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3 years ago

The following system of equations is _____.

1 answer:

7 0

First equation: y = -1/3x + 2/3
We can write it as : 1/3x + y = 2/3
Now, multiply the equation with 6,
2x + 6y = 4
Which is equal to 2nd equation!!

In short, The following system of equation is "Equivalent"

Hope this helps!

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Which graph shows the solution of the inequality −|x − 2| + 9 > 6?

mariarad [96]

answer is -1 < x < 5

-|x - 2|+ 9 > 6

Rearrange the terms

-|x - 2| > 6 - 9

-|x - 2| > - 3

then divide both sides of the inequality by the co- efficient of variable

|x - 2| < 3

convert the absolute inequality to standard inequality

-3 <x - 2 < 3

separate compound inequalities into system of inequality

{x - 2}> -3

{x - 2 < 3}

Rearrange variable to the left side of the equation

x > -3 + 2

calculate the sum or difference

x > -1

x -2 < 3

Rearrange variable to the left side of the equation

x < 3 + 2

calculate the sum or difference

x < 5

x > -1 and x < 5

Find intersection

-1 < x < 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

learn more about inequality equation here :https://brainly.in/question/15934172

SPJ9

4 0

8 months ago

At a given time of day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 4-ft

Gre4nikov [31]

4/0.8=X/7.04
0.8x=28.04
X= 35.05’

4 0

1 year ago

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

HELPLSPLSPLPSLPSLPSL

babunello [35]

Answer:

25.5

Step-by-step explanation:

first find the area od the rectangle than the triangle.

to find the area count the number of squares and use A=b*h

than do the same for the triangle using A=.5*b*h

15=3*5

10.5=.5*3*7

10.5+15=25.5

3 0

2 years ago

Item 10 A bacterial culture quadruples in size every hour. You begin observing the number of bacteria 3 hours after the culture

Vinvika [58]

Answer:

There will be 200 000 bacteria after 8 hours

Step-by-step explanation:

The crop quadruples every hour.

x represents the number of hours that pass after preparing the crop

y represents the number of bacteria after x hours.

The equation for y in function of x 3 hours after observing the crop is:

$y = 192(4^{x - 3})$

We want to know after how long there will be 200 000 bacteria.

Then we make y = 200 000 and clear x.

$200\ 000 = 192(4^{x - 3})\\\\log(200\ 000) = log(192(4^{x-3}))\\\\log(200\ 000) = log(192) + log(4 ^{x-3})\\\\log(200\ 000) - log(192) = (x-3)log(4)\\\\\frac{log(200\ 000) - log(192)}{log(4)} = (x-3)\\\\x = 3 + \frac{log(200\ 000) - log(192)}{log(4)}\\\\x = 8\ hours$

5 0

3 years ago