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2 years ago

The shaded octagon is transformed to the unshaded octagon in the coordinate plane below.

Mathematics

2 answers:

lions [1.4K]2 years ago

8 0

Answer:A

Step-by-step explanation:

bogdanovich [222]2 years ago

7 0

Answer:

The un-shaded octagon is a reflection because it is a flip over a diagonal line (y = -x) ⇒ answer A

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

- If the point (x , y) translated horizontally to the right by h units

∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

∴ Its image is (x , y - k)

* Lets solve the problem

- Look to the answer

# Answer D is wrong because the un-shaded octagon is not a vertical

translation because it is not directly under the shaded octagon.

# Answer C is wrong because the un-shaded octagon is not a

horizontal translation because it is not directly to the left of

the shaded octagon

# Answer B is wrong because the un-shaded octagon is not a dilation

because it is not smaller or bigger than the shaded octagon it has

the same size

# The answer A is the right because:

∵ The shaded octagon in the first quadrant and the un-shaded

octagon in the third quadrant

∵ The vertex of (2 , 1.5) has image (-1.5 , -2)

- The coordinates are replaced by each other the their signs are

changed

∴ The shaded is reflected across the line y = -x

* The un-shaded octagon is a reflection because it is a flip over a

diagonal line (y = -x)

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A poll found that 64% of a random sample of 1076 adults said they believe in ghosts.

Dennis_Churaev [7]

Answer:

Margin of error at 90% is 0.024

Margin of error at 99% is 0.037

Step-by-step explanation:

Sample size = 1076

A poll found that 64% of a random sample of 1076 adults said they believe in ghosts.

So, No. of adults said they believe ghosts = $\frac{64}{100} \times 1076=688.64\sim 688$

So, x = 688

n = 1076

$\widehat{p} = \frac{x}{n}$

$\widehat{p} = \frac{688}{1076}$

$\widehat{p} = 0.639$

$ME=z \times \sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}$

z at 90% confidence is 1.64

$ME=1.64 \times \sqrt{\frac{0.639(1-0.639)}{1076}}$

$ME=0.024$

So, margin of error at 90% is 0.024

Find the margin of error needed to be 99% confident.

z at 99% confidence is 2.58

$ME=2.58 \times \sqrt{\frac{0.639(1-0.639)}{1076}}$

$ME=0.024$

So, margin of error at 99% is 0.037

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2 years ago

The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the act

stealth61 [152]

Answer: 0.2551

Step-by-step explanation:

Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.

Significance level : $\alpha=1-0.95=0.05$

The critical z-value for 95% confidence : $z_{\alpha/2}=1.960$ (1)

Since , $z=\dfrac{x-\mu}{\sigma}$ (where x be any random variable that represents the temperature reading from a thermocouple.)

Then, from (1)

$\dfrac{x-\mu}{\sigma}=1.96\\\\ x-\mu=1.96\sigma$ (2)

Also, all readings are within 0.5° of μ,

i.e. $x-\mu$

i.e. $1.96\sigma$ [From (2)]

i.e. $\sigma$

i.e. $\sigma\approx0.2551$

The required standard deviation : $\sigma=0.2551$

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2 years ago

f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex

DerKrebs [107]

Answer:

see below

Step-by-step explanation:

f(x) = −16x^2 + 24x + 16

Set equal to zero to find the x intercepts

0 = −16x^2 + 24x + 16

Factor out -8

0 = -8(2x^2 -3x-2)

Factor

0 = -8(2x +1) (x-2)

Using the zero product property

2x+1 =0 x-2 =0

x = -1/2 x=2

The x intercepts are -1/2 ,2

Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum

The x value of the maximum is 1/2 way between the zeros

(-1/2+2) /2 = 1.5/2 =.75

To find the y value substitute into the function

f(.75) = -8(2x +1) (x-2)

=-8(2*.75+1) (.75-2)

= -8(2.5)(-1.25)

=25

The vertex is at (.75, 25)

We have the zeros, and the vertex. We know the graph is symmetrical about the vertex

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2 years ago

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timurjin [86]

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