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
write 3/4 as a decimal. Use method 1
Answers
Answer:
0.75
Step-by-step explanation:
A principal of $6000 is invested in an account paying an annual rate of 5%. Find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly. (a) The amount in the account after 4 years if the account is compounded semiannually is $ nothing. (Round to the nearest cent.)
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Solution :
Given :
Principal amount deposited, P = $ 6000
Rate of interest, r = 5%
Number of years, t = 4 years
When the deposited amount is compounded semiannually, i.e. n = 2
Therefore,
Future value,
[tex]$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$[/tex]
[tex]$FV = 6000\left( 1 +\frac{0.05}{2}\right)^{2 \times 4}$[/tex]
[tex]$FV = 6000 \times (1.025)^8$[/tex]
= 6000 x 1.2184
= 7310.4
Therefore, after 4 years there will be $ 7310.4 in the amount when compounded semi annually.
When the deposited amount is compounded quarterly, i.e. n = 4
Therefore,
Future value,
[tex]$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$[/tex]
[tex]$FV = 6000\left( 1 +\frac{0.05}{4}\right)^{4 \times 4}$[/tex]
[tex]$FV = 6000 \times (1.0125)^{16}$[/tex]
= 6000 x 1.219889
= 7319.334
Therefore, after 4 years there will be $ 7319.334 in the amount when compounded quarterly.
When the deposited amount is compounded monthly, i.e. n = 12
Therefore,
Future value,
[tex]$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$[/tex]
[tex]$FV = 6000\left( 1 +\frac{0.05}{12}\right)^{12 \times 4}$[/tex]
[tex]$FV = 6000 \times (1.0041667)^{48}$[/tex]
= 6000 x 1.22089
= 7325.34
Therefore, after 4 years there will be $ 7325.34 in the amount when compounded monthly.
Help asaaaaap please
Answers
Answer:
A. 1
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
-5x - 1 ≤ -9
Step 2: Solve for x
Add 1 to both sides: -5x ≤ -8Divide -5 on both sides: x ≥ 8/5Here we see that any value x greater than or equal to 1.6 would work as a solution.
Therefore, our answer is A. 1, as it doesn't work as a solution.
Ben is now 3 times as old as his brother Jerry. In 5 years, Ben will be twice as old as Jerry will be then. Find their present ages.
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Answer:
30 I am a little confused
PLS help ASAP thank you
Answers
Answer: they are not similar
Step-by-step explanation:
there will no be no steps
What do you know about the following System of Equations?
y=3x + 4
y 3x + 9
The graph of the lines will have one come point of intersection
The graph of the lines will have no common point of intersection
The graph of the lines will have an infinite amount of points in common
The lines are the same
Answers
Answer:
graph have no common points of intersection
Step-by-step explanation:
since both slopes have a value of 3, the system of equations are two parallel lines.
parallel lines will never meet.
since the y intercepts (plug in 0 for x or look at the constant) are different, they are not the same line
A 12 cm by 20 cm painting hangs in a museum. The museum curator wants to hang other paintings in the gallery that are proportional in size. The dimensions of several paintings are shown. Which paintings' dimensions are proportional to the original painting? Select all that apply. A. 1.5 cm by 2.5 cm B. 27 cm by 45 cm C. 9 cm by 15 cm D. 30 cm by 50 cm E. 6 cm by 14 cm
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Answer:
A. 1.5 cm by 2.5 cm
B. 27 cm by 45 cm
C. 9 cm by 15 cm
D. 30 cm by 50 cm
Step-by-step explanation:
The dimensions of the original painting = 12 cm by 20 cm painting
Hence, the proportion is:
12/20 = 0.6
Hence, we compare the options given in the question.
A. 1.5 cm by 2.5 cm
= 1.5/2.5 = 0.6 , option A is correct
B. 27 cm by 45 cm
27cm/45 cm = 0.6 Option B is correct
C. 9 cm by 15 cm
9cm/15cm = 0.6 , Option C is correct
D. 30 cm by 50 cm
30 cm /50 cm = 0.6 Option D is correct
E. 6 cm by 14 cm
6cm/14 cm = 0.4285714286
Option E is not correct
Therefore, Options A to D are the correct options
First one
11
12
23
1
Second one
11
12
23
1
Answers
Answer:
Step-by-step explanation:
AD is 11 and BC is 12. We know this because AD and BC are parallel, as well as AB and DC. This means all the right triangles are congruent. I hope you understand. Let me know if you need more explanation! Please mark brainliest if correct, too.
