MATHEMATICS HIGH SCHOOL

While scuba diving, Alex counted the number of sea turtles and jellyfish he saw. After a few minutes, he counted 4 seaturtles and 12 jellyfish. This ratio remained consistent during the remainder of his dive.
Part A
Using the given ratio, complete the table.
Number of
Number of
Sea Turtles
Jellyfish
1
4
24
14
60

Answers

Answer 1

Answer:

Answer:

The values which are added to the table are;

Sea turtles = 1, Jellyfish = 3

Sea turtles = 4, Jellyfish = 12

Jellyfish = 24, Sea turtles= 8

Sea turtles = 14, Jellyfish = 42

Jellyfish = 60, Sea turtles= 20

Step-by-step explanation:

The given parameters are;

The ratio of sea turtles to jellyfish = 4:12

Therefore, the ratio of sea turtles to jellyfish = 1:3

Which gives;

When the number of sea turtles = 1, the jellyfish = 1 × 3 = 3 Jellyfishes

When the number of sea turtles = 4, the jellyfish = 4 × 3 = 12 Jellyfishes

When the number of sea jellyfishes = 24, the number of sea turtles = 24/3 = 8 sea turtles

When the number of sea turtles = 14, the jellyfish = 14 × 3 = 42 Jellyfishes

When the number of sea jellyfishes = 60, the number of sea turtles = 60/3 = 20 sea turtles

The values given in the table can be presented as follows;

Number of Sea Turtles ${}$ Number of Jellyfish

1 ${}$ 3

4 ${}$ 12

8 ${}$ 24

14 ${}$ 42

20 ${}$ 60

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Select the correct answer.What is the factored form of 1,458x3 − 2?

A.
2(9x − 1)(81x2 + 9x + 1)
B.
2(9x + 1)(81x2 − 9x + 1)
C.
(9x − 2)(81x2 + 18x + 4)
D.
(9x + 2)(81x2 − 18x + 4)

Answers

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

What is the factored form of 1,458x³ − 2?

A. 2(9x − 1)(81x² + 9x + 1)

B. 2(9x + 1)(81x² − 9x + 1)

C. (9x − 2)(81x² + 18x + 4)

D. (9x + 2)(81x² − 18x + 4)

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\sf \: 1458 x ^ { 3 } - 2$

Factor out 2 (common factor).

$\sf \: 2\left(729x^(3)-1\right)$

Consider $729x^(3)-1$ . Rewrite $729x^(3)-1$ as $\left(9x\right)^(3)-1^(3)$ . The difference of cubes can be factored using the rule: $a^(3)-b^(3)=\left(a-b\right)\left(a^(2)+ab+b^(2)\right)$ .

$\sf\left(9x-1\right)\left(81x^(2)+9x+1\right)$

Rewrite the complete factored expression. Polynomial 81x²+9x+1 is not factored as it does not have any rational roots.

$\boxed{ \boxed{ \bf A) \: \: 2\left(9x-1\right)\left(81x^(2)+9x+1\right) }}$

factor each expression: 4n^2-8n+3, 4p^2+7p+3, 6r^2-23r+20, 5z^2+19z-4, 2k^2-13k-24, 6t^2+7t-5, 3x^2+23x-36, 4w^2-5w-6, 4d^2-4d-35

Answers

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these are the answers in order, hope I helped :) please choose my answer as the best xx

1. A rectangular picture 6cm by 8cm is enclosed by a frame 1/2cm wide. Calculate the area of the frame. A.15sq cm B. 20 sq cm C. 13 sq cm D. 16 sq cm E. 17

Answers

Answer:

The area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Step-by-step explanation:

Length of rectangular picture frame = 6 cm

Width of rectangular picture frame = 8 cm

Area of rectangular picture frame = 6×8 cm² = 48 cm²

Length, excluding 1/2 cm wide frame of rectangular picture = (6–1/2-1/2) = 5 cm

Width, excluding 1/2 cm wide frame of rectangular picture = (8–1/2-1/2) = 7 cm

Area, excluding 1/2 cm wide frame of rectangular picture = 5×7 cm² = 35 cm²

Area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Therefore, the area of 1/2 cm wide frame = 48 - 35 = 13 cm²

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D.p = 28

Answers

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Answers

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The product of a + 3 and –2a2 + 15a + 6 is –2a3 + xa2 + 51a + 18. What is the value of x?

Answers

Value of x is 9 As when we multiply a + 3 by -2a2 + 15a + 6 We get (a + 3) (-2a2 + 15a + 6) -2a3 + 15a2 + 6a - 6a2 + 45a + 18 -2a3 + 9a2 + 51a + 18 If we compare the coefficients of a2, we get x = 9

Answer:

Step-by-step explanation:

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