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3 years ago

Find rules for quadratic functions with graphs meeting these conditions.

1 answer:

8 0

1.) (x - 4)(x + 1) = 0
x^2 + x - 4x - 4 = 0
y = x^2 - 3x - 4

2.) (x - 2)(x - 6) = 0
x^2 - 6x - 2x + 12 = 0
x^2 - 8x + 12 = 0
since the function has a maximum point the leading coefficient is negative.
Therefore, required equation is y = -3x^2 + 24x - 36

3.) a(x + 3)^2 = ax^2 + 6ax + 9a
since the y intercept is at y = 18 => 9a = 18 => a = 2
Therefore, required function is y = 2x^2 + 12x + 18

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student randomly receive 1 of 4 versions(A, B, C, D) of a math test. What is the probability that at least 3 of the 5 student te

alexdok [17]

Answer:

1.2%

Step-by-step explanation:

We are given that the students receive different versions of the math namely A, B, C and D.

So, the probability that a student receives version A = $\frac{1}{4}$ .

Thus, the probability that the student does not receive version A = $1-\frac{1}{4}$ = $\frac{3}{4}$ .

So, the possibilities that at-least 3 out of 5 students receive version A are,

1) 3 receives version A and 2 does not receive version A

2) 4 receives version A and 1 does not receive version A

3) All 5 students receive version A

Then the probability that at-least 3 out of 5 students receive version A is given by,

$\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{3}{4}\times \frac{3}{4}$ + $\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{3}{4}$ + $\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}$

= $(\frac{1}{4})^3\times (\frac{3}{4})^2+(\frac{1}{4})^4\times (\frac{3}{4})+(\frac{1}{4})^5$

= $(\frac{1}{4})^3\times (\frac{3}{4})[\frac{3}{4}+\frac{1}{4}+(\frac{1}{4})^2]$

= $(\frac{3}{4^4})[1+\frac{1}{16}]$

= $(\frac{3}{256})[\frac{17}{16}]$

= 0.01171875 × 1.0625

= 0.01245

Thus, the probability that at least 3 out of 5 students receive version A is 0.0124

So, in percent the probability is 0.0124 × 100 = 1.24%

To the nearest tenth, the required probability is 1.2%.

4 0

2 years ago

What is 130% converted into a decimal?

Free_Kalibri [48]

Move the percent two places to the left 1.30

8 0

2 years ago

HELP I WILL GIVE BRAINLIEST!!!

lys-0071 [83]

T= 250 + 45a.

Since the cost of the medicine costs $250, and there is $45 dollars per appointment then 45 a would represent the 45 dollars for every appointment she chooses to have.

Hope this helps and have a nice day.

-R3TR0 Z3R0

7 0

2 years ago

Please help for brainlist !!

Elena-2011 [213]

Answer:

Step-by-step explanation:

First substitute x for 9

Then your problem is m(9)=2(9)+8

Now it is m(9)=18+8

Then add 18 and 8 for 26

Answer:

5 0

2 years ago

Fill in the blank. In the triangle below, y=

arsen [322]

Answer:

47.10

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

... Cos = Adjacent/Hypotenuse

The value y is the length of the hypotenuse, and the given length 35 is the side adjacent to the given angle. Thus, the cosine relationship will be helpful.

Filling in the given values, we have ...

... cos(42°) = 35/y

Multiplying by y/cos(42°), we can find y to be ...

... y = 35/cos(42°) ≈ 35/0.7431

... y ≈ 47.10

Y will be approximately 47.10 in length

Step-by-step explanation:

we will use this form that we memorized in our schools ............. SOH CAH TOA

CAH means , Cos ∅= Adjacent/Hypotenuse

Given values

∅ =42°

hypotenuse= y

adjacent side length = 35

now putting in our values into

Cos ∅= Adjacent/Hypotenuse

cos(42°) = 35/y

by multiplying y on both sides we get

y= 35/cos( 42°)

cos(42°)= 0.743

so y= 35/0.743

y = 47.10632

y ≈ 47.10

3 0

2 years ago