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olga_2 [115]
3 years ago
15

Graph f(x)= -(x-2)²+4

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Mathematics
1 answer:
Mandarinka [93]3 years ago
7 0

Answer: See the graph attached.

Step-by-step explanation:

The standard form of a quadratic function is:

f(x)=a(x-h)+k

Where (h,k) is the vertex of the parabola.

If a is negative, then the parabola opens down.

Then, for the function:

f(x)=-(x-2)^2+4

You can identify:

h=2\\k=4

Then the  vertex of the parabola is at (2,4)

Note that a=-1, therefore the parabola opens down.

Find the intersection with the x-axis. Substitute f(x)=0 and solve for x:

0=-(x-2)^2+4\\0=x^2-4x\\0=x(x-4)\\\\x_1=0\\x_2=4

Knowing that the vertex is at (2,4), the parabola opens down and it intersects the x-axis at x=0 and x=4, you can graph the function, as you observe in the figure attached.

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A genetics experiment involves a population of fruit flies consisting of 1 male named Bart and 3 females named Charlene, Diana,
kenny6666 [7]

Answer:

(b) \frac{1}{2}

Step-by-step explanation:

1 male named Bart (b)

3 females named Charlene(c), Diana(d), and Erin(e).

Since there is replacement, the possible samples are:

bb, bc, be, bd, cb, cc, cd, ce, db, dc, dd, de, eb, ec, ed, and ee.

Total Number of pairs = 16

Event of picking 2 males:bb

Event of 1 male:bc,cb,bd,db,be,eb

Event of picking 0 males:

cc, cd, ce, dc, dd, de, ec, ed, and ee.

\begin{equation*} \begin{matrix}Proportion of males & Probability \\0 & 9/16 \\1 & 6/16 \\2 & 1/16 \end{matrix} \end{equation*}

b. The mean of the sampling distribution

\mu = (\frac{9}{16} X0 ) +(\frac{6}{16} X 1)+(\frac{1}{16} X 2) = \frac{8}{16} = \frac{1}{2}

c.  No; the proportion of males is \frac{1}{4} while the mean is \frac{1}{2}.

B. No, the sample mean is not equal to the population proportion of males. These values are not always equal, because proportion is an unbiased estimator.

7 0
2 years ago
X+3=12 solve for x. x =
NeX [460]

Answer:

X is 9

Step-by-step explanation:

9 + 3 = 12

3 0
3 years ago
Need an answer to this
Firlakuza [10]

Answer:

x=20⁰

Step-by-step explanation:

The angle 6x is next to a 3x one.

And 6x+3x=180⁰

9x=180⁰

x=20⁰

3 0
2 years ago
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40 is 20% if what number?
Mamont248 [21]

Answer:

200

Step-by-step explanation:

Use the ratio: 20/100 = 40/X

Simplify the ratio: 1/5 = 40/X

Cross Multiply: 1X = 200

Divide both sides by 1: 1X/1 = 200/1

Simplify: X = 200

6 0
3 years ago
Plsss help!!!<br>y = ??<br>X =???​
Lyrx [107]

Answer:

x=80* y=20* and X=100*

Step-by-step explanation:

If we assume PQ || OR then by alternate interior angles x is equal to 80 degrees and y is equal to 20 degrees.

We know that a triangle adds up to 180 degrees.

Angle ROX and XRO add up to 100 degrees. Leaving RXO equal to 80 degrees. (180-100=80).

By opposite angles, QXP is equal to 80 degrees also.

Then we are left with solving for X.

Supplementary angles add up to 180 degrees.

Subtract angle OXR from 180 and we are left with angle OXP = X = 100 degrees.

8 0
3 years ago
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