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3 years ago

The area of triangle PQR is 231 cm2 , and PQ = 21 cm. Find the altitude SR. Help me solve this

Mathematics

1 answer:

Shtirlitz [24]3 years ago

3 0

Answer:

SR = 22 cm

Step-by-step explanation:

area = bh/2

(21 cm)(h)/2 = 231 cm^2

21h = 462 cm

h = 22 cm

SR = 22 cm

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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

Peter's Party Zone sells cups in packages of 6 and plates in packages of 8 . Shaniya is hosting a birthday party for her little

kirill [66]

Answer:

Step-by-step explanation:

find a common factor

6*8=48

8*6=48

8 0

3 years ago

Which ordered pair is a solution to the system of linear equations Negative 4 x + y = 8 and x minus 5 y = 17?

Zinaida [17]

Answer:

(-3, -4).

Step-by-step explanation:

-4x + y = 8

x - 5y = 17 Multiply this by 4:

4x - 20y = 68 Add this to the first equation:

-19y = 76

y = 76/-19

y = -4.

Plug this into the second equation:

x - 5(-4) = 17

x = 17 - 20

x = -3.

CHECK this result in equation 1:

-4(-3) + -4 = 8

12 - 4 = 8

8 = 8 <------ OK.

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3 years ago

As an estimation we are told 5 miles is 8 km. Convert 27.4 miles to km.

kicyunya [14]

Answer:

43.8 km to the nearest tenth.

Step-by-step explanation:

5 miles is 8 km

so 1 mile = 8/5 km

and 27.4 miles = 27.4 * 8/5

= 43.84 km

7 0

3 years ago

Read 2 more answers

From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21

ankoles [38]

Answer:

Step-by-step explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:

We are going to take 4 of the 5 even numbers in the box so we have

$5C4=5$

Case 2: When all 4 numbers are odd:

We are going to take 4 of the 5 odd numbers in the box, so we have

$5C4=5$

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

$5C2 * 5C2$

Remember that we obtain the probability from

$\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}$

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:

We are taking 4 of the 10 cards:

$10C_4=210$

Hence we have that the probability that their sum is even

$\frac{5+5+100}{210}=\frac{11}{21}$

8 0

3 years ago