Triangle QRS is a right triangle with the right angle at vertex R. The sum of m∠Q and m∠S must be equal to 45°. greater than 45°

Response:

A quadratic equation has solutions of 6 and -2.

Thus, if the variable is denoted by X, the factors of the polynomial function will be (X - 6) and (X + 2).

Thus, the equation can be represented as

(Response)

Answer:

i) A total of 40320 different arrangements

ii) For the initial 3 spots, there are 336 different combinations.

Step-by-step explanation:

Given: The total finalists = 8

The count of boys = 3

The count of girls = 5

To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!

The number of possible arrangements equals 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.

nPr =

Here n = 8 and r = 3

Substituting n = 8 and r = 3 into the formula, we arrive at

8P3 =

=

= 6.7.8

= 336

Thus, there are 336 different arrangements for the first 3 spots.

Answer:

86/105

Step-by-step explanation:

May possesses 4/15 meters of lace

Lovie has lace that exceeds May's by 2/7 meters

4/15 + 2/7

= 58/105

Consequently, the total amount of lace they have is calculated as

= 4/15 + 58/105

= 86/105

Thus, together they own 86/105 meters of lace

Response:

x² + -6x = -13

Detailed breakdown:

8x² - 48x = -104

Rearranging gives us x² - 6x = -13