The mathematical function known as a logarithm expresses the degree to which a base number must be raised in order to obtain a specific value. The symbol logb(x), where b is the logarithm's base and x is the value being evaluated, stands for the logarithm of a number. The natural logarithm, which has a base of e, is the most widely used logarithm (approximately 2.71828). The inverse function of exponentiation is the logarithm, according to this definition. The exponent to which we must raise b in order to obtain a number x is its logarithm to base b.
It reads log2(3x + 8) = 5.
logb(a^n) = n * logb(a) where b is the base of the logarithm, is a property of logarithms that can be used to rewrite expressions. Since the base in this instance is 2, we obtain log2(3x + 8) = 5.
corresponding to 2^5 = 3x + 8
Now that x is on one side of the equation, we can solve for it.
32 = 3x + 8
After deducting 8 from both sides, we arrive at 24 = 3x, which we then multiply both sides by to get 8
Thus, x = 8 is the corresponding equation.
and the solution is 8.
Therefore, the x=8 is the solution of this problem .
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Answer:
1. a 2. 8
Step-by-step explanation:
The grocery store has bulk pecans on sale, which is great since you're planning on making 6 pecan pies for a wedding. How many pounds of pecans should you buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
You will need to buy ____ pounds of pecans.
Give your answer accurate to at least one decimal place.
Answer:
2.29 pounds.
Step-by-step explanation:
The following is the analysis for the response to this query:
There must be some relationship among both the volume and the weight.
According to the given label's information, one cup weighs 99 grams. Given that there are 99/453.6 pounds for every cup as well as you require 7*1 1/2 cups, multiplying 10.5 cups by 99/453.6 pounds for every cup results in 2.3 pounds. A pound (avoirdupois) is defined as 453.6 grammes.
Another way to write this would be:
7 (pecan pie) * 1.5 (cup/pecan pie) * 99 (gram/cup) * 0.0022 (pounds/gram) = 2.292 pounds
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(a) this is part of thr fibonacci sequence;21,34,55
what is the next term of the sequence
a 68
b 76
c 88
d 89
Answer:
89
Step-by-step explanation:
fibonacci sequence is a famous sequence where each number is the sum of the last two.
Therefore :
34+55 will give us the next number which is 89
URGENT!
find the value of x in each supplementary angle pair
[tex] \frac{x}{3° } + 49° = 180° \\ [/tex]
Cross multiply
[tex]x + 147° = 180°[/tex]
simplify
x = 180° - 147°
answer : x = 33°
What does the subtraction of 7 from 9 mean?
Answer: it mean 7-9.
Step-by-step explanation:
7 is smaller than 9, so the answer is going to be negative. I like to do
7-9
Is basically just 9-7, just put a negative label
So 7-9 can be solved as 9-7=2 slap on a negative sign and -2! Hope this helps!
What are the two 2 methods used in solving a system of linear equations?.
Two different methods used to solve the system of linear equation is given by :
a. Elimination method.
b. Substitution method
As given in the question,
Let us consider system of linear equation be :
2x + 5y = 3 __(1)
3x + 4y = 1 __(2)
a. Elimination method :
Multiply (1) by 3 and ( 2) by -2 and add them we get,
6x + 15y = 9
-6x -8y = -2
7y = 7
⇒ y = 1
b. Substitution method :
Substitute the value of y = 1 in any one equation we get,
2x + 5(1) = 3
⇒ 2x = 3 - 5
⇒ x = -1
While solving two equation substitute the value of one variable from one equation into the other.
Therefore, the two methods used to solve the system of linear equation is equal to :
a. Elimination method.
b. Substitution method
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Larry and Bonny began saving money the same week. The table below shows the
models for the amount of money Larry and Bonny had saved after x weeks.
Larry's Savings
f(x)=8x+15
Bonny's Savings
g(x)=5,5x+25
After how many weeks will Larry and Bonny have the same amount of money saved?
Equation:
Answer:
Answer:
4
Step-by-step explanation:
8x + 15 = 5.5x +25
so 2.5x =10
x=4
I need some help please
Answer:
x = 39
m ∠1 = 63°
m ∠2 = 117°
Step-by-step explanation:
m∠1 + m∠2 = 180° since they are adjacent linear angles lying on the same straight line
Therefore x + 24 + 3x = 180
4x + 24 = 180
4x = 180-24 = 156
x = 156/4 = 39
Therefore x = 39 (a)
FOr (b) substitute this value of x = 39 into each equation
m∠1 = x + 24 = 39 + 24 = 63°
m∠2 = 3x = 3(39) = 117°
Painter A can paint the house in 50 hours. Painter B can paint the same house in 35 hours. If they work together, about how many hours should it take them to paint the house?
It will take 20.6 hours to paint the house if both painter A and painter B worked together.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Let F represent the house fully painted.
Painting done by painter A in 50 hours = F
Painting done by painter A in 1 hour = F/50
Painting done by painter B in 35 hours = F
Painting done by painter B in 1 hour = F/35
If they both paint together,
Painting done by painter A and painter B in 1 hour = F/50 + F/35
= 85/1750 F
= 17/350 F
Time taken to paint 17/350 F = 1 hour
Time taken to paint F = 1 / (17/350)
= 20.588
≈ 20.6 hours
Hence time taken to paint the house by both working together is 20.6 hours.
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DIG DEEPER There is a total of 4,752 passengers on 3 subway
trains. Each subway train has 8 cars. The number of
passengers in each car is the same. How many
passengers are in each car?
There are 198 passengers in each car.
What is division?
The division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication.
To determine the number of passengers in each car, we need to divide the total number of passengers by the total number of cars.
We know that:
There are 4,752 passengers in total
There are 8 cars per train and 3 trains
So, the total number of cars is 8 cars/train x 3 trains = 24 cars
To find the number of passengers per car, we divide the total number of passengers by the total number of cars:
4,752 passengers / 24 cars = 198 passengers per car.
Hence, there are 198 passengers in each car.
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What are the 3 methods in solving system of nonlinear equations?.
There are several methods that can be used to solve a system of nonlinear equations, but three common ones are: substitution method, elimination method and graphing method.
Substitution method: This involves isolating one variable in one equation and substituting it into the other equation to eliminate that variable. You can then solve for the remaining variable and substitute it back into the original equation to find the solution.
Elimination method: This method involves adding or subtracting the equations in such a way as to eliminate one of the variables. Then you can solve for the remaining variable and substitute it back into the original equation to find the solution.
Graphical method: This method involves graphing both equations on the same coordinate plane and finding the point of intersection of the two lines. The coordinates of this point will be the solution to the system of equations.
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What is the value of X? 3 ,4,5,6,8
Answer:
but it is not possible to determine the value of X with the information provided. The numbers 3, 4, 5, 6, and 8 are all different values, and without any additional context or information, it is impossible to determine which one is X.
It would be helpful if you could provide more information such as an equation or some context, to help determine the value of X.
please answer fast its due tomorrow
Is co-prime a number 9?.
Yes, the numbers 2 and 9 are co-prime numbers, i.e., HCF(2,9) = 1.
Two numbers a and b are relatively prime if their only common divisor is 1. If the only highest common factor of two numbers a and b is 1, then a and b are co-prime numbers. In this case,(a, b) is said to be a co-prime pair. Properties of relatively prime numbers:
The greatest common divisor (HCF) of two relatively prime numbers is always 1.The least common multiple (LCM) of two relatively prime numbers is always their product.Two even numbers must not be relatively prime.Every pair of two consecutive numbers is primeWe have, two numbers say 2 and 9 and we have to check they are co-prime or not. The factors of 2 are 1 and 2. Factors of 9 are 1, 3 and 9. So, highest common factor between 2 and 9 is 1. As 9 and 2 have no common factor other than 1, they are co-prime.
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Complete question:
Is 2 co-prime number with 9?.
How do you write 10 more than a number?.
To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.
To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.
In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.
This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.
Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.
Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.
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What is the factor of 9x2 24xy 16y2?.
The factor of 9x² 24xy 16y² is (3x−4y)²
A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, usually smaller or simpler things of the same kind.
Factorization in mathematics is the method of dividing a large number into tiny ones that, when multiplied together, give you the original number. Factorization is the split of a number into its factors or divisors.
9x²−24xy+16y²
=(3x)²−24xy+(4y)²
=(3x)²−2(3x)(4y)+(4y)²
Using (a−b)²=a²−2ab+b², we get
=(3x−4y)²
Factorization, also known as factoring, is the process of dividing or decomposing a thing into factors that, when multiplied together, form the original number, matrix, etc.
