pages in 8 days. What is her unit rate in pages per day?
Answers
Answer:
31.75 round it off to 32 pages per day
Step-by-step explanation:
254/8=31.75 but you cant but a decimal so its 32
When is the function positive?
Answers
When f(x) > 0.
Let ⟨s
n
⟩ be a bounded sequence that does not converge. By Theorem 3.5.1 there is a subsequence ⟨s
n
i
⟩ that converges to some real number ℓ. Show that there is another subsequence of ⟨s
n
⟩ that converges to a real number different than ℓ.
Answers
We have shown that there is another subsequence of ⟨s_n⟩ that converges to a real number different than ℓ.
To show that there is another subsequence of ⟨s_n⟩ that converges to a real number different than ℓ, we can make use of the fact that ⟨s_n⟩ does not converge.
Since ⟨s_n⟩ does not converge, there exists an ε > 0 such that for every N ∈ ℕ, there exists an n > N such that |s_n - ℓ| ≥ ε.
Now, let's construct a subsequence ⟨s_ni⟩ as follows:
- Start with i = 1.
- Choose n_1 such that |s_n1 - ℓ| ≥ ε.
- For each subsequent i, choose n_i > n_{i-1} such that |s_ni - ℓ| ≥ ε.
By construction, we can see that the subsequence ⟨s_ni⟩ satisfies the condition that |s_ni - ℓ| ≥ ε for every i ∈ ℕ.
Since ε > 0, we can choose a smaller δ > 0 such that |ℓ - (ℓ ± δ)| = δ.
Now, consider the subsequence ⟨s_ni⟩. By construction, for every i ∈ ℕ, we have |s_ni - ℓ| ≥ ε.
But since |ℓ - (ℓ ± δ)| = δ, we have |s_ni - (ℓ ± δ)| ≥ ε - δ.
Thus, we can see that the subsequence ⟨s_ni⟩ converges to a real number different than ℓ, specifically ℓ ± δ.
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y= 2x + 1 and - 4x + y = 9, solve the system of equations without graphing
Answers
After solving the given equations we know that the value of x and y are -4 and -7 respectively.
What are equations?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Ax+By=C is the usual form for two-variable linear equations.
A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
This form is also highly useful when solving systems involving two linear equations.
So, we have the equations:
y=2x+1 ...(1)
-4x+y=9 ...(2)
Now, substitute y=2x+1 in equation (2):
-4x+y=9
-4x+2x+1=9
-2x=8
x=-4
Now, insert x=-4 in equation (1):
y=2x+1
y=2(-4)+1
y=-8+1
y=-7
Therefore, after solving the given equations we know that the value of x and y are -4 and -7 respectively.
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The principal advantage of the Dodge-Romig tables is: A. minimum inspection B. its desirability for receiving inspection C. smaller lot sizes D. simplicity
Answers
The principal advantage of the Dodge-Romig tables is their simplicity. Therefore, the correct answer is D. simplicity.
The Dodge-Romig tables are statistical sampling tables used in quality control to determine the acceptance or rejection
of a production lot based on sample size and the number of defects found in the sample.
The principal advantage of the Dodge-Romig tables is their simplicity.
They provide a quick and easy method for determining the acceptability of a production lot, without the need for
extensive calculations or statistical knowledge.
This means that they can be used by personnel with limited training in quality control.
The principal advantage of the Dodge-Romig tables is their simplicity. While they can be used for receiving inspection,
their main benefit is in minimizing inspection time and effort by providing clear guidelines for lot sampling and
acceptance based on size and level of defects.
Additionally, their use can facilitate smaller lot sizes and more efficient quality control processes.
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camilla leans a 18foot ladder against a wall so that it forms an angle of 71 with the ground. how high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary
Answers
The wall is 17.0 ft from the point ladder touches the wall
Explanation:The length of the ladder = 18 ft
The angle the ladder makes with the wall = 71°
We need to find the distance betwen the base of the wall and the point the ladder touches the wall.
To solve this, we will do an illustration of the scenario:
Let x = distance between the base of the wall and the point the ladder touches the wall
To get x, we will apply sine ratio (SOH):
\(\begin{gathered} si\text{ n }71\degree\text{ = }\frac{opposite}{hypotenuse} \\ \text{opposite = x, hypotenuse = }18 \\ \\ \sin \text{ }71\degree=\text{ }\frac{x}{18} \end{gathered}\)\(\begin{gathered} x\text{ = 18(}\sin 71\degree) \\ x\text{ = 18(}0.9455) \\ x\text{ = 17.019} \\ To\text{ the nearest tenth, x = 17.0} \end{gathered}\)The wall is 17.0 ft from the point ladder touches the wall
Rachelle graphs a point at (4, 2). She says that she can move her
point four or more units to the left and two or more units down to arrive at a point in the third quadrant. Is Rachelle correct? Explain why or why not.
Answers
Answer: yes, Rachelle is correct.
Step-by-step explanation:
first, if you're moving left, you're subtracting from the x value.
4-4=0
next, if you're moving down then you're subtracting from the y value.
2-2=0
if you subtract more than the given numbers, like said in the problem, you would have coordinates like (-1,-1) or (-3,-4)
therefore, you would be in the third quadrant.
If x is added to 4 and then multiplied by 2, then the function is f(x) = 2(x +4)
What are the steps to find the inverse to this function?
a.) Divide by 2, then subtract 4
b.) Subtract 4, then divide by 2
c.) Multiply by 4, then add 2
d.) Add 2, then multiply by 4
Answers
Answer:
A
Hope this helps!!
