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Alja [10]
3 years ago
6

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

Mathematics
1 answer:
Paha777 [63]3 years ago
7 0

Step-by-step explanation:

f(x) = 3 {x}^{2}  \: and \: g(x) = x + 2 \\ (f.g)(x)  \\ = f(x).g(x) \\  = 3 {x}^{2} .(x  + 2) \\ \red{ \boxed{ \bold{  \therefore f(x).g(x)= 3 {x}^{3}  + 6 {x}^{2} }}} \\

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Solve the following system of equations.
Elan Coil [88]

Answer:

(2,-3)

Step-by-step explanation:

I am not sure if you meant the first equation to be y or -y.  I solved it as y.

y = x-5                       -x -3y =7

I am going to take the second equation and write it as x =

-x - 3y = 7  Give equation

-x = 3y +7   Add 3y to both sides

x = -3y-7  Multiplied each term in the equation by -1 so that x could be positive

I am going to substitute -3y-7 for x in the first equation up above

y = x - 5

y = -3y -7 - 5  Substitute -3y-7 for x

y = -3y -12  Combined -7-5

4y = -12  Added 3y to both sides

y = -3  Divided both sides by 4.

I now know that y is -3, I will plug that into x = -3y-7 to solve for x

x = -3(-3) -7

x = 9-7   A negative times a negative is a positive

x = 2

5 0
2 years ago
Name the three similar triangles correspondingly. Start with the original right triangle LMK, then the remaining two right trian
aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

5 0
3 years ago
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Find the value of x.round to the nearest tenth
Nata [24]

Answer:

\displaystyle x \approx 8.2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Trigonometry</u>

[Right Triangles Only] SOHCAHTOA

[Right Triangles Only] sinθ = opposite over hypotenuse

Step-by-step explanation:

<u>Step 1: Identify Variables</u>

Angle θ = 23°

Opposite Leg = <em>x</em>

Hypotenuse = 21

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in variables [sine]:                                                                         \displaystyle sin(23^\circ) = \frac{x}{21}
  2. [Multiplication Property of Equality] Isolate <em>x</em>:                                              \displaystyle 21sin(23^\circ) = x
  3. Rewrite:                                                                                                           \displaystyle x = 21sin(23^\circ)
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  5. Round:                                                                                                             \displaystyle x \approx 8.2
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3 years ago
A box has twice as many grapes as a basket. Once 2kg of grapes were added to the basket, it contained 0.5 kg more than the box.
pav-90 [236]

By solving a system of equations, we will see that now there are 3.5kg of grapes on the basket.

<h3>How many kilograms of grapes are in the basket now?</h3>

Let's define the variables:

  • x = kg of grapes on the box originally.
  • y = kg of grapes on the basket originally.

We know that:

x = 2y

When we add 2kg to the basket, it has 0.5k more than the box, then:

y + 2 = x + 0.5

Then we have a system of equations:

x = 2y

y + 2 = x + 0.5

We want to solve this for y, then we can replace the first equation into the second one:

y + 2 = (x = 2y) + 0.5

y + 2 = 2y + 0.5

2 - 0.5 = 2y - y

1.5 = y

This means that, originally, there are 1.5 kg of grapes on the basket. And then we added 2kg, so now there are:

1.5kg + 2kg = 3.5kg

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

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2 years ago
The slope of the line whose equation is 3y + 2x =1 is
frez [133]
3y + 2x =1
3y = - 2x + 1
y = - 2/3x + 1/3

slope : - 2/3
7 0
3 years ago
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