Simplify each expression.

log₃(x+1)-log₃(3 x²-3 x-6)+log₃(x-2)

The function is equal to zero when x = -3 or +4

We know that a function is a mathematical rule. It is an instruction to perform an operation on a given set of values. In this case, we have the function given as; f(x)= x^2-x-12/x^2+x-12. Recall that the function is equal to zero when the numerator is equal to zero.

Now we have to solve the quadratic equation;

x^2-x-12 =0

x^2 - 4x + 3x - 12 = 0

x(x - 4) + 3(x - 4) = 0

(x - 3) (x - 4) =0

x = -3 or +4

We can now see that the function is equal to zero when x = -3 or +4

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Answer:

y=3

Step-by-step explanation:

Step 1: Cross-multiply.

14/3y+5=3/y

14*y=3*(3y+5)

14y=9y+15

Step 2: Subtract 9y from both sides.

14y−9y=9y+15−9y

5y=15

Step 3: Divide both sides by 5.

5y/5=15/5

y=3

Lines and mare perpendicular is The same result is obtained by reflecting Q over the Line M as well as rotating Q 180 degrees using the center P.

As a reminder, perpendicular lines are those that cross at a 90-degree angle. Two non-vertical lines are said to be perpendicular when they are in the same plane and intersect at a right angle.

The axes of the coordinate plane, or the horizontal and vertical lines, are simply perpendicular to one another. Additionally, the slopes of the parallel lines have negative reciprocal slopes.

Since Lines L and M are perpendicular lines, or lines that meet at a right angle (90°), rotating Q 180 degrees using the center P has the same result as reflecting Q across Line M.

Q will therefore be identical to reflecting Q over any of the perpendicular lines when rotated 180 degrees from the center.

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The ball would go 44 yards in 1 seconds

Hunter kicked a soccer ball

It went 33/2 yards in 3/8 seconds

The distance it will travel in 1 second can be calculated as follows

33/2 = 3/8

x= 1

Cross multiply both sides

3/8x = 33/2

x= 33/2 ÷ 3/8

x= 33/2 × 8/3

x= 44

Hence the ball will move 44 yards in 1 second

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Answer:

52.5 minutes

Step-by-step explanation:

[tex]21/6=3.5\\3.5*15=52.5[/tex]

Answer: 52 minutes and 30 seconds

Step-by-step explanation:

You are going to do cross multiplication for this. So 6 miles over 21 minutes is equal to 15 miles over x minutes. When we cross multiply this brings us to 315 over 6. Then we divide 315 by 6 getting us 52.5 minutes and .5 of a minute is 30

Capella is  1.09 times brighter than Rigel.

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

[tex]log_ax=N[/tex]

where, a is the base of function or equation

            x =expression or equation

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations. Some of them are listed below.

Some important formulas of logarithms are :

In the question given here to us,

We use the given formula:

[tex]m_2-m_1= -2.5log\frac{b_2}{b_1} \\[/tex]

Here, m1 = magnitude of Rigel = 0.12

          m2 = magnitude of Capella =0

put the values in eq.

[tex]= > m_2-m_1= -2.5log\frac{b_2}{b_1} \\\\= > - 0.12 = -2.5log\frac{b_2}{b_1}\\\\= > 0.04 = log \frac{b_2}{b_1}\\ \\= > \frac{b_2}{b_1} = 10^{0.04} = 1.09 approx[/tex]

Hence, Capella is  1.09 times brighter than Rigel.

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Type of solutions the function f(x)=[tex]x^2[/tex]+9 will have Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}. Range is [-9,[tex]\infty[/tex]),{y|y≥-9}.

Given function [tex]f(x)=x^{2} +9[/tex]

To determine the function's domain and range.

Domain and range is nothing but the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. For instance, if the relation is R ={(1, 2), ( 2, 2), ( 3,3 ), ( 4, 3)}

Domain is the set of all x-coordinates with values of {1, 2, 3, 4}.

The set of all y-coordinates in the range is equal to {2, 3}.

Domain and range for the function is

Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}.

range is [-9,[tex]\infty[/tex]),{y|y≥-9}

Therefore, the function has the domain and range as

Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}.

range is [-9,[tex]\infty[/tex]),{y|y≥-9}.

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The ride that has the greatest elevation based on the information is B. Lightning bolt : 327 feet.

The term elevation is typically used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.

Elevations show how your house will appear from various perspectives. Regarding these particular angles, there are many elevation kinds. Some varieties include split elevations, rear elevations, side elevations, and front elevations.

