Michael needs to memorize words on a vocabulary list for German class. He has 12 words to memorize,and he is one-fourth done. How many words has Michael memorized so far?

9514 1404 393

Answer:

  a) y = (x -4)² -4

  b) (4, -4)

  c) translated 4 right, 4 down

Step-by-step explanation:

a) Apparently "graphing form" is a reference to "vertex form." That form is ...

  y = a(x -h)² +k . . . . . . parabola with vertex (h, k) and vertical scale factor 'a'

The coefficient of x² in your given equation is 1, so a=1. The values of h and k can be found as follows.

'h' is the opposite of half the x-coefficient in your equation, so is h = -(-8/2) = 4. The value of k is the square of h, subtracted from the constant in your equation: k = 12 -h² = 12 -16 = -4. (This applies when a=1, as here.) These calculations are the "cut to the chase" version of "completing the square."

The method of "completing the square" has you consider the x-terms separately from the constant term:

  y = (x² -8x) +12

To "complete the square", you want to make the terms in parentheses be a perfect square trinomial. You do that by adding the square of half the x-coefficient. In order to keep the same equation, you need to subtract an equivalent amount outside parentheses:

  y = (x² -8x +(-8/2)²) +12 -(-8/2)² . . . . . add and subtract (-8/2)²

  y = (x -4)² +(12 -16)

Then the vertex form is ...

 y = (x -4)² -4 . . . . and the vertex is (h, k) = (4, -4).

The graphing calculator plot attached confirms this vertex value.

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The problem statement tells you that you can also find this form by averaging the x-intercepts. If you factor your equation, you get ...

  y = (x -6)(x -2)

The x-values that make these factors zero {6, 2} are the x-intercepts. Their average (6+2)/2 = 4 is the x-coordinate of the vertex (h). You can find the y-coordinate of the vertex by evaluating y when x=4: y = 4² -8·4 +12 = -4. So, the vertex by this method is (h, k) = (4, -4), and the equation in graphing form is ...

  y = (x -4)² -4 . . . . as above.

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b) As we saw above, the vertex coordinates are (h, k) = (4, -4).

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c) The vertical scale factor 'a' is 1, so the only transformation done on the graph is to move the parent vertex (0, 0) to the location (4, -4). That is, the graph has been translated 4 units right and 4 units down. (In the attached, the parent function is shown with a dashed line.)

9514 1404 393

Answer:

  B, E

Step-by-step explanation:

You are give a table of values of x and f(x). You are told that g(x) = (1/2)f(x), and you are asked for points (x, g(x)) that match that description.

It can be useful to mentally, or actually, add a third column to the table that shows the values of g(x). Each of those is half the corresponding value of f(x), because that is what g(x) = (1/2)f(x) means.

Having done that, you can then compare the ordered pairs (x, g(x)) to those in the answer list to see which ones match. The ones that match are highlighted in green in the attachment:

  (-1, -2) . . . . . . 2nd choice

  (6, 3/2) . . . . . 5th choice

Answer:

The answer is

[tex]y = 2x + 13[/tex]

Step-by-step explanation:

Remember:

[tex]Slope-intercept form: \: \\ y = mx + b \\ \\ m = slope \\ b = y - intercept[/tex]

[tex]M = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

First: Find the slope.

[tex]M = \frac{13 - 5}{0 - ( - 4)} = \frac{8}{4} = 2[/tex]

.

Second: Solve for the y-intercept

[tex]y = mx + b \\ 5 = 2( - 4) + b \\ 5 = - 8 + b \\ \frac{+ 8 = + 8 \: \: \: \: \: \: \: \: }{13 = b} [/tex]

.

Third: Plug in.

[tex]y = mx + b \\ y = 2x + 13[/tex]

Answer:

The First Graph (top left)

Step-by-step explanation:

bottom left: y = 3x

top right: y = 2x

bottom right: y = 3x

The top left is the only correct one

Answer:

Step-by-step explanation:

this is okay  ... use the point-slope formula [y-y1=m(x-x1)] with your given point.. also m is the slope.. which as is.. is undefined.. so just leave it like that.. the teacher is making this too abstract thou.. to make sense

y-2=m(x-(-3))

y-2 = m(x+3)

y-2 = mx +3m

y = mx +3m +2

that's all you could do for now.. until the slope is defined  :)

Answer:

y-2=m(x-(-3))

y-2 = m(x+3)

y-2 = mx +3m

y = mx +3m +2

Step-by-step explanation:

Step-by-step explanation:

Since the sum of the digits must be an integer, the number itself must also be a multiple of 5.

Lowest common multiple of 5 and 9 = 45.

Therefore the number could be 45 or 90.

5(9 + 0) =/= 90, so 90 is incorrect.

Since 5(4 + 5) = 45, 45 is the answer.

