An exponential function gives a variable raised to the power of x, where the variable is a positive real number
Yes, [tex]\underline{f(x) = 3 ^{(2 \cdot x - 3)}}[/tex] is an exponential function
Reason:
An exponential function is a function that can be written in the form;
f(x) = eˣ
Where;
e = Euler's number, which is the number approximately 2.71828
In the general form, an exponential number is a number given in the form;
f(x) = a·bˣ
Where;
b = A positive real number
The given function; [tex]f(x) = 3 ^{(2 \cdot x - 3)} = \dfrac{3^{2\cdot x}}{3^3} = \dfrac{1}{27} \times 9^x[/tex] is an exponential function
Where;
a = [tex]\dfrac{1}{27}[/tex]b = 9Therefore, the correct response is; Yes, [tex]f(x) = 3 ^{(2 \cdot x - 3)}[/tex] is an exponential function
Learn more here:
https://brainly.com/question/17153778
I'm confused. Hopefully, you can help me.
Answer:
C
Step-by-step explanation:
a straight line is 180, 180-40=140
There is a meeting in Conference Room A.
The ratio of women to men is 3 to 4. If there
are 18 women at the meeting, how many men are there?
A) 21 men
B) 54 men
C) 24 men
D) 72 men
Answer:
I think 21 is it right ...
Need help with this one please show it step by step.
Thank you!
Answer:
which class you are plz say dude
3. Write an exponential function that represents the table and graph. y=0-b*
please help!!
Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Property 1: Every integer is a rational number. Property 2: The sum of any two rational numbers is rational. Property 3: The product of any two rational numbers is rational. Note: Property 1 is Theorem 4.3.1, Property 2 is Theorem 4.3.2, and Property 3 is Exercise 15 in Section 4.3. Using these properties, choose explanations for each step in the given proof.
Given:
Expression is
[tex]3r^2-2r+4[/tex]
To prove:
If r is any rational number, then [tex]3r^2-2r+4[/tex] is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,
[tex]3r^2-2r+4[/tex]
It can be written as
[tex]3(r\times r)-2r+4[/tex]
Now,
3, -2 and 4 are rational numbers by property 1.
[tex]r^2=r\times r[/tex] is rational by Property 3.
[tex]3r^2\text{ and }-2r[/tex] are rational by Property 3.
[tex]3r^2+(-2r)+4[/tex] is rational by property 2.
So, [tex]3r^2-2r+4[/tex] is rational.
Hence proved.
We want to prove that if r is rational, then:
[tex]3*r^2 - 2r + 4[/tex] Is also rational.
The proof is below:
Remember that a rational number is any number that can be written as a quotient of two integer numbers.
Then we have:
[tex]r = \frac{a}{b}[/tex]
Where a and b are integers.
If we replace that in our equation, we get:
[tex]3*(\frac{a}{b}) ^2 - 2*(\frac{a}{b}) + 4\\\\\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}[/tex]
Note that if a is an integer, then 3*a^2 is also an integer.
If b is an integer, then b^2 is also an integer.
Now we can perform the sum of these fractions to get:
[tex]\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}\\\\\frac{3a^2 - 2ab + 4b^2}{b^2}[/tex]
And because integers are closed under the addition, then the numerator of that fraction is also an integer, then we have that the given expression can be written as a quotient of two integers, thus, it is a rational number.
If you want to learn more, you can read:
https://brainly.com/question/15815501
The third term of an A.P is 4m - 2n. If the ninth term of the progression is 2m - 8n. Find the common difference in terms of m and n
Let [tex]a_n[/tex] denote the n-th term in the progression. So
[tex]a_n=a_{n-1}+d[/tex]
for some constant difference between terms d.
