Answer:
x = 1
Step-by-step explanation:
Given exponential equation:
[tex]3^{2x}-9=0[/tex]
Add 9 to both sides of the equation:
[tex]\implies 3^{2x}-9+9=0+9[/tex]
[tex]\implies 3^{2x}=9[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(3^2\right)^{x}=9[/tex]
[tex]\implies9^{x}=9[/tex]
[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]
[tex]\implies9^{x}=9^1[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies x=1[/tex]
Does the following relation represent a function? {(16,7), (7,26), (15,16), (-7,15), (-8,26)} ?
Yes, No, There is not enough information to answer this question
PLEASE HELPPP!!!! DESPERATEEEEEEE
Pablo has a goal to lose 25lb. He has lost 16lb. What percent of his goal has been reached
A writer earns $3400 a month. Last month she spent 204 on food. what percent of her income was spent on food
In triangle ABC, the measure of angle C is 6 times the measure of angle B. 2 times angle A is 20 more than 3 time angle B. Find the measure of each angle in degrees.
Answer:
∠
A
=
x
=
32
∘
∠
B
=
3
x
=
3
⋅
32
=
96
∘
∠
C
=
x
+
20
=
32
+
20
=
52
∘
Step-by-step explanation: Every triangle adds up to 180.
Need some help on this question:
The rule to get from one term to the next in a sequence is
Un+1 = 2Un
If U1=4, work out the values of U2, U3 and U4.
Will mark as Brainliest if correct answer is given. Thanks.
Answer:
8, 16, 32
Step-by-step explanation:
using the recursive formula [tex]U_{n+1}[/tex] = 2[tex]U_{n}[/tex] and U₁ = 4 , then
U₂ = 2 U₁ = 2 × 4 = 8
U₃ = 2 U₂ = 2 × 8 = 16
U₄ = 2 U₃ = 2 × 16 = 32
What is the ratio of 1 1/2 hours to 50 minutes
Answer:
50 mins: 1 and a 1/2 hours
Answer:
9:5
Step-by-step explanation:
1.5 hours is equivalent to 90 minutes (60 x 1.5)
so it's a ratio of 90:50
this can be simplified to a ratio of 9:5 by dividing both sides by their shared factor of 10
52% of all americans are home owners. if 41 americans are randomly selected, find the probability that a. exactly 19 of them are are home owners. b. at most 24 of them are are home owners. c. at least 23 of them are home owners. d. between 19 and 27 (including 19 and 27) of them are home owners.
With the help of permutanions and combinations we can conclude the answer.
What is permutations and combinations?By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.Here is a detailed explanation of permutation and combination, along with their distinctions.acc to our question-
a= total americans -41 probability of 19 of them is house owner= 41C19b= total americans -41 probability of 24 of them is house owner41C24Hence ,permutanions and combinations concept helped us to reach our solution.
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Identify the kind of sequence shown: 2,-1,-4, -7, -10, ... *
O Arithmetic
O Geometric
ONeither
Ojojo and fifi shared an amount of
ratio 3. 4 respectively.
money
If frifi had 140000 had much was
Shared ?
The total amount that was shared $245000 .
In the question ,
the ratio of amount shared by JoJo and Frifi is given
the ratio is given as 3:4 .
the amount that JoJo get = 3x
the amount that Frifi get = 4x
given that Frifi got $140000 .
So , 4x = 140000
Dividing both sides by 4 ,
we get ,
x = 140000/4
x = 35000
total amount shared = 3x + 4x = 7x
Substituting the values of x = 35000 , we get
total amount shared = 7*35000
= 245000
Therefore , The total amount that was shared $245000 .
The given question is incomplete , the complete question is
JoJo and Frifi shared an amount in the ratio 3:4 respectively , if Frifi had $140000 , then find the total amount that was shared ?
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Any nonzero integer divided by 0 equals 0.
Answer: False
Step-by-step explanation:
Can not divide a number by 0.
f(x) = |x|-3; vertical shrink by a factor of 1/3
An equation that represents a vertical shrinkage of the graph of g(x)=1/3|x|-1 by a factor of three.
What is vertical shrink?A vertical stretch/shrink by a factor of k also means that the point (x, y) on the f (x) graph is transformed to the point (x, ky) on the g graph (x). Vertical Stretches and Shrinks Examples Consider the base functions (1) f (x) = x2 - 2, and (2) g(x) = sin (x). Stretches and shrinks, unlike translations, effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without changing its shape. Multiply or divide the output by a constant to stretch or shrink the graph in the y direction.Given,
f(x) = |x|-3;
vertical shrink by a factor of = 1/3
Therefore,
g(x)=1/3|x|-1
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Use the real number line shown below to complete each statement.
The letter best represents −0.1525.
The letter best represents 9
5
.
The letter best represents −1
5
.
A number line goes from negative 0.5 to positive 1.8 and shows points negative 0.5, 0, positive 0.5, 1, and 1.5. Marks divide the space between each number into 5 equal parts. Point a is on the third mark and point b is halfway between the third and fourth mark to the right of negative 0.5, point c is on the second mark after 0, point d is between the second and third mark after positive 1, point e is on positive 1.5, and point f is on the third mark after positive 1.5.
