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3 years ago

What’s the equation

Mathematics

1 answer:

OLga [1]3 years ago

5 0

Answer:

y = 4. $3^{x}$

Step-by-step explanation:

For an exponential function in the form

y = a $b^{x}$

Use ordered pairs from the table to find a and b

Using (0, 4 ), then

4 = a $b^{0}$ ( note $b^{0}$ = 1 ), thus

a = 4

y = 4 $b^{x}$

Using (1, 12 ), then

12 = 4 $b^{1}$ = 4b ( divide both sides by 4 )

b = 3

Thus

y = 4 . $3^{x}$ ← exponential equation

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Dennis_Churaev [7]

For what.. could you finish the question ?

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3 years ago

John ordered a large three topping pizza for $7. 50 and a large 8 topping pizza for $10. Write an equation in slope-intercept fo

yKpoI14uk [10]

to get the equation of any straight line, we simply need two points off of it, well, let's use the provided values hmmm

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2 years ago

what is the sum of two numbers is "-7." Two times the first number equals 4 the second number. Find the two numbers.

skelet666 [1.2K]

Answer:

$\sf \text{The numbers are $\dfrac{-14}{3} $ and $\dfrac{-7}{3}$}$

Step-by-step explanation:

Let the numbers be x , y

Sum of two numers = -7

x + y = -7------------(I)

Two times the first number equals 4 the second number.

2x = 4y ----------(II)

Divide both sides by 2

$\sf \dfrac{2x}{2}=\dfrac{4y}{2}$

x = 2y

Subtitute x = 2y in equation (I)

2y + y = -7

3y = -7

y = -7/3

Plugin y = -7/3 in equation (II)

$\sf 2x = 4*\dfrac{-7}{3}\\\\2x = \dfrac{-28}{3}\\\\x =\dfrac{-28}{3*2}\\\\x = \dfrac{-14}{3}$

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2 years ago

Leona has a bag containing letter tiles. Which describes dependent events?

serious [3.7K]

Answer:

a) removing a vowel, not replacing it, and then removing another vowel

Step-by-step explanation:

This question is from the topic Probability. In Probability, a dependent event is one in which the outcome of one event alters or changes the outcome of another event. A classic example of this is seen when sampling without replacement is done. When sampling without replacement is done, the outcome of another event within the same set changes. When sampling with replacement is done, the outcome of the events are independent because every item in the population still has an equal chance of being chosen. However, in the case of sampling without replacement, once an item has been selected from a population, the outcome of every other event after it is altered based on the item that was initially chosen.

Let's assume that the bag has 26 tiles (one for each alphabet from a - z)

Population = 26, consonant = 21, vowel = 5

If a vowel or consonant is removed & is replaced, we have:

Pr (choosing "a") = number of item ÷ population

Pr = 1 ÷ 26 = 1/26

Pr (choosing "y") = 1 ÷ 26 = 1/26

Doing this for over & over again, produces the same probability

However, if an item was selected without replacement, we have:

Pr (choosing "a") = 1 ÷ 26 = 1/26

Without replacement implies that if I choose tile letter "a", tile letter "a" will not be included in subsequent events, hence:

Population = 25

Pr (choosing "u") = 1 ÷ 25 = 1/25

Without replacement, population = 24

Pr (choosing "y") = 1 ÷ 24 = 1/24

So, we see the dependent nature of the events in how that the outcome of the next event is being altered. As such, option a describes a dependent event & is the correct answer

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3 years ago

Solve the system by substitution(show your work)

Gnesinka [82]

Answer:

x = 3 , y = 6 , z = -1

Step-by-step explanation using substitution:

Solve the following system:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

In the first equation, look to solve for x:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Add y + z to both sides:

{-x = -8 + y + z

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Multiply both sides by -1:

{x = 8 - y - z

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Substitute x = 8 - y - z into the second and third equations:

{x = 8 - y - z

4 y - 4 (8 - y - z) + 5 z = 7

2 (8 - y - z) + 2 z = 4

4 y - 4 (8 - y - z) + 5 z = 4 y + (-32 + 4 y + 4 z) + 5 z = -32 + 8 y + 9 z:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

2 (8 - y - z) + 2 z = 4

2 (8 - y - z) + 2 z = (16 - 2 y - 2 z) + 2 z = 16 - 2 y:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

16 - 2 y = 4

In the third equation, look to solve for y:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

16 - 2 y = 4

Subtract 16 from both sides:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

-2 y = -12

Divide both sides by -2:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

y = 6

Substitute y = 6 into the second equation:

{x = 8 - y - z

9 z + 16 = 7

y = 6

In the second equation, look to solve for z:

{x = 8 - y - z

9 z + 16 = 7

y = 6

Subtract 16 from both sides:

{x = 8 - y - z

9 z = -9

y = 6

Divide both sides by 9:

{x = 8 - y - z

z = -1

y = 6

Substitute z = -1 into the first equation:

{x = 9 - y

z = -1

y = 6

Substitute y = 6 into the first equation:

{x = 3

z = -1

y = 6

Collect results in alphabetical order:

Answer: {x = 3 , y = 6 , z = -1

3 0

3 years ago