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
torresn06 where are you i need your help....
567*875
Answers
Answer:
The answer is 496125.
Step-by-step explanation:
Simply multiply the two numbers together to get 567*875 = 496125.
Hope this helped!
Answer:496,125
Step-by-step explanation:
Please help me please
Answers
Answer:
The graph of f is shifted 6 units up to create the graph of g
Option A is correct option.
Step-by-step explanation:
We are given f(x)=x
and g(x)=f(x)+6
We need to find how f(x) and g(x) are related.
We know that according to translation rules:
if we have f(x) as original graph and f(x)+d as translated graph it means the original graph f(x) is shifted d units up.
So, in our case f(x)=x
g(x)=f(x)+6
The graph of f is shifted 6 units up to create the graph of g
Option A is correct option.
3(x+1)-2x=-6
Slove this
Answers
Answer:
x = -9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
3(x + 1) - 2x = -6
Step 2: Solve for x
Distribute 3: 3x + 3 - 2x = -6Combine like terms: x + 3 = -6Isolate x: x = -9Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 3(-9 + 1) - 2(-9) = -6Add: 3(-8) - 2(-9) = -6Multiply: -24 + 18 = -6Add: -6 = -6Here we see that -6 does indeed equal -6.
∴ x = -9 is the solution to the equation.
Sophia spent $75.00 of her $225.00 paycheck on new shoes. What percent of her paycheck did she spend on the new pair of shoes?
Your answer:
if you do solve please make an explanation :)
Answers
Answer:
33.33%
Step-by-step explanation:
75*100=7500
7500/225=33.3333333
50 points for good answ.
car moves with constant speed. from A to B, car had to arrive on time, but he ride half of the road with 2/3v speed. with what speed car has to ride the rest of the road to go on B location on time?
Answers
Answer:
2vStep-by-step explanation:
Let the distance be d and average speed be v.
Half of the distance the speed was 2/3v
Let the speed be xv in the second half of the distance.
Then time is:
d/v = d/2 : (2/3v) + d/2 : (xv)d/v = 3/4(d/v) + (1/2x)(d/v)1 = 3/4 + 1/2x1/2x = 1 - 3/4 1/2x = 1/42x = 4x = 2The rest of the road car has to ride with speed of 2v
Exercise 21
Let x represents a length in cm where x > 1.5.
AB = 2x - 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Si.
. CBFG is a rectangle of area S2.
. ADEB is a right trapezoid of area S3.
1) Express S1 and S2 and S3 in terms of x
Plzzz I need help
Answers
Answer:
see explanation
Step-by-step explanation:
area of Δ ABC is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 4x - 6 and h = 2x - 3 , then
A = [tex]\frac{1}{2}[/tex] (4x - 6)(2x - 3) ← expand using FOIL
= [tex]\frac{1}{2}[/tex](8x² - 24x + 18) ← distribute
= 4x² - 12x + 9
----------------------------------------------------------
Area of rectangle CBFG is calculated as
A = lb ( l is length, b is breadth )
Here l = 4x - 6 and b = 3x - 2, then
A = (4x - 6)(3x - 2) ← expand using FOIL
= 12x² - 26x + 12
----------------------------------------------------------
Area of trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases
Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then
A = [tex]\frac{1}{2}[/tex] (2x - 3)(4x + 1 + 2x + 3)
= [tex]\frac{1}{2}[/tex] (2x - 3)(6x + 4) ← expand using FOIL
= [tex]\frac{1}{2}[/tex] (12x² - 10x - 12) ← distribute
= 6x² - 5x - 6
What is mZG?
Enter your answer in the box.
FGH
(x-5)°
(3x+24)°
x°
Answers
Answer:
The angle for G is 121°.
Step-by-step explanation:
Given that total angles in a triangle is 180° so in order to find the angle of G, first, you hav eto find the value of x :
x + (x - 5) + (3x + 25) = 180°
5x + 20° = 180°
5x = 160°
x = 32°
Next, you have to find the angle of G :
G = 3x + 25
G = 3(32) + 25
G = 96° + 25°
G = 121°
solve for x
3(x - 2) = 6x - 12
Answers
Answer:
The answer is 2
Step-by-step explanation:
Here's how I got it:
3(x - 2) = 6x - 12
Multiply 3 times x and 3 times 2, this is what you would get
3x - 6 = 6x - 12
Then, subtract the lowest x with the bigger X, this way you would have x on one side:
3x - 6 = 6x - 12
-3x -3x
This is what you should have after this:
-6 = 3x - 12
Now, to get the variable (letter that represents a number) by itself, you have to add 12 to both sides like this:
-6 = 3x - 12
+12 +12
You would get this:
6 = 3x
Finally, you have to get x by itself, so you have to divide 3 on both sides like this
6/3 = 3/3 x
That's why, your answer is 2
Sapphire and Abe are shelving books at a public library. Sapphire shelves 12 books at a time, whereas Abe shelves 18 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved.
Answers
Answer: 36
Step-by-step explanation:
Given: Sapphire shelves 12 books at a time, whereas Abe shelves 18 at a time.
If they end up shelving the same number of books, what is the smallest number of books each could have shelved = LCM (12,18)
12 = 2 x 2 x 3
18 = 2 x 3 x 3
LCM (12, 18) = 2 x 2 x 3 x 3 = 36
Hence, the smallest number of books each could have shelved = 36
Answer:
36
Step-by-step explanation:
nrly
A museum recorded that it had 988 visitors in 4 hours .What is the unit rate in visitors per hour?