Based on the real number line shown below, each statement should be completed as follows:
The letter b best represents −0.1525.The letter f best represents 9/5.The letter a best represents −1/5.What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Therefore, both -0.1525 and -1/5 would be represented by the letters that are on the left hand side of the real number line while 9/5 would be represented by a letter that is on the right hand side, which are letters b, a, and f respectively;
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Angles ABC and CBD are a linear pair. If m∠CBD=90°, what is m∠ABC in degrees?
NO LINKS OR FILES.
Measurement of ∠ ABC is 90°
What is Linear pair?A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Given that ∠ CBD and ∠ ABC are linear pairs,
Therefore, m∠ CBD + m∠ ABC = 180°
m∠ ABC = 180° - 90° = 90°
Hence, Measurement of ∠ ABC is 90°
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Which equation has the solution x = 9? Select each correct answer 0 +7=8 24-2x = 13 | | 4 + 5x = 18 0¹²-3=6 02x-3 = 15 3x + 2 = 25
HELP PLS!
For x to be a solution, there must be the quantity x in the equation.
All the equations that contain x are :
+) 24 - 2x = 13
+) 4 + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25
We will solve for the value of x for each of the equation :
+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5
+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8
+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9
+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.
We can see, only the equation 2x-3 = 15 has x=9 as a solution.
Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?
The total amount of the money earned by Paige will be $1591.92.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.
The total amount of earnings will be,
TA = ( 50 x 30 ) + ( 0.02 x 4596)
TA = 1500 + 91.92
TA = $1591.92
Therefore, the total amount of the money earned by Paige will be $1591.92.
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If Tristan borrows $4000 at an interest rate of 7.4% with a loan term of 3 years, how much does Tristan pay interest
The amount of Interest Tristan pays is $955.2
Given:
Tristan borrows $4000 at an interest rate of 7.4% with a loan term of 3 years.
we are asked to determine the interest Tristan pays for it:
we know:
P = $4000
r = 7.4%
t = 3 years.
Evaluate :
I = 4000(1+7.4%)³ - 4000
I = 4000(1+0.074)³ - 4000
I = 4000(1.074)³ - 4000
I = 4000(1.2388) - 4000
I = 4955.2 - 4000
I = 955.2
Hence we get the required interest as $955.2
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Please help with algebra. Find the formula for an exponential equation that passes through the points, (0,2) and (1,6). The exponential equation should be of the form y=abx.
The exponential function has an equation of f(x) = 2(3)^x
How to determine the equation of the exponential function?From the question, we have the following points that can be used in our computation:
(0, 2) and (1,6)
Also, we understand that
Function type = Exponential function
An exponential function is represented as
f(x) = ab^x
At point (0, 2), we have
2 = ab^0
Evaluate
a = 2
Substitute a = 2 in f(x) = ab^x
f(x) = 2b^x
At point (1, 6), we have
6 = 2b^1
This gives
2b = 6
Divide
b = 3
So, we have
f(x) = 2(3)^x
Hence, the equation of the exponential function is f(x) = 2(3)^x
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x³+10<9 help pls pls pls pls pls pls
Answer:
x< -1
Step-by-step explanation:
x^3 < 9 - 10
x^3 < -1
x< -1
Answer:
x < -1
Step-by-step explanation:
x³<9-10
x³<-1
x < -1
Please mark as brainliest
Solve the equation given a domain of {-3}.
3x - 2y = 5
Solution of the equation 3x-2y = 5 for domain {-3} is (-3,-7).
Given,
Eq => 3x - 2y = 5
Domain = x = -3
Put x = -3 in equation
3(-3) - 2y = 5
-9 - 2y = 5
-9 - 5 = 2y
-14 = 2y
y = - 14 / 2
= -7
Hence, solution is (-3,-7).
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which graph represents a by traveling at a constant rate of 12 mph
There is no graph in your question
explain how to select a cluster sample of fans. what is the benefit of using a cluster sample in this context?
The cluster sample represents the the characteristic of group of same types objects.
What is the cluster sampling?
A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.
A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.
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Find the AGI and taxable income:
$23,670 and $12,400
$12,400 and $11,270
$11,270 and $23,670
$23,670 and $11,270
The AGI and taxable income is $23,670 and $11,270
How to calculate AGI(Adjusted gross income) ?
