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professor190 [17]

1 year ago

7

Billy plans to paint baskets. The paint costs $14.50. The baskets cost $7.25. Write an equation that gives the total cost as a f

unction of the number of baskets made. Determine the cost of 4 baskets

1 answer:

andreyandreev [35.5K]1 year ago

7 0

Let 'x' represent the number of baskets and let 'y' be the total cost.

Since the paint costs 14.50 and each basket cost 7.25, then we have the following function:

$y=7.25x+14.50$

To find the cost of 4 baskets, we can make x = 4 and solve for y:

$\begin{gathered} x=4 \\ \Rightarrow y=7.25(4)+14.50=29+14.50=43.50 \\ y=43.50 \end{gathered}$

therefore, the cost of painting 4 baskets is $43.50

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Simplify the expression state any excluded values<br> 2a^2-4a+2<br> ---------------<br> 3a^2-3

chubhunter [2.5K]

Answer:

The simplified form is $\dfrac{2(x-1)}{3(x+1)}$ .

$x =1$ is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

$\dfrac{2a^2-4a+2}{3a^2-3}$

Let us simplify the numerator and denominator separately.

The numerator is given as $2a^2-4a+2$

2 is a common factor in all the three terms. So, we factor it out. This gives,

$=2(a^2-2a+1)$

Now, $a^2-2a+1=(a-1)(a-1)$

Therefore, the numerator becomes $2(a-1)(a-1)$

The denominator is given as: $3a^2-3$

Factoring out 3, we get

$3(a^2-1)$

Now, $a^2-1$ is of the form $a^2-b^2=(a-b)(a+b)$

So, $a^2-1=(a-1)(a+1)$

Therefore, the denominator becomes $3(a-1)(a+1)$

Now, the given expression is simplified to:

$\frac{2a^2-4a+2}{3a^2-3}=\frac{2(x-1)(x-1)}{3(x-1)(x+1)}$

There is $(x-1)$ in the numerator and denominator. We can cancel them only if $x\ne1$ as for $x=1$ , the given expression is undefined.

Now, cancelling the like terms considering $x\ne1$ , we get:

$\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}$

Therefore, the simplified form is $\dfrac{2(x-1)}{3(x+1)}$

The simplification is true only if $x\ne1$ . So, $x =1$ is the excluded value for the given expression.

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