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s2008m [1.1K]
3 years ago
5

For f(x)=3x+1 and g(x)=x squared - 6 find (f- g)(x)

Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0
It helps to first clarify that the notation (f - g)(x) simply means f(x) - g(x). Given that, let's look at our f(x) and our g(x) here, and use their definitions to find their difference.

f(x)=3x+1\\g(x)=x^2-6

When we're taking (f - g)(x), we simply substitute the expression 3x + 1 for f(x) and the expression x² - 6 for g(x) to obtain:

(3x+1)-(x^2-6)=3x+1-x^2+6

Or, ordering the polynomial from highest power to lowest and combining the constants:

-x^2+3x+7

Edit: By request, here's what would happen if you had something instead like:

(f\times g)(x)

In this case, you'd have to *multiply* the two function expressions together. Here's what that would look like:

(3x+1)(x^2-6)

Using the distributive property, we can distribute the expression 3x+1 to the terms x^{2} and -6:

(3x+1)x^2-(3x+1)6

Distributing again, we get:

3x(x^2)+x^2-3x(6)+6=3x^3+x^2-18x+6

And we're done.
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goldenfox [79]

Answer:

The possible combinations are (4 & 6) ,(8 &3), (2 &12), (24 &1)

Step-by-step explanation:

The area of a flower bed is 24 square feet.

Now, the factors of 24 are 2 x 2 x 2 x 3.

Hence, if the other sides were whole number dimensions, then the possible combinations will be (4 & 6) ,(8 &3), (2 &12), (24 &1)

3 0
4 years ago
In a random sample of 28​ families, the average weekly food expense was​ $95.60 with a standard deviation of​ $22.50. determine
garik1379 [7]
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3 years ago
Item 7
Mariulka [41]

Answer:

A = 74.7^\circ

B = 42.5^\circ

C = 62.8^\circ

Step-by-step explanation:

Given

A = (-1,2) \to (x_1,y_1)

B = (2,8) \to (x_2,y_2)

C = (4,1) \to (x_3,y_3)

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2

For AB

A = (-1,2) \to (x_1,y_1)

B = (2,8) \to (x_2,y_2)

d = \sqrt{(-1 - 2)^2 + (2 - 8)^2

d = \sqrt{(-3)^2 + (-6)^2

d = \sqrt{45

So:

AB = \sqrt{45

For BC

B = (2,8) \to (x_2,y_2)

C = (4,1) \to (x_3,y_3)

BC = \sqrt{(2 - 4)^2 + (8 - 1)^2

BC = \sqrt{(-2)^2 + (7)^2

BC = \sqrt{53

For AC

A = (-1,2) \to (x_1,y_1)

C = (4,1) \to (x_3,y_3)

AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2

AC = \sqrt{(-5)^2 + (1)^2

AC = \sqrt{26

So, we have:

AB = \sqrt{45

BC = \sqrt{53

AC = \sqrt{26

By representation

AB \to c

BC \to a

AC \to b

So, we have:

a = \sqrt{53

b = \sqrt{26

c = \sqrt{45

By cosine laws, the angles are calculated using:

a^2 = b^2 + c^2 -2bc \cos A

b^2 = a^2 + c^2 -2ac \cos B

c^2 = a^2 + b^2 -2ab\ cos C

a^2 = b^2 + c^2 -2bc \cos A

(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A

53 = 26 +45 - 2 * 34.21 * \cos A

53 = 26 +45 - 68.42 * \cos A

Collect like terms

53 - 26 -45 = - 68.42 * \cos A

-18 = - 68.42 * \cos A

Solve for \cos A

\cos A =\frac{-18}{-68.42}

\cos A =0.2631

Take arc cos of both sides

A =\cos^{-1}(0.2631)

A = 74.7^\circ

b^2 = a^2 + c^2 -2ac \cos B

(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B

26 = 53 +45 -97.67 * \cos B

Collect like terms

26 - 53 -45= -97.67 * \cos B

-72= -97.67 * \cos B

Solve for \cos B

\cos B = \frac{-72}{-97.67}

\cos B = 0.7372

Take arc cos of both sides

B = \cos^{-1}(0.7372)

B = 42.5^\circ

For the third angle, we use:

A + B + C = 180 --- angles in a triangle

Make C the subject

C = 180 - A -B

C = 180 - 74.7 -42.5

C = 62.8^\circ

8 0
3 years ago
Find, to the nearest integer, the number of feet in the length
OLEGan [10]

Answer:

Length of shadow on the ground = 11 ft (Approx)

Step-by-step explanation:

Given:

Height of pole = 15 ft

Angle of elevation of the sun = 53°

Find:

Length of shadow on the ground = ?

Computation:

⇒ Tan A = Height / Base

⇒ Tan A = Height of pole / Length of shadow on the ground

⇒ Tan 53° = Height of pole / Length of shadow on the ground

⇒ Tan 53° = Height of pole / Length of shadow on the ground

⇒ 1.327 = 15 / Length of shadow on the ground

⇒ Length of shadow on the ground = 15 ft / 1.327

⇒ Length of shadow on the ground = 11.3 ft

Length of shadow on the ground = 11 ft (Approx)

7 0
4 years ago
20 + 5 + 0.03 + 0.006 in standard form
svetlana [45]
The answer to your problem 20 + 5 + 0.03 + 0.006 is -25.036
5 0
4 years ago
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