All categories

2 years ago

Rewrite the equation in vertex form. y = x2 - 6x + 18

2 answers:

8 0

Complete square!
Vertex form is (x-h)^2+k
meaning that the vertex is located at (h,k).

$y=x^2-6x+18$
$=(x^2-2(3x)+9)+9$ 3^2=9
$=(x-3)^2+9$
vertex form, h=3, k=9, vertex is located at (3,9)

Edited 2018-03-18
There was a suggestion to explain the completion of square as
x^2-6x=(x-3)^2-9.

However, this does not show where the (x-3) come from.
If this is a better explanation for any or all of you, here it is.

7nadin3 [17]2 years ago

4 0

The answer is <span>y= (x-3)^2 + 9

I hope this helps</span>

You might be interested in

Benito embroiders and sells T-shirts. The graph shows his profit as a function of the number of shirts sold. After selling a cer

vovikov84 [41]

Answer:

The correct option is;

The x-intercept represents the shirts he has to sell before making a profit

Step-by-step explanation:

The given data are;

(0, -20), (1, -10), (2, 0), (3, 10), (4, 20), (5, 30), (6, 40), (7, 50), (8, 25), (9, 40), (10, 55), (11, 70)

The data show a linear relationship because successive data point increases by the same amount of 10 for x between 0 and 7 and 15 for x between 8 and 11;

Therefore;

Slope, m of the first linear portion using points (2, 0), and, (4, 20) gives;

m = (20 - 0)/(4 - 2) = 10

The equation of the line is therefore;

y - 20 = 10·(x - 4)

y = 10·x - 40 + 20

y = 10·x - 20

The y-intercept (x = 0) is y = -20

The x-intercept (y = 0) is found as follows;

0 = 10·x - 20

20 = 10·x

10·x = 20

x = 20/10 = 2

Therefore, when x = 2 we have;

Profit = y = 10·x - 20 = 10×2 - 20 = 0

Which can be expressed as, he has to sell more than 2 shirts to make profit

Therefore, the correct option is that the x-intercept represents the shirts he has to sell before making a profit.

4 0

2 years ago

Which length is 10 6 times greater than a nanometer?

crimeas [40]

A nanometer (nm) is 10⁻⁹ m.

Therefore
10⁶ x 1 nm = 10⁶(10⁻⁹ m) = 10⁻³ m

By definition,
10⁻³ m = 1 mm (millimeter)

Answer: 1 millimeter

8 0

2 years ago

Kain graphs the hyperbola (y+2)^2/64 − (x+5)^2/36 = 1 . How does he proceed? Drag a value, phrase, equation, or coordinates in t

cupoosta [38]

Answer:

1st box: (-5,-2)

2nd box: up and down

3rd box: 8

4th box: +-4/3

5th box: y+2 = +-4/3 (x+ 5)

Step-by-step explanation:

Just took the k12 unit test, hope this helps!

7 0

2 years ago

Read 2 more answers

What common angle do ACE and ACD share?

SCORPION-xisa [38]

The answer is the second option, <ACE = <ECA.

This is because C is in the middle of both, so it's referring to the same angle. The other options are all comparing different angles, that aren't congruent, so they're incorrect.

6 0

2 years ago

Read 2 more answers

An example problem in a Statistics textbook asked to find the probability of dying when making a skydiving jump.

MArishka [77]

Answer:

(a) 0.999664

(b) 15052

Step-by-step explanation:

From the given data of recent years, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.

So, the probability of death is $\frac{21}{3000000}==0.000007$ .

Assuming, this probability holds true for each skydiving and does not change in the present time.

So, as every skydiving is an independent event having a fixed probability of dying and there are only two possibilities, the diver will either die or survive, so, all skydiving can be regarded as is Bernoulli's trial.

Denoting the probability of dying in a single jump by $q$ .