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4 years ago

6

A rectangle with a width of 2.5 cm and a length of 3 cm is dilated by a scale factor of 4. Which statements about the new rectan

gle are true? Check all that apply.
The dimensions of the new rectangle will be 10 cm by 12 cm.
The dimensions of the new rectangle will be 40 cm by 48 cm.
The new perimeter will be 4 times the original perimeter.
The new perimeter will be 16 times the original perimeter.
The new area will be 4 times the original area.
The new area will be 16 times the original area.
The new perimeter will be 44 cm.
The new area will be 30 square cm

1 answer:

jeka57 [31]4 years ago

6 0

Answer:1,3,5,7,

Step-by-step explanation:

When you are dilating the perimeter grows by the scale factor, and when you are dilating the area, it grows by the scale factor squared(16).

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago

Which set of ordered pairs in the form of (x,y) does not represent a function of x? {(-1,2), (3,-2),(0,1),(5,2}

serg [7]

For a relation to be a function it must be $one-to-one or many-to-one.$

$One-to-many$ relation is not a function.

In the above options, C is $One-to-many$ relation therefore cannot be a function.

The reason is that 3 alone maps onto -2 and 5, in the ordered pairs (3,-2) and (3,5). This disqualifies it from being a function.

Hence the graph of this relation will not pass the vertical line test

$The correct answer is C$

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3 years ago

Given the function f(x) = 3x + 1, evaluate f(a + 1). <br> A. 3a + 1 <br> B. a + 2<br> C. 3a + 4

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Answer:

Given the function f(x) = 3x + 1, evaluation of f(a + 1) gives:

C. 3a + 4

Step-by-step explanation:

Given function:

f(x) = 3x + 1

We have to find f(a+1).

For this purpose, we will take x = a+1 and

substitute it in the function f(x) = 3x+1:

f(x) = 3x + 1

f(a+1) = 3(a+1) +1

f(a+1) = 3(a) + 3(1) +1

f(a+1) = 3a+3+1

f(a+1) = 3a + 4

So the function f(a+1) is equal to option C. 3a + 4.

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zaharov [31]

Answer:

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Step-by-step explanation:

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SCORPION-xisa [38]

Answer:

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Step-by-step explanation:

<CGE:

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3 years ago

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