Step-by-step explanation:
The inverse of the function will be y = x / 2 - 4. Then the correct option is A.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by the swapping of x with y and y with x.
If x is added to 4 and then multiplied by 2, then the function is f(x) = 2(x +4). Then the inverse of the function will be
x = 2(y +4)
Simplify the equation, then the inverse function will be
x / 2 = y + 4
y = x / 2 - 4
The inverse of the function will be y = x / 2 - 4.
Then the correct option is A.
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Explain how recapturing a higher percent of marked alligators affects the estimated total population
Answers
Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.
What is Population?This is referred to as the total number of species or organisms in an area at a given period of time.
Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.
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A standard number cube, numbered 1 through 6 on each side, is rolled 3 times. What is the probability of rolling a 2 on all three rolls?
Express your answer as a fraction.
Answers
Answer:
1/216
Step-by-step explanation:
probability of rolling a 2 and a 2 and a 2 = 1/6(1/6)(1/6) = 1/216
What is the difference of 67.5 and 23.678
Answers
Answer:
43.822
Step-by-step explanation:
67.5
- 23.678
43.822
can anyone help me pls
Answers
Answer:
4x - 5 ft
Step-by-step explanation:
Perimeter = 4 × side
16x - 20 = 4 × side
(16x - 20)/4 = side
4x - 5 = side
Answer:
\(perimeter = 2(l + b) \\ 16x - 20 = 2(2l)(square \: so \: l = b) \\ 16x - 20 = 4l \\ l =( 16x - 20 )\div 4 = 4x - 5 \\ thank \: you\)
Jim needs to divide 762 coupon books equally among 9 stores. In which place is the first digit of the quotient? Select the word that makes the sentence true. The first digit of the quotient is in the ones place.
Answers
Answer:
ones
Step-by-step explanation:
It is given that Jim wants to divide 762 coupons equally among 9 stores.
So dividing 762 by 9, we get
\($=\frac{762}{9}$\)
= 84.66
The position of the digit before the decimal place start with 'ones' and then proceeds to tens, hundreds, thousands, etc.
Therefore, the first digit of the quotient is in the ones place of the position value or place value.
Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 45 bacteria are present o begin with the total number present after a days is f(x) = 45 - 64* Find the total number present after 1, 2 and 3 days. There will be bacteria present after 1 day, after 2 days and after 3 days.
Answers
A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
The problem can be solved using the exponential growth model.
In the given problem, the formula for the growth model is given, that is:
f(x) = 45 (64)^(x)
Where:
f(x) = total number of bacteria present after x days
To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.
f(1) = 45 (64)¹ = 2,880
f(2) = 45 (64)² = 184,320
f(3) = 45 (64)³ = 11,796,480
Hence,
after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
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dante's commedia is divided into three books, each containing thirty-three
Answers
Dante's Commedia consists of three books, each containing 33 cantos, for a total of 100 cantos.
The Commedia is a famous literary work by Dante Alighieri, an Italian poet from the 14th century. It is divided into three books: Inferno, Purgatorio, and Paradiso. Each book consists of 33 cantos, making a total of 100 cantos in the entire work.
Inferno is the first book and depicts Dante's journey through Hell. It starts with Dante being guided by the Roman poet Virgil and encountering various sinners and punishments in the different circles of Hell.
Purgatorio is the second book and portrays Dante's ascent up Mount Purgatory, where souls undergo purification to reach Heaven. In this book, Dante is guided by Virgil and later by Beatrice, his beloved.
Paradiso is the final book and represents Dante's ascent to Heaven. In Paradiso, Dante is guided by Beatrice and encounters various heavenly spheres, learning about theology, cosmology, and the nature of God's love.
Each book explores different themes, symbolism, and allegorical representations. Dante's Commedia is renowned for its vivid imagery, complex allegories, and its profound exploration of moral, spiritual, and philosophical themes.
In conclusion, Dante's Commedia consists of three books, each containing 33 cantos, for a total of 100 cantos. It is a monumental work of Italian literature that delves into the realms of Hell, Purgatory, and Heaven, offering a rich exploration of various themes and ideas.
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What is the answer to, 2/3 / -1/2?
Answers
Answer:
\( \frac{ \frac{2}{3} }{ \frac{ - 1}{2} } \\ = \frac{2}{3} \times \frac{ - 2}{1} \\ = \frac{ - 4}{3} \\ thank \: you\)
Answer:
-4/3
Step-by-step explanation:
\(\frac{2}{3} /\frac{-1}{2} \\\\\frac{2}{3} *\frac{-2}{1} \\\\\frac{-4}{3}\)
I NEED HELP ASAP PLSSS
The matrix equation represents a system of equations.
A matrix with 2 rows and 2 columns, where row 1 is 2 and 7 and row 2 is 2 and 6, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 8 and row 2 is 6.
Solve for y using matrices. Show or explain all necessary steps.
Answers
The solution to the system of equations is
x = -3 and y = 2How to solve the matrix equationThe matrix equation is written as a linear equation by using matrix multiplication to get
2x + 7y = 8
2x + 6y = 6
Then solving simultaneously by substitution method we have
Step 1:
Solve 2x + 6y = 6, in terms of x.
From the second equation:
2x = 6 - 6y
x = 3 - 3y
Step 2:
Substitute the expression for x in terms of y into the other equation.
2(3 - 3y) + 7y = 8
6 - 6y + 7y = 8
y = 2
Step 3:
Substitute the value of y back into one of the original equations to solve for x.
2x + 7(2) = 8
2x + 14 = 8
2x = -6
x = -3
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