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?.

Answer:

The correct answer is A

Step-by-step explanation:

2 is exactly 7 units away from -5.

Answer:

x=y-p+q

Step-by-step explanation:

y=x+p-q

x=y-p+q

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
           

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

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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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

Answer:

207

Step-by-step explanation:

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

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

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]

Answer:

It's very interesting 4

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

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

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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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.

Answer:

4

Step-by-step explanation:

5

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

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

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

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

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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The value of y is 2.33924.

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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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.

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

Answer:

See below

Step-by-step explanation:

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.

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.

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

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.

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]

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

Step-by-step explanation:

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

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

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

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.

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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Answer:

8

Step-by-step explanation:

3 - -5 = 8

filling space here dont mind this

Answer:

it's helps with learning the difference of thr compound

Answer:

92

Step-by-step explanation:

46 + 46 = 92

value of a = 3

value of b = 2

a + b = 3 + 2 = 5 .