Solve for [tex]a_n[/tex] explicitly:
[tex]a_4=a_3+d[/tex]
[tex]a_5=a_4+d=a_3+2d[/tex]
[tex]a_6=a_5+d=a_3+3d[/tex]
and so on, up to
[tex]a_n=a_3+(n-3)d[/tex]
We're told that the third term is [tex]a_3=4m-2n[/tex], and the ninth term is [tex]a_9=2m-8n[/tex], and according to the recursive rule above, we have
[tex]a_9=a_3+6d[/tex]
Solve for d :
[tex]2m-8n=(4m-2n)+6d[/tex]
[tex]-2m-6n=6d[/tex]
[tex]d=-\dfrac{2m+6n}6=\boxed{-\dfrac{m+3n}3}[/tex]
Jamie has a sprinkler than covers a circular area with diameter 16 feet. What is the area of lawn that the
sprinkler covers?
Answer:
64π or 201.0619298297
Step-by-step explanation:
Area of a circle: πr²
To find r, the radius of the circle, take the diameter (16) and halve it to get 8. You can now place 8 into the equation to get π8². Square 8 to get 64. You now now have π64, or 201.0619298297.
PLZ, HELP WILL GET BRAINLIEST AND A LOT OF POINTS.
What is the exponential function rule for the following points
x f(x)
1 8
2 32
3 128
4 512
Answer:
y=2(4^x)
Step-by-step explanation:
if you notice, all the y-values are multiplied by 4 for each x-value. this means 4 is raised to the power of x. however, when you plug this in, you realize that the value produced is only half the actual y-values, so you multiply this whole thing by 2.
y=2(4^x)
Answer:
f(x) = 2^(2x+1)
Step-by-step explanation:
You can tell that each of the outputs of f(x) are powers of 2, so all you have to do is figure out the pattern of the exponents.
2^3 = 8
2^5 = 32
2^7 = 128
2^9 = 512
the relationship between the sequence
3,5,7,9
when you start on 1 is
2x+1
2(1)+1 = 3
2(2)+1 = 5
etc.
Drag the divisor fraction to the dividend bar to see how many
parts of the divisor are in the dividend
Use fraction bars and the rules of dividing signed
numbers to divide
15
Dividend
15 3
5 5
o
18
cila
o
Divisor
o
12
O -5
Answer:
Is B
Step-by-step explanation:
The dividend is 2 and the divisor is 2/5
What is Division?A division is a process of splitting a specific amount into equal parts.
The given fraction is 2 ÷ 2/5
The number which is getting divided here is called the dividend.
The number which divides a given number is the divisor.
In the given division the dividend is 2
The divisor is 2/5
Hence, the dividend is 2 and the divisor is 2/5
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ7
I"LL MARK YOU BRANLIEST IF YOU ANSWER CORRECT! Ayana's favorite brownie recipe calls for 1/2 of a cup of flour for every 1/3 of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?
Answer:
either a full cup or 1 1/2
Which expression shows how to convert 60 hours into days?
Answer: so, 60 hours = 60/24 days = 2 days 12 hrs
Step-by-step explanation:
Which of the following steps would you use to
evaluate (a + b)??
Answer:
(a+b)(a+b)
Step-by-step explanation:
Work out 2 1/3 divided by 1/4
Answer:
9.3333333
Step-by-step explanation:
Answer:
[tex] \frac{9}{4} \div \frac{1}{4}
\frac{9}{4} \times \frac{4}{1}
= \frac{34}{4} \\ \\ \\ \\ = 9[/tex]
Geometry The sides of a yield sign all have the same
length (see figure). The perimeter of a roadway yield
sign is 225 centimeters. Find the length of each side.
YIELD
Figure for 51
Figure for 52
Answer:
75 cm
Step-by-step explanation:
Given:
Perimeter of the triangular yield sign = 225 cm
Side lengths = x, x and x
Required:
Length of each side
SOLUTION:
Perimeter of the triangular yield sign = sum of all sides of the triangular yield sign
225 cm = x + x + x
Solve for x
225 = 3x
Divide both sides by 3
225/3 = 3x/3
75 = x
x = 75
The length big each side is 75 cm
HELP NEEDED ASAP MATHS PLEASE!!!
A bacteria population increases exponentially at a rate of r% each day. After
32 days, the population has increased by 309%. Find the value of r.
Answer:
r=4.5% daily
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.
