The expression for f(x) using exponent properties is 8x+11.
Let's first simplify the following statement in order to determine f(x):
[tex]\[\left(\frac{1}{49}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11}\][/tex]
Rewrite now with [tex]\(\left(\frac{1}{49}\right)^x\)[/tex] and [tex]\(\left(\frac{1}{7}\right)^{6x + 11}\)[/tex] as a single term's powers:
[tex]\[\left(\frac{1}{7^2}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11} \][/tex]
Now, using the rule for exponents [tex](a^{(m*n)} = (a^m)^n)[/tex],
Combine the following words using the same base (1/7 in this case):
[tex]\[ \left(\frac{1}{7}\right)^{2x} \cdot \left(\frac{1}{7}\right)^{6x + 11} \][/tex]
Add their exponents to multiply phrases with the same base:
[tex]\[ \left(\frac{1}{7}\right)^{2x + (6x + 11)} \][/tex]
[tex]\[ \left(\frac{1}{7}\right)^{(8x + 11)} \][/tex]
Now, the given expression becomes:
[tex]\[ \left(\frac{1}{7}\right)^{(8x + 11)} \][/tex]
Now, compare [tex]\(\left(\frac{1}{7}\right)^{f(x)}\)[/tex],and [tex]\(f(x) = 8x + 11\)[/tex] gives f(x) = 8x+ 11.
So, the expression for f(x) is: [tex]\[ f(x) = 8x + 11 \][/tex].
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The question attached here is in appropriate form the appropriate form is
Find the expression for f(x) when rewriting the following expression in the form [tex]\(\left(\dfrac{1}{7}\right)^{f(x)}(7^1) ^{\dfrac{1}{49}^x \cdot \dfrac{1}{7}^{6x+11}}\):[/tex]
[tex]\(\left(\frac{1}{49}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11}\)[/tex]
Please answer fast! this is my first question so I think I'm giving 10 points? I'm not sure how it works-
if the producer in a food chain has 1000 kcal of energy available, how much energy would each of the consumers have?
Answer:
100kcal
10kcal
1kcal
Step-by-step explanation:
Each level you go up, you only get 10% of the total energy
What is the solution to the system Y 3x 7 and 6x 2y 12?
The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.
To solve a system of equations, you can use substitution or elimination.
One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.
Solving for y in the first equation:
y = 3x - 7
Then substitute the result in the second equation:
6x - 2(3x - 7) = 12
6x - 6x + 14 = 12
14 = 12
That clearly is not true and this system of equations has no solution.
--The question is incomplete, answering to the question below--
"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?
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Define an exponential function, f(x), which passes through the points (0,125) and (3,8). Enter your answer in the form a*b^x
Answer:
Step-by-step explanation:
put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8
b^3=8/125
b=2/5
then the answer is 125*(2/5)^x
You need to split it in half then multply then add
Answer: 322in 2
Step-by-step explanation:
1. Cut it in half
2. 8*21=168 (first half)
3. 11*14=154 (second piece)
4. Add 168 and 154, equals to 322in 2
What is the solution to the inequality below?
√x <9
Answer:
x<81 I hope this is the correct answer.
what is 8 1/4/d=2/11
[tex]8\frac{1}{4}d =\frac{2}{11}[/tex]
a) Simplify both sides of the equation.
[tex]\frac{33}{4}d=\frac{2}{11}[/tex]
b) Multiply both sides by 4/33.
[tex](\frac{4}{33} ) \times (\frac{4}{33}d)=(\frac{4}{33}) \times (\frac{2}{11} )\\[/tex]
d = [tex]\frac{8}{363}[/tex]
[tex]8\frac{1}{4} \div d=\frac{2}{11}[/tex]
= [tex]\frac{33}{4d} =\frac{2}{11}[/tex]
a) Cross Multiply.
[tex](33)\times(11)=2\times 4d[/tex]
[tex](363) =8d[/tex]
b) Flip.
[tex]8d=(363)[/tex]
c) Divide both sides by 8
[tex]\frac{8d}{8} = \frac{363}{8}[/tex]
[tex]d=\frac{363}{8}[/tex]
can you find the proportion pwease :)
Answer: 15/10
Step-by-step explanation:
Answer:
15 cookies and 10 brownies
Step-by-step explanation:
Need help ASAP !!! Right answer please
Answer:
[0,∞) or x ≥0
Notice that the graph doesn't go to the left of x = 0. It only goes right. This means that the domain (all possible values of x), can only be the values above 0.
