Final answer:
While it's not necessary to use the binomial theorem to multiply binomials, it can greatly simplify the process. This theorem is handy for higher powers and in cases where technology tools are not available.
Explanation:
The formulas for special products, like the binomial theorem, are not always necessary for multiplying binomials, but they can simplify the process significantly, especially for higher powers. When multiplying binomials without these formulas, one would have to apply the distributive property multiple times, which can be tedious and prone to error. The binomial theorem provides a direct way to expand binomials raised to a power in a series expansion: (a + b)n = an + n*an-1*b + ... + bn. Utilizing this formula can speed up calculations and help avoid mistakes.
In understanding series expansions, working with exponents, and creating formulas based on logical sense and unit consistency, students can sometimes simplify problems without needing to memorize formulas. However, for complex problems or when working with large exponents, knowing and applying the binomial theorem can be much more efficient.
Moreover, technologies like calculators and computer software often have functions that apply these theorems or carry out the multiplications of binomials, which can make manual calculations unnecessary, provided you have access to these tools. But understanding the underlying principles is important for a strong mathematical foundation.
The original is rice of a computer was reduced by $ 250. The new discounted price is $1499
If p= the computers original price in dollars, which mathematical sentence expresses the information above?
A. P-250<1499
B.250-p<1499
C.250-p=1499
D.p-250=1499
Answer:
D
Step-by-step explanation:
D, because he first reduces the price by 250 yuan from the original price, so it is P-250, and then obtains a new discounted price, which indicates that the answer is P-250=1499
What is the area of this figure? Select from the drop-down menu to correctly complete the statement. The area of the figure is cm². A square with sides measuring 6 cm. A trapezoid attached to the side of the square has a top length of 7 cm, a long leg side of 10 cm, and the bottom length, when combined with the length of the square, measures out at 21 cm.
Answer: 102
A=1/2 (b1 + b2)h
Michael bought a $25.00 gift for a friend. After he bought the gift, Michael had $176.89. Write and solve an equation to calculate how much money Michael had before he bought the gift.
Michael had 201.89 before he bought the gift.
What is the equation ?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given
Michael bought a $25.00 gift for a friend
Michael have $176.89 after buying the gift .
Therefore, we can write the equation as,
Money with Michael before buying gift card = Money with Michael before after gift card
Money with Michael before buying gift card = 25 + $176.89
Money with Michael before buying gift card = $201.89
Therefore, Michael had $201.89 before he bought the gift.
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The east room of the White House is 79 feet long by 36 feet wide what is the area and what is the perimeter of the east room
Based on the dimensions of the White House east room, the perimeter must be 230 feet and the area is 2,844 feet.
The measurements of the east room give the impression that this is a rectangular shaped room.
The area of a rectangle is:
= Length x Width
= 79 x 36
= 2,844 feet²
The perimeter is:
= (2 x length) + (2 x Width)
= (2 x 79) + (2 x 36)
= 230 feet
In conclusion, the perimeter of the east room is 230 feet and its area is 2,844 feet².
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Starting from her hotel,Angie walked 2/3 mile along the beach in one direction.She turned around and walked 1/2 mile toward her hotel.How much farther does she need to walk to get to the hotel?
What is the area of the shape shown?
Write two equivalent fractions for 2/5 and 1/3 and 3/4
The relation {(-1, 4), (2, 7), (3, 7)} is a function. True False
Answer:
True
Step-by-step explanation:
I did the quiz and got 100%
jorge has a recipe that calls for 2 1/3 cups of flour he plans to make 1 1/2 times the recipe will the amount of flour jorge needs be equal to greater than or less than the amount of flour his recipe calls for
Alvin’s age is two times Elgas age. The sum of their ages is 18. What is Elgas age?
Last week 1200 burgers were served at the Burger Barn.
a. This week 1176 burgers were served. What is the percent of change?
b. Use the percent of change from part (a) to predict the number of burgers served next week. Round to the nearest whole number, if necessary.
The percent of change between the number of burgers served at the Burger Barn last week versus this week shows a 2% decrease. Using this information, the projected number of burgers to be served next week is approximately 1152.
Explanation:To calculate the percent of change, we subtract the final number (in this case, the number of burgers served this week) from the initial number (the number of burgers served last week), divide the result by the initial number, and then multiply by 100 to convert to percent.
