Recognizing the specific forms of square trinomials and the difference of squares allows you to rewrite them as separate factors, simplifying algebraic expressions and facilitating further mathematical operations.
Knowing when to rewrite square trinomials and the difference of squares as separate factors depends on the algebraic expression you are dealing with. Let's consider each case separately.
1. Square Trinomials:
- Square trinomials have the form [tex]\(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\)[/tex], where(a) and (b) are algebraic expressions.
- These trinomials can be factored into the square of a binomial: [tex]\((a + b)^2\) or \((a - b)^2\).[/tex]
- You should rewrite a square trinomial as separate factors when you encounter an expression that matches the form of a perfect square trinomial. Recognizing this pattern allows you to simplify the expression.
2. Difference of Squares:
- The difference of squares has the form [tex]\(a^2 - b^2\),[/tex] where (a) and (b) are algebraic expressions.
- This expression can be factored into the product of conjugates: [tex]\((a + b)(a - b)\).[/tex]
- You should rewrite a difference of squares as separate factors when you have an expression in the form [tex]\(a^2 - b^2\)[/tex]. Recognizing this pattern helps you simplify and factor the expression efficiently.
A personal identification code consists of five digits (0 through 9). how many codes are possible?
a. 50
b. 252
c. 100,000
d. 30,240
There are 30,240 codes that are possible which consist of five digits (0 through 9).
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
There are 10 options for each of the 5 digits in the personal identification code (0 through 9). Since the order of the digits matters, we can use the formula for the number of permutations of n items taken r at a time, which is:
n!/(n-r)!
In this case, n is the number of options (10) and r is the number of items (5). Plugging these values into the formula gives us:
10!/(10-5)! = 10!/(5!) = 109876 = 30,240
Therefore, the correct answer is (d) 30,240.
Learn more about permutation here:
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Jorge bought a car for $41,902 . He paid for the car with a check. Round the price to the nearest:
What is the degree of each monomial -9
The degree of a monomial is the sum of the exponents of the variables.
For example:
monomial: 257 x^3 y^5 z^21.
The degree is the sum of the exponents of x, y and z, this is 3 + 5 + 21 = 29.
When a monomial is just a number, it means that the exponents of the variables are zero. For example:
- 9 x^0 y^0 z^0 = - 9 * 1 * 1 * 1 = - 9.
This is your case, the monomial -9 has degree 0, which is the option B.
a(1)=20
a(n)=a(n−1)−17
Find the 3rd term in the sequence
Answer:
-14
Step-by-step explanation:
khan academy
The sides of a triangle are in the ratio 5:12:13. what is the length of each side of the triangle if the perimeter of the triangke is 15 inches
An acute angle θ is in a right triangle with sin θ = two thirds . What is the value of cot θ?
Answer:
six divided by the square root of thirteen
Step-by-step explanation:
hey there,
< sin θ = [tex]\frac{O}{H}[/tex]
So that means O = 2 and H = 3. In order to find cot θ, first let's find tan θ.
tan θ = [tex]\frac{O}{B}[/tex]
We only know what O is equal to, not B. So let's draw out a triangle.
7
◢ 6
B
As you can see (sorry for the poor triangle), this is a right triangle. In order to find an unknown part, use [tex]a^2 + b^2 = c^2[/tex]!
[tex]6^2 + B^2 = 7^2[/tex]
B = ±√13
Obviously, a side of a triangle can't be negative, so it stays positive. Now we can find tangent!
tanθ = [tex]\frac{6}{\sqrt{13} }[/tex]
But, we're not done here. We're trying to find cotθ.
cotθ = [tex]\frac{1}{tan}[/tex]θ
[tex]\frac{1}{\frac{6}{\sqrt{13} } }[/tex] = [tex]\frac{\sqrt{13} }{6}[/tex]
That's your final answer! >
Hope this helped! Feel free to ask anything else.
If today is tuesday what day will it be in 100 days
Which equation is not a quadratic equation?
y = 3x2 + 2
y = 5x - 2
y = -x2
y = 5x2 - 2x + 7
4xy - 9xy + -3xy Simplify the polynomial
How to determine the direction of a vector?
What does b belong with?