A triangle ha an area of 142. 74 quare feet and a height of 18. 3 feet. What i the length of the bae?
A triangle having an area of 142. 74 ft^2 and a height of 18. 3 ft, has a base of 15.6 ft.
What is the area of a triangle?
In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.
The area of the triangle is 142.74 ft^2.
The height of the triangle is 18.3 ft.
Let the base of the triangle be x.
The formula for area of a triangle is -
Area = (height × base)/2
Plugging in the values in the equation -
142.74 = (18.3 × x)/2
142.74 = 18.3x/2
18.3x = 285.48
x = 285.48/18.3
x = 15.6
Therefore, the base of the triangle measures 15.6 ft.
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Alonzo went to a baseball game. The game started at 10:50 AM, and it was 3 hours 27 minutes long. When did the game end? PLEASE ANSWER IT I NEED IT
Answer:
The game ends at 2:17 PM.
Step-by-step explanation:
The basketball game started at 10 hours and 50 minutes and the game lasted 3 hours and 27 minutes. We can use addition to find out the time. Simply add the hours and the minutes.
10 hours + 3 hours = 13 hours
50 minutes + 27 minutes = 77 minutes = 1 hour and 17 minutes
⇒ 14 hours and 17 minutes ⇒ 2:17 PM
Is (1, 1) a solution to this system of equations?
4x + 14y = 18
9x + y = 10
Answer:
yes
Step-by-step explanation:
Please help, I need answers ASAP.......
Answer:
hope it is helpful to you
Nolan is a waiter at a restaurant. Each day he works, Nolan will make a guaranteed wage of $25, however, the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on. How much would Nolan expect to earn in a day on which he waits on 12 tables? How much would Nolan expect to make in a day when waiting on tt tables?
Nolan would expect to earn $157 in a day when he waits in 12 tables.
Now, According to the question:
We have the following information:
Each day Nolan works, Nolan will make a guaranteed wage of $25, however the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on.
Now, for waiting on 12 tables, he will get the fixed amount of 25 dollars and the amount for 12 tables.
So, the total amount will be:
25+11 × 12
$157
Hence, Nolan would expect to earn $157 in a day when he waits in 12 tables.
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What is the simplest form of this expression? 2m^3(-m - 3) + 7m^4
hiii so image below, this is super easy bt its hard when you're sleep deprived like me, so please help
You in seventh grade? or nah
The red line on this graph is y=-2x-1
The dotted line is y=x.
Write the equation of the inverse of this function
Answer:
Step-by-step explanation:
HELP DUE IN 15 MINS!
In rhombus ABCD, m∠CDE = 50°, DB = 12 ft, and AC = 16 ft
1. m∠CEB =?? degrees
2. m∠BCE =?? degrees
3. m∠ADE =?? degrees
4. ° DE =?? degrees
5. CB =?? degrees
Answer:
1.) m∠CEB = 90 degrees => The intersection is perpendicular
2.) m∠BCE = 40 degrees => 180 - (50 + 90)
3.) m∠ADE = 50 degrees => 180 - (40 + 90)
4.) DE = 6 ft => half of DB: 12/2
5.) CB = 10 ft => Using Pythagorean Theorem, solve:
=> 8² + 6² = CB²
=> 64 + 36 = CB²
=> 100 = CB²
=> [tex]\sqrt{100}[/tex] = CB
=> 10 = CB
Hope this helps!
Answer:
Step-by-step explanation:
I'm just adding the answer to 3. Give the other answerer the Brainliest.
Given a Rhombus, The diagonals bisect the angle that the diagonal is connect to
Therefore <ADE = 50 degrees, same as <CDE.
Michelle has four white socks two black socks and two gray socks in her drawer she pulled that one sock on the drawer without looking she's not put it back then Michelle Pulls a second Sock from the drawer .what is the probability that Michelle pulls two white socks from the drawer a.3/14 b. 3/16 c. 1/16 d. 1/2
Answer:
3/14
Step-by-step explanation:
prob for the 1st sock=4/8=1/2
prob for the 2nd sock=3/7(there's 7 socks left now and only 3 were white since she pulled one out and didn't put it back)
so the prob of both being white is 1/2*3/7=3/14
Round your answer to the nearest hundredth.
