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
31q=7.037 what is the value of q??
Answers
Answer:
0.227
Step-by-step explanation:
q=7.037/31
q=0.227
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}
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 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:
What’s the answer ? Im too tired fa this shi
Answers
Answer:
90-39=51 thats a 90° angle
what is 3/4 divided by 1/2
Answers
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]
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
-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!
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
please help and answer this question
Answers
Answer:
-2x+9
This is the answer you are looking for
YOUR WELCOME! :D
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:
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
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).
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
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:
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.
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
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.
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
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
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
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
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
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
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
I need help it khan 4q+3+2q-1
Answers
Answer: 6q + 2
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
What is the inverse of the function f(x) = 2x-10?
Answers
Answer:
One sec
Step-by-step explanation:
standard form for y=mx+b
Answers
Answer:
that's standard form for slope
Step-by-step explanation:
have a nice day :)