From the information, it was stated that the lightning bolt starts at an elevation of 15ft from the platform and speeds the passengers to an elevation of 327 ft.

It should be noted that the information is to simply find the elevation that is the greatest.

Based on the figures given, the appropriate elevation will be 327 feet.

Therefore, the correct option is B.

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The length of the actual hotdog is 15 cm

The graph that completes the question is added as an attachment

The length of the hotdog in the figure is given as

Length = 9 units

The scale is given as

Scale: 6 units = 10 cm

So, we have

6 * 9 units = 10 * 9 cm

Divide both sides by 6

So, we have

9 units = 15 cm

Substitute 9 units = 15 cm in Length = 9 units

Length = 15 cm

Hence, the length of the actual hotdog is 15 cm

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Answer:

x = 4

Step-by-step explanation:

-8x = -x - 28

Move the -x on the right side to the left

-8x + x = -28

-7x = -28

Cross out the negatives

7x = 28

Divide by 7

x = 4

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

[tex]-8x = -x - 28 \text{ / Add 8x}\\-8x + 8x = -x - 28 + 8x\\\to 0 = 7x - 28 \text{ / Add 28}\\0 + 28 = 7x - 28 + 28\\\to 28 = 7x \text{ / Divide by 7}\\\frac{28}7 = \frac{7x}7\\4 = x[/tex]

Answer:

Step-by-step explanation:

Company A:

The recursive formula is, aₙ=aₙ₋₁+4,000, where a₁=42,000

Company B:

The recursive formula is, aₙ₊₁=(1+0.09) x aₙ, where a₁= 42,000

I'm sure she should go for company B, in the long run, she would make much more money. This is proven because company a is increasing using an arithmetic sequence; based on this all they're doing is adding 4,000. But company B is increasing at a percentage of 9 after a while that can really amount to a lot.

Hope this helps, if you are still confused don't hesitate to ask :))

Josie's pay [tex]a_n[/tex] from company A in the [tex]n[/tex]-th year is given recursively by

[tex]\begin{cases} a_1 = 42000 \\ a_{n+1} = a_n + 4000 & \text{for } n\ge1 \end{cases}[/tex]

while her pay [tex]b_n[/tex] from company B is

[tex]\begin{cases} b_1 = 42000 \\ b_{n+1} = 1.09 b_n & \text{for } n \ge1 \end{cases}[/tex]

From these recurrences, we have

[tex]a_2 - a_1 = 4000[/tex]

[tex]a_3 - a_2 = 4000[/tex]

[tex]a_4 - a_3 = 4000[/tex]

and so on - this is just confirming that the pay from company A increases at flat rate of $4000 each year.

Similarly,

[tex]b_2 = 1.09 b_1 = 45780 \implies b_2 - b_1 = 3780[/tex]

[tex]b_3 = 1.09 b_2 \approx 49900 \implies b_3 - b_2 \approx 4120[/tex]

[tex]b_4 = 1.09 b_3 \approx 54391 \implies b_4 - b_3 \approx 4491[/tex]

and we see here that [tex]b_n[/tex] increases at a larger rate year. In only 2 years of working at company B, Josie would be making more money, and the amount by which her salary increases each year is also increasing.

Assuming Josie hopes to make more money, invest in her future, etc, she should take the offer from company B.

A situation in the real world that the equation can simulate. A corporation charges 19.25 per hour, whereas another charges 17.25 per hour plus a one-time fee of 26.77. This is represented by 19.25x =17.25x +26.77. How many hours do they cost the same?

An equation is used to show the relationship between the variables that are illustrated.

In this instance, a situation from the actual world that the equation can simulate.

A corporation charges 19.25 per hour, whereas another charges 17.25 per hour plus a one-time fee of 26.77.

This is represented by 19.25x =17.25x +26.77. How many hours do they cost the same?

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Answer:

9

Step-by-step explanation:

keep adding

If two trains going in opposite directions leave at the same time and train b travels 10 mph faster than train a and in 7 hours the trains are 630 miles apart, then the speed of the faster and slower train is equal to 50mph and 40mph respectively.

The speed of each train can be determined by using an algebraic

expression.

As one train travels 10 miles per hour faster than the other, consider x to be the speed of the slower train. In this case, the algebraic expression to find the speeds of each train can be given as,

7x + 7(x + 10) = 630

7x + 7x + 70 = 630

14x = 630 - 70

14x = 560

x = 560 ÷ 14

x = 40 mph

Therefore, x + 10 = 40 mph + 10 mph = 50 mph

Hence, the speed of the faster train is 50 mph and the speed of the slower train is 40mph.