?
B
С
50°
7
9514 1404 393
Answer:
BC ≈ 5.87
Step-by-step explanation:
The law of sines is applicable.
a/sin(A) = 7/sin(50°)
Angle A is the complement of angle B, so we have ...
a = 7(sin(40°)/sin(50°))
a ≈ 5.8736974
The length of BC is about 5.87 units.
What is the formula for directed line segment?
The formula for a directed line segment is A = (x2 - x1, y2 - y1). It is a vector equation, meaning that it describes the direction and magnitude of a line segment, rather than its endpoint coordinates.
A directed line segment is a line segment with a starting point and an ending point, where the direction of the line can be described in terms of its magnitude and direction. To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points, and then calculate the difference between the y-coordinates of the start and end points. The result is the vector A, which describes the magnitude and direction of the line segment.
For example, consider a line segment with start point (1, 2) and end point (4, 6). To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points (4 - 1 = 3). Then, calculate the difference between the y-coordinates of the start and end points (6 - 2 = 4). The result is the vector A = (3, 4). This vector describes the magnitude and direction of the line segment, with the magnitude being the length of the line segment, and the direction being the direction from the start point to the end point.
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Help me pleaseeeeeee
Answer:
only y= 8x-6
Step-by-step explanation:
in order know of an equation is linear is if the equation when graphed makes a straight line the equation should be in the format y=mx+b or y=mx if it is a proportional relationship.
Has a slope of 2/3 and passes through the point (-12, 3) in y intercept form
Miranda conducted a survey on how many hours per day students spend surfing the internet versus how many pets they have. She surveyed ten of her classmates and recorded the data in the scatter plot below.
Use technology to determine which equation best models the data in the scatter plot.
A.
y = -0.4x + 6.3
B.
y = -7.4x + 0.7
C.
y = -0.7x + 7.4
D.
y = -6.3x + 0.4
Answer:
Step-by-step explanation:
a
What is the slope of the linear regression prediction equation if a person with 12 years of schooling
On solving the provided question, we can say that the e slope of the linear regression prediction equation if a person with 12 years of schooling is 1.
what is linear regression?When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.
the e slope of the linear regression prediction equation if a person with 12 years of schooling
a. 1(correct)
b. 12
c. 13
d. 1,500
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*Can someone please help me out with this one?*
A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is
plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of , for the resulting
scatterplot is 0.83.
How would the value of the correlation coefficient change if sodium was plotted on the x-axis
and calories plotted on the y-axis?
A.The value of r would increase
B.The value of r would not change
C.The value of r would change to -0 83.
D.The value of r could increase or decrease, depending of the strength of the new relationship.
Answer:
B) The value of r would not change
Step-by-step explanation:
If there's a positive association between sodium and calories, that's like saying there's a positive association between calories and sodium. Therefore, the value of r would not change because both variables are still increasing with each other.
Estimate number of jelly beans in 1 litre jar.
The cost of tuition at a college is $12,000 and is increasing at a rate of 11% each year. Use an exponential function to find the cost of tuition after 4 years.
Answer:
17280
Step-by-step explanation:
11% of 12000= 1320
1320x4=5280
5280+12000=17280
Please mark brainliest
Determine whether each system of equations has no solution, one solution, or infinitely many solutions
Show work please:)
Answer:
One solutionStep-by-step explanation:
Given system:
y = -3-3(x + 9) = yThe first equation is a horizontal line, the second equation is a line with a slope of -3.
Since the lines have different slopes, they intersect at one point.
As there is one intersection, the system has one solution.
hi can someone pls help me
:)
A cone and a sphere have the same volume the base of the cone has a radius of 8 feet and the sphere has a radius of 6 feet what is the height of the cone?
Step-by-step explanation:
Volume of Cone=
[tex] \frac{1}{3} \pi \: r {}^{2} h[/tex]
Volume of Sphere=
[tex]\frac{4}{3} \pi \: r {}^{3} [/tex]
Since VC = VS
[tex] \frac{1}{3} \times 3.14 \times 8 {}^{2} \times h = \frac{4}{3} \times 3.14 \times 216[/tex]
66.99h = 904.32
h = 904.32 ÷66.99
h= 13.5 feet