Which sets of three numbers could represent the lengths of the sides of a right triangle? 12, 15, 21

Y + 2 = -2x +6 3x + 9y = 6

OleMash [197]

Answer:

hey u have any pictures that can explain it

8 0

2 years ago

K = [ 14 -13 0 3 8 -1 -10 -2 5 ] find the determinant of K

spin [16.1K]

I suppose K is the matrix

$K = \begin{bmatrix}14 & -13 & 0 \\ 3 & 8 & -1 \\ -10 & -2 & 5\end{bmatrix}$

To compute det(K), you can use a simple cofactor expansion along the first row:

$\det(K) = 14\times\det\begin{bmatrix}8 & -1 \\-2 & 5\end{bmatrix} - (-13)\times\det\begin{bmatrix}3 & -1 \\ -10 & 5\end{bmatrix} + 0\times\det\begin{bmatrix}3 & 8 \\ -10 & -2\end{bmatrix} \\\\ \det(K) = 14\times(8\times5-(-1)\times(-2)) + 13\times(3\times5-(-1)\times(-10)) + 0 \\\\ \det(K) = 14\times38 + 13\times5 = \boxed{597}$

8 0

2 years ago

How do I find the answer to number 8?

Sonbull [250]

Multiply both sides of the equation by (x+1), on the right hand side the denominator then goes away and on the left hand side you get (x+1)(x+1), foil that out then just solve for x

8 0

2 years ago

Two cards are drawn in succession from a standard 52-card deck.1. What is the probability that the first card is red and the sec

rodikova [14]

Answer:

52 cards:

26 red and 26 black

P(R) = probability of picking a red card

P(B) = probability of picking a black card

P(R) = P(B) = ¹/₂

If with replacement:

P(R∩B) = (¹/₂)(¹/₂) = ¹/₄

If without replacement:

P(R∩B) = (¹/₂)(²⁶/₅₁) = ¹³/₅₁

8 Balls:

3 red and 5 white

P(R) = probability of picking a red ball

P(W) = probability of picking a white ball

P(R) = ³/₈

P(W) = ⁵/₈

If with replacement:

P(R∩W) ∪ P(W∩R) = (³/₈)(⁵/₈) + (⁵/₈)(³/₈)

= ¹⁵/₆₄ + ¹⁵/₆₄

= ³⁰/₆₄

= ¹⁵/₃₂

If without replacement:

P(R∩W) ∪ P(W∩R) = (³/₈)(⁵/₇) + (⁵/₈)(³/₇)

= ¹⁵/₄₂ + ¹⁵/₄₂

= ³⁰/₄₂

= ⁵/₇

8 0

2 years ago

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.).