Tell whether the data show a direct variation. If so, Identify the constant of the variation. With steps.

How to do fractions Equations multiplication and division

anygoal [31]

Add subtraction multiplication and division

6 0

3 years ago

Read 2 more answers

Is 7 a solution of the equation 4x = 54? Explain.

vladimir1956 [14]

Answer: No

Step-by-step explanation:Divide 4 from both sides to find that x actually equals 13.5

6 0

3 years ago

The following set of coordinates most specifically represents which figure? (−5, 6), (−1, 8), (3, 6), (−1, 4) (6 points) Paralle

Vladimir [108]

Answer:

Rhombus

Step-by-step explanation:

The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).

We use the distance formula to find the length of AB.

$|AB|=\sqrt{(-1--5)^2+(8-6)^2}$

$|AB|=\sqrt{16+4}$

$|AB|=\sqrt{20}$

The length of AD is

$|AD|=\sqrt{(-1--5)^2+(6-4)^2}$

$|AD|=\sqrt{16+4}$

$|AD|=\sqrt{20}$

The length of BC is:

$|BC|=\sqrt{(-1-3)^2+(8-6)^2}$

$|BC|=\sqrt{16+4}$

$|BC|=\sqrt{20}$

The length of CD is

$|CD|=\sqrt{(-1-3)^2+(6-4)^2}$

$|CD|=\sqrt{16+4}$

$|CD|=\sqrt{20}$

Since all sides are congruent the quadrilateral could be a rhombus or a square.

Slope of AB $=\frac{8-6}{-1--5}=\frac{1}{2}$

Slope of BC $=\frac{8-6}{-1-3}=-\frac{1}{2}$

Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be a square. It is a rhombus

7 0

3 years ago

Read 2 more answers

3.

natima [27]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.

The store keeps an inventory of 80 shovels, then

x+y+z=80

The store always buy twice as many spade shovels as square, so

x=2z

The total cost of all shovels is

16x+9.60y+12.80z=1,072

a) The system of three equations is

$\left\{\begin{array}{l}x+y+z=80\\ \\x=2z\\ \\16x+9.60y+12.80z=1,072\end{array}\right.$

b) In matrix form this is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}80\\0\\1,072\end{array}\right)$

c) The determinant is

$\left\|\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right\|=0-32+9.60-0+19.20-12.80=-16$

d) Find three determinants:

$\left\|\begin{array}{ccc}80&1&1\\ 0&0&-2\\ 1,072&9.60&12.80\end{array}\right\|=0-2,144+0-0+1,536-0=-608$

$\left\|\begin{array}{ccc}1&80&1\\ 1&0&-2\\ 16&1,072&12.80\end{array}\right\|=0-2,560+1,072-0+2,144-1,024=-368$

$\left\|\begin{array}{ccc}1&1&80\\ 1&0&0\\ 16&9.60&1,072\end{array}\right\|=0+0+768-0-0-1,072=-304$

So,

$x=\dfrac{-608}{-16}=38\\ \\y=\dfrac{-368}{-16}=23\\ \\z=\dfrac{-304}{-16}=19$

e) If the store doubled all prices and inventory, then the new matrix is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 32&19.20&25.60\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}160\\0\\2,144\end{array}\right)$

7 0

3 years ago

What is the value of the expression below? (-8)^4/3 A. 32 B. 16 C. -16 D. 3

son4ous [18]

Answer:

-16

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers