log_6⁡(x+1)+log_6⁡x=1

Answers

Answer 1

Answer:

x = -3, 2

Step-by-step explanation:

[tex]log_6⁡(x+1)+log_6⁡x=1 \\ \\ log_6⁡ \{x(x+1) \} = 1 \\ \\ x(x + 1) = {6}^{1} \\ \\ {x}^{2} + x = 6 \\ \\ {x}^{2} + x - 6 = 0 \\ \\ {x}^{2} + 3x - 2x - 6 = 0 \\ \\ x(x + 3) - 2(x + 3) = 0 \\ \\ (x + 3)(x - 2) = 0 \\ \\ x + 3 = 0 \: \: or \: \: x - 2 = 0 \\ \\ x = - 3 \: \: or \: \: x = 2 \\ \\ x = - 3, \: \: 2[/tex]


Related Questions

Understand the question explain and u will be brainiest

Answers

The answer is 1/7
This is because the question asks if a student DOES NOT have any pets, so you find the total outside of the ‘has pets’ area. This is 30 that have siblings and 5 which do not:
30+5 = 35
Then the question asks for the probability that they DO NOT have siblings so that is 5 people.
5/35 = 1/7

Which of the following are exterior angles? Check 2 that apply.

Answers

Answer:

D, A,B I think that’s it

Step-by-step explanation:

In a video game, Agnes scored 20% fewer than Amy. Amy scored 860
points. How many points did Agnes score? *

Answers

Answer:

[tex]\huge\boxed{\sf Agnes\ Score = 688\ points}[/tex]

Step-by-step explanation:

[tex]\sf = 20 \% \ of \ 860 \\\\= \frac{20}{100} * 860\\\\= 2 * 86\\\\= 172 \ points[/tex]

Since, Agnes scored 20 % fever than Amy.

So,

Agnes Score = Amy's Points - 20 % of Amy's Points

Agnes Score = 860 - 172

Agnes Score = 688 points

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

Hope this helped!

~AnonymousHelper1807

To increase attendance for a flower show, the organizers have chosen flower shops in the area to offer discount coupons to their customers. Half of the stores receive discount coupons for admission, while the other half of the stores receive two-for-one admission coupons. The organizers then compare the number of each type of coupon redeemed at the show.

What are the explanatory and response variables in this scenario?

The explanatory variable is the number of coupons redeemed. The response variable is the type of coupon.
The explanatory variable is each chosen flower shop. The response variable is the number of coupons redeemed.
The explanatory variable is the type of coupon. The response variable is number of number of coupons redeemed.
The explanatory variable is the attendance at the flower show. The response variable is the number of attendees who used coupons.

Answers

Answer:

Because the weather was generally better this year compared to last year, the attendance may have increased.

Step-by-step explanation:

took test

Answer:

C.) The explanatory variable is the type of coupon. The response variable is number of number of coupons redeemed.

Step-by-step explanation:

edge 2020

box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the amount of material used. sides of base

Answers

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

Given that f(x) = x – 2 and g(x) = x2 + 3x – 4, find (f – g)(x). Question 1 options:A. (f – g)(x) = –x2 –2x + 2 B.(f – g)(x) = x2+ 2x – 4 C. (f – g)(x) = –x2+ 4x – 6 D. (f – g)(x) = x2+ 4x + 6

Answers

Answer:

A

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\=(x-2)-(x^2+3x-4)\\=x-2-x^2-3x+4\\=-x^2-4x+2\\[/tex]

Therefore, answer is A.

Answer:

Step-by-step explanation:

Algebra II: Part 2 James Madison

Your quiz has been submitted successfully. 100%

Question 1  5 / 5 points

Given that f(x) = x – 2 and g(x) = x2 + 3x – 4, find (f – g)(x).

A: (f – g)(x) = –x2 –2x + 2

Question 2  5 / 5 points

Given that f(x) = x + 4 and g(x) = x + 7, find (g – f)(x).

A: (g – f)(x) = 3

Question 3  5 / 5 points

Let f(x) = 4x – 1 and g(x) = 2x. Find (f ∘ g)(–5).

