Simplify: 9(a + b) + 4(3a + 2b)

Mathematics

2 answers:

Alborosie2 years ago

6 0

Answer:

21a + 17b

Step-by-step explanation:

To simplify, we need to distribute the 9 to the terms inside of the parentheses that it is being multiplied by and 4 to the terms inside of the parentheses that it is being multiplied by like so:

9(a)+9(b)+4(3a)+4(2b)

9a+9b+12a+8b

Add like terms

21a + 17b

nydimaria [60]2 years ago

5 0

Step-by-step explanation:

first, multiply 9 with both a and b also 4 with 3a and 2b

second, collect the variables which means the a's together and the b's together

third, add the variables

finally, since different variables can not be added the answer will be 21a+17b

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AlladinOne [14]

Remember that for a function of the form $y=a x^{2}$ , a parabola, the focus will be: $(0, \frac{1}{4a} )$ .
We know that the vertex of the parabola is (0,0), and the sun is the focus of the parabola; we also know that the focus is in the positive y-axis and when the comet is as its vertex, the distance between them is 60'000.000 km; therefore the focus of our parabola is (0, 60'000.000).
Now that we know the focus, we can find $a$ using the focus of the parabola:
$\frac{1}{4a} =60'000.000$
$1=(60'000.000)(4a)$
$1=240'000.000a$
$a= \frac{1}{240'000.000}$

Now, the only thing left is replacing the value of $a$ in our equation $y=a x^{2}$ :
$y=( \frac{1}{240'000.000)} ) x^{2}$
$y= \frac{ x^{2} }{240'000.000}$

We can conclude that the equation that represents the path of the comet is $y= \frac{ x^{2} }{240'000.000}$