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4 years ago

8

Expand and simplify 3(x-2)+2(4x-1)

1 answer:

aliya0001 [1]4 years ago

5 0

3(x-2)+2(4x-1)
=3x-6+8x-2
=11x-8

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3 years ago

Determine g(x + a) – g(x) for the following function.<br> g(x) = 5x2 + 2x

dusya [7]

Answer:

$g(x + a) - g(x) = 10ax + 5a^2 + 2a$

Step-by-step explanation:

We are given the function:

$g(x) = 5x^2 + 2x$

And we want to determine:

$\displaystyle g(x+a) - g(x)$

Substitute:

$\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \end{aligned}$

And simplify:

$\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \\ \\ &= \left(5(x^2 + 2ax + a^2) + (2x + 2a) \right) + \left(-5x^2 - 2x\right) \\ \\ &= \left((5x^2 + 10ax + 5a^2) + (2x + 2a)\right) + \left(-5x^2 - 2x\right) \\ \\ &= (5x^2-5x^2) + (10ax + 2x - 2x) + (5a^2+2a) \\ \\ &= 10ax + 5a^2 + 2a \end{aligned}$

In conclusion:

$g(x + a) - g(x) = 10ax + 5a^2 + 2a$

3 0

2 years ago

Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “nor

Olenka [21]

Answer:

He have <u>47</u> ducks and <u>7</u> cows.

Step-by-step explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.

Let the number of ducks be $x.$

And the number of cows be $y.$

So, total number of animals are:

$x+y=54$

$x=54-y$ ....( 1 )

As, the feet of cows are 4 and ducks are 2.

Now, the total number of feet are:

$2(x)+4(y)=122$

$2x+4y=122$

Substituting the value of $x$ from equation (1) we get:

$2(54-y)+4y=122$

$108-2y+4y=122$

$108+2y=122$

<em>Subtracting both sides by 108 we get:</em>

$2y=14$

<em>Dividing both sides by 2 we get:</em>

$y=7.$

<em>The number of cows = 7.</em>

Now, to get the number of ducks we substitute the value of $y$ in equation (1):

$x=54-y\\x=54-7\\x=47.$

<em>The number of ducks = 47.</em>

Therefore, he have 47 ducks and 7 cows.

4 0

3 years ago