Quadrilateral PRST is transformed according to the rule (x, y) → (x + 9, y +4) to create quadrilateral P'R'S'T'.

Mathematics

1 answer:

malfutka [58]3 years ago

3 0

Answer:

C. The angle measures of quadrilateral P’R′S’T′ are equal to the corresponding angle measures of quadrilateral PRST.

Step-by-step explanation:

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PRACTICE ANOTHER A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into an

sergejj [24]

Answer:

Step-by-step explanation:

We have the equations

4x + 3y = 18 where x = the side of the square and y = the side of the triangle

For the areas:

A = x^2 + √3y/2* y/2

A = x^2 + √3y^2/4

From the first equation x = (18 - 3y)/4

So substituting in the area equation:

A = [ (18 - 3y)/4]^2 + √3y^2/4

A = (18 - 3y)^2 / 16 + √3y^2/4

Now for maximum / minimum area the derivative = 0 so we have

A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0

-3/8 (18 - 3y) + √3 y /2 = 0

-27/4 + 9y/8 + √3y /2 = 0

-54 + 9y + 4√3y = 0

y = 54 / 15.93

= 3.39 metres

So x = (18-3(3.39) / 4 = 1.96.

This is a minimum value for x.

So the total length of wire the square for minimum total area is 4 * 1.96

= 7.84 m

There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.

3 0

2 years ago

What is a true statement about negative exponents?

Nadya [2.5K]

Answer:

Raising something to a negative exponent is just taking the reciprocal of the amount.

Step-by-step explanation:

Let's assume that you wanted to know what $x^{-2}$ is.

To find it, you would take the reciprocal of the x amount. So $x^{-2}$ becomes $\frac{1}{x^{2}}$ .

This works because of the nature of exponents. Exponents represent the number of times you are multiplying a value by itself. So $a^{3}$ would be equal to a · a · a. To increase the exponent, you increase the number of times the value is multiplied by itself: To increase $a^{3}$ to $a^{5}$ , you would have to multiply a with $a^{3}$ two more times (a · a · a · a · a). To decrease the exponent, you must divide the value by itself. So to decrease $a^{5}$ to $a^{2}$ , you would have to divide $a^{5}$ by a 3 times.

If the exponent is 0, the value is equal to 1. But you can still decrease the exponent into negative numbers. You just divide 1 by a the desired amount of times: $\frac{1}{a^{3}}$ means that you are dividing 1 by a 3 times.