The logarithmic equation log2(8) = 3 convert to exponential form as 2^3 = 8.
Converting the logarithmic equation log2(8) = 3 to exponential form involves recognizing the base and the exponent.Logarithms state that if logb(A) = C, then the equivalent exponential form would be bC = A. In this case, since 2 is the base and 3 is the exponent to which 2 must be raised to get 8, we can write 2^3 = 8.
To further clarify, logarithms are simply a way to represent exponents, and they are widely utilized in mathematics to simplify the multiplication and division of exponents. A logarithm with a base of 10 is known as the common logarithm and is often written without a base as log(A). In contrast, when another base is used, it is indicated as logb(A). The relationship between logarithms and exponents is leveraged in various scientific and engineering fields to represent and calculate large numbers conveniently.
The rectangles garden is 25ft by 15ft what is the area of the garden ?
Solve the system using elimination.
5x + 4y = 12
3x – 3y = 18
Final answer:
To solve the system of equations using elimination, multiply one equation by a constant so that the coefficients of one variable will be the same in both equations. Then add or subtract the equations to eliminate that variable. Finally, solve for the remaining variable and substitute back to find the complete solution.
Explanation:
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying the first equation by 3 and the second equation by 4. This will give us:
15x + 12y = 36
12x - 12y = 72
Next, we can add the two equations together to eliminate y:
27x = 108
Dividing both sides by 27, we find that x = 4.
Substituting this value of x back into one of the original equations, we can solve for y:
5x + 4y = 12
5(4) + 4y = 12
20 + 4y = 12
Subtracting 20 from both sides, we get 4y = -8.
Dividing both sides by 4, we find that y = -2.
Therefore, the solution to the system of equations is x = 4 and y = -2.
Find the roots of the polynomial equation.
2x3 + 2x2 – 19x + 20 = 0
Answer:
1. a, -3,-1,1,3
2. a, 3+i/2, 3-i/2, -4
3. d, 6- sqrt 6
4. a, x3-8x2-11x+148=0
5. d, there are either 2 or 0 positive roots and one negative
Step-by-step explanation:
I did the quick check.
Final answer:
The roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0 are complex.
Explanation:
To find the roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0, we can use the factoring method or the quadratic formula. Let's use the quadratic formula. The formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 2, and c = 20. Plugging the values into the quadratic formula, we get:
x = (-2 ± √(2² - 4(2)(20))) / (2(2))
x = (-2 ± √(4 - 160)) / 4
x = (-2 ± √(-156)) / 4
Since we cannot take the square root of a negative number in the real number system, the roots of the given equation are complex, which means there are no real solutions.
The school that Scott goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 1 senior citizens tickets and 12 students tickets for a total of $130. The school took in $80 on the second day by selling 5 senior citizens tickets and 3 student tickets. Find the price of a senior citizens ticket and the price of a student tickets
A moves points a specified distance along a line parallel to a specified line.
a. translation
b.reflection
c. rotation
d. dilation
Answer:
It's A. translation
Step-by-step explanation:
Multiply, expressing the product in scientific notation. (9.16X10−3)(5.5X1016)
To multiply numbers in scientific notation, multiply the coefficients and add the exponents.
Explanation:To multiply numbers in scientific notation, we multiply the coefficients and add the exponents.
In this case, we have (9.16 × 10-3) multiplied by (5.5 × 1016).
The product of the coefficients is 9.16 × 5.5 = 50.38.
The sum of the exponents is -3 + 16 = 13.
Therefore, the product in scientific notation is 5.038 × 1013.
what is the answer to this 10-4b
What are the roots of the equation 2x2 + 9x + 6 = 0?
How many 1/6 are in 1/2?
Answer:
3 1/6
Step-by-step explanation: it is because you would have to divide the 1 and the 6 well not really divide more of the multiplying then after that you switch 1 and 2 and the 2 is and the top and 1 at the bottom and you to butterfly some of you should know then you get 3 1/6
On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday?
The number of hamburgers will be 348.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.
The number of hamburgers will be calculated as below:-
Cheeseburgers= x
Hamburgers= 3x
3x+x=464
4x=464
x=116
Substitute the value of x in expression.
Hamburgers= 3x
Hamburgers= 3 x 116 = 348
Therefore, the number of hamburgers will be 348.
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The local hamburger shop sold 116 hamburgers on Saturday. We determined this by setting up an equation where the number of hamburgers (H) plus three times the hamburgers (3H) equaled the total sales of 464 burgers, and then solving for H.
