If a^2+3a+9=0, What is a^3?

(x – 6)2 = y + 7, find the vertex.

Anna007 [38]

Would be the answer 16

3 0

3 years ago

Write the function notation for the transformation that would change f(x) to have a vertical

koban [17]

Function is $4 - \frac{f(x)}{8}$ .

Step-by-step explanation:

We have a function notation for the transformation that would change f(x) to have a vertical compression by a factor of $\frac{1}{8}$ , reflection over the x axis, up 6 and right 2.

Step 1:

Vertical compression by a factor $\frac{1}{8}$ , this means decreasing value of function by a factor of $\frac{1}{8}$ . Function becomes $\frac{f(x)}{8}$ .

Step 2:

Reflection over x-axis means rotating f(x) by 180° over origin . Function now is $-\frac{f(x)}{8}$ .

Step 3:

Up 6 , means value of function is increased by 6 , Function now is $\frac{-f(x)}{8} + 6$ .

Step 4:

Right 2, means shifting function to 2 units on right side i,e, on x-axis.

∴Function finally becomes, $\frac{-f(x)}{8} +6 - 2$ which is $4 - \frac{f(x)}{8}$ .

6 0

3 years ago

John has a die and a coin. The die is labeled 1 through 6 and the two sides of the coin are heads and tails. The tables below sh

Alenkasestr [34]

Answer:

n = 60

Step-by-step explanation:

Total outcomes, while tossing a coin are 2, given as:

{Heads, Tails}

The probability of getting a heads up, while tossing the coin is:

P(Heads) = Favorable Outcome/Total Outcomes

P(Heads) = 1/2 = 0.5

Now, the total outcomes, while rolling a die are 6, given as:

{1, 2, 3, 4, 5, 6}

5 of these numbers are factors of 12, which are:

{1, 2, 3, 4, 6}

Thus, the probability of getting a factor of 12, while rolling a die is:

P(Factor of 12) = Favorable Outcome/Total Outcomes

P(Factor of 12) = 5/6 = 0.83

So, the probability of getting both heads and factor of 12 will be:

P(Heads and Factor of 12) = P(Heads ∪ Factor of 12)

P(Heads and Factor of 12) = P(Heads) * P(Factor of 12) = 0.5 * 0.83

P(Heads and Factor of 12) = 0.417 = 41.7%

So, for 144 trials, the number of trials in which we get heads and factor of 12, are given by:

n = P(Heads and Factor of 12) * 144

where,

n = no. of trials John would expect to roll a number on the die that is a factor of 12 and toss a coin that lands heads-up out of next 144 trials

n = 0.417 * 144

n = 60

7 0

3 years ago

a windowpane is 5.7 Inches by 7.1 inches. what is the distance between opposite corners of the windowpane? if necessary, round t

nikitadnepr [17]

Answer:

the distance is 9.1 inches (please give brainliest)

Step-by-step explanation:

we must use the pythagorean theorem:

5.7^2 + 7.1^2 = c^2

(c being the distance being the two corners)

c^2 = 82.9

c = sqrt(82.9) ≈ 9.1

7 0

3 years ago

Find a solution to the system. Make sure to write as a coordinate.

RUDIKE [14]

Answer:

x=2, y=3

Step-by-step explanation:

This is a system of equations.

To solve a system of equations, we use the substitution method.

We can plug in the first equation, $x=2y-4$ , into the value for x in the second equation. Now, the second equation looks like this:

$2*(2y-4)+y=7$

We simplify and solve for y:

→ $4y-8+y=7$

→ $5y=15$

→ $y=3$

Now, we plug in the value for y, which is 3, into either equation. I will just use the first equation:

→ $x=2*3-4$

→ $x = 2$

Let me know if my explanation is unclear.

3 0

3 years ago