Simplify: (12j2)5(25j3)2.

Answer:

The value of the rational expression when x = -3 is undefined.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Rational Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]

Step 2: Find Value

∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.

___

Topic: Algebra II

Answer:

Step-by-step explanation:

Two legs of a right triangle measure 3 inches and 4 inches. Which of the following choice for the length of the third side will make the triangle a right triangle?

x = √(3²+4²)

x = √(9 + 16)

x = √25

Answer:

Step-by-step explanation:

An coincident system of equations means that it has infinite solutions, because one line is on the other one. This happens when their equation are the same, or their "parent" line is the same.

So, given equations are:

6x + 4y = 2 and 3x + 2y = 1

Observe that if we divide the first by 2, we have

[tex]\frac{6x+4y}{2} =\frac{2}{2}[/tex]

[tex]\frac{6x}{2}+\frac{4y}{2} =1[/tex]

[tex]3x+2y=1[/tex]

As you can see, using the first equation, we found that it has the same "parent" equation than the second equation. In other words, they are basically the same. This means that they represent the same line, so, the system is coincident and they have infinite solutions.

The answer is coincident :)

Answer:

lol

Step-by-step explanation:

A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.

In this question we are provided with the perimeter of a rectangle fence that is 200 feet. It is also given that the length of the fence is twice its breadth. We are asked to calculate it's dimensions.

First we will form an equation.

Let us assume the breadth as x

Then, length = 2x

It is given that the perimeter is 200 feet.

We know,

[tex] \bull \: \small\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]

Substituting the values we get

[tex] \small\sf{ 200 = 2(2x + x)}[/tex]

Now we will solve this equation and find out the value of x.

[tex] \small\sf{ 200 = 2(2x + x)}[/tex]

[tex] \longmapsto \small\rm{ 200 = 2(3x )}[/tex]

[tex] \longmapsto \small\rm{200 = 6x} [/tex]

[tex] \longmapsto \small\rm{ \dfrac{ \cancel{200} \: \: 33.33}{ \cancel{6}} = x } [/tex]

[tex] \small\sf{x = 33.33} [/tex]

We will substitute the value of x = 33.33.

Length = 2x = 2 × 33.33 = 66.66 feet

Breadth = x = 33.33 feet

The graph is showing the equation of circle x²+y²=4

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.

The equation will be as follows:-

x²+y²=4

Hence the graph is showing the equation of circle x²+y²=4

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Step-by-step explanation:

If you agree that increasing age (for elementary school children) causes increasing foot size, and therefore increasing shoe size, then you expect a correlation between age and shoe size. Correlation is symmetric, so shoe size and age are correlated.

Answer:

The answer should be $1127.74

Answer: The formula for area of a triangle is area equals base times height divided by 2. the height is 5 units.

Step-by-step explanation:

It is a quadrilateral, parallelogram, and a rhombus

Answer:

quadrilateral, parallelogram, and rhombus.

Step-by-step explanation:

All quadrilaterals have 4 sides, all parallelograms have 2 sets of parallel sides, and a rhombus has diagonals that bisect each other perpendicularly.

Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .

Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.

First find the difference in longitudes:

= Singapore - Quito

= 104 - (-78.5) because Quito is west

= 104 + 78.5

= 182.5°

Then subtract this from 360°:
= 360 - 182.5

= 177.5°

Every 1° longitude along the Equator is 111 km so the shortest distance is:

= 177.5 x 111

= 19,702.5 km

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Answer:

288 m^3

Step-by-step explanation:

V=(1/3)Bh, where B is base, and h is height

The base will use the equation A=(1/2)bh

B = (1/2)12x9

B = 54

the height is given: 16m

substitute into Volume equation:

V=(1/3)54x16

V=288

Answer:

Using 22/7 as pi, the area of a circle with a diameter of 14 metres is:

154 m²

Step-by-step explanation:

To solve, use the formula for the area of a circle.

Remember the formula for area of a circle. Be careful not to mix up the formula for area with the formula for circumference!

[tex]A = \pi r^{2}[/tex]

From the question, we know:

To use the formula, we need the radius ("r").

The radius is a line that goes from the centre point of the circle to the circle outline. It is half the length of the diameter.

The diagram shows the diameter ("d"), which goes through the centre point of the circle. It is twice the length of the radius.

Solve for "r".

r = d/2

r = (14 m)/2

r = 7 m

Substitute r = 7 m and π = 22/7  into the formula for the area of a circle.

[tex]A = \pi r^{2}[/tex]                         Start with the formula and substitute.

[tex]\displaystyle{A = \frac{22}{7} (7\ m)^{2}}[/tex]                Square "7" and the "m".

Remember that the answer for area is always squared units.

[tex]\displaystyle{A = \frac{22}{7} (49\ m^{2})}[/tex]      

Multiplying a fraction and whole number is the same as multiplying the whole number in the numerator (top of the fraction).

[tex]\displaystyle{A = \frac{22*49}{7}m^{2}}[/tex]              Simplify the numerator.

[tex]\displaystyle{A = \frac{1078}{7}m^{2}}[/tex]                  Divide.

[tex]A = 154\ m^{2}[/tex]                   Final answer

∴ The area of the circle is 154 m².

Answer:

448 fl oz/week

Step-by-step explanation:

1 week = 7 days

4 pints per day × 7 days/week = 28 pints per week

1 pint = 16 fl oz

28 pints/week × 16 fl oz/pint = 448 fl oz/week

a) Line AE, and Line BC are parallel

b) Line ED, and Line CD

c) 3

Step-by-step explanation:

Answer:

so first do nothing and just fail health class

The value of y that satisfies given conditions is y = - 8.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

We also know that slope(m) = (y₂ -y₁)/(x₂ - x₁).

So, lines parallel to each other have the same slope hence to find the value of y we'll equate their slopes.

∴ (3 - 9)/(4 + 4) = (y - 1)/(4 + 8).

-6/8 = (y - 1)/12.

-3/4 = (y - 1)/12.

-36/4 = y - 1.

- 9 = y - 1.

 y = - 8.

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Answer:

  x = -47.1

  x = -3.35454... (2-digit repeat)

Step-by-step explanation:

Each of the absolute value functions causes the overall behavior of the equation to change where that absolute value function's argument is zero. Those values of x are -7, -5/2, -2/5.

These breakpoints cause the domain of the equation to be divided into 4 parts. A graphing calculator shows us that solutions exist only in the two regions ...

In those regions, the equation simplifies to ...

  2(-(x +2/5)) -2(-(x +7)) = 2/3x +(-(x +5/2))

  x(-2 +2) -4/5 +14 = x(2/3 -1) -5/2 . . . . collect terms

  15.7 = -1/3x . . . . . . add 5/2

  x = -47.1 . . . . . . . multiply by -3

__

  2(-(x +2/5)) -2(x +7) = 2/3x +(-(x +5/2))

  x(-2 -2) -4/5 -14 = x(2/3 -1) -5/2 . . . . collect terms

  (-3 2/3)x = 12.3 . . . . . . . . add 1/3x +14.8

  x = -36.9/11 = -369/110

  x = -3 39/110 ≈ -3.35454... (2-digit repeat)

The option (A) 63 inches to 81 inches is correct after using the empirical Rule.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have:

The mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height

99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.

The lower range = 72 – 3(3) = 63 inches

The upper range = 72 + 3(3) = 81 inches

Thus, the option (A) 63 inches to 81 inches is correct after using the empirical Rule.

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Answer:

24 ft

Step-by-step explanation:

to find the perimeter of rug is you have to add 9+9+3+3= 24

Since the variable x is the numerator of the fraction, we first need to multiply each side by 6, since the denominator is 6. After doing this, the equation should now look like this: [tex]18 = x + 31[/tex]. Next, we subtract 31 from 18 following the rule. 18 - 31 = -13. x is equal to -13.

For shown work in order:

[tex](6) 3 = x +31[/tex]

[tex]18 = x + 31[/tex]

[tex]18 - 31 = x[/tex]

[tex]x = -13[/tex]

Step-by-step explanation:

the area of a triangle is always

baseline × height / 2

where baseline and height are perpendicular (at a 90° angle) to each other.

so, in our case the area is

7 × 2 / 2 = 7 × 1 = 7 units²

The equation that can be used to find out the total time it will take to William to mow the lawn is (75n) / 100=33.

This is a mathematical expression that represents a situation including a value that is not known.

In this case the best equation would be 75n / 100=33 as this is the only one that includes all the factors:

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Answer:

Step-by-step explanation:

4x + 2 = 11

4x = 9

x = 9/4

2(9/4) - 1

9/2 - 2/2= 7/2

The possible number represented by the 9 counter is 27

The counters are given as:

12 counters and 15 counters

When added, we get a number that can be represented by 9 counters.

This means that:

12 + 15 = 9x

Evaluate the sum

27 = 9x

Divide by 9

x = 3

When subtracted, you need more than 9 counters.

This means that:

x = 15 - 12 = 3

So, we conclude that the number is a multiple of 3 and 9

In other words, the decimal number is a multiple of 9 (i.e. 27)

Hence, the possible number is 27

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Answer:

D. 60

Step-by-step explanation:

210 baseballs divided evenly between 7 trash bins = 30 balls per bin

2 trash bins multiplied by 30 balls per bin = 60 balls in two bins

Hope this helps!

Answer:

[tex]\huge\boxed{\sf x > -1.25}[/tex]

Step-by-step explanation:

0.2 (x + 20) - 3 > -7 - 6.2x

Distribute

0.2x + 4 - 3 > -7 - 6.2x

0.2x + 1 > -7 - 6.2x

Add 6.2x to both sides

0.2x + 6.2x + 1 > -7

6.4x + 1 > -7

Subtract 1 to both sides

6.4x > -7 - 1

6.4x > -8

Divide 6.4 to both sides

x > -8/6.4

x > -1.25

[tex]\rule[225]{225}{2}[/tex]

Answer:

x > -1.25

Step-by-step explanation:

Using the distributive property: a(b + c) → ab + ac

1. Distribute '0.2'

0.2(x) + 0.2(20) - 3 > -7 - 6.2x

0.2x + 4 - 3 > -7 - 6.2x

0.2x + 1  > -7 - 6.2x

2. Add '6.2x' to both sides

0.2x + 6.2x + 1  > -7 - 6.2x + 6.2x

6.4x + 1 > -7

3. Subtract '1' from both sides

6.4x + 1 - 1 > -7 - 1

6.4x > -8

4. Divide both sides by '6.4' to isolate the variable

6.4x ÷ 6.4 > -8 ÷ 6.4

x > -1.25

Final answer: x > -1.25

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Answer:

B. None of these

Step-by-step explanation:

There are a total of 12 coins in your pocket.

The probability of drawing a nickel first is 5/12

Since you return the coin, the total number of coins in your pocket doesn't change.

The probability of drawing a dime second is 7/12

Since this is a compound probability problem, multiply the two probabilities together.

5/12 x 7/12 = 35/144

35/144  = 0.243

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

[tex] log_{4}x = k \\ \\ \longrightarrow \: log_{4}x = log_{2 {}^{2} }x \\ \\ \longrightarrow \: 2 log_{2}x \\ \\ now , \\ \\ log_{2}x = k \\ \\ \therefore \: 2( log_{2}x) = 2(k) \\ \\ \longrightarrow \: 2k[/tex]

hope helpful ~