Explanation:The question asks us to solve a basic algebra problem involving hamburgers and cheeseburgers. Let's define the number of hamburgers sold as H. Since the number of cheeseburgers sold was three times the number of hamburgers sold, we can represent the number of cheeseburgers as 3H. The total number of burgers sold was 464. Now, we can write down the equation:
H + 3H = 464
This simplifies to:
4H = 464
Now, we divide both sides by 4 to find the value of H:
H = 464 / 4
H = 116
So, the local hamburger shop sold 116 hamburgers on Saturday.
find the inverse of f informally. verify that f(f^-1(x))=x and f^-1(f(x))=x
f(x)= (x-1)/5
To find the inverse of a function, switch x and y and solve for y. The inverse of f(x) = (x-1)/5 is f^-1(x) = 5x + 1. Verify that f(f^-1(x)) = x and f^-1(f(x)) = x.
Explanation:To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation y = (x-1)/5 for x. Let's do that:
Step 1: Replace y with x and x with y: x = (y-1)/5.
Step 2: Solve for y: Multiply both sides by 5: 5x = y - 1. Add 1 to both sides: 5x + 1 = y.
So, the inverse of f(x) = (x-1)/5 is f-1(x) = 5x + 1.
To verify that f(f-1(x)) = x, substitute f-1(x) into f(x) and simplify:
f(f-1(x)) = f(5x + 1) = ((5x + 1) - 1)/5 = 5x/5 = x.
Similarly, to verify that f-1(f(x)) = x, substitute f(x) into f-1(x) and simplify:
f-1(f(x)) = f-1((x-1)/5) = 5((x-1)/5) + 1 = x-1+1 = x.
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How many solutions are there to the equation below?
16(x + 2) - 8 = 16x + 24
A.
Infinitely many
B.
1
C.
0
Answer:
There are infinitely many solution.
Step-by-step explanation:
Given : 16(x + 2) - 8 = 16x + 24.
To find : How many solutions are there to the equation below.
Solution : We have given
16(x + 2) - 8 = 16x + 24.
On distributing 16 over ( x +2) .
16 x + 32 - 8 = 16x + 24 .
16 x + 24 = 16x + 24.
We can see left hand side is equal to right hand sides .
Therefore, There are infinitely many solution.
The letters from the word “integer” are placed on cards and put in a hat. If someone picks 1 card out of the hat, how many different outcomes are possible?
A.
1 outcome
B.
5 outcomes
C.
6 outcomes
D.
7 outcomes
What is the explicit rule for this geometric sequence?
4,4/5,4/25,4/125,…
The sum of three consecutive even integers is 36. Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.
Which equation can be used to find the first integer?
3x = 2x + 6
2x + 6 = 36
3x + 6 = 36
3x + 36 = 2x + 6
Answer:
C. [tex]3x+6=36[/tex]
Step-by-step explanation:
Let x represent the first integer, [tex]x+2[/tex] represent the second integer, and [tex]x+4[/tex] represent the third integer.
The sum of these integers would be [tex]x+x+2+x+4[/tex].
We have been given that the sum of three consecutive even integers is 36. We can represent this information in an equation as:
[tex]x+x+2+x+4=36[/tex]
Combine like terms:
[tex]3x+6=36[/tex]
Therefore, the equation [tex]3x+6=36[/tex] can be used find the first integer.
What is the value of x? If necessary, round your answer to two decimal places.
What is nine tenths as a percentage?
The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T(t)=(4t)/(t^2 +1), where t represents time elapsed. What is the meaning of the horizontal asymptote for this function? The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses. The horizontal asymptote of y = 0 means that the person’s temperature will approach 0ºF as time elapses. The horizontal asymptote of y = 4 means that the person’s temperature will approach 102.6ºF as time elapses. The horizontal asymptote of y = 4 means that the person’s temperature will approach 4ºF as time elapses.
The person's body temperature will approach 98.6ºF as time lapses. Option A is correct.
How to calculate the horizontal asymptotes of a function?A horizontal asymptote for a function is an imaginary line that is not part of the graph and lies along the x-axis of the graph either to the left or right.
The horizontal asymptote of the given function can be described as the nature of the function T(f) as t approaches infinity.
This is the point where the line y=0 which means that the person's body temperature will approach 0ºF above 98.6ºF as t goes to infinity.
