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3 years ago

If f(x) = 3 x2 + 2 and g(x) = x2 - 9, find (f - g)(x).

Mathematics

1 answer:

Tom [10]3 years ago

6 0

Answer:

2x^2 +11

Step-by-step explanation:

(x) = 3 x^2 + 2

g(x) = x^2 - 9

(f - g)(x) =3 x^2 + 2 - (x^2 - 9)

Distribute the minus sign

= 3x^2 +2 - x^2 +9

Combine like terms

= 2x^2 +11

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Solve for q. a=qb+r What is q equal to? q=a−r−b q=a−r/b q=a/b −r q=a/rb

Mademuasel [1]

The given equation is $a=qb+r$

We need to solve the equation for q.

Value of q:

The value of q can be determined by solving the equation $a=qb+r$ for q.

Thus, subtracting both sides of the equation by r, we get;

$a-r=qb$

Now, dividing both sides of the equation by b, we have;

$\frac{a-r}{b}=\frac{qb}{b}$

Simplifying the terms, we get;

$\frac{a-r}{b}=q$

Therefore, the value of q is $q=\frac{a-r}{b}$

Hence, Option B is the correct answer.

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3 years ago

Question 3 Find 250% of 4.4

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Step-by-step explanation:

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3 years ago

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3 years ago

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Hey could someone please help me with this really hard assignment is taking me forever. Thank you marking brainliest!

rewona [7]

Answer:

Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

Step-by-step explanation:

Exercise 1:

Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

$y = \sqrt{l^{2}-x^{2}}$ (1)

Where:

$l$ - Hypotenuse, in inches.

$x$ - Known leg, in inches.

$y$ - Unknown leg, in inches.

If we know that $l = 11\,in$ and $x = 10\,in$ , then the length of the unknown leg is:

$y = \sqrt{21}$

Since 4 is the least whole number closest to $\sqrt{21}$ , then we conclude that the length of the unknown leg is 4 inches.

Exercise 3:

The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:

$x + y > l > x-y$ (2)

Where:

$x$ - Greater side, in inches.

$y$ - Lesser side, in inches.

$l$ - Missing side, in inches.

If we know that $x = 8\,in$ and $y = 6\,in$ , then we have the following range of missing sides:

$14\,in > l > 2\,in$

The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4:

Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:

(i) $x = 4\,in, y = 2\,in$

$6\,in>l>2\,in$

Possible choices: 5 inches.

(ii) $x = 5\,in, y = 2\,in$

$7\,in > l > 3\,in$

Possible choices: 4 inches, 6 inches.

(iii) $x = 6\,in, y = 2\,in$

$8\,in > l > 4\,in$

Possible choices: 5 inches, 6 inches.

(iv) $x = 10\,in, y = 2\,in$

$12\,in > l > 8\,in$

Possible choices: None.

(v) $x = 5\,in, y = 4\,in$

$9\,in > l > 1\,in$

Possible choices: 2 inches, 6 inches.

(vi) $x = 6\,in, y = 4\,in$

$10\,in > l > 2\,in$

Possible choices: 5 inches.

(vii) $x = 10\,in, y = 4\,in$

$14\,in > l > 6\,in$

Possible choices: None.

(viii) $x = 6\,in, y = 5\,in$

$11\,in > l > 1\,in$

Possible choices: 2 inches, 4 inches, 10 inches.

(ix) $x = 10\,in, y = 5\,in$

$15\,in > l > 5\,in$

Possible choices: 6 inches.

(x) $x = 10\,in, y = 6\,in$

$16\,in > l > 4\,in$

Possible choices: 5 inches.

Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

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3 years ago

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