An experiment consists of dealing 5 cards from a standard 52-card deck. what is the probability of being dealt aa 10, jack, queen, king, ace, all in the same suit
Bella made a drawing of her rectangular bedroom with the scale of 1 inch = 3 feet. The drawing was 6 inches long by 4 inches wide. What are the dimensions of Bella's room? What is the actual area? Show your work.
Bella's actual room dimensions are 18 feet by 12 feet, resulting in an actual area of 216 square feet. This was determined by applying the scale factor from the drawing to the actual room size.
To determine the actual dimensions of Bella's room based on her drawing, we first need to use the provided scale factor. According to the scale, 1 inch on the drawing is equal to 3 feet in actual size. We can calculate the actual dimensions by multiplying the length and width of the drawing by the scale factor.
The drawing is 6 inches long by 4 inches wide.
Actual length: 6 inches × 3 feet/inch = 18 feet
Actual width: 4 inches × 3 feet/inch = 12 feet
Now, to determine the actual area of Bella's room, we multiply the actual length by the actual width:
Actual area = actual length × actual width
Actual area = 18 feet × 12 feet = 216 square feet
What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x plus 24
Answer:
x= -6 is the point of discontinuity.
Step-by-step explanation:
We have been given the expression
[tex]\frac{x^2-16}{4x+24}[/tex]
The first thing to find the discontinuity is to factorize the given rational function:
After factorization we get:
We will use [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]here, a=x\text{and}b=4[/tex] we will get:
[tex](x+4)(x-4)=x^2-4^2[/tex]
we will get:
[tex]\frac{(x+4)(x-4)}{4(x+6)}[/tex]
Discontinuity is the point where value of the function becomes not defined
Here, the point of discontinuity is -6 because when denominator becomes zero. function becomes not defined.
It has vertical asymptote but function is not defined.
Hence it is the point of discontinuity.
Which complex number has a distance of √17 from the origin on the complex plane?
A;2 + 15i
B:17 + i
C:20 – 3i
D:4 – i
Answer:
The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
D is correct
Step-by-step explanation:
We are given the absolute value of complex plane.
If complex number is a+ib then absolute value [tex]\sqrt{a^2+b^2}[/tex]
We have to check the absolute value of each option and check which is equal to [tex]\sqrt{17}[/tex]
Option A: 2+15i
[tex]d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\neq \sqrt{17}[/tex]
Option B: 17+i
[tex]d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\neq \sqrt{17}[/tex]
Option C: 20-3i
[tex]d=\sqrt{20^2+3^2}=\sqrt{400+9}=\sqrt{409}\neq \sqrt{17}[/tex]
Option D: 4-i
[tex]d=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}= \sqrt{17}[/tex]
Hence, The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
Which of the following statements is the converse of the statement "If each of two angles has a measure of 28 degrees, then the two angles are equal in measure"?
Answer:
If two angles are equal in measure then each of the two angles has a measure of 28 degrees.
Step-by-step explanation:
The converse of a statement is found by switching the hypothesis and conclusion of a conditional statement.
The hypothesis is the part that comes after "if" and the conclusion is the part that comes after "then."
This means the hypothesis is "each of two angles has a measure of 28 degrees" and the conclusion is "the two angles are equal in measure."
This gives us the converse "If two angles are equal in measure then each of the two angles has a measure of 28 degrees."
If you had 5 green marbles and 8 red marbles, what's the probability that you'll pull out a marble that is green?
5+8 = 13 total marbles
5 are green
so you would have a 5/13 probability of picking a green one
What is the equation of a circle with a center (-2, 3) and a radius r = 5?
Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?
Maggie’s brother is 12 years younger that three times her age . The sun of their ages is 44 . How old is Maggie
Which formula is used to find circular mil area?
una pizzeria hace pizzas de varios tamaños y las vende en cajas hexagonales de 39 cm de lado y 4.7 cm de alto ¿que cantidad de cartón se anestesia para cada caja teniendo en cuenta q la caja esta formado por dos partes compuestas de una base lateral ?
Final answer:
To calculate the amount of cardboard used for each box, we need to find the surface area of the hexagonal base and the lateral surface area. We can use the formula for the surface area of a hexagon to find the base area. Then, we multiply it by the height of the box and add the two areas together.
