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3 years ago

6

Evaluate d/2 + c/3 for c = 6 and d = 10 a) 10 b) 16/5 c) 7 d) 6

1 answer:

pshichka [43]3 years ago

4 0

D/2 + c/3

10/2 + 6/3

5+6/3

=5+2

=7

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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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3 years ago

What is the value of the x variable in the solution to the following system of equations?

Mazyrski [523]

Correct answer is A.

$3x + 2y = 8
\\2x + 3y = 2 
\\
\\9x+6y=24
\\-4x-6y=-4
\\
\\5x=20
\\x=4$

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3 years ago

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a dvd costs twice as much as a music cd. Jack buys 2 dvds and 2 cds and spends $45. Determine how much one cd costs. in dollars

VMariaS [17]

$dvd=d \\ cd=c \\ \\ \left \{ {{d=2c} \atop {2d+2c=45}} \right. \\ \\ 2(2c)+2c=45 \\ 4c+2c=45 \\ 6c=45 \\ c=7.5 \\ \\ d=2(7.5) \\ d=15$

One CD costs $7.50.
One DVD costs $15.00.

3 0

3 years ago

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Is 7.5 greater or less than 48.75?

fomenos

Answer:

Less than

Step-by-step explanation:

7.5 < 48.75

48.75 is a bigger number than 7.5

Therefore, 7.5 is less than it.

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3 years ago

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A town has a population of 2000 and grows at 4% every year write an equation to represent the scenario

vfiekz [6]

Answer: $P=2000(1.04)^t$ .

Step-by-step explanation:

It is given that,

Initial population of a town = 2000

Growth rate = 4% = 0.04 per year

The exponential growth function for population is

$P=P_0(1+r)^t$

where, $P_0$ is initial population, r is growth rate and t is number of years.

Substitute $P_0=2000,r=0.04$ in the above equation.

$P=2000(1+0.04)^t$

$P=2000(1.04)^t$

Therefore, the required equation is $P=2000(1.04)^t$ , where P is population after t years.

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3 years ago