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3 years ago

The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry?

Mathematics

1 answer:

Andrew [12]3 years ago

6 0

First, simplify the expression of the function $f(x)=x^2-4x+6$ highlighting the perfect square:

$f(x)=x^2-4x+4-4+6=(x-2)^2+2.$

Then find the vertwx of parabola. When x=2, f(2)=2 and the coordinates of the vertex are (2,2). The axis of symmetry passes through the vertex and is parallel to the y-axis. Therefore, its equation is x=2 (see attached graph for details).

Answer: x=2.

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Answer:

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3 years ago

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2 years ago

How many blue counters must be added so that the ratio of yellow counters to total counters is 1 to 6

Ivahew [28]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

If the diameter of the circle below is 16 in., what is the area of the circle?

mote1985 [20]

Answer:

64π inches² (approximately 201.06 inches²)

Step-by-step explanation:

$A=\pi r^2$ where $r$ is the radius

To find the radius, divide the diameter by 2

16 ÷ 2 = 8 inches

Plug in 8 as the radius

$A=\pi (8)^2\\A=64\pi$

$A=201.06$ (approximately)

Therefore, the area of the circle is 64π inches², or approximately 201.06 inches².

I hope this helps!

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3 years ago

Read 2 more answers

An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip is drawn.

Harlamova29_29 [7]

Answer:

(A) 0.04

(B) 0.25

Step-by-step explanation:

Let R = drawing a red chips, G = drawing green chips and W = drawing white chips.

Given:

R = 8, G = 10 and W = 2.

Total number of chips = 8 + 10 + 2 = 20

$P(R) = \frac{8}{20}=\frac{2}{5}\\P(G)= \frac{10}{20}=\frac{1}{2}\\P(W)= \frac{2}{20}=\frac{1}{10}$

As the chips are replaced after drawing the probability of selecting the second chip is independent of the probability of selecting the first chip.

(A)

Compute the probability of selecting a white chip on the first and a red on the second as follows:

$P(1^{st}\ white\ chip, 2^{nd}\ red\ chip)=P(W)\times P(R)\\=\frac{1}{10}\times \frac{2}{5}\\ =\frac{1}{25} \\=0.04$

Thus, the probability of selecting a white chip on the first and a red on the second is 0.04.

(B)

Compute the probability of selecting 2 green chips:

$P(2\ Green\ chips)=P(G)\times P(G)\\=\frac{1}{2} \times\frac{1}{2}\\ =\frac{1}{4}\\ =0.25$

Thus, the probability of selecting 2 green chips is 0.25.

(C)

Compute the conditional probability of selecting a red chip given the first chip drawn was white as follows:

$P(2^{nd}\ red\ chip|1^{st}\ white\ chip)=\frac{P(2^{nd}\ red\ chip\ \cap 1^{st}\ white\ chip)}{P (1^{st}\ white\ chip)} \\=\frac{P(2^{nd}\ red\ chip)P(1^{st}\ white\ chip)}{P (1^{st}\ white\ chip)} \\= P(R)\\=\frac{2}{5}\\=0.40$

Thus, the probability of selecting a red chip given the first chip drawn was white is 0.40.

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2 years ago