A:  (f ∘ g)( – 5) = –41

Question 4  5 / 5 points

Which of the following is the inverse relation of the set below?

A:  {(3,–2), (–4,7), (7,3), (4,8)}

Question 5  5 / 5 points

What is the inverse of f(x) = 2x2 –4?

A:  y = ±x+24−−−√

Question 6  5 / 5 points

Which of the following function pairs are inverses?

A: f(x) = 2x – 3 and g(x) =x+32

Question 7  5 / 5 points

Which of the following is true?

A:  The horizontal line test is used to determine if a function's inverse will be a function.

Question 8  5 / 5 points

Evaluate81−−√4

A: 3

Question 9  5 / 5 points

Evaluate 1251⁄3.

A: 5

Question 10  5 / 5 points

Use the properties of exponents to simplify the expression 2(x13)65⋅y23.

A: 2x25⋅y23

Question 11  5 / 5 points

A population culture begins with 15 strands of bacteria and then doubles every 4 hours. This can be modeled as 15(2)t4, where t is time in hours. How many strands of bacteria are present at 12 hours?

A: 120 strands of bacteria

Question 12  5 / 5 points

Simplify 36√3√.

A: 23–√

Question 13  5 / 5 points

Simplify 73–√+12−−√−75−−√.

A: 43–√

Question 14  5 / 5 points

Simplify 2–√×22–√.

A: 4

Question 15  5 / 5 points

Simplify 83−−√.

A: 26√3

Question 16  5 / 5 points

Select the equation of the function shown in the graph.

A: f(x)=2x−−√4−5

Question 17  5 / 5 points

Identify the graph of f(x)=x−2−−−−√3−3.

t would not allow me to add the graft. But it is the answer with the line that goes all the way across the graft starting at -10 thru -4.5 and up to 10. The line looks like an "S"

Question 18  5 / 5 points

Identify the graph of f(x)=6x−−√4−1.

It would not allow me to add the graft. But it is -1 up to the right to about 9.5. Document uploaded

Question 19  5 / 5 points

Select the equation of the function shown in the graph.

A: f(x)=x−1−−−−√5+5

Question 20  5 / 5 points

Solve the inequality x+2−−−−√4>2.

A: x>14

Question 21  5 / 5 points

Solve the inequality −2x−−−−√−1<3.

A: −8<x≤0

Question 22  5 / 5 points

Solve the equation 2x−1−−−−−√=5.

A: x = 13

Question 23  5 / 5 points

Solve the equation x+1−−−−√+5=3.

A: There is no solution.

Question 24  5 / 5 points

Given thatf(x)=4x3x+3−−−−−√ and g(x)=2x+1−−−−√, find (fg)(x).

A: 2x3–√

Completing the Square
Solve each equation by completing the square.
1) 7x2 + 14x - 65--9

Answers

Answer:

2(30-7x)

Step-by-step explanation:

=14+14x-65-9

=14+14x-79

=60+14x

=2(30-7x)

The two triangles are similar, What is the length of DE?

Answers

Answer:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.

I hope this might help you

Mark it as brainliest answer and follow me

Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation.

"The sum of a number and its opposite is always 1."

Answers

Answer:

Never applies

Step-by-step explanation:

Given

Argument: The sum of a number and its opposite is always 1

Assume a positive number x

The opposite of the number is negative x (i.e. -x)

The sum of both numbers is:

[tex]Sum = x + (-x)[/tex]

Open Bracket

[tex]Sum = x -x[/tex]

[tex]Sum = 0[/tex]

Now, take for instance.

[tex]Number = 5[/tex]

Opposite would be

[tex]Opposite = -5[/tex]

Their sum is:

[tex]Sum = 5 + (-5)[/tex]

[tex]Sum = 5 -5[/tex]

[tex]Sum = 0[/tex]

Another instance is:

[tex]Number = -8[/tex]

Opposite would be

[tex]Opposite = 8[/tex]

Their sum is;

[tex]Sum = -8 + 8[/tex]

[tex]Sum = -0[/tex]

Hence, the argument never applies because the sum is never 1

what is the greatest common factor of 14x+28+21

Answers

Answer:

7 (2x+7)

Step-by-step explanation:

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︎ ︎ ︎︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎

︎ ︎ ︎︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎

Answer:

The greatest common factor is 7.

Step-by-step explanation:

7 x 2 = 14

7 x 4 = 28

7 x 3 = 21

Sofia used these steps to find the inverse of function f

She made a mistake in step__(2,6,4,3,5)?

She should have_____
.dived each side by 8 instead of multiplying
.replaced x with f(x)
.divided each side by 3 instead of multiplying
.added 4 to each side instead of subtract
.restricted the domain to x>0

Answers

Answer:

Step-by-step explanation:

Step 1             f(x) = [tex]\frac{3x+4}{8}[/tex]                 Given

Step 2            y = [tex]\frac{3x+4}{8}[/tex]                    Change f(x) to y

Step 3            x = [tex]\frac{3y+4}{8}[/tex]                    Switch x and y

Step 4            8x = 3y + 4              multiply each side by 8

Step 5            8x - 4 = 3y               Subtract 4 from each side

Step 6            [tex]\frac{8x-4}{3}=y[/tex]                   Divide by 3 on each side

Step 7            [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]           Replace y by [tex]f^{-1}(x)[/tex]

Therefore, inverse of the function will be,

[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]

Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.

Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].

It is required to calculate the inverse of the function.

So, the steps involved in finding the inverse of the function will be,

Step 1:

Write the given function as,

[tex]f(x)=\dfrac{3x+4}{8}[/tex]

Step 2:

Change the function f(x) to y as,

[tex]y=\dfrac{3x+4}{8}[/tex]

Step 3:

Switch x and y as,

[tex]x=\dfrac{3y+4}{8}[/tex]

Step 4:

Multiply each side of the equation by 8 as,

[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]

Step 5:

Now, subtract 4 from each side of the equation as,

[tex]8x-4=3y+4-4\\8x-4=3y[/tex]

Step 6:

Now, it is required to divide each side by 3.

[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]

Step 7:

Now, replace y with [tex]f^{-1}(x)[/tex] as,

[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]

So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].

Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

For more details, refer to the link:

https://brainly.com/question/19606498

Round 4,287,965 to the nearest thousand

Answers

Answer:

It is 4,288,000.

Step-by-step explanation:

To round to the nearest thousand, you need to find the thousands place. In the thousands place there is a "7". Okay, we've found it, so the next step is rounding.

To round, there is a handing phrase that we can use to know whether we should round the place up or down. It is "4 or less, let it rest. 5 or more, add 1 more." We need to apply this phrase to the number behind the place we need to round (so apply it to the place behind the thousands place).

When we look behind the thousands place, we see there is a 9. Apply the rule to that. Since 9 is above 5 and not less than 4, we need to add one more to the thousands place.

That means after we round, the 7 turns into a 8. That's how you get 4,288,000.

Hope this makes sense <3

Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page

Answers

Answer:

13 pages : 1/2 hour Multiply both sides by 2

26 pages : 1 hour ------>> 26 pages/hr

Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages

Split up the fraction: (1/26) hr / page

Answer:

26

Step-by-step explanation:

13 in 1/2 hour

13:1/2

26:1

The fourth term of a geometric progression is 4 and the seventh term is 32/125. Find the first term, the common ratio and the sum of the first nth terms. Hence, deduce the sum to infinity.​

Answers

Answer:

common ratio is 2/5

First term is  125/2

The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]

The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]

Step-by-step explanation:

The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:

[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]

Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:

[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]

So, the common ratio is 2/5

we can now determine the first term:

[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]

The sum of the first n terms is given by the formula:

[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]

and therefore, the infinite sum is:

[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]

Can someone help me with this.. It is timed I WILL MARK YOU AS BRAINLIEST

Answers

(2p+13)(p−3)/2p-7
​​

Answer:

1) dividend

2) divisor

3) quotient

help me please in this problem

Answers

I think it’s 12.67 I’m not so sure

12 divided by 1/4 please help got a test next Monday

Answers

Answer:

48

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

When dividing fractions flip and multiply.

So 12 would become 1/12

and 1/4 would become 4/1

Now multiply

[tex]\frac{1}{12}*\frac{4}{1}= \frac{4}{12} = \frac{1}{3}[/tex]

So the answer is 1/3

When dividing fraction remember to flip then multiply much easier that way!

Hope this helps!!

The length of a rectangle is four times its width.
If the perimeter of the rectangle is 90 yd, find its length and width.

Answers

Answer:

Length of rectangle = 36 yd and width of rectangle = 9 yd

Step-by-step explanation:

Let width of rectangle = w

Length of rectangle = 4w (four times the width)

Perimeter of rectangle = 90 yd

We need to find length and width of rectangle.

The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]

Where l is length and w is width

Putting values and finding length and width of rectangle

[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]

So,width (w) of rectangle is w= 9 yd

Finding length of rectangle = 4w = 4*9 = 36 yd

So, length of rectangle = 36 yd and width of rectangle = 9 yd

Now move vertices A, B, and C of ∆ABC to create a triangle of your choice. (Note: the tool will allow you to create only certain kinds of triangles.) Does the relationship between the base angles change as the vertices change? If so, how?

Answers

Answer:

The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.

Step-by-step explanation:

Here is the answer from Plato. Hope this helps :)

Answer:

The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.

Step-by-step explanation:

Exact Edmentum sample answer

Cassandra has $2000 dollars in a bank account that she uses to make automatic $900.01 mortgage
payments each month. If Cassandra stops making deposits to that account, when would automatic
payments make the value of the account zero? Use a table to estimate the solution. Then use a graphing
calculator to approximate the x-intercept

Answers

Answer:

no

Step-by-step explanation:

it's CASSANDRA business so she solve it herself

im not sure this one is confusing

Which scenario describes this picture?

Answers

Answer:

It"s the second answer, "An 8-foot ramp leans....".

Step-by-step explanation:

Answer:

Step-by-step explanation:

An 8-foot ramp leans against a building 5 feet away.  

cos x = [tex]\frac{5}{8}[/tex] ⇒ x ≈ 51.3178°

Can 14,18 and 19 form a triangle?

Answers

Answer:

Yes

Step-by-step explanation:

Using the triangle formula: a+b>c , b+c>a , and c+a>b, we can conclude that these values can form a triangle because 14+18>19 , 14+19>18 , and 18+19>14.

Answer:

To confirm if this can form it, we take the lower of the two numbers , square them, and equal it to the biggest number squared. (AKA The Pythagorean Theorem).

Step-by-step explanation:

[tex]14^{2} +18^{2} = 19^{2}[/tex]

Now solve to see if it equates to be true.

196 + 324 = 361

520 [tex]\neq[/tex] 361

That means 14, 18, and 19 can't form a triangle.

what number is represented by this number discs​

Answers

Answer:

15

Step-by-step explanation:

Solve two fifths minus one seventh equals blank.

solve this and you will get 25 points

Answers

Answer:

9/35

Step-by-step explanation:

9/35 is the answer, hope this helped

How many times does 35 go into 100 please give correct answer max points.

Answers

Answer:

100/35 = 2

35 goes into 100 2 times

Step-by-step explanation:

Is that a perfect square

Answers

Answer:

im gonna go with yes

Step-by-step explanation:

Answer:

is what a perfect square?

Step-by-step explanation:

there is no pic attached

What is the graph of the function rule?
1. y= 3x - 2 (1 point)
Algebra 1

Answers

This should be what you're looking for.

Bob has a coin collection made up of pennies and nickels. If he has three times as many pennies as nickels and the total face value of the coins is $416, how many coins of each kind are in the collection?

Answers

Answer:

I think its 15600..

Step-by-step explanation:

what is 12+12 and give good reson why

Answers

Answer:

24

Step-by-step explanation:

you have 12 of something and Are adding 12 to it.

Simplify (6x ^ 2 + 11x - 3) + (2x ^ 2 - 17x - 4) . (1 point)
1 ) 8x ^ 2 + 6x - 1
2) 8x ^ 2 - 6x - 7
3 ) 8x ^ 2 + 6x + 1
4 ) 8x ^ 2 - 6x + 7

Answers

Answer:

2) 8x^2 -6x-7 hope this helps

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