All categories

2 years ago

Please help!!! The question is in the image below.

Mathematics

1 answer:

Sergeeva-Olga [200]2 years ago

7 0

<h3>Answer:</h3>

Vertical scaling by a factor of 1/2
Vertical translation 5 units downward

<h3>Explanation: </h3>

Multiplying a function value by a constant effectively applies a vertical scale factor to that function. The scale factor is the constant. Here, the parent function x² is multiplied by 1/2 (to give 1/2x²). The vertical scale factor is 1/2.

Adding a constant to a function value causes a vertical translation of that function. Every output value is moved upward (translated) by the amount that is added. Here, that added amount is -5, so the vertical movement is downward 5 units.

For f(x) = x², vertical scaling by a factor of 1/2 makes it 1/2x². Translating that downward 5 units makes it ...

... y = 1/2x² - 5 . . . . . . . . . x² scaled and translated

You might be interested in

Which is equivalent to V180x11 after it has been simplified completely?

inna [77]

Question:

Which is equivalent to $\sqrt{180x^{11}}$ after it has been simplified completely?

Answer:

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

Step-by-step explanation:

Given

$\sqrt{180x^{11}}$

Required

Simplify

We start by splitting the square root

$\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}$

Replace 180 with 36 * 5

$\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}$

Further split the square roots

$\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}$

Replace power of x; 11 with 10 + 1

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}$

From laws of indices; $a^{m+n} = a^m * a^n$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}$

Further split the square roots

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}$

From laws of indices; $\sqrt{a} = a^{\frac{1}{2}}$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}$

Rearrange Expression

$\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}$

From laws of indices; $\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}$

So, we have

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}$

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

<em>The expression can no longer be simplified</em>

Hence, $\sqrt{180x^{11}}$ is equivalent to $6x^{5}\sqrt{5x}$

7 0

2 years ago

Read 2 more answers

There are 28 students in the class and 1316 blocks. If the blocks are divided equally among the students, how many does each stu

Yanka [14]

Answer:

Step-by-step explanation:

5 0

2 years ago

Two choices greater than 3/5

Nata [24]

Answer:

39/50 is larger than 3/5.

Step-by-step explanation:

2/3 is larger than 3/5.

4 0

1 year ago

An object consisting of two endpoints and all of the points between them

Over [174]

that'd be a segment.

⭕-------------------------------------⭕

3 0

2 years ago

If the area of the larger circle is 25 times the area of the smaller circle, then the radius of the larger circle is how many ti

IrinaVladis [17]

Answer:

easy peasy (again)

Step-by-step explanation:

given is that, area of the larger one is 25 times more than the smaller one

so, just put it in the area formula,

let the radius of the larger circle be represented by = R

and of the smaller circle be = r

then, (pi) (R)^2 =25 x (pi) (r)^2

=> dividing the equation by pi on both sides, also taking square root on both sides

=> R = 25 r

that would be the radius of the larger circle is 25 times bigger than the smaller radius

(all u need is to pay attention to the data given in the question and the relation between all that data itself) then it'll look like magic of how the question gets solved...the answer is always in front of you, only thing is to look harder ...good luck with what you are aiming to achieve

3 0

2 years ago