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3 years ago

Determine if the following lengths make an acute, right or obtuse

Mathematics

1 answer:

Rzqust [24]3 years ago

4 0

Answer:

acute

Step-by-step explanation:

cause

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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 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.

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

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

8 0

3 years ago

Add 3/14+4/14 simply your answer

Mila [183]

Answer:

$\Large \boxed{\frac{1}{2}}$

Step-by-step explanation:

$\displaystyle \frac{3}{14} +\frac{4}{14}$

Add the fractions since the denominators are the same.

$\displaystyle \frac{3+4}{14}$

$\displaystyle \frac{7}{14}$

Simplifying the fraction.

$\displaystyle \frac{7(1)}{7(2)}$

$\displaystyle \frac{1}{2}$

5 0

3 years ago

State of the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement

Vinil7 [7]

Answer:

b. not similar

Step-by-step explanation:

The given sides* have the ratio 30:39 = 10:13 in one triangle and the ratio 20:27 = 10:13.5 in the other triangle. Since these ratios are different, the triangles cannot be similar.

____

* These are the sides bracketing the vertical angles at T. If the triangles were similar, the three sides would have to have the ratios 10 : 13 : 13.5.

However, the geometry shown would require that the angle opposite side 13.5 in one triangle have the same measure as the angle opposite side 13 in the other triangle. That is not possible, so it is not possible for these triangles to be similar.

6 0

3 years ago

Name a pair of lines that apear to be parallel

Nitella [24]

The sides of a square or rectangle

8 0

3 years ago

Can someone help me .

insens350 [35]

Y-y1=m(x-x1)
m= slope =-3
y-y1=-3(x-x1),
y1=-7, x1=5
y--7=-3(x-5)
y+7=-3(x-5) this is C

7 0

3 years ago