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qaws [65]
3 years ago
10

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.

Mathematics
2 answers:
OverLord2011 [107]3 years ago
8 0

Answer: the answer is C

Step-by-step explanation:

I took the test

seraphim [82]3 years ago
4 0

Keywords:

<em>Quadratic equation, vertex shape, parabola </em>

For this case we have to rewrite the given quadratic equation, in the form of vertex, for this, we must take into account that a quadratic equation of the form ax ^ 2 + bx + c = 0, can be rewritten in the form of vertex as: y = a (x-h) ^ 2 + k. Vertice is the lowest or highest point of the parabola. The vertex is given by: (h, k). So, let: f (x) = 4x ^ 2 + 48x + 10, to find the equation in the form of vertex, we follow the steps below:

Step 1:

We take the common factor to the first two terms of the equation:

f (x) = 4 (x^2 + 12x) + 10

Step 2:

We work square:

We divide the coefficient of the term "12x" by 2 and its result is squared, that is:

(\frac {12} {2}) ^ 2 = 36

So, we have:

f (x) = 4 (x^2 + 12x + 36-36) + 10

Step 3:

We simplify:

f (x) = 4 (x^2 + 12x + 36) + 10- (4 * 36)

Step 4:

We factor:

f (x) = 4 (x + 6) ^ 2-134

Thus, h = -6\ and\ k = -134

Answer:

The equation in the form of vertex is: f (x) = 4 (x + 6) ^ 2-134, and the vertex is (h, k) = (- 6, -134)

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<span> The </span>associative property<span> states that you can add or multiply regardless of how the numbers are grouped. By"grouped" we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis</span>
3 0
3 years ago
Which is the solution to the inequality?<br> (Look at pic pls hurry)
Reil [10]

Answer:

3

Step-by-step explanation:

5 0
2 years ago
Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. If Smith always bets that the outcome will be
zimovet [89]

Answer:

0.003

Step-by-step explanation:

Given: A roulette wheel consists of 38 numbers 1 to 36, 0, and double 0.

Smith bets that the outcome will be one of the numbers 1 through 12.

To find: probability that Smith will lose his first 5 bets

Solution:

Probability refers to chances of occurrence of some event.

Probability = Number of favourable outcomes/Total number of outcomes

Total number outcomes = 38

As Smith bets that the outcome will be one of the numbers 1 through 12, number of favourable outcomes is equal to 12.

So,

probability that Smith will loss his first bet = \frac{12}{38}=\frac{6}{19}

Therefore,

Probability that Smith will lose his first 5 bets = (\frac{6}{19} )^5=0.003

4 0
2 years ago
If Betty makes monthly deposits at the end of each month in an account that earns 8% interest compounded monthly,
Svetlanka [38]

9514 1404 393

Answer:

  (a) $254.08

  (b) $767.34

  (c) $12,449.36

Step-by-step explanation:

These questions are best answered by a financial calculator or app. Such are available for your phone or tablet. A spreadsheet also has built-in functions for making these calculations.

(a) FV = $40,000, i = 8% per year, n = 9 years (108 months), compounding 12 times per year. The monthly deposit needs to be $254.08.

__

(b) Payment = $254.08, n = 3 months, i = 8%/year, compounding 12 times per year. FV = $767.34.

__

(c) The sum of 108 payments of $254.08 is ...

  108 × $254.08 = $27,440.64

The interest earned is enough to bring the account value to $40,000, so is ...

  $40,000 -27,440.64 = $12,559.36

_____

<em>Additional comment</em>

The amount $254.08 is rounded down to the nearest cent, so the balance after 9 years will be $39,999.70, which is $0.30 short of $40,000. We used $40,000 as the final account balance, so overestimated the interest by $0.30.

There may be additional small changes in the values if you round interest to the nearest cent each month the way a financial institution would. It is hard to tell in these problems how accurate you're intended to be in your calculations.

4 0
2 years ago
Peter wants to make for necklaces that are the same way. He asked his friends to cut the string for the necklace is 15 paper cli
postnew [5]

Correct question is;

Peter wants to make four necklaces that are the same way. He asked his friends to cut the string for the necklace 15 paper clips long. Would all the lengths be the same? Explain your think

Answer:

No, the lengths would not be the same. This is due to the fact the the paper clips could be in different sizes.

Step-by-step explanation:

We are told that he wants to make four necklaces that are the same way and that he told his friends to cut the string for the necklace 15 paper clips long.

Now, we are not told the sizes of the paper clips and we know that paper clips come in different sizes. Thus the paper clips in which the strings are cut could be in different sizes. Therefore, the lengths wouldn't be the same due to that.

5 0
2 years ago
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