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3 years ago

1. Which of these transformations are isometries? The diagrams are not drawn to scale.

Mathematics

1 answer:

lisov135 [29]3 years ago

6 0

In math, an isometry is a congruent transformation in which the distance (or length) and the angle is preserved or remains the same even after the transformation.

The transformation can be translation, rotation, reflection, etc.

Let us not use this definition of isometry to answer our question, one at a time.

(I) In here, as we can see the distances 10 and 5 and the angle 43 degrees has been preserved. So, this is an isometry.

(II) In here, distances have been halved, so this is not an isometry, even though the angles have been preserved.

(III) In here, the corresponding distances and the angles have been preserved. So, this is an isometry.

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Step-by-step explanation:

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3 years ago

Find the domain and range of f(x). Please explain your answer. f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

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2 years ago

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yKpoI14uk [10]

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3 years ago

The batting averages for seven baseball players are listed below. 0.176, 0.235, 0.272, 0.158, 0.201, 0.255, 0.303 What is the in

bonufazy [111]

Answer:

Interquartile Range= 0.079.

Step-by-step explanation:

Given,

The batting averages for seven baseball players are

0.176, 0.235, 0.272, 0.158, 0.201, 0.255, 0.303

First we have arrange the data in descending order or ascending order.

The ascending order of the data is

0.158, 0.176, 0.201, 0.235, 0.255, 0.272, 0.303

Median: The middle term of the data is the median of the data.

Here

Median = 0.235

First quartile: The median of the lower half of data.

The lower half of the data is 0.158, 0.176, 0.201

$Q_1=0.176$

Third quartile: The median of the upper half of data.

The upper half of the data is 0.201, 0.255, 0.303

$Q_3=0.255$

Interquartile: The difference between first quartile and third quartile.

Interquartile Range = $Q_3-Q_1$

=(0.255- 0.176)

=0.079

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3 years ago