The AGI calculation can be done as,
It is determined by subtracting specified deductions, or "adjustments," that you are qualified to claim from the total income you report that is subject to income tax, such as wages from a job or self-employment, dividends, and interest from a bank account.Before you take the standard or itemized deductions, which you record in later sections of your tax return, your AGI is computed.We have given that,
Gross income = $23670
1 Exemption = $12400
Adjustment = 0
Deduction = 0
Find AGI and Taxable income
AGI = Adjusted gross income
we know,
AGI = Total income - Any deduction or any adjustment
AGI = ($23,670 + $12400) - (0 + 0)
AGI = $36070
Now, Calculate taxable income
Taxable income = Gross income - 1 Exemption
= $23670 - $12400
= $11,270
Hence, the AGI and taxable income is $36,070 and $11,270
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Answer: D is the answer
Step-by-step explanation:
$23,670 and $11,270
What is the correct standard form for 400+3+0.07+0.001 need answer asap
Answer:
403.071
Step-by-step explanation:
add
Which of the following sets of numbers can be the lengths of the sides of a triangle?
2.6, 8.1, 10.2
6, 7, 13
1.2, 10.5, 2.1
6, 6, 12
Answer:6, 6, 12
Step-by-step explanation
2 sides must be equal which means 6 and 6 points are moving towards each other and 12 is the length
what kind of autocorrelation is assumed in the classical linear regression model? what kind of autocorrelation is assumed in the classical linear regression model? positive autocorrelation negative autocorrelation no autocorrelation serial correlation g
We use the Serial Autocorrelation in the classical linear regression model.
In the classical linear regression model the serial autocorrelation is assumed to solve the problem.
Hence, we use the Serial Autocorrelation in the classical linear regression model.
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rove by induction that 3n < n! for all integers n greater than 6. state whether you are using regular or strong induction
We can use both regular and strong induction.
The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).
In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.
Regular Induction form
N>6 = n=7 in basic case
3n = 37 = 2187
N! = 7! = 5040
For n= 7 3n<n! is true
Induction hypothesis
Let for n= k and k>6
Assume 3k<k! is true
We prove that for k = k+1 the assumption holds true then the assumption must be true for k
K = k+1
3k+1 < (k+1)!
3k. 3 < (k+1) k!
3k < (k+1)/3.k!
For k>6
(k+1)/3 >1 and let (k+1)/3 = p
3k < P.k!
But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1
Therefore 3k<k! for k>6
3n < n! for all integers n greater than 6.
Therefore we can use both regular and strong induction
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how many ways are there to select 5 scoops of ice cream to put into a bowl, chosen from baskin robbins 31 flavors? a flavor may be selected multiple times.
In permutation, ³¹C₅ are there to select 5 scoops of ice cream to put into a bowl .
What are some examples of permutation?
A permutation is a set up of things in a specific order. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. The components of set A cannot be arranged in any other way, as you can see.Total ice cream flavor n = 31 flavor
selection of (r) = 5 scoop
total number of ways to select 5 scoops of ice cream from 31 flovers
= ³¹C₅
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What’s the answer 60 points plus brainliest also explanation needs to be included
Answer:
both a and b
Step-by-step explanation:
It is because in the elimination method it does not matter whether you eliminate x or y so if you use option a which multiplies -2 by 1st equation so it will become:
-4x+6y=40
4x+6y=8
so the -4x and 4x cancels and a is a valid option.
If you use the b which multiplies the second with 3 it becomes:
2x-3y=-10
4x+3y=24
so -3y and 3y cancel which also makes this a valid option.
Answer: both a and b
students deliver newspapers and magazines to houses.
one day,they have to deliver 875 newspapers and 1200 magazines.
each student can deliver 35 newspapers or 50 magazines in 1 hour.
each student can only work for 8 hours
work out the minimum number of students needed
Answer:
4 students for newspapers & 3 students for magazines are needed for the deliveries to be made in a day.
Step-by-step explanation:
According to the question,
875 newspapers & 1200 magazines are to be delivered in a day by students.In an hour each student can deliver 35 newspapers or 50 magazines & each student can only work for 8 hoursSo, In 8 hours each student can deliver:
35 × 8 = 280 newspapers
50 × 8 = 400 magazines
To find out minimum number of students needed to work we need to divide work done by each student in 8 hours by total deliveries to be made.
[tex] \therefore[/tex]
For Newspapers:
875/280 = 3.125
So, by rounding of the figure we will need 4 students to deliver newspapers as each student can work only for 8 hours.
For magazines:
1200/400 = 3
3 students are needed to deliver magazines.
In thi quetion, aume that the car ue the ame amount of petrol for each mile it travel. A car ue 55 litre of petrol to travel 495 mile. How much petrol would the car ue on a trip of 160 mile?
Give your anwer to the nearet litre
The car use 6.67 liters of petrol to travel 160 miles of distance.
Given, the car use the same amount of petrol for each mile it travels.
A car use 55 liters of petrol to travel 495 miles.
we have to find the petrol used to travel 160 miles.
As, 55 liters = 495 miles
495 miles = 55 liters
1 mile = 55/495 liters
Now, 160 miles = 55/495×160 liters
160 miles = 6.67 liters
So, the car use 6.67 liters of petrol to travel 160 miles of distance.
Hence, the car use 6.67 liters of petrol to travel 160 miles of distance.
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A 10 pound bag of apples costs $9.85 - what is the price per pound?
Answer:
Step-by-step explanation:
$9.85 / 10 ≈ $0.99
