a is 2q^2r
b is 3s^2t
the expression factored is...
(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)
The given expression is a sum of two cubes. The factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
Given:
The given identity is, [tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex].
It is required to factorize [tex]8q^6r^3 + 27s^6t^3[/tex] using the given identity.
The given expression can be written in the form of sum of two cubes as,
[tex]8q^6r^3 + 27s^6t^3=2^3q^6r^3 + 3^3s^6t^3\\=(2q^2r)^3+(3s^2t)^3[/tex]
Here, a and b are [tex]2q^2r[/tex] and [tex]3s^2t[/tex] respectively.
Now, the factorization of the given expression can be one as,
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r)(3s^2t)+(3s^2t)^2)\\=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex]
Therefore, the factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
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Find the missing measure for a right circular cone given the following information. Find L.A. if r = 6 and h = 8 48 60 96
Final answer:
The Lateral Area (L.A.) of a right circular cone with a base radius of 6 and a height of 8 is 60π square units, calculated by finding the slant height using the Pythagorean theorem and then applying the formula for L.A.
Explanation:
The student is asked to find the Lateral Area (L.A.) of a right circular cone given the base radius (r) is 6 and the height (h) is 8. First, we need to find the slant height of the cone, which can be done using the Pythagorean theorem in a right triangle where one leg is the height of the cone, the other leg is the radius of the base, and the hypotenuse is the slant height (l). The formula is l = [tex]\sqrt{(r^2 + h^2)[/tex]. After calculating l, we use the formula for the Lateral Area: L.A. = π r l.
Calculating the slant height: l = [tex]\sqrt{(6^2 + 8^2)}[/tex] = [tex]\sqrt{(36 + 64)[/tex]= [tex]\sqrt{100[/tex]= 10.
Now, we calculate the Lateral Area: L.A. = π * 6 * 10 = 60π. Hence, the Lateral Area of the cone is 60π square units.
Brian deposited $4000 into an account with 5.4% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 6 years?
find all the zeros for each function.
p(x)=2x^3-3x^2+3x-2
*show work*
The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = –16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet.
Can someone check my answers?
1. Simplify the sum or difference.
sqrt 5 + 6 sqrt 5
A) 6 sqrt 5
B) 30
C) 6 sqrt 10
D) 7 sqrt 5
2. Simplify the sum or difference.
4 sqrt 2 - 7 sqrt 2
A) negative sqrt 6
B) -3 sqrt 2
C) -11 sqrt 2
D) 11 sqrt 2
3. Simplify the sum or difference.
3 sqrt 7 - sqrt 63
A) -2 sqrt 7
B) -6 sqrt 7
C) -4 sqrt 3
D) 0
4. Simplify the sum or difference.
-6 sqrt 10 + 5 sqrt 90
A) 9 sqrt 10
B) -9 sqrt 10
C) -39 sqrt 10
D) -10
5. Simplify the product.
sqrt 6 (sqrt 2 + sqrt 3)
A) sqrt 8 + 3
B) sqrt 30
C) 2 sqrt 3 + 3 sqrt 2
D) 4 sqrt 2 + 3
1 - D
2 - B
3 - D
4 - A
5 - C
6 - A
7 - D
8 - B
9 - B
10 - C
i just took the "Operations with Radical Expressions practice" for WA connexus, these answers are 100 percent correct
i need to know how to make the equations
Which of the following functions best represents the graph?
A. f(x) = x3 + x2 − 4x − 4
B. f(x) = x3 + x2 − x − 1
C. f(x) = x3 + 3x2 − 4x − 12
D. f(x) = x3 + 2x2 − 2x − 1
Answer:
B. f(x)=x³+x²-x-1
Step-by-step explanation:
The value of the graph f(x) shows that at x=1 and x=-1 must yield f(x)=0
which is true in case B.