Answers
Answer:
247
Step-by-step explanation:
247 visitors per hour
Could someone help me with this? Please provide an explanation! Thank you!
Answers
Answer:
if you are solving for x then the answer would be -17/6 or -2 5/6 (mixed number form)
Step-by-step explanation:
John has 14 coins that are nickels and dimes. He has $.95 altogether. How
many of each coin does John have?
Answers
Answer:
7 nickels the rest are dimes
Step-by-step explanation:
9 times 5 cents= 45
5 times 10 cents=50
I need help with a math question ASAP!! please Below is a screenshot of the problem
Answers
Answer:
Pretty sure it's B, the second one from the top
Answer:
Soda tax — Should people have to pay an extra tax on soda or junk food?
Your conversation should include the following:
A total of at least five entries for each side (10 entries total—two to three sentences each)
Accurate facts used to support both perspectives
At least two properly cited sources used for research
Step-by-step explanation:
prove that:
tan80°=2tan 70°+ tan10°
Answers
2tan70+tan10=5.67
So tan80=2tan70+tan10
Answer:
kunjal brother answer is correct hope it's help you have a good day ☺☺ keep smiling be happy stay safe ☺☺
I have no use for them just take them pls
Answers
Noooooo wayssssssss
I wontttttttt
Need help ASAP !!!!!!!!
Answers
Answer:
b 1 1/7
Step-by-step explanation:
pretty sure its B 1 1/7
1 1/7 hope it helps
Find the sum
14.3 + 7.36 = ?
Answers
Answer:
21.66
Step-by-step explanation:
Nico rolled two number cubes 250 times. use the complement to find the experimantal propability of not rolling a 3 on the blue number cube, NC2.
Answers
Answer:
the probability is 0%
Step-by-step explanation:
is there options like
A
B
C
options
3(23−2v)+3v=48
what is v?
Answers
Answer:
v=7
Step-by-step explanation:
my previous answer was incorrect, my bad
Answer: v=-7
Step-by-step explanation:
3(23−2v)+3v=48
Distribute:
69-6v+3v=48
Combine like terms:
-6v+3v=-3v
69-3v=48
Subtract 69 on both sides:
69-69-3v=48-69
-3v=-21
Divide 3 on both sides:
-3v/3=-21/3
v=-7
Ethan Planted a tree that was 1.85 meters tall. Several years later, the tree is 5.30 meters tall. Which equation can be used to find x, the number of meters the tree has grown?
A. 1.85x= 5.30
B. 1.85+ x= 5.30
C. 1.85+ 5.30= x
D. 1.85 (5.30)= x
Answers
Explanation:
The starting height of the tree was 1.85 meters. To find the number of meters the tree grew, you would subtract the current height from the previous height.
5.30-1.85=x. This equation is the same as 1.85 + x = 5.30 if you switch the 5.30 and x.
Answer:
x = B the answer is b
Step-by-step explanation:
How do I find the value of X?
Answers
hope that helps :3
What is the correct answer? Please hurry
Answers
Answer:
2.5m
Step-by-step explanation:
5/2 = 2.5
Carlos graphs the equations y = 0.5x2 + 3 and y = –4x2 + 24x – 35 and generates the graph below. Which conclusion is supported by the graph?
Answers
I got you fam 1. (0,3) 2. (3,1)
Answer:
The equation 0.5x2 + 3 = –4x2 + 24x – 35 has no real solutions.
Step-by-step explanation:
the lines don't intersect at all so theres no solutions
Line L is shown in the coordinate plane. a. What are the coordinates of points and ? b. Is the point (16,20) on line L ? Explain how you know. c. Is the point (20,24) on line L? Explain how you know. d. Is the point (80,100) on line L? Explain how you know. e. Write a rule that would allow you to test whether (, ) is on line L.
Answers
Answer:
so its will be the equal number
Step-by-step explanation:
pls dont get mad if I'm wrong I tried :)
Warren was drawing a shape on the grid below. He started at (2,0) and drew a line to (2,5), then to (4,3), then to (6,5) and finally a line to (6,0). What was made after all the points were connected?
Answers
Answer:
concave pentagon
Step-by-step explanation:
Answer:
c edge 2021
Step-by-step explanation:
what is the total surface area of three of these ice cubes (pic attached)
Answers
Answer:
9ft2
Step-by-step explanation:
Answer:
18 ft
Step-by-step explanation:
A cell phone plan costs $200 to start. Then there is a $50 charge each month.
Is there a proportional relationship between time and the cost of the cell phone plan? Explain how you know.
Answers
Answer:
I cant speak English well. I dont understand what it says. can u explain what do u want. I'll help u
11) Which of the following are examples of the HL Theorem? Select 2. *
Answers
Answer:
Step-by-step explanation:
All of them are examples of Hypotenuse Leg Theorem
Mollie bought 12 packages of carrots for a total of $48. She realized she needed to purchase another 10 more packages. How much will she have spent IN ALL on the carrots?
Answers
Answer:
$88
Step-by-step explanation:
48/12= 4
for another 10 she pays another $40
Answer:
$88
Step-by-step explanation:
determine whether g(x)=x2-5x+2 has a minimum of maximum
Answers
Answer:
g(x) has a minimum
Step-by-step explanation:
Given a quadratic in standard form
g(x) = ax² + bx + c ( a ≠ 0 )
• If a > 0 then vertex is a minimum
• If a < 0 then vertex is a maximum
Given
g(x) = x² - 5x + 2 ← in standard form
with a > 0 , thus
g(x) has a minimum