Why is it important to keep the two sides of an equation balanced when solving? what other properties do we use to rewrite expressions and equations?.

Answers

Answer 1

"Law of conservation of Mass and Energy", is the reason for which it is important to keep the two sides of an equation balanced when solving.

The other properties that we should consider while rewriting the expressions of an equation is that we should not multiply or divide the expressions by zero on both the sides.

According to the law of conservation of mass, mass is neither generated nor destroyed during a chemical process. For instance, when coal is burnt, the carbon atom in it transforms into carbon dioxide. The carbon atom transforms from a solid to a gas, yet its mass remains constant. Similar to this, according to the law of conservation of energy, energy cannot be generated or destroyed. For instance, kinetic energy is converted to potential energy when a toy vehicle is rolled down a ramp and collides with a wall.

While rewriting expressions of an equation, we should not multiply or divide them by zero, as multiplying or dividing by zero makes two non-equal expressions equal (0 and ∞ respectively.

This is the reason why is it important to keep the two sides of an equation balanced, and that the expressions should not be multiplied or divided by zero.

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Related Questions

Solve the equation for 0 <= x < 2pi.

(2sin x - 1)(2cos^2 x - 1) = 0

Answers

If

(2 sin(x) - 1) (2 cos²(x) - 1) = 0

then either

2 sin(x) - 1 = 0   or   2 cos²(x) - 1 = 0

sin(x) = 1/2   or   cos(2x) = 0

The first equation gives two families of solutions,

x = arcsin(1/2) + 2nπ = π/6 + 2nπ

x = π - arcsin(1/2) + 2nπ = 5π/6 + 2nπ

where n is any integer; we get the solutions x = π/6 and x = 5π/6 in the interval 0 ≤ x < 2π when n = 0.

The second equation also gives two families of solutions,

2x = arccos(0) + 2nπ = π/2 + 2nπ

2x = -arccos(0) + 2nπ = -π/2 + 2nπ

Divide both sides by 2 :

x = π/4 + nπ

x = -π/4 + nπ

Then the solutions we want are x = π/4 and x = 5π/4 (when n = 0 and 1 in the first family, respectively) and x = 3π/4 and x = 7π/4 (when n = 1 and 2 in the second family).

We have 6 solutions, so A is the correct choice.

the expression 5 3/2 is equivalent to
to √5³

Answers

Step-by-step explanation:

[tex] = {5}^{ \frac{3}{2} } [/tex]

[tex] = \sqrt[2]{ {5}^{3} } [/tex]

[tex] = \sqrt{ {5}^{3} } [/tex]

Which function is increasing at the highest rate? A. B. A linear function on a coordinate plane passes through (minus 1, 3), and (2, minus 3) which intercepts axis at (0.5, 0), and (0, 1) C. A linear function, f, with an x-intercept of 8 and a y-intercept of -4. D. x 1 2 3 4 5 g(x) -5 -4 -3 -2 -1

Answers

The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.

The options are given in the image attached with the answer

What is a Function ?

A function is a law that relates a dependent variable and an independent variable.

It is asked among the options given , which is increasing at the highest rate.

To increase at a rate , the value of the slope , m should be > 0

For the Option 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

For Option 2

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

For option 3

m = (-4 + 5)/(2-1) = 1

For Option 4

(8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

The highest rate on increasing is of 12x -6y = -24

Therefore Option B is the correct answer.

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Please help!!
Construct the circle that circumscribes image DEF.

Answers

Answer:

See below

Step-by-step explanation:

General outlineConstruct the perpendicular bisectors of DE, EF, and DF.Identify the circumcenter. Draw the circumcircle.

Circles & Circumcircles

To construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.

Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle.  The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.

Constructing perpendicular bisectors

To construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).

So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.

Finding a point that is equidistant from two given points

Set the compass to any radius that is larger than half the distance between the two endpoints.  If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.

Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice.  If uncertain, draw the entire circle.  Keeping the radius saved.