A. f(1)=1+1-4-4= -6≠0
C. f(1)= 1+3-4-12=-12≠0
D. f(-1)= -1+2+2-1= 2≠0
Hence, option B is correct
i.e. f(x)= x³+x²-x-1
What is the sum of the first eight terms of the series?
(−600)+(−300)+(−150)+(−75)+(−37.5)+...
Round the answer to two decimal places.
−1200.50
−1195.31
−1190.63
−1181.25
Tamara says that raising the number i to any integer power results in either -1 or 1 as the result, since i^2 = -1. Do you agreed or disagree with Tamera? Explain
Tamara's claim that raising the complex number i to any integer power results in either -1 or 1 is incorrect. The powers of i follow a cyclic pattern which includes i, -1, -i, and 1.
Explanation:I must disagree with Tamara's statement that raising the complex number i to any integer power results in either -1 or 1. The powers of i actually follow a recurring pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then the pattern repeats.
For i to the power of 1, the result is just i itself.For i to the power of 2 (i^2), the result is indeed -1.For i to the power of 3 (i^3), the result is -i.For i to the power of 4 (i^4), the result is back to positive 1.So, while -1 and 1 are indeed in the sequence of results, they're not the only possibilities. Specifically, -i and i are also possible results of raising i to an integer power.
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What is the sum of 2 numbers is 100 and their difference is 6?
Bc¯¯¯¯¯ is parallel to de¯¯¯¯¯. what is ab? enter your answer in the box.
The probability that a bakery has demand for 2 3 4 or 5 birthday cakes on any given day are 0.32, 0.24, 0.25 and 0.19 respectively. construct a probability distribution for this data
Which ordered pair (a, b) is a solution to the given system?
Two cities are 124 miles apart from each other. The cities are 4cm on a map, what is the Scale factor?
What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be defined if you multiplied it by 2? Would it be defined if you subtracted some real number from it? Would it be defined if you squared it? Would it be defined if you cubed it?
Final answer:
In the complex number system, types of numbers that are undefined under a radical sign in the real number system, such as negative real numbers, become defined. For example, the square root of -1 is i, an imaginary unit. This allows operations like multiplication, subtraction, squaring, and cubing on complex numbers to be defined, illustrating the comprehensive nature of the complex number system.
Explanation:
The types of numbers that are undefined under a radical sign (specifically the square root) are negative real numbers in the context of the real number system. However, when we introduce the concept of complex numbers, every number, including negative ones, can have a defined square root. For example, the square root of -1 is defined as i, which is an imaginary unit.
When you handle the expression √-1 (which is i) in various operations:
If multiplied by 2, the result is still defined as 2i, which is a complex number.If a real number is subtracted from it, such as √-1 - 3, this is also defined and results in i - 3, another complex number.If squared (√-1)^2, it simplifies to -1, which is a defined real number.If cubed (√-1)^3, it results in -i, still defined within the complex number system.This illustrates that with the incorporation of complex numbers, operations on what would be undefined values in the real number system become fully defined. Additionally, the complex number system ensures that every polynomial equation has a root, fulfilling the Fundamental Theorem of Algebra. Complex numbers are a critical development in mathematics, allowing for the full spectrum of polynomials to be solvable and expanding our capability to model and solve a wide array of problems.
Quick question!
Which investment vehicles historically provide the lowest annual rates of return?
A)Government bonds and U.S. Treasury bills
B)Large company stocks and government bonds
C)Small company stocks and large company stocks
D) U.S. Treasury bills and small company stocks
Use the quadratic formula to solve 9x2 + 6x – 17 = 0.
Answer:
The person that answered “C” is completely wrong. The answer is D. Mark me brainliest after you get the answer right :)
Step-by-step explanation:
What is the measure of AC ? (First Picture)
Enter your answer in the box.
What is the measure of BC ? (Second Picture)
Enter your answer in the box.
