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2 years ago

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

Mathematics

1 answer:

Tom [10]2 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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The total area of the figure to the right is 299 cm². Use this fact to write an equation involving x. Then solve the

Sliva [168]

Answer:

i. $x^{2}$ + 26x + 144 - 299 = 0

ii. x = 5

Step-by-step explanation:

The area of the figure = 299 cm²

The figure has a shape of a rectangle, so that;

Area of rectangle = length x width

length of the figure = 18 + x

width of the figure = 8 + x

Area of the figure = (18 + x) x (8 + x)

299 = (18 + x) x (8 + x)

299 = $x^{2}$ + 26x + 144

$x^{2}$ + 26x + 144 - 299 = 0

$x^{2}$ + 26x - 155 = 0

applying the trigonometric formula;

x = (-b ± $\sqrt{b^{2} - 4ac}$ ) ÷ 2a

= (-26 ± $\sqrt{(26)^{2} - 4(1*-155)}$ ) ÷ 2

= (-26 ± $\sqrt{676 +620}$ ) ÷ 2

= (-26 ± $\sqrt{1296}$ ) ÷ 2

= (-26 ± 36) ÷ 2

x = (-26 + 36) ÷ 2 OR x = (-26 -36) ÷ 2

= 10 ÷ 2 OR -62 ÷ 2

= 5 OR -31

Thus, x = 5

5 0

3 years ago

Simplify. 4−16÷4+42 −16 13 15 16 PLEASE HELP

jok3333 [9.3K]

PEMDAS. 16/4 = 4. 4+42 = 46. 46-4 = 42. Answer is 42!

3 0

3 years ago

Read 2 more answers

Identify the zeros of the function f(x) = 2x^2 − 4x + 5 using the Quadratic Formula

Nostrana [21]

For this case we have that by definition, the roots, or also called zeros, of the quadratic function are those values of x for which the expression is 0.

Then, we must find the roots of:

$2x ^ 2-4x + 5 = 0$

Where:

$a = 2\\b = -4\\c = 5$

We have to: $x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Substituting we have:

$x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (5)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-40}} {4}\\x = \frac {4 \pm \sqrt {-24}} {4}$

By definition we have to:

$i ^ 2 = -1$

So:

$x = \frac {4 \pm \sqrt {24i ^ 2}} {4}\\x = \frac {4 \pm i \sqrt {24}} {4}\\x = \frac {4 \pm i \sqrt {2 ^ 2 * 6}} {4}\\x = \frac {4 \pm 2i \sqrt {6}} {4}\\x = \frac {2 \pm i \sqrt {6}} {2}$

Thus, we have two roots:

$x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}$

Answer:

$x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}$

3 0

3 years ago

Two objects are moving along separate linear paths where each path is described by postion, d, and time, t. The variable d is me

fiasKO [112]

Linear equation: d = m t + b
If the graph of the position of the second object is parallel to d = 2.5 t +2.2, than m = 2.5
t = 0, d = 1
1 = 2.5 · 0 + b
b = 1
Answer: A ) d = 2.5 t + 1

3 0

3 years ago

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A section of ground measures 1.5 cubic meters and contains 0.78 gram of gold. What is the amount of gold per cubic meter? Enter

Marta_Voda [28]

To find the gold per cubic meter you have to divide the amount of gold by the size of the area. So you would do .78/1.5 which would give you .52g/m3

3 0

3 years ago