Choose the true statement. -8 < 8 -8

The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant

ira [324]

$\bf \qquad \qquad \textit{double proportional variation}
\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\textit{\underline{y} varies directly with the square of \underline{x} and inversely with \underline{z}}}{y=\cfrac{kx^2}{z}}
\\\\\\
\textit{we also know that }
\begin{cases}
x=9\\
z=27\\
y=6
\end{cases}\implies 6=\cfrac{k9^2}{27}
\\\\\\
\cfrac{27\cdot 6}{9^2}=k\implies 2=k$

4 0

3 years ago

Julio’s rotation maps point K(–6, 9) to K’(9, 6). Which describes the rotation? A. 90 degrees clockwise rotation B. 180 degrees

andreyandreev [35.5K]

Answer:

The correct option is;

A. 90 degrees clockwise rotation

Step-by-step explanation:

From the given information, we have;

The coordinates of the pre-image is K(-6, 9)

The coordinates of the image is k'(9, 6) which is similar to a transformation of a pre-image of (x, y) to an image of (y, -x)

The transformation from (x, y) to (y, -x) can be obtained from either;

1) A rotation of 90° (clock wise)

2) A rotation of 270° counter clockwise

Therefore, the correct option that maps K(-6, 9) to K'(9, 6) is a 90 degrees clockwise rotation.

4 0

3 years ago

9x - 3y = -2 -3x + y = -3

morpeh [17]

Multiply 2nd equation by 3 and add to first
9x-3y=-2
-9x+3y=-9 +
0x+0y=-7

0=-7
false
no solution
these lines aer paraalell so no solution

6 0

3 years ago

Hi could you please tell me the answer to this?

devlian [24]

Answer:

5

Step-by-step explanation:

5

4 0

3 years ago

Question is down below

Bingel [31]

This is a great question!

To determine the probability with which two sweets are not the same, you would have to subtract the probability with which two sweets are the same from 1. That would only be possible if she chose 2 liquorice sweets, 5 mint sweets and 3 humburgs -

$Probability( 2 Liquorice) = 12 / 20 * 11 / 19$

As you can see, the first time you were to choose a Liquorice, there would be 12 out of the 20 sweets present. After taking that out however, there would be respectively 11 Liquorice out of 19 remaining. Apply the same concept to each of the other sweets -

$Probability(2 Mint ) = 5 / 20 * 4 / 19,\\Probability( 2 Humbugs ) = 3/20 * 2/19$

____

Calculate the probability of drawing 2 of each, add them together and subtract from one to determine the probability that two sweets will not be the same type of sweet!

$1-\left(\frac{132}{380}+\frac{20}{380}+\frac{6}{380}\right) =\\\frac{111}{190}$

Thus, the probability should be 111 / 190

5 0

3 years ago

Choose the true statement. -8 < 8 -8 > 8 -8 = 8