With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times.  If it doesn't intersect two times, the radius chosen at the beginning was too small.  Start the entire process over with a larger radius.

These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.

Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.

Process

Steps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):

Set compass radius to length DEDraw circle, centered at D, through E.  Keep radius set.Draw circle, centered at E, through D.Identify points of intersection of the circles from steps 2 & 3, M & NDraw line  MNSet compass radius to length EFDraw circle, centered at E, through F.  Keep radius set.Draw circle, centered at F, through E.Identify points of intersection of the circles from steps 7 & 8, Q & RDraw line  QRSet compass radius to length DFDraw circle, centered at D, through F.  Keep radius set.Draw circle, centered at F, through D.Identify points of intersection of the circles from steps 12 & 13, S & TDraw line  STIdentify point of concurrency of line MN, line QR, and line ST;  label it point PSet compass radius to length DP (or EP, or FP)Draw circle, centered at P, through points D, E, and F.

Note:  Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three.  So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.

Kyla has the number of cherries that Denise has. If Kyla has 46 cherries, how many cherries do they have altogether?​

Answers

Answer:

92

Step-by-step explanation:

46 + 46 = 92

Answer: 92
Explanation:
46+46=92

Add the following two numbers in scientific notation.

Answers

Answer:

3.31 x 10^4

Step-by-step explanation:

3.111 x 10^4 is 31110

2 x 10^3 is 2000

31110 + 2000 = 33100 or 3.31 x 10^4

Answer:

b) 3.31 × 10⁴

Explanation:

[tex]\sf \rightarrow \left(3.11\cdot 10^4\right)+ \left(2\cdot 10^3\right)[/tex]

remove parenthesis

[tex]\rightarrow \sf 3.11\cdot \:10^4+2\cdot \:10^3[/tex]

simplify

[tex]\rightarrow \sf 31100+2000[/tex]

add the numbers

[tex]\sf \rightarrow 33100[/tex]

convert to scientific form

[tex]\sf \rightarrow 3.31 \ x \ 10^4[/tex]

the question is below

Answers

Answer:

B. $4.75

Step-by-step explanation:

3(4) + 7 = 19

19/4=4.75

Answer:

B

Step-by-step explanation:

First, 3n + 7 while n = 4 then 3*4 = 12 + 7 = 19. Next, you do 19/4 which is
            n
equal to 4.75.



I Hope This Helped :D
           

Can someone help me please?

Answers

Answer:

C.

Step-by-step explanation:

The reds are counting up in whole numbers by one integer.

Hope this helps!

If not, I am sorry.

180 is equivalent to π/2 radians

true
false

Answers

Answer:

[tex]\fbox {False}[/tex]

Step-by-step explanation:

To convert a degree measure to radian measure, multiply with π/180.

⇒ 180 × π/180

⇒ π radians

false is the answers

please mark me as brainlest

What is the area of Victor’s storage space?

Answers

The area of victor's storage space is 28 square inches

What is a polygon?

A polygon is a plane shape with at least three sides.

Analysis:

Area of storage = area of triangle + area of rectangle

Height of triangle = 5 - 3 = 2 inches

Base of triangle = 12 - 4 = 8 inches

length of rectangle = 5 inches

width of rectangle = 4 inches

Area of storage = 5 x 4 + 1/2 x 8 x 2 = 28 square inches

In conclusion, the area of the storage space is 28 square inches.

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r=
help me please thank u​

Answers

Answer:

[tex]\fbox {r = 34}[/tex]

Step-by-step explanation:

Finding IQ and RJ by tangent rule :

⇒ IQ = QK = 10

⇒ KR = RJ = 8

Finding PJ :

⇒ PJ = 32 - 8

⇒ PJ = 24

∴ But PJ = PI (by tangent rule)

⇒ PI = 24

Finding r :

⇒ PI + IQ

⇒ 24 + 10

r = 34

Please can someone help asap thank you !x

Answers

Answer:

Step-by-step explanation:

Gradient is the slope, the rise over run, change in y over change in x.