Substitute the given values into the model function:
[tex]409\%P_o=100\%P_o(1+r)^{32}[/tex]
Simplifying:
[tex]4.09=(1+r)^{32}[/tex]
We need to solve for r. Taking the 32nd root:
[tex]\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}[/tex]
Simplifying:
[tex]1+r=\sqrt[32]{4.09}=1.045[/tex]
Solving:
[tex]r=1.045-1\Rightarrow r=0.045[/tex]
r=4.5% daily
Translation is a congruency transformation. True or false
Answer:
True
Step-by-step explanation:
In a translation, the figures face the same direction and are congruent.
What is the minimum number of x-intercepts that a polynomial of degree 10 can have?
Given m||n, find the value of x.
t
>m
(3x+14)
(7x-4)
Answer:
(3x+14°) + (7x-4)° = 180°
=> 10x + 10 = 180
=> 10x = 180 – 10
=> x = 170/10
=> x = 17
The value of x is 17
What is | -8|
—16
-8
8
16
Answer:
8
Step-by-step explanation:
scince it has the lines that mean that it will always be positive.
Answer:
8
Step-by-step explanation:
Have a nice day!
How do you know if a sum or product will result in a rational or irrational number?
Types of Data
Numbers
Yes/No
Longer response
What is the campus like?Is there on-campus housing?Is financial aid available?Are engineering scholarships offered?What majors are available?How much is the tuition?How many students are enrolled?What is the average class size?What percentage of those who apply are accepted?What dining options are offered on campus?
jfjkejkiydtmhfsngdjfs
3)
Blair expects an increase of 3% in her current annual
salary of $42,000. What would her new annual salary
be?
Answer:
$43,260
Step-by-step explanation:
You have the 3% annual income, which you can convert to a decimal. This gives:
42000 * 1.03
42000 represents Blair's initial income, and 0.03 represents the 3% increase.
I chose 1.03 because I don't have to subtract 97% and add it to 42000.
I need help on this ASAPPPPPPP
Which is greater, 9 x 10^-2 or 3 x 10^-4? How many times greater is the number you chose than the other number? Explain your reasoning.
Answer:
The solution to 9x10^-2 is 0.09 or (3/10)^2. The solution to 3x10^-4 is 0.0003 or 3/10000. Based on that, 9x10^-2 fits into 3x10^-4 three-hundred (300) times.
plz help I will mark brainlest!
Answer:
-1.71 the answer is d
Step-by-step explanation:
.........
are fractions with the same denominator?
Answer:
To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.
Step-by-step explanation:
For example, 2/3 + 3/6
The denominators in this case have a common denominator which is 6.
All you have to do is multiply the 2/3 by 2 in the numerator and the denominator. Once you do, you'll get 4/6 which you could then add to 3/6 to get 7/6 which would equal 1 1/6 or 7/6 either is fine.
Hope this helps! :)
Answer:
To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.
Step-by-step explanation:
jamie and her 2 friends decide to buy a pizza pie and split the cost. The pizza pie cost $12.78. If Jamie has $5, how much does she have left over after they buy the pizza pie?
Answer:
she has no more money
Step-by-step explanation:
Answer:
7.78 if u subtract
but no more money i guess
2х - Зу= 2
х= бу - 5
X=
Y=
Answer:
2x-3y=2
x=6y-5
2(6y-5)-3y=2
use the distributive property.
2*6y=12y
2*-5=-10
12y-10-3y=2
combine like terms
12y-3y=9y
9y-10=2
add 10 to both sides.
9y-10+10=9y
2+10=12
9y=12
divide both sides by 9
9y/9=y
y=about 1.33
plug in the value of y in the expression equal to the value of x.
x=6(1.33)-5
solve
6*1.33=7.98
x=7.98-5
7.98-5=2.98
Step-by-step explanation:
x=2.98
y=1.33
On a map, 1 inch equals 5 miles. If two cities are 7 inches apart on the map, how far are they actually apart
Answer:
35
Step-by-step explanation:
7 * 5 = 35