Henry saw 28 blue, 16 red and 24 white cars drive by his house in 1 hour. What percent of the cars were blue? (Round answer to the nearest percent)
A. 24%
B. 65%
C. 41%
D. 35%
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Answer:
C
Step-by-step explanation:
The percentage is calculated as
% = [tex]\frac{blue}{total}[/tex] × 100%
Total number of cars = 28 + 16 + 24 = 68
number of blue cars = 28, then
% blue = [tex]\frac{28}{68}[/tex] × 100% = 41% ( to the nearest percent )
Zoey has a bag that contains orange chews, apple chews, and watermelon chews. She
performs an experiment. Zoey randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Zoey performs the experiment 57 times. The
results are shown below:
A orange chew was selected 39 times.
A apple chew was selected 6 times.
A watermelon chew was selected 12 times.
Based on these results, express the probability that the next chew Zoey removes from
the bag will be apple chew as a decimal to the nearest hundredth.
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Answer: 54%
Step-by-step explanation:
Find the area of a circle with radius = 12cm give your answer rounded to 3SF
Answers
Answer:
452.4
Step-by-step explanation:
area is given by πradius squared which gives answer as 452.389
Answer:
452.39 because you have to take the radius squared times pie or 3.14 to get the area so your answer would be 452.39
Step-by-step explanation:
Hope it helps
Please help! I think of a number, I double it, and then add 3. The result is 19. Write this in the form of an equation and then solve the equation to find the number I was thinking of.
Answers
Answer:
8
Step-by-step explanation:
Y×2+3=19
19-3=16
16÷2=8
You subtract the 3 first to get what the number was when doubled. After getting that number you would divide it by 2 to get the number that you thought of.
I need help fast! Given the diagram below, find the length of CH.
Answers
Answer:19.8
Step-by-step explanation: if you look at the lines it describes the length of the area it’s on. Since there is 4 lines on right side it would be 9.9+9.9 which would give you and answer of 19.8 so CH=19.8
Answer:
CH=12
Step-by-step explanation:
CH=12
9.9+9.9=19.8
19.8x19.8=392.04
8x8=64
392.04-64=328.04
v328.4=18
18-6=12
What angles are they ?
Answers
number 2 is your answer
Answer:
number 2 is your answer
Step-by-step explanation:
Why do parallel lines never cross?
Answers Are
Answers
Answer:
C. Because they have the same slopes and different y-intercepts
Step-by-step explanation:
Answer:
Your answer would be the 3rd one.
Because they have the same slopes and different y-intercepts.
I hope that this is the answer you were looking for!
Have a great day!
The ratio of buckets of yellow paint to buckets of red paint in the store is 3 to 4. There are 60 buckets of yellow paint. How many buckets of red paint are in the store?
Answers
Answer:
80 buckets of red paint
Step-by-step explanation:
Given
The ratio of buckets of yellow paint to buckets of red paint in the store to be 3:4
Total ratio = 3 + 4 = 7
Amount of yellow paint = 60
Required
Amount of red paint.
First get the total amount of paint used.
3/7 * x = 60
x is the total paint used
3x/7 = 60
3x = 7*60
x = 420/3
x = 140 buckets of paint
Amount of red paint = Total - Amount of yellow paint
Amount of red paint = 140 - 60
Amount of red paint = 80
Hence there are 80 buckets of red paint in the store
Explain how you can use the vertex form of a quadratic function to locate the vertex of the function's graph.
Answers
Answer:
quadratic function can find and write with the vertex and function the graph better.
Step-by-step explanation:
If f(x)=7x+2 and x=1 what is the output value? Plzzz help ASAP
Answers
The output is 9
Please help me please help!!
Answers
Answer:
(1) -27
Step-by-step explanation:
[tex]-2(-3)^2+3(-3)[/tex][tex]-2(9)+(-9)[/tex][tex]-18-9[/tex][tex]-27[/tex]Karen says the functions f(×)=×+3 and g(×)= -×+7 intersect at x=2 is she correct
Answers
Answer:
Yes.
Step-by-step explanation:
To find the point of intersection we solve the system:
y = x + 3
y = -x + 7 Subtract:
0 = 2x - 4
2x = 4
x = 2.
She is correct.
Answer:
yes
Step-by-step explanation:
Given the 2 equations
y = x + 3 → (1)
y = - x + 7 → (2)
Substitute y = x + 3 into (2)
x + 3 = - x + 7 ( add x to both sides )
2x + 3 = 7 ( subtract 3 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Thus the functions intersect at x = 2
craig went to the store yesterday. he bought a pack of ice cream for $0.98, bottle of soda for $1.19, and a lunchable for $4.89. How much money did he spend altogether? Show work don't forget label
Answers
Answer: $7.06
Step-by-step explanation:
$0.98 + $1.19 + $4.89 = $7.06
Tell whether the angles are adjacent or vertical. Then find the value of x.
Answers
Porción indefinida de plano limitada por dos líneas que parten de un mismo punto o por dos planos que parten de una misma línea y cuya abertura puede medirse en grados.
ángulos adyacentes Ángulos que tienen el vértice común, un lado común que los separa y los otros dos lados en línea recta.
Answer:
They are adjacent. x=10/3
Step-by-step explanation:
which is bigger 1 2/7 or 1 1/5
Answers
Answer:
1 2/7 is bigger
Step-by-step explanation:
HELP ASAP! WILL MARK BRAINLIEST
Answers
Answer:
it will be the first the 5th the 2nd and the 3rd
the width of a rectangle is ycm and its length is y+2 cm. if the perimeter of the rectangle is 32cm what is the width of the rectangle
Answers
Answer:
[tex]\huge\mathtt{{\colorbox{silver}{ANSWER~~~↴}}}[/tex]
ꜰɪʀꜱᴛ ᴡᴇ ᴡʀɪᴛᴇ ᴛʜᴇ ɢɪᴠᴇɴ↴
⇒WIDTH = Y cm
⇒LENGTH =( y+2 )cm
⇒PERIMETER = 32cm
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
solution ↴
perimeter of rectangle = 2 ( length + width)
[tex]32cm = 2( (y +2) +y )cm \\ \frac{32}{2} cm = 2y + 2cm \\ 16cm = 2y - 2cm \\ 16 cm- 2 cm=2y\\ 14cm = 2y \\ y = \frac{14cm}{2} \\ y = 7cm
[/tex]
☛ so the width of the rectangle is 7cm
so we all done :D
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
PLZ HELP ME
look at the picture above
Answers
b. To reflect it across the x axis you would need to change the coefficient and make it negative. In this case, it would be:
g(x)= -3(2)^x
Brandie lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend, then up 3 flights to deliver a message to a neighbor. Which integer best represents the number of flights Brandie must walk to get back to her starting point?
A). -12
B). -1
C). 5
D). 7
Answers
Answer:
Option (B) is the correct answer.
Step-by-step explanation:
Let 'x' the starting point be
She walks down 2 flights to visit a friend.
so walking down means we need to add 2 units to the starting point x
[tex]x+2[/tex]
Then he walks up 3 flights to deliver a message to a neighbor.
now subtracting 3 units from (x+2)
[tex]x + 2 - 3 = -1[/tex]
x = -1 means now he is UP to 1 point where he started his flight.
Thus, he needs to walk down 1 more flight to reach her starting point
Thus, -1 is the number of flights Brandie must walk to get back to her starting point.
Therefore, option (B) is the correct answer.
. help needed please
Answers
3x+2(2x−1)=33
what is x?
Answers
Answer:
x = 5
Step-by-step explanation:
3x + 2(2x − 1)= 33
simplify
3x + 4x - 2 = 33
7x - 2 = 33
add 2 to both sides
7x - 2 + 2 = 33 + 2
7x = 35
divide both sides by 7
7x/7 = 35/7
x = 5
I don’t know if this correctly !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!! PLEASE ANSWER !!!!!!!!!!!!!!
Answers
Step-by-step explanation:
the three angles =180
because they are supplementary angles
I hope this help