Reduce 36 42 to its lowest form

What is the factorization of 729^15+1000?

igomit [66]

Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

$1000=10^{3}$ then $\sqrt[3]{10^{3}} =10$

So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a sum of cubes.

Sum of cubes

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

with $a= 9x^{5}$ y $b=10$

2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)$

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8 0

3 years ago

At the theater, tickets for adults cost $4.75

shutvik [7]

X+y= 26 and 4.75x + 2.25y= 83.50

y=26-x( substitute this into second equation for y and solve for x)

4.75x + 2.25(26-x)= 83.50

4.75x + 58.5-2.25x= 83.50

x= 10

Now solve for y by substituting your answer for x

10+ y= 26

y=16

Therefore, 16 tickets were purchased for kids and 10 for adults.

7 0

3 years ago

The figure below shows a shaded region and a non-shaded region. Angles in the figure that appear to be right angles are right an

scoundrel [369]

Answer:Area of part 1:

A1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

Area of part 2:

A2=length*width=(8+2)*1=10 ft2

Area of part 3:

A3=length*width=8*2=16 ft2

Total shaded area : A1+A2+A3=41 ft2

Total area of the reactangle : A=16*8=128 ft2

Total area of the nonshaded region : 128-41=87 ft2

Step-by-step explanation: Plz make brainliest

5 0

3 years ago

Each day a cashier counts the number of pennies left in the "take a penny, leave a penny" dish. Estimate the probability that th

jeka94

Answer:

B.4/11

Step-by-step explanation:

hope it helps

consider making my answer as BRAINLIST

7 0

3 years ago

The highest temperature recorded in Greensburg was 35C. Write the opposite temperature.

hichkok12 [17]

Answer: the opposite answer is 35F

Step-by-step explanation: the C goes to a F

8 0

3 years ago