Answer:
Part 1) [tex]arc\ AC=33\°[/tex]
Part 2) [tex]arc\ BC=130\°[/tex]
Step-by-step explanation:
Part 1) What is the measure of AC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<ABC=\frac{1}{2}(arc\ AC)[/tex]
substitute the values and solve for x
[tex]2.5x+4=\frac{1}{2}(7x-2)[/tex]
[tex]5x+8=(7x-2)[/tex]
[tex]7x-5x=8+2[/tex]
[tex]2x=10[/tex]
[tex]x=5\°[/tex]
Find the measure of arc AC
[tex]arc\ AC=7x-2=7(5)-2=33\°[/tex]
Part 2) What is the measure of BC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<BDC=\frac{1}{2}(arc\ BC)[/tex]
substitute the values
[tex]65\°=\frac{1}{2}(arc\ BC)[/tex]
[tex]2*65\°=(arc\ BC)[/tex]
[tex]arc\ BC=130\°[/tex]
7 cakes cost £5.60 , what would be the cost of:
10 cakes
5 cakes
12 cakes
Given the whole number 3,257,098, in what place value is the 2? Ten thousands Millions Thousands Hundred thousands
Final answer:
In the number 3,257,098, the digit 2 is in the hundred thousands place, which is the sixth position from the right or the second position from the left.
Explanation:
In the number 3,257,098, the digit 2 is in the hundred thousands place. When examining place values, we count the positions of the digits from right to left, starting with the ones position immediately to the left of the decimal point (imaginary for whole numbers). The digit to the immediate left is in the tens place, followed by hundreds, thousands, ten thousands, and so on. In this case:
9 is in the ones place,8 is in the tens place,0 is in the hundreds place,7 is in the thousands place,5 is in the ten thousands place,2 is in the hundred thousands place,3 is in the millions place.If p is a true statement and q is false then p V q is true
Answer:
Step-by-step explanation:
True
A principal of $400 is invested in an account at 6% per year compounded annually. What is the total amount of money in the account after 5 years? A. $526.00 B. $531.37 C. $535.29 D. $520.00
The total amount of money in the account after 5 years is $535.29.
To calculate the total amount of money in the account after 5 years, we can use the compound interest formula: [tex]A = P{(1 + r/n)}^{(nt)[/tex], where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.
Given that the principal is $400, the annual interest rate is 6%, and the compounding is done annually, we have:
A = 400(1 + 0.06/1)^(1*5) = 400(1.06)^5 = 400 * 1.338225 = $535.29
Therefore, the total amount of money in the account after 5 years is $535.29.
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A 45 degree sector in a circle has an area of 13.75pi cm^2, what is the area of the circle? Enter your answer as a decimal.
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game? answer= $2 Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? answer= $2 What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point. Let X = the points you have after one spin. Fill out the missing values in the table. Xi P(xi) If you take one spin, what is your expected value? What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 What is the expected value for each choice? Should he pass the ball or take the shot himself? Explain. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?
Answer:
To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.
HELP!!!!! 8 POINTS!!!!!! Rachel decided to have bouncy balls as a party favor. She determines that her ratio of bouncy balls to guests is 9:3. Explain how to find the number of balls needed for 30 guests.
A recipe calls for 1/4 cup of flour.Carter only a measurement cup that holds 1/8 cup. How can carter measure the flour he needs for his recipe
Answer:
Carter can measure the flour he needs for his recipe by filling his measurement cup twice.
Step-by-step explanation:
Since Carter has a smaller cup, he would have to fill his cup a number of times until the sum of the number of cups he has fill repeatedly adds up to the recipe requirement.
The number of times Carter would have to measure his cup with flour to get the recipe call may be computed by dividing the recipe call amount with the size of Carter's measurement cup
= 1/4 ÷ 1/8
= 1/4 × 8/1
= 2
a(1)= -2
a(n)=a(n-1)-5
whats the 4th term in the sequence?