Answer: 45

Step-by-step explanation:

We know that it has to be a 2-digit number. Its the multiple of 9. We see there is a number in the question. Five. I simply took 9 and multiplied it by 5 which gave me a total of 45.

Step-by-step explanation:   2(x+4)(x-4)        is the factored form of 2x^2-32.

Answer:

2[(x+4)(x-4)]

Step-by-step explanation:

2x2-32

2(x2-16)

2(x2-4^2)

2[(x+4)(x-4)]

Answer:

1. 3

2. 3

5. 3

6. 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. y = -17

2. x = 3

5. r = 3

6 y = 3

Answer:

Step-by-step explanation:

Putting value of z = 3

6(3)2+ 2(3) + 10

6(9) + 6 + 10

54 + 16

70

Step-by-step explanation:

I dont know I need help I have this answer in my test and I need help plz

Answer:

25

Step-by-step explanation:

Answer:

Number of tickets sold in advance = 310

Number of tickets sold  at the door = 340

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at the door than in advance, and $2630 was collected. How many of each kind of ticket were sold?

The explation of the answer is now given as follows:

Let a represents number of tickets sold in advance. Therefore, we have:

a = number of tickets sold in advance at $3 each

a + 30 = number of tickets sold  at the door at $5 each

The total amount collected can be represented by this equation:

3a + 5(a + 30) = 2630

Solving for a, wee have:

3a + 5a + 150 = 2630

8a = 2630 - 150

8a = 2,480

a = 2,480 / 8

a = 310

Therefore, this implies:

Number of tickets sold in advance = 310

Number of tickets sold  at the door = a + 30 = 310 + 30 = 340

Answer:

.

Step-by-step explanation:

we are asked to write an expression that shows how to multiply 4 and 362 using place value ans expanded form. The expanded form of 362 is 300 + 60+ 2. IN this case, the expression is 4*(300 +60+ 2) that is we distribute 4 to the numbers inside that is 1200 + 240 + 8 equal to 1448

Answer:

Step-by-step explanation: substitute 0 in for x for the y intercept

Answer:

[tex]2\sqrt{10}[/tex]

Step-by-step explanation:

Take [tex]a^{2} +b^{2} +c^{2}[/tex], let x represent a, 9 represent b, and 11 represent c.

Now, plug your variables into the equation:

[tex]x^{2} +9^{2} =11^{2}[/tex]

Simplify:

[tex]x^{2} +81=121[/tex]

Subtract:

[tex]x^{2} =40[/tex]

Take the square root of 40:

[tex]x=2\sqrt{10}[/tex]

Answer:

$3960

Step-by-step explanation:

12% of $4,500 is 540.

Subtracting the 12% means taking away $540 from $4,500, which gives you $3960

Answer:

x = 5

Answer:

[tex]3x + 2 = 17 \\ 3x = 15 \\ \boxed{x = 5}[/tex]

Answer:

-3c

Step-by-step explanation:

Answer:

-3c

Step-by-step explanation:

according to my calculations this is right

Answer:

Step-by-step explanation:

first put the inequality into slope intercept form (y-mx+b)

x-3y</=18

-3y</=-x+18

y>/=1/3x-6 (you have to flip the sign since you are dividing by a negative number)

then graph it (i attached a picture)

to figure out what side to shade in you can substitute the point (0,0) in for x and y. if it is true you shade in the part of the graph that includes (0,0).

0>/=1/3(0)-6

0>/=-6

Answer:

B. the temperature decreasing by 18º

Step-by-step explanation:

decreasing means to take away or less so therefore its b

Answer:

B. the temperature decreasing by 18º

Step-by-step explanation:

i just took it

Answer:

Step-by-step explanation:

lag is Determine the​ flag's wlag is Determine the​ flag's wlag is Determine the​ flag's w this mena that the wiatgh

Answer:

I need help on this.

Step-by-step explanation:

First convert all th fractions into decimal :

3/7 =0.428

7/16=0.4375

0.43=remain same (already given in decimal form)

43.8%=0.438

now arrange them in one row (horizontally) then it will be easy to arrange it.

0.428 , 0.4375 , 0.43 ,0.438

=0.428 , 0.43, 0.4375 ,0.438

= ans) 3/7, 0.43, 7/16, 43.8%

Answer:

It is c

Step-by-step explanation:

(y x 40) + (y x 8)

40y + 8y

48y

y x 48 = 48y

the answer's 85

Step-by-step explanation:

pemdas ig

Answer:

Step-by-step explanation:

-3 = -x - 2

the equation is a bit hard to read in your questions but if that is the correct equation then the slope is  -1

Answer:

try looking at the codes in it, in the coding it says the answer!

Step-by-step explanation:

my brother told me, I tryed it out and it worked, just don't get caught!

Answer:

the nswer is 37

Step-by-step explanation: