Answers
=========================================================
Explanation:
Recall that quadratic form is ax^2+bx+c.
So we need an x^2 term followed by an x term, then a constant at the end.
It may not look it, but the given equation is nearly in quadratic form.
Rewrite 9^(2x) as (9^x)^2
We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0
From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0
From here we can use the quadratic formula or factor. I'll factor.
w^2 - 2w - 3 = 0
(w - 3)(w + 1) = 0
w-3 = 0 or w+1 = 0
w = 3 or w = -1
---------------------
Now we use these values of w to find x
If w = 3, then,
w = 9^x
3 = 9^x
log(3) = log(9^x)
log(3) = x*log(9)
x = log(3)/log(9)
x = log(3)/log(3^2)
x = log(3)/(2*log(3))
x = 1/2
At the last step, we have the log(3) terms cancel.
Repeat for w = -1
w = 9^x
-1 = 9^x
log(-1) = log(9^x)
We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.
In short, w = -1 is extraneous so it doesn't lead to any x value solution.
So only w = 3 is useful.
Ultimately, the only solution is x = 1/2.
Related Questions
What is the inverse of the function f(x) = 2x-10?
Answers
Answer:
One sec
Step-by-step explanation:
HELP THIS IS DUE IN 1:00 PM AND I WILL GIVE BRAINLIEST
Answers
Answer:
1) They were multiplied by one power of ten because 2.5x 1^10 is 25, and so that it is easier to divide.
19.625/ 2.5 * 10/10 = 196.25/25
Hope this helps plz hit the crown ;D
Pls help. I don't know how to do this and pls don't answer if you don't know the answer.
Answers
Answer:
m = 3 5/18
All you need to do is rewrite the equation as 8 1/9- 4 5/6
how do we find the place value of 3a + b given that a=4, b=3, and c=-2
Answers
Answer:
3a+b
3(4)+3
12+3
15
Step-by-step explanation:
You substitute the variables with the given numbers. I think this is correct.
I need help it khan 4q+3+2q-1
Answers
Answer: 6q + 2
Step-by-step explanation:
use the diagram below to find the lengths of the following answer question 18-25. Be sure to include all necessary work. Leave your answer in the simplest radical form when necessary.
Answers
Answer:
18. AE = 6
19. BG = 6
20. CF = 5
21. GF = 2
22. CE = 3
23. AC = 3·√5
24. A_F = 10
25. DA = 3·(√5 - 1)
Step-by-step explanation:
Whereby the point C is the center of the circle, we have;
CB = CG = CE = 3 = The radius of the circle with center at C
CE = 3
CF = √(4² + 3²) = 5 by Pythagoras' theorem
CF = 5
GF = CF - CG = 5 - 3 = 2
GF = 2
BG = CB + CG = 3 + 3 = 6
BG = 6
Whereby, BC is a tangent to the circle with center, C, we have;
A_F = √(8² + 6²) = 10 by Pythagoras' theorem
A_F = 10
AE = A_F - EF = 10 - 4 = 6
AE = 6
AC = √(6² + 3²) = 3·√5 by Pythagoras' theorem
AC = 3·√5
DA = AC - CD = 3·√5 - 3 = 3·(√5 - 1)
DA = 3·(√5 - 1).
Is the following relation a function?
Answers
Answer:
yes
Step-by-step explanation:
A function is any graph that the x values do not repeat.
You can check this by using this vertical line test
Run your finger or a pencil down a specific vertical (top to bottom) line on the graph, if you can see that it intersects into the graph more than once, then it's not a function.
Erica went bowling with her friends. She paid $3 to rent shoes and then $5 for each game of bowling. If she
spent a total of $23, then how many games did Erica bowl?
Answers
Answer:
4 games
Step-by-step explanation:
23 - 3 = 20
20 / 5 = 4
What's 4/5 as a percentage?
Answers
Answer:
80%
Step-by-step explanation:
% is out of 100 so make the denominator of 4/5 to be 100:
4/5 times 20/20 = 80/100 = 80%
Answer:
80%
Step-by-step explanation:
4 divided by 5 equal .8
.8 x 100 equals 80
It's multiplied by 100 because usually percentages are out of 100.
OR
You can move the decimal in .8 to 2 space to the right
7.5d = 2.5d Lin divided each side by 2.5d and Elena subtracted 2.5d from each side with both leads to the solution
Answers
Answer:
Elena's move will lead to the solution of the problem
Step-by-step explanation:
To solve the equation 7.5d=2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side. Will both moves lead to the solution? Explain your reasoning
Given:
7.5d = 2.5d
Lin divides each side by 2.5d, Lin:
7.5d / 2.5d = 2.5d / 2.5d
3 = 1
This can not be the solution to the problem because 3 can not be Equal to 1
Elena subtracts 2.5d from each side
7.5d = 2.5d
7.5d - 2.5d = 2.5d - 2.5d
5d = 0
This can lead to the solution of the problem
Elena's move will lead to the solution of the problem
will make you BRAINLIEST please help me please
Answers
Answer:
You have to substitute the x-values into the function :
[tex]f(x) = {11}^{x} [/tex]
[tex]f( - 2) = {11}^{ - 2} = \frac{1}{121} [/tex]
[tex]f( - 1) = {11}^{ - 1} = \frac{1}{11} [/tex]
[tex]f(0) = {11}^{0} = 1[/tex]
[tex]f(1) = {11}^{1} = 11[/tex]
[tex]f(2) = {11}^{2} = 121[/tex]
-6n-4n please help because I have an improvement test
Answers
Answer:
-10n
Step-by-step explanation:
-6n-4n=-10
Explain: -6n - 4n
Step-by-step:
Collect like terms and calculate the coefficients
(-6 - 4)n
Calculate the difference
10n
Explain: Solved using the variables by collecting terms and there coefficients. Then calculated the difference.
ANSWER: 10n
Hope this helps!
An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Consider the trinomial 6x2 + 13x + 6. The value of ac is . The value of b is . The two numbers that have a product of ac and a sum of b are 4 and .
Answers
Answer:
1. ac = 36
2. b = 13
3. 4 and 9
Step-by-step explanation:
Given
6x² + 13x + 6
Required
Fill in the gaps
Solving (1): The value of AC
The general form of an equation is:
ax² + bx + c
By comparison:
a = 6
b = 13
c = 6
So,
ac = a * c
ac = 6 * 6
ac = 36
Solving (2): The value of b
In (1) above, we showed that
b = 13
Solving (3): Two numbers that satisfy product ac and sum b
We have that.
ac = 36
If one of the numbers is 4, then the other number is
Other number = 36/4
Other number = 9
Alternatively, we have that.
b = 13
If one of the numbers is 4, then the other number would be:
Other number = 13 - 4
Other number = 9
Answer:
ac = 36
b = 13
The two numbers that have a product of ac and a sum of b are 4 and 9
Step-by-step explanation:
What’s the answer ? Im too tired fa this shi
Answers
Answer:
90-39=51 thats a 90° angle
Sharon correctly answered 21 out of 24 questions on a math quiz. Which is this ratio as a decimal?
0.625
0.667
0.840
0.875
pls help♡
Answers
Answer:
0.875
Step-by-step explanation:
To find the decimal, you divide the 21 by the 24.
21/24 = 0.875
what is the total area of the four walls of a rectangular room 12 ft long by 13 ft wide by 9 ft high?
Answers
Answer:
your mom
i dunno what else to put here lol
Answer:
Total area of four walls is 450ft
Step-by-step explanation:
First to find area of one wall is lenghth times height 2(12 x 9)
Second to find the area of the two other walls it’s height times width 2(13 x 9)
third add then up and you get 450
standard form for y=mx+b
Answers
Answer:
that's standard form for slope
Step-by-step explanation:
have a nice day :)
Luna entered a raffle for a new pair of running shoes. She purchased 20 tickets and was told that she had a 20% chance of winning. How many tickets were sold? P (Luna winning) = StartFraction Number of tickets purchased over Total number of tickets sold EndFraction. 20 percent = StartFraction 20 over x EndFraction. One-fifth = StartFraction 20 over x EndFraction. x = tickets
Answers
Answer:
100 ticketsStep-by-step explanation:
Probability of winning = amount of tickets purchased/Total number of tickets
20% = 20/total number of tickets
20/100 = 20/total number of tickets
cross multiply
20 * total number of tickets = 20 * 100
20 * total number of tickets = 100
total number of tickets sold = 100 tickets
Answer:
100 tickets
Step-by-step explanation:
Hi and goodbye
Which lines are parrallel check all that apply
Answers
Answer:
b // f
c // e
Step-by-step explanation:
b // f
89.5 = 180 - 90.5
89.5 = 89.5 {corresponding angles are congruent.So b // f}
c//e
91.5 = 180 - 88.5
91.5 = 91.5 {corresponding angles are congruent.So b // f}
Which equations and/or functions represent the graphed line? Select three options.
f(x)=1/5x-4
f(x)=1/2x+2
f(x)=1/2+1
y-3=1/2(x-2)
y-1=1/2(x+2)
Answers
Answer:
The second one, the fourth one, and the fifth one.
f(x)=(1/2)x+2
y-3=1/2(x-2)
y-1=1/2(x+2)
The three equations that represent the graphed line are:
f(x) = (1/2)x + 2
y - 1 = (1/2)(x + 2)
y - 3 = (1/2)(x - 2)
To identify which equations and/or functions represent the graphed line, we can compare the given equations with the characteristics of the graph.
The graphed line appears to have a slope of 1/2 and passes through the point (0, 1). Let's check the options:
f(x) = (1/5)x - 4: This equation has a slope of 1/5, not 1/2, so it does not represent the graphed line.
f(x) = (1/2)x + 2: This equation has the correct slope of 1/2, but it does not pass through the point (0, 1), so it does not represent the graphed line.
f(x) = (1/2) + 1: This equation is not in slope-intercept form and does not represent the graphed line.
y - 3 = (1/2)(x - 2): This equation has the correct slope of 1/2 and passes through the point (2, 3). However, it does not pass through the point (0, 1), so it does not represent the graphed line.
y - 1 = (1/2)(x + 2): This equation has the correct slope of 1/2 and passes through the point (−2, 1) (after rearranging to slope-intercept form). It also passes through the point (0, 1), which matches the graph.
The three equations that represent the graphed line are:
f(x) = (1/2)x + 2
y - 1 = (1/2)(x + 2)
y - 3 = (1/2)(x - 2)
To know more about equations:
https://brainly.com/question/10724260
#SPJ2
Eliot needs to replace a window that is in the shape of a
semicircle.
K 1.5 ft
>
What is the area of the window? Use 3.14 for 1. Round your
answer to the nearest hundredth of a square foot.
Answers
353.25
a=(3.14*15^2)/2
a=706.5/2
a=353 sq in
Which of the following equations is equivalent to 4x -y=3`?
Answers
Answer:
x-intercept = (3/4,0)
y'intercept = (0,-3)
Step-by-step explanation:
Not sure what conversion you need but here are the intercepts
What is the x intercept of the graph of 3x-y+6=0
Answers
Answer: It would be 2,0 :) Please tell me if I'm wrong
Step-by-step explanation:
PLZ HELP ITS URGENT!!! Which of the following represents the value of the series below? Also maybe if possible, could you please add an explanation?
Answers
Answer:
first one
Step-by-step explanation:
the sum of (9k-4) =3542
so it will be the first one because
28((5+248)/2)=3542
Answer:
a
Step-by-step explanation:
cuz i milk da cows homie, all fo my edge brothas, no cap on jaw, j keepin it real fo yall homies
what is the slope of y= -1/6x - 3/2
Answers
Answer:
-1/6
Step-by-step explanation:
Answer: -1/6
Step-by-step explanation:
Use the slope-intercept form y=mx + b to find slope m
31q=7.037 what is the value of q??
Answers
Answer:
0.227
Step-by-step explanation:
q=7.037/31
q=0.227
Plz help fast answer
Answers
Coastal
Graphic
Heroic
Dramatic
Angelic
Betrayal
Bacterial
Answer:
1: Patriotic
2: Global
3: Graphic
4:heroic
5: betrayel
6:angelic
7: dramatic
8: bacterial
Step-by-step explanation:
I think this is it
Sarah’s job at a cellphone store pays 6% commission on the sales she makes. She also makes $1400 base pay. What will Sarah’s total paycheck be if she had $4000 in sales?
Answers
Answer:
255
Step-by-step explanation:
please help and answer this question
Answers
Answer:
-2x+9
This is the answer you are looking for
YOUR WELCOME! :D
what is 3/4 divided by 1/2