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Elena is 59 inches. Some people are taller than Elena
Answer:
that even a complete problem?
How do you solve 2nd degree equations with 2 variables?.
The solution is the set of values for the two variables (x, y) that satisfy both equations.
To solve a system of two equations with two variables that are both quadratic (2nd degree), you can use the following steps:
Write the two equations in standard form, which is ax² + bx + c = 0 for each equation, where a, b, and c are coefficients.
Solve each equation separately for one variable by factoring or by using the quadratic formula.
Substitute the value of one variable from one equation into the other equation, and solve for the other variable.
Substitute the value of the other variable from the previous step back into one of the original equations to find the value of the first variable.
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Mr. Berry had $120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years?
What is the slope of this line y =- 3x 3?.
The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.
What is slope ?
Slope, also known as gradient, is a measure of the steepness of a line. It is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two distinct points on the line. It is represented by the letter "m" in the slope-intercept form equation of a line y = mx + b, where m is the slope, x is the independent variable, y is the dependent variable and b is the y-intercept, the point where the line crosses the y-axis.
The slope of a line is a measure of its steepness or incline. It is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope is represented by the letter "m" and it is the coefficient of the x variable in the equation of the line y = mx + b, where b is the y-intercept.
In this case, the equation of the line is y = -3x + 3,
The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.
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Point A represents a positive number. Which point represents the opposite of that number?
A number line. Point E is 5 units to the left of zero. Point D is 3 units to the left of zero. Point C is 2 units to the right of zero. Point A is 2 units to the right. Point B is 4 units to the right.
The point opposite to point A is not labeled in the number line.
What is a number line?A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
Given a number line,
for any number line points left of zero are negative numbers and points right to the zero are positive numbers,
Given points, Point A is 2 units to the right = +2
Point B is 4 units to the right = +4
Point C is 2 units to the right of zero = +2
Point D is 3 units to the left of zero = -3
Point E is 5 units to the left of zero = -5
so the point opposite to +2 is -2 which is 2 units left of zero,
but it is not given on the labeled points.
Therefore, the opposite point of A is not labeled.
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What are the solutions of the quadratic equation 3x² 14x 5 0?.
On simplifying the given quadratic equation , we get that the solution of the quadratic equation 3x² -14x -5 = 0 are x = -1/3 and x = 5 .
The Quadratic Equation are given as : 3x² -14x -5 = 0 ;
to find the solutions of this equation , we use the split the middle term method ;
⇒ 3x² -14x -5 = 0 ;
we split "-14" as the sum of -15 and 1 .
⇒ 3x² -15x + x -5 = 0 ;
⇒ 3x(x - 5) +1(x - 5) = 0;
⇒ (3x + 1)(x - 5) = 0 ;
Solving the factors separately ,
we have ;
⇒ 3x + 1 = 0 and x - 5 = 0 ;
⇒ x = -1/3 and x = 5 ;
Therefore , the solutions of given quadratic are x = -1/3 and x = 5 .
The given question is incomplete , the complete question is
What are the solutions of the quadratic equation 3x² -14x -5=0 ?
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yo help i dont get this at all pls
[tex]x~~ : ~~(x+5)~~ = ~~4~~ : ~~5\qquad \implies \qquad \cfrac{x}{x+5}=\cfrac{4}{5} \\\\\\ 5x=4x+20 \implies x=20[/tex]
What are the 3 types of multiplication?.
Answer: Commutative, associative, distributive
Step-by-step explanation: I hope this helped!
Can someone please help solve this math problem? There are two boxes underneath the graph. I have to find the domain/range in this math problem, it is listed in the picture below, Thanks!