Explanation:
To find the amount of cardboard used for each box, we need to calculate the surface area of the hexagonal base and the lateral surface area. The surface area of a hexagon can be found using the formula:
Surface Area = 3 x √3 x s^2
where s is the length of the side of the hexagon. Given that the side length is 39 cm, we can substitute this into the formula to find the surface area of the hexagonal base. Once we have the surface area, we can calculate the lateral surface area by multiplying it by the height of the box, which is 4.7 cm. Adding the two areas together will give us the total amount of cardboard used for each box.
Write the set of points greater than or equal to −5−5 but strictly less than 44, excluding 00, as a union of two intervals (if you're having trouble with this, try drawing a number line):
The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
Z= k/x
when x is 6, Z= 2
2=k/6
k=2*6
k=12
Z=12/X
when x = 13
Z=12/13
Z=0.923
Ship A receives a distress signal from the northeast and ship B receives a distress signal from the same vessel from the west. At what location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences.
Coordinate geometry is the use of a 2D plane to represent the location of points. The position or location of the distress is in the first quadrant.
The coordinates of ship A and B are not given. So, I will give a general explanation.
On the four cardinal points,
North is upwardsEast is at the rightWest is at the leftSouth is downwardSo, if ship A receives a distress from the northeast, then it means that the distress is coming from a location at the top right of A. i.e. the first quadrant.
Also, ship B receives distress from the west. This means that ship B is at the right-hand side of the distress.
So, we can conclude that the position or location of the distress is at the first quadrant.
It is impossible to determine the actual coordinates of the distress because the coordinates are not given (see attachment possible illustration)
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Because the car that has a terrible oil leak not only as a new battery for the van but also slows him down because he needs the Atwell after every hundred miles of driving he drives 100 miles every two hours it takes him 15 minutes to add oil how long should it take him to drive 500 miles
To drive 500 miles, taking into account both driving time and oil stop time, it would take 11 hours and 15 minutes.
He drives 100 miles every 2 hours, so to drive 500 miles he would take 10 hours (5 segments of 100 miles each).He needs to add oil every 100 miles, which takes 15 minutes each time. Therefore, for the 500-mile trip, he would spend an additional 75 minutes (5 segments x 15 minutes each).Adding the driving time and oil stop time, he would take 10 hours (driving) + 1 hour 15 minutes (oil stops) = 11 hours 15 minutes to drive 500 miles.Daniella wrote the equation shown to represent “four less than – 3.7 times a number is –11.9.” 4n – (–3.7) = 11.9 Explain her error, include the correct equation in your response.
Answer:
The correct equation is [tex]-3.7n-4=-11.9[/tex]
Step-by-step explanation:
Let
n-------> the number
we know that
The equation that represent the expression “four less than [tex]-3.7[/tex] times a number is [tex]-11.9[/tex] " is equal to
[tex]-3.7n-4=-11.9[/tex]
The equation that Daniella wrote represents the expression "[tex]-3.7[/tex] less than four times a number is [tex]11.9[/tex] "
Answer:
The coefficient of the variable should be -3.7 because of the word “times.” The words “four less than” mean that 4 will be subtracted from 3.7n. “Is” represents the equals sign, and “-11.9” is the second expression. The correct equation is -3.7n – 4 = -11.9.
Step-by-step explanation:
Edg math
Your teacher is giving you a test worth 100 points containing 40 questions. there are two-point and four-point questions on the test. let the number of two-point questions be x and the number of four-point questions be y. how many of each type of question are on the test?
Answer:
t=30 f=10
Step-by-step explanation:
t= 100*1 - 40*4 = 30
2*1 - 1*4
f= 2*40 - 1*100 = 10
2*1 - 1*4
t=30 f=10
Use the distributive property to expand the following expression. -3(6.3x + 7y - 2.5)
The expression -3(6.3x + 7y - 2.5) expands to -18.9x - 21y + 7.5 using the distributive property by multiplying each term inside the parentheses by -3.
To use the distributive property to expand the expression -3(6.3x + 7y - 2.5), you multiply each term inside the parentheses by -3. The distributive property lets you reverse the distributive law and turn it into factors (multiples).
-3 × 6.3x = -18.9x
-3 × 7y = -21y
-3 ×-2.5 = 7.5
Once each term is multiplied, the expanded expression is: -18.9x - 21y + 7.5
Suppose you draw a card from a well-shuffled pack of playing cards. What is the probability the card you draw will be an ace? A. 4/50 B. 1/13 C. 4/13 D. 1/52