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3 years ago

6

Estimate the perimeter of the figure to the nearest whole number. perimeter: about_units

1 answer:

AlexFokin [52]3 years ago

3 0

Answer:

The shape is about 16 units in diameter.

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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 <em>sum and difference of cubes</em>, 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 <u><em>perfect cube numbers</em></u> (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 <em>sum and difference of cubes </em>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 <em>sum of cubes.</em>

<em>Sum of cubes</em>

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

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

2.) Solving the sum of cubes.

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

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

.

8 0

3 years ago

A charity fundraiser charges 102 dollars per plate. If there are 85 guests at the fundraiser , how much money did they earn

Naddik [55]

Answer:

8,670

Step-by-step explanation:

because if 102 dollars per plate you take 102x85 = 8,670

5 0

3 years ago

Read 2 more answers

An individual is at a restaurant with two other people and they are trying to determine the tip for their check total which came

zlopas [31]

Answer:

c. The tip is $10.00

Step-by-step explanation:

The total bill in the restaurant is = $ 68.42

They wanted to pay a gratuity of 15%

Therefore the correct tip can be calculated as :

= 68.42 of 15%

= $68.42 \times \frac{15}{100}$

= 68.42 x 0.15

= 10.263

≈ 10 (approx.)

Thus the individual along with the other two wishes to pay a tip $10.00 for the total value.

7 0

3 years ago

The two spheres above have the same center one has a radius of 2 cm and the other one has a radius of 3 cm approximately how muc

Paladinen [302]

Answer:

79.6 cm^3

Step-by-step explanation:

The formula for the volume of a sphere is V = 4/3 πr³.

sphere A radius 2 cm so r[A] = 2 cm

sphere B radius 3 cm so r[B] = 3 cm

distance between the surfaces of the 2 spheres is 1 cm

To find volume of each sphere and the difference in volume:

pi r^2 * r - (1/3) pi r^2 * r = (2/3) pi r^3

8 0

3 years ago

Write the inequality represented by each graph..

igomit [66]

Answer:

Step-by-step explanation:

HERE ARE THE ANSWERS

6 0

3 years ago