Domain:
Range:
Answer:
Domain: is -4 ≤ x ≤ 1
which can be expressed in interval notation as
[-4, 1]
Range is -3 ≤ y ≤ 2
or in interval notation: [-3, 2]
Step-by-step explanation:
The domain is the set of x values from minimum to maximum
The range is the set of y values again from minimum to maximum
Minimum value of x = -4
Maximum value = 1
So range is -4 ≤ x ≤ 1 which can be expressed in interval notation as
[-4, 1]
Minimum y-value is -3 and maximum y-value is 2
Range is -3 ≤ y ≤ 2
or in interval notation: [-3, 2]
Please help I need answers asap please show your work
Answer:
#1) [tex]\frac{1}{7}[/tex]
#2) 4
Step-by-step explanation:
#1) 37x=9x+4
37x=9x+4
-9x
28x=4
28 28
answer: [tex]\frac{4}{28} = \frac{1}{7}[/tex]
#2) 2x+3=11
2x+3=11
-3
2x= 8
2 2
answer: [tex]\frac{8}{2} =4[/tex]
spara
2:
Back to task
Calculate the coordinates of the midpoint of point P and point Q, which are
shown below.
12
11
10
9
8
7
65
Calculator
Bookwork code: J44 not allowed
6
5-
43
3
2-
1
P
Q
#I
0 1 2 3 4 5 6 7 8 9 please can u help me this is due soon and I’m stuck on it
Answer:
(3, 8 )
Step-by-step explanation:
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then
midpoint = ( [tex]\frac{1+5}{2}[/tex], [tex]\frac{6+10}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{16}{2}[/tex] ) = (3, 8 )
What relation exists between x and y so that
the two solids have the same volume? Please help!
The volume of solid₁ and solid₂ is related with y = x + 1 where x = 1 × 2 units.
What is volume?The amount of actual space a 3D object takes up is measured by its volume. It represents the area in three dimensions of a two-dimensional shape. It is measured in cubic units like cm3, for example. This can be determined by multiplying the object's length, height, and width.
Based on a fundamental equation, which is one of the first equations that students encounter in school, this method of measuring volume was developed. Because it lays the foundation for further equation study, math volume is very important.
We cane see that
y = x + 1
1/2 of 2 = x/2 = 1
x = 2
Lets find the value of the variables
y = (2)+ 1
y = 3
Volume of solid₁ = x × y × 2 = 2 × 3 × 2 = 12 cube unit
Volume of solid₂ = x × y × 2 = 2 × 3 × 2 = 12 cube unit
Thus, the volume of solid₁ and solid₂ is related with y = x + 1 where x = 1 × 2 units.
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Write a function of the form f(x) = A sin (Bx-C) for the given graph.
The sine function graphed is given as follows:
y = 0.5sin(x - π/4).
How to define the sine function?The sine function for this problem is defined as follows:
y = Asin(Bx - C).
For which the parameters are given as follows:
A is the amplitude.The period is of 2π/B.C is the phase shift.The difference between the highest value and the lowest value is of 1, hence the amplitude of the function is givne as follows:
2A = 1
A = 1/2
A = 0.5.
The period of the function is of 2π, hence the parameter b is obtained as follows:
2π/B = 2π
B = 1.
The sine function, without phase shift, should pass through the origin, while the function here was shifted right π/4 units, hence the parameter C is given as follows:
C = π/4.
Hence the function is:
y = 0.5sin(x - π/4).
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What is the factored form of x² +8x +16?.
To find the factored form of the quadratic equation x^2 + 8x + 16, we can use the technique of factoring by grouping.
First, we write the equation in the form of (x^2 + ax + b) + (x + c) = 0
x^2 + 8x + 16 = 0
Next, we find two numbers that multiply to b and add to a, in this case, b = 16 and a = 8
We can factor out a common factor of x from the first two terms and x + 4 from the last two terms: x^2 + 8x + 16 = (x^2 + 8x) + (16)
Finally, we can factor out a common factor of x + 4 from both terms:
x^2 + 8x + 16 = x(x + 8) + 4(4)
So the factored form of x^2 + 8x + 16 is (x+4)^2.
You can also find the factored form of the quadratic equation x^2 + 8x + 16 by using the difference of squares method:
x^2 + 8x + 16 = (x+4)^2
It's worth noting that this is a perfect square trinomial, which means that it can be factored into the square of a binomial.
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What type of graph is used for two variable analysis?.
A scatter plot or scattergram chart will show the relationship between two different variables or reveals distribution trends.
Now, According to the question:
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Use a scatter plot to determine whether or not two variables have a relationship or correlation. Are you trying to see if your two variables might mean something when put together? Plotting a scattergram with your data points can help you to determine whether there's a potential relationship between them.
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