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Answer:

8936111

Step-by-step explanation:

2+(889*567)+8402773+29273 =

2 + 504063 + 8402773 + 29273 =

8936111

Answer:

6.51326 is greater than √38

Step-by-step explanation:

6.51326 compared with √39

6.51326 compared with 6.244998

means 6.51326 is greater than √38

Answer:

5/20 is not equivalent to 1/5.

Step-by-step explanation:

We can start by simplifying all of the fractions, by finding numbers we can divide both the numerator and denominator by the same number.

[tex]\frac{3}{15} =\frac{1}{5}[/tex] by dividing by 3.

[tex]\frac{2}{10} =\frac{1}{5}[/tex] by dividing by 2.

[tex]\frac{5}{20} =\frac{1}{4}[/tex] by dividing by 5.

and last but not least

[tex]\frac{15}{75} =\frac{1}{5}[/tex] by dividing by 15.

We can see that 5/20 is the only one that equals to 1/4 when simplified.

Therefore, 5/20 is not equivalent to 1/5.

Hope this helped! Have a great day!

The length of the diagonal is 7.05cm of a square.

The perimeter of the square is 20 cm.

The formula of the perimeter of the square is 4a, where a is the length of the side of the square.

So, 4a = 20

       a = 5

Now we have to find the diagonal of the square.

In a square there is two diagonal, each of equal length

Therefore,

    diagonal = [tex]\sqrt{2}[/tex]a

                    = 1.41 × 5

                    7.05cm

Therefore the diagonal of the square is 7.05cm.

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Answer:

The Distributive Law

Step-by-step explanation:

Answer:

answer is D

how ?

when doing long division it will give 24.0833333333 so to 3dp is 24.083

Answer:

on how to do this

I'm no sure

Answer:

I'm no sure

Step-by-step explanation:

Answer: White rose ratio: 4/12 (simplify) Red rose ratio: 8/12 (simplify)

But you ask for total then red rose so 12/8

Step-by-step explanation: 4+8=12 That is total number of roses. You have 4 white rose so 4 out of 12. Have 8 red rose so 8 out of 12

Based on the Abby, Chantral, Dougie, Kajan, Minh, and Zara being equally fast, the probability that Abby and Chantral will be the first two finishers is 1/15.

The probability that Abby and Chantral will be the first two finishers can be found by the formula:
= Number of successful outcomes where Abby and Chantral will be the first two finishers / Total number of outcomes

Solving gives:

= (21! - 4!) / 6!

= 48 / 720

= 1 / 15

In conclusion, the probability that Abby and Chantral will finish first is 1/15.

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Answer:

Step-by-step explanation:

Perimeter = 110 in

Area = 490 in²

Answer:

that would 14 jars LoL in of pop tarts

   The number -√17, expressed as a value or number exponential is -17¹/².

  An exponential number is a mathematical expression and one of the many mathematical operations of reduction, it involves the successive multiplication of a number, it has the form:

aᵇ

Where:

  To convert a root into a exponential we must know the way in which these are related, and it is by means of the following property:

√a = a¹/²

  Now in our case we have -√17 which can be expressed as.

(-1)√17, where 17 = a, then

(-1)17¹/²

-17¹/²

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The correct answer of the question is {-1+√61}/ 10 or {-1-√61}/ 10 .

The given quadratic equation is 5 x²+x=3

First, we have to convert the equation in the form

ax² + bx + c = 0, then apply the quadratic formula i.e.

x = {-b±√(b²- 4ac)}/ 2a .

Now,

5 x²+x=3

⇒ 5 x²+ x - 3 = 0

Here, a = 5, b = 1 and c = -3

Now, applying quadratic formula

{-b±√(b²- 4ac)}/ 2a

= {-1±√(1²- 4 × 5 × -3)}/ (2 × 5)

= {-1±√(1 + 60)}/ 10

= {-1±√61}/ 10

= {-1+√61}/ 10 or {-1-√61}/ 10

Therefore the final answer to the given equation is is {-1+√61}/ 10 or {-1-√61}/ 10 .

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When two functions are combined so the range of one becomes the domain of the other, the resulting function is called a Composite Function .

Composite Function : If f ( x ) is a function with domain x and f ( x ) = y is its range , then g [ f ( x ) ] is a composite function , where f ( x ) is the domain  and g [ f ( x ) ] = z is the range of function g [ f ( x ) ] .

Hence , when two functions are combined so the range of one becomes the domain of the other, the resulting function is called a composite function .

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