Answer:
The fourth term in the sequence is -17
Step-by-step explanation:
To find the 4th term of the sequence, we will simply follow the steps below;
a(1) = -2
a(n) = a(n-1)-5
We will find the value of the sequence when n = 1, n= 2 n =3 n=4
The first one has been done for us, so we have the first term to be a(1) = -2
The next thing to do, is to find the second term, ie. when n=2
a(n) =a(n-1)-5
a(2) =a(2-1)-5
=a(1) - 5
but a(1) = -2
a(2) =a(1) - 5
=-2-5
=-7
a(2) = -7
next is to find the third term, ie. when n=3
a(n) =a(n-1)-5
a(3) =a(3-1)-5
=a(2) - 5
but a(2) = -7
a(3) =a(2) - 5
=-7-5
=-12
a(3) = -12
next is to find the fourth term, ie. when n=4
a(n) =a(n-1)-5
a(4) =a(4-1)-5
=a(3) - 5
but a(3) = -12
a(4) =a(3) - 5
=-12-5
=-17
a(4) = -17
Therefore, the fourth term in the sequence is -17
can someone help me find the y-intercept and explain how you got that answer?
There are many penguins on a hill. 53 penguins waddled off the hill. Now 21 penguins remain on the hill. How many penguins were on the hill to start?
74 penguins
72 penguins
32 penguins
34 penguins
Answer:
74 Penguins
Step-by-step explanation:
1. 53+21
2. =74
Penguins are my favorite animal. What's yours?
Answer:
There were originally 74 penguins on the hill.
Step 1: Determine the Values we NeedFor starters, we need to define the variable that we will use to solve this equation. I will use x.
We know that our original amount is x, and we need to find it to solve the problem.
The Factsx stands for the original amount of penguins on the hill.53 penguins waddle off of the hill.21 penguins remain after the 53 penguins waddle off of the hill.To find x, we will set up an algebraic equation that allows us to find the value easily.
Step 2: Set up the Algebraic EquationNow, we will need to set up the equation with the facts we have determined.
We know that we need to set our equation equal to x to find our total. To do this, we know that our initial amount is x, and we remove 53 penguins from this total since they waddle off of the hill.
Since we "remove" from the total, this means that we will subtract 53 penguins from x, our initial amount. We are left with the 21 penguins that do not leave the hill, or otherwise, remain on the hill.
[tex]x - 53 = 21[/tex]
Step 3: Rearrange and Solve the EquationFinally, we are ready to solve the equation to find our initial amount of penguins.
To solve this equation, we must combine our like terms.
Because our numbers (constants) do not have any letters (variables) attached to them, we will combine them.
The main goal of an algebraic equation is to get the variable (in this case, x) by itself. To do this, we can perform reverse operations to get the constants together.
You'll notice that 21 does not have a sign associated with it, but 53 does, and it is a subtraction symbol.
The reverse operation of subtraction is addition. Therefore, to combine the two values, we can add both 53 and 21 to each other to find x.
[tex]x = 53 + 21[/tex]
Using any method of choice, add the two values together.
[tex]x = 53 + 21 = 74[/tex]
Then, to simplify, remove the operation and only leave the sum of the operation.
[tex]\boxed{x = 74}[/tex]
Therefore, the initial number of penguins—the number of penguins on the hill to start—is equivalent to 74 penguins.
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What is the length of JK, to the nearest tenth of a millimeter?
The length of JK to the nearest tenth is; 4.5 mm
What is the Length of a side of the triangle?From the given triangle, we see the following parameters;
JL = 3 mm
KL = 5 mm
angle JLK = 62 °
Use the Law of Cosines, we can find the length of JK as;
|JK| = √(3² + 5² − 2(3 * 5) cos62°)
|JK| = √(34 - 14.084)
|JK| = 19.916
|JK| = √19.916
|JK| = 4.463
Approximating to the nearest tenth; JK = 4.5 mm
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