For line A

6/3=2

Gradient=2

For Line B

5/5 =1

Gradient =1

Answer:

•The coordinates of line A (0,1) and (1,3)

gradient formula : y2-y1/x2-x1

gradient :

3-1/1-0=2

Actually you can take any other coordinates for reference!

example :

the other coordinates of line A (0,1) and (2,5)

=5-1/2-0

=2 (same)

•The coordinates of line B (3,2) and (4,1)

Gradient : =1-2/4-3

=-1

or

the coordinat B =(7,-2) and (-2,7)

=7-(-2)/-2-7

=9/-9

=-1

Note:The line to the right has a positive gradient, and the line to the left has a negative gradient

solve for y in 1/8^2-3y=2^y-2

Answers

The value of y is 2.33924.

What is equation?

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

Given:

(1/8)²-3y = [tex]2^{y}[/tex]-2

1/64 - 3y =  [tex]2^{y}[/tex]-2

1/64+ 2 =  [tex]2^{y}[/tex]+3y

129/2 =  [tex]2^{y}[/tex]+3y

Taking log on both side

log 129 - log 2 = y log 2 + 3 log y

2.11 - 0.301 = 0.301 y + 3 log y

1.809 = 0.301 y + 3 log y

1.809/3= 0.1 y + log y

0.603 = 0.1 y + log y

y = [tex]10^{\frac{603-100y}{1000}}[/tex]

y= 2.33924

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2.2.5a (Part 1): For the graph below, what is the x-intercept? *
-4 -2
2
-2
-4
y
2
4
0 points
X

Answers

An x-intercept is the point where the line of a graph passes through the x-axis. Thus, you should look for this point on the given graph.

What is a graph?

A graph can be defined as a type of chart that is used for the graphical representation of data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.

In Mathematics, x-intercept refers to the point where the line of a graph passes through the x-axis as shown in the image attached below. Since the graph wasn't provided for this question, you should look for the point where the line passes or crosses through the x-axis.

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What is the difference between -5 and 3?

Answers

Answer:

8

Step-by-step explanation:

3 - -5 = 8

filling space here dont mind this

8 because 3- -5=8 when u subtract a negative from a negative it becomes positive

The subject of the formula below is y.
y=X+p-q
Rearrange the formula to make x the subject.

Answers

Answer:

x=y-p+q

Step-by-step explanation:

y=x+p-q

x=y-p+q

Which is the simplified form of x-12?
O 12
O
O
*12
12
17/7/22

Answers

Applying the negative exponent rule, the simplified form of  [tex]x^{-12}[/tex] is: [tex]\frac{1}{x^{12}}[/tex].

What is the Negative Exponent Rule?

The negative exponent rule states that, if [tex]x^{-a}[/tex] then, it can be rewritten as, [tex]\frac{1}{x^a}[/tex].

Given the expression, [tex]x^{-12}[/tex], we can apply the negative exponent rule to rewrite the expression in simplified form as:

[tex]\frac{1}{x^{12}}[/tex].

Therefore, expressing  [tex]x^{-12}[/tex] in a simplified form will give us: [tex]\frac{1}{x^{12}}[/tex].

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Solve the following quadratic by
completing the square.
y = x2 - 6x +2

Answers

Answer: [tex]3 \pm \sqrt{7}[/tex]

Step-by-step explanation:

[tex]1) \text{ } x^{2}-6x+2=0\\\\2) \text{ } x^{2}-6x=-2\\\\3) \text{ } x^{2}-6x+\left(\frac{-6}{2} \right)^{2}=-2+\left(\frac{-6}{2} \right)^{2}=7\\\\4) \text{ } (x-3)^{2}=7\\\\5) \text{ } x-3 =\pm \sqrt{7} \longrightarrow \boxed{3 \pm \sqrt{7}}[/tex]