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a building with a height of 14 m casts a shadow that is 16m long while a taller building casts a 24 meter long shadow. what is the height of the taller building
If Sawyer makes $15 an hour, which equation represents his earnings?
W = 15h
W = 15/h
W = h/15
W = 15 + h
The graph shows the production of cars per day at a factory during a certain period of time. What is the domain of this function during this period?
The domain is all real numbers 0 through 9.
The domain is all integers 0 through 9.
The domain is all positive real numbers.
The domain is all positive integers.
Answer:
The domain is all real integers 0 through 9.
I've done the test, hope this helps
.002 times 900000 scientific notation
Find the exact area of a circle having the given circumference.
4(sqrt3 PI ) ...?
Answer:
12(pi)
Step-by-step explanation:
Find the common ratio of the following geometric sequence.
If necessary, use the slash bar ( / ) to enter a fraction. Reduce fractions to their lowest terms.
(5/12),(1/3),(4/15),(16/75),(64/375)
Consider the equation y = 8 - 3x. for every increase of 1 in the x- variable, what is the change in the y- variable?.
a. increase of 3.
b. increase of 8.
c. decrease of 3.
d. decrease of 8
Management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution.
Value of X
0
1
2
3 or more
Probability
0.60
0.35
0.04
0.01
Reference: Ref 9-7
The probability that a randomly chosen table orders at least one appetizer is
A. 0.35.
B. 0.39.
C. 0.40.
D. none of the above.
integrate 1 / sqrt(25 - 16x^2) dx
To integrate 1 / sqrt(25 - 16x^2) dx, we use trigonometric substitution with x = (5/4)sinθ. After substitution, integration, and back-substitution, the result is arcsin(4x/5) + C, where C is the constant of integration.
Explanation:The integral to solve is ∑ (1 / sqrt(25 - 16x^2)) dx, which resembles the inverse trigonometric function, specifically the arcsine function. To solve this integral, we can use a trigonometric substitution. Since the integral involves a square root of a difference of squares, we can substitute x with (5/4)sinθ, which simplifies the integral considerably.
After substitution, we can then use the derivative of sinθ, which is cosθ, in order to find the full differential dx to replace in our integral. The resulting integral in terms of θ can be integrated using standard techniques, yielding an arcsine function as the antiderivative. After integrating, we must then convert back from θ to x to express the solution to the original integral in the original variable.
The answer to the integral ∑ (1 / sqrt(25 - 16x^2)) dx is arcsin(4x/5) + C, where C is the constant of integration. The substitution step is crucial in solving this type of problem and is a commonly used method in calculus.
Carol buys a reference book that originally cost $87.50 for 15% off. She pays a sales tax of 4.5%. What is the total cost of the book?
Answer:
$77.72
Step-by-step explanation:
This is the total cost of the book with tax.
Rich bought 5 cupcakes and one pie. He knows his total bill and knows the pie was $6.89, but he wants to find the price of the cupcakes. How can he determine the price of each cupcake?
To determine the price of each cupcake, subtract the price of the pie from the total bill and then divide the result by the number of cupcakes. Each cupcake costs $1.62.
Explanation:To determine the price of each cupcake, Rich can subtract the price of the pie from the total bill and then divide the result by the number of cupcakes:
Let's say the total bill is $15.00.Subtract the price of the pie ($6.89) from the total bill: $15.00 - $6.89 = $8.11.Divide the remaining amount by the number of cupcakes (5): $8.11 ÷ 5 = $1.62.Therefore, each cupcake costs $1.62.
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Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth. A)0.005 B)0.008 C)0.213 D)0.227
Answer:
The correct option is C. 0.213
Step-by-step explanation:
Percentage of students at high school who takes chemistry = 40%
So, probability of students who take chemistry = 0.4
So, probability of students who do not take chemistry = 1 - 0.4
= 0.6
Total number of students taken for survey = 12
Now, we need to find the probability that exactly 4 students have taken chemistry among the 12 surveyed students.
By using binomial distribution :
n = 12 , p = 0.4 , q = 0.6 , k = 4
[tex]\text{Required Probability = }_{k}^{n}\textrm{C}\cdot(p)^k\cdot(q)^{n-k}\\\\\implies\text{Required Probability = }_{4}^{12}\textrm{C} \cdot(0.4)^4 \cdot(0.6)^8 \\\\\implies \text{Required Probability = }0.2128\approx 0.213[/tex]
Therefore, The correct option is C. 0.213