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3 years ago

The perimeter of the blueprint is represented by the equation P=8x. What is the equation of the perimeter when solved for x

Mathematics

1 answer:

Korvikt [17]3 years ago

5 0

Answer:

x = P/8

Step-by-step explanation:

The perimeter of the blueprint is given by the equation :

P = 8x

We need to solve the above equation for x.

Dividing both sides of the equation by 8.

$\dfrac{P}{8}=\dfrac{8x}{8}\\\\x=\dfrac{P}{8}$

Hence, the value of x is P/8

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3 years ago

in a five character password the first two characters must be digits and the last three characters must be letters if no charact

Vilka [71]

Answer:

1,404,000 unique passwords are possible.

Step-by-step explanation:

The order in which the letters and the digits are is important(AB is a different password than BA), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this question:

2 digits from a set of 10(there are 10 possible digits, 0-9).

3 characters from a set of 26. So

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3 years ago

How is the graph of the parent quadratic function transformed to produce the graph of y = negative (2 x + 6) squared + 3?

bearhunter [10]

We start with the parent function

$f(x)=x^2$

The first child function would be

$g(x)=(2x)^2$

We have multiplied the input of the function by a constant: we have

$g(x)=f(2x)$

This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.

The second child function would be

$h(x)=(2x+6)^2$

We added 6 to the input of the function: we have

$h(x)=g(x+6)$

This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.

The third child function would be

$l(x)=-(2x+6)^2$

We changed the sign of the previous function (i.e. we multiplied it by -1): we have

$l(x)=-h(x)$

This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.

The fourth child function would be

$m(x)=-(2x+6)^2+3$

We added 3 to previous function: we have

$m(x)=l(x)+3$

This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.

Recap

Starting from the parent function $y=x^2$ , we have to:

Compress the graph horizontall, with scale factor 2;
Translate the graph 6 units to the left;
Reflect the graph across the x axis;
Translate the graph 3 units up

Note that the order is important!

5 0

3 years ago

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