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3 years ago

Put these numbers in order from least to greatest. -8/20, 3/5, -16/32.

Mathematics

1 answer:

maksim [4K]3 years ago

3 0

Answer:

least to greatest: -16/32, -8/20, 3/5

Step-by-step explanation:

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brilliants [131]

Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

4 0

3 years ago

15y^-11/3y^-11, show steps I need help please don't understand how to do it.

tester [92]

One may note, you never quite asked anything per se, ahemm, if you meant simplification.

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\
-------------------------------\\\\
\cfrac{15y^{-11}}{3y^{-11}}\implies \cfrac{15}{3}\cdot \cfrac{y^{-11}}{y^{-11}}\implies 5\cdot y^{-11}\cdot y^{+11}\implies 5\cdot y^{-11+11}
\\\\\\
5y^0 \implies \boxed{5}$

8 0

3 years ago

For concreatting a tower cement, sand, stones are in the ratio 1:2:4 For 144kg sand.. What amount of cement is required?

Verdich [7]

Answer:

72 kg

Step-by-step explanation:

For concreatting a tower cement, sand, stones are in the ratio 1:2:4 For 144kg sand.. What amount of cement is required?

We are given the ratio

cement: sand:stones

= 1:2:4

The sum of proportion =

1 + 2 + 4 = 7

We are given the kg of sand = 144kg

Step 1

We find the total kg of cement, sand and stones = x

Using the proportion of sand,

2/7 of x = 144kg

2/7 × x = 144kg

2x/7 = 144kg

Cross Multiply

2x = 7 × 144kg

x = 7 × 144kg/2

x = 504kg

Therefore the total kg of cement, sand and stone = 504kg

Step 2

The amount of cement required is calculated as:

1/7 × 504 kg = 72 kg

Therefore, 72kg of cement is required.

4 0

3 years ago

Fernando has $50 in a savings account that earns 10% interest per year. The interest is not

DENIUS [597]

Answer: $5

Step-by-step explanation:

i = 50 x .10 x 1

i = 5

6 0

3 years ago

What is 8.461785 rounded to the nearest hundredth tenths

Pepsi [2]

8.46...hundredth. 8.5....tenths

4 0

3 years ago

Read 2 more answers