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2 years ago

Please explain 12 and13and please please please hurry!

Mathematics

1 answer:

pantera1 [17]2 years ago

6 0

Answer:

12. a = 2

13. $x = \dfrac{4}{3}$

Step-by-step explanation:

12.

6a(a + 3) = 2a(3a + 5) + 16

First, distribute 6a on the left side, and distribute 2a on the right side.

6a² + 18a = 6a² + 10a + 16

Subtract 6a² from both sides.

18a = 10a + 16

Subtract 10a from both sides.

8a = 16

Divide both sides by 8.

a = 2

13.

$\dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{1}{3}(x + 2)$

The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.

$6 \times \dfrac{1}{3}x + 6 \times \dfrac{1}{2}x = 6 \times \dfrac{1}{3}(x + 2)$

$\dfrac{6}{3}x + \dfrac{6}{2}x = \dfrac{6}{3}(x + 2)$

$2x + 3x = 2(x + 2)$

Combine like terms on the left side. Distribute the 2 on the right side.

$5x = 2x + 4$

Subtract 2x from both sides.

$3x = 4$

Divide both sides by 3.

$x = \dfrac{4}{3}$

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3 years ago

Please find the general limit of the following function:

valentinak56 [21]

Answer:

The general limit exists at <em>x</em> = 9 and is equal to 300.

Step-by-step explanation:

We want to find the general limit of the function:

$\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))$

By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.

So, let's find each one-sided limit: the left-hand side and the right-hand side.

The left-hand limit is given by:

<h3> $\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))$ </h3>

Since the given function is a polynomial, we can use direct substitution. This yields:

$=(9)^2+2^7+(9.1\times 10)$

Evaluate:

$300$

Therefore:

$\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300$

The right-hand limit is given by:

$\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))$

Again, since the function is a polynomial, we can use direct substitution. This yields:

$=(9)^2+2^7+(9.1\times 10)$

Evaluate:

$=300$

Therefore:

$\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300$

Thus, we can see that:

$\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300$

Since the two-sided limits exist and are equivalent, the general limit of the function does exist at <em>x</em> = 9 and is equal to 300.

8 0

3 years ago

Read 2 more answers

Best and Correct answer gets BRAINLIEST!!!!!

hichkok12 [17]

Answer:

Step-by-step explanation:

3/1 = 3

3 is the correct answer

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3 years ago

What is the probability of spinning a 5 and rolling a 1 , 2 or 3 ??

ch4aika [34]

Answer: The answer is A 1/16

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4 years ago

At smith lake boat rentals it costs $25 per hour to rent a boat plus one time charge for cleaning. The bengal family rented a bo

vesna_86 [32]

Answer: the Jones family paid $164

Step-by-step explanation:

Let x represent the one time charge that smith lake boat rentals charge for cleaning.

The bengal family rented a boat from 11 am- 6:30pm and paid $226.50. This means that the number of hours for which they rented the boat is

11 - 6:30/= 7.5 hours

Therefore,

25 × 7.5 + x = 226.5

187.5 + x = 226.5

x = 226.5 - 187.5

x = $39

If the jones family rented a boat from 8am-1pm, the number of hours would be 5 hours.

The amount that they paid is

39 + 5 × 25 = 39 + 125

= $164

3 0

3 years ago