Percent of Change = ((Initial number - Final number) / Initial number) * 100
So in this case, the percent of change = ((1200 - 1176) / 1200) * 100 = 2% decrease.
To predict the number of burgers served next week, we can assume the same percent of change. If there's a 2% decrease expected, then we subtract 2% of this week's total burgers from this week's total burgers.
Projected number of burgers served next week = This week's total - (2% of This week's total) = 1176 - (2/100 * 1176) = 1152.32 → If we round to the nearest whole number, we get 1152.
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Bailey’s Cakes and Pastries baked a three-tiered cake for a wedding. The bottom tier is a rectangular prism that is 18 centimeters long, 12 centimeters wide, and 8 centimeters tall. The middle tier is a rectangular prism that is 12 centimeters long, 8 centimeters wide, and 6 centimeters tall. The top tier is a cube with edges of 4 centimeters each. What is the volume of each tier and of the entire cake?
Answer:
the top tier is 64 cubic centimeters
the middle tier is 576 cubic centimeters
the bottom tier is 1728 cubic centimeters
the entire cake is 2368 cubic centimeters
Step-by-step explanation:
A circle has a diameter of 20 inches. Find the exact area and find the approximate area using π 3.14
Express this equation in logarithmic form.
23 = 8
24 squared + 10 squared = x squared
express 68 as a product of prime numbers by completing the factor tree
Can i get some help please.
Which expressions are equivalent to( 5^3 x 5^2 )^4
A:25^20
B:(25^5)^4
C: none of the above
Thanks!!
Your friend finds 192 divided by 6 by writing (6 x 30) + (6 x 2). She says the answer is 12. Is your friend correct? EXPLAIN!
No, your friend is not correct. The answer to 192 divided by 6 is 32, not 12.
Explanation:No, your friend is not correct. When dividing 192 by 6, we need to find how many times 6 can go into 192. One way to do this is by subtracting multiples of 6 from 192 until we reach 0. This method is called long division. Let's work through it step by step:
Write 192, the dividend, inside the division symbol.Write 6, the divisor, outside the division symbol.Divide 6 into the first digit of 192, which is 1. The answer is 0, as 6 cannot go into 1.Bring down the next digit, which is 9.Divide 6 into 19, which gives us 3. Write the 3 above the line, in the quotient, as our first digit.Multiply 6 by 3, which gives us 18. Subtract 18 from 19, which leaves us with 1.Bring down the next digit, which is 2.Divide 6 into 12, which gives us 2. Write the 2 above the line, in the quotient, as our next digit.Multiply 6 by 2, which gives us 12. Subtract 12 from 12, which leaves us with 0.So the answer to 192 divided by 6 is 32. Your friend's method of using (6 x 30) + (6 x 2) is incorrect because it does not result in the correct quotient.
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If x = 12 cm, y = 8 cm, z = 10 cm, and w = 3 cm, what is the surface area of the geometric shape formed by this net?
A. 288 cm2
B. 144 cm2
C. 192 cm2
D. 160 cm2
Here's the shape: https://media.studyisland.com/pics/127804pic7.png
What is the area of the frame in square units around the picture?
PLEASE HELP ME! On a coordinate grid, the distance between point F and point G is 13 units. Point F is located at (-1, 3). Point G is located at (x, -9). Which value could be the value of x?
A 4
B 8
C 11
D 24
Find the length of BC.
What is 3.4 mph (miles per hour) converted to feet per seconds?
at the park, 4/7 of the children are boys. if there are 8 boys at the park, how many are girls?
A pool pump fills 1/6 of the pool in 1/3 hour. How much of the pool is filled in one hour
Find the ordered triple (x,y,z) that satisfies the following system:
x-2y&=0
y-2z&=0
x+z&=5.
can their be smaller integer than 0.5
Solve for x.
−1/4x+5=3/4
Enter your answer in the box.
Answer:
16
Step-by-step explanation:
this is correct
Heather has $500 in her savings account. She withdraws $20 per week for gas. Write an equation Heather can use to see how many weeks it will take her to have a balance of $220.
Select the equation that has c = 56.08 as a solution. A c × 12 = 672.96 B 2c = 112.14 C c + 97 = 154.08 D 49 + c = 105.80