A cone with radius 2 units is shown below. Its volume is 29 cubic units.
2
h
Find the height of the cone.
Use 3.14 for π and round your final answer to the nearest hundredth.
units

Answers

Answer:

It's very interesting 4

Answer = 6.93
Reason
Formula for cone
V= 1/3 pi r^2 h
Fill in the values we know
29 = (1/3) (3.14) (2^2) h
29 = (1/3) (3.14) (4) h
Multiply numbers in parenthesis
29 = 4.187 h
Now isolate “h” by dividing both sides by 4.187

6.93 = h

What is the probability of drawing a red card, replacing it, and then drawing an odd card?
4 red 5 blue 6 red 7 blue 8 blue

Answers

Answer:

4

Step-by-step explanation:

5

Jack goes to a restaurant in a state with a 7.25% sales tax. He buys a
meal and tips 20% before tax. Select the meal cost that would allow his
total bill, including tip and tax, to have a total cost equal to $15.

Answers

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the meal cost, hence:

Total cost = x + 0.2x + 0.0725x

15 = 1.2725x

x = 11.79

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

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what is 3x+2y=6 ordered pair?

Answers

The ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

What is an equation?

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

We have an equation 3x + 2y = 6 now the ordered pair of the equation will be found by the graph will be ( 0,3) and ( 2, 0). The graph is also attached with the answer below.

Therefore the ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

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What is the equation of the line that passes through (-3, 4) and (3, -2)?

y = - x - 1
y = x + 7
y = x - 1
y = - x + 1

Answers

Answer:

y = -x +1

Step-by-step explanation:

p1 (-3,4)

p2 ( 3, -2)

line equation y = mx + b

The slope m equals

[tex] \frac{y2 - 21}{x2 - x1} [/tex]

[tex] \frac{ - 2 - 4}{3 - - 3} = \frac{ - 6}{6} = - 1[/tex]

y = - x + b

from any point

-2 = -3 + b

b = 1

line equation = y = -x +1

Just plugging the points into the equations, both fit y=-x+1

Hope this helps

It Sami anual Compound interest is applied interest, what instead of anual compound will be the profit of an investor It Sami anual Compound interest is applied interest , what instead of anual compound will be the profit of an investor.​

Answers

Answer:

it's helps with learning the difference of thr compound

Find the values of a and b 3 * 2 = a + b if​

Answers

value of a = 3

value of b = 2

a + b = 3 + 2 = 5 .

Pls answer this asap

Answers

A and C should be right

Answer:

The correct answer is A

Step-by-step explanation:

2 is exactly 7 units away from -5.

The price of one kilograms of apple at a fruit mart is $4.00. If there is a special price this week with a
15% discount, how much do I need to pay if I buy 3 Kg of apple?

Answers

Answer
$10.20
Step by step explanation

4.00 × 15 ÷ 100 = 0.6

4.00 - 0.6 = 3.4

3.4 × 3 = 10.2

24. Kyla has 2/7the amount of cherries that Denise has. If Kyla has 46 cherries, how many cherries do they have altogether​

Answers

Answer:

207

Step-by-step explanation:

Denise has 46(7/2) = 161 cherries.

So, they have a total of 161 + 46 = 207 cherries

The answer is 161 cherries.

You can find this out by doing a reverse division problem. Take the 46 and put it over 1 as so (46/1). You will then want to multiply it by the reciprocal or the opposite of 2/7th which is 7/2. Once you do the equation (46/1)•(7/2) you will get 161!

(02.01)
Solve for x: (x+20)/2=3x

Answers

When this equation is solved, the answer is X = 4

Find the values of the variables indicated below

M=

K=

Answers

Answer:

m=120

k=60

Step-by-step explanation:

a trapezoid has 360 degrees. subtract 120 degrees to get 240 degrees. we know that m=2k. 240=2k+2k which is 4k. 240 is 4k. k=60. m=2k, so mulitply 60 by 2 to get m=120

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