Jim, Carla and Tomy are members of the same family.  Carla is 5 years older than Jim.  Tomy is 6 years older than Carla.  The sum of their 3 ages is 31 years. How old is each one of them?

Answers

Answer 1
Answer: let the age of jim be x
carla's age= x+5
tomy's age= 6+5+x
sum of their ages=31
x+x+5+x+5+6=3x+16=31
3x=31-16
   =15
x=15 divided by 3
     = 5
jim's age=5
carla's age=10
tomy's age = 16
Answer 2
Answer: x - Jim
y - Carla
z - Tomy

y=x+5\n z=y+6\n x+y+z=31\n\n x=y-5\n z=y+6\n x+y+z=31\n\n y-5+y+y+6=31\n 3y=30\n y=10\n\n x=10-5\n x=5\n\n z=10+6\n z=16

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Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?A.f(x) = (x – 8)2 – 56
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Answers

f(x) = x² + 8 - 16x

I'll rearrange it using y and x.

y = x² - 16x + 8
y - 8 = x² - 16x
y - 8 + 64 = x² - 16x + 64
y + 56 = (x-8)²
y = (x-8)² - 56

(x - 8)(x - 8) = x(x-8) - 8(x-8) = x² - 8x -8x + 64 = x² - 16x + 64

Choice A.) f(x) = (x-8)² - 56

By completing the square, the function in vertexform f(x) = (x - 8)² - 56 is equivalent to the function in standardform f(x) = x² + 8 - 16 · x. (Correct choice: A)

How to determine the vertex of the quadratic function by algebraic means

In this question we must transform a quadraticfunction in standardform into vertexform. An analytical approach is completing the square, which consists in transforming part of the polynomial into a perfect squaretrinomial. Now we proceed to present the procedure:

1) x² + 8 - 16 · x     Given

2) x² - 16 · x + 8    Commutative property

3) x² - 16 · x + 64 - 56     Modulative property/Existence of additive inverse/Definition of addition

4) (x - 8)² - 56     Associative property/Perfect square trinomial/Result

By completing the square, the function in vertexform f(x) = (x - 8)² - 56 is equivalent to the function in standardform f(x) = x² + 8 - 16 · x. (Correct choice: A)

To learn more on quadratic functions: brainly.com/question/5975436

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Frankie paid $11.75 for the movie ticket and $4.75 for popcorn and a drink. How much did Frankie spend?
a. $7.00
b. $15.50
c. $15.75
d. $16.50

Answers

He spent $16.50. Add the two amounts up.

Its 16.50

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Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the solution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c.Which equation can be used to determine c, the unknown concentration?

Answers

Taking the 3 solutions as 3 different terms, we can create an equation as follows:

Solution 1 : 10mL with 20% acid
Solution 2 : 30mL with x% acid
Solution 3 : 40mL with 32% acid

Since solution 1 + solution 2 = solution 3, let us substitute the given values we have:

10(0.2) + 30(x) = 40(0.32)
2 + 30x = 12.8

To solve for the unknown concentration x, we subtract 2 from both sides:
2 + 30x - 2 = 12.8 - 2
30x = 10.8

Dividing both sides by 30:
30x/30 = 10.8/30
x = 0.36

Therefore the unknown solution is 36% acid.

Answer:

Therefore the unknown solution is 36% acid.

Step-by-step explanation:

Which set of ordered pairs represents a function?{(3,3), (-9,-1),(-4,3), (3,1)}
{(2,4), (2,9), (-2,-8), (7,5)}
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{(5,9), (-6,1),(6,5),(-8,5)}
Submit Answer

Answers

Answer:

{(5,9), (-6,1),(6,5),(-8,5)}

Step-by-step explanation:

There is no repeating X factor

I don’t think my answer is right I believe but I think it’s the first one because it functions in a pattern.

How to do recurring decimal and fraction

Answers

Answer:

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A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that bestrepresents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer.Hint: Use the formula, f(x) = P(1 + r)x.

Answers


The question gives you the formula to use, but it's printed wrong.
The 'x' is an exponent after the (1 + r).

All you have to do is take the formula, and write the numbers into it
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The key thing to spot is that the forest is decreasing, so the 'r' is negative,
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So the formula to use is       f(x)  =  P (1 + r) ^x

P = 2000
r = -0.06
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The amount left after 12 years is
        
                                   2000 (0.94)¹² =

                                   2000 (0.476)  =  951.8 square kilometers.
                  

hope this helps- i did the test :)

Answer: