Simplify each expression:
12^log base 12 of 144
The simplification of the mathematical expression 12^log base 12 of 144 is 144, according to the properties of logarithms.
Explanation:To simplify 12^log base 12 of 144, you need to understand the definition of logarithms. A logarithms in base b of a number x is the power to which we have to raise b to get x. In other words, if y = log base b of x, then b^y = x.
Applying this to our example, since log base 12 of 144 is 2 (because 12^2 = 144), then 12^log base 12 of 144 = 12^2 = 144.
Therefore, the simplification of the expression 12^log base 12 of 144 is 144.
Learn more about Logarithms here:https://brainly.com/question/37287488
#SPJ12
To simplify the expression 12^log base 12 of 144, evaluate the logarithm, substitute the value back into the expression, and perform exponentiation.
Explanation:In essence, the logarithm with base 12 and argument 144 essentially asks, "To what power must 12 be raised to obtain 144?" The answer, as established, is 2. Consequently, when we raise 12 to the power of 2, we retrieve the original value of 144. This simplification showcases the inherent relationship between logarithms and exponentiation, providing a clearer understanding of the expression's evaluation.
To simplify the expression 12^log12(144), we need to evaluate the logarithm first. Since the base of the logarithm is the same as the base of the exponentiation, we can simplify it to just log(144). Using a calculator, we find that log(144) = 2.158. Now we can substitute this value back into the original expression: 12^2.158. Evaluating the exponentiation gives us the final answer: 205.08.
Learn more about Simplifying expressions here:https://brainly.com/question/29003427
#SPJ12
Rewrite (-9)^-2 without an exponent
On a coordinate grid, both point (−4, −1) and (2, 6) point are reflected across the y-axis. what are the coordinates of the reflected points?
A computer uses 239 watts per hour. How many watts would it use if it is on for 8 days?
Answer:
29 watts
Step-by-step explanation:
239 ÷ 8 = 29.875
a function can only be represented by a straight line on the coordinate plain
True or False
In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is
usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut,N( t ) = N0e ^-0.2t , where N o is the initial size of the cohort.
Approximate the percentage of the original number still alive after 7 years. Round to one decimal place, if necessary.
please show the steps
Using the exponential decay function for Pacific halibut, it is calculated that approximately 24.7% of the original cohort is still alive after 7 years.
Explanation:To approximate the percentage of the original number of Pacific halibut still alive after 7 years, we use the exponential decay model provided, N(t) = N0e^-0.2t. Plugging in t = 7 years into the equation gives us:
N(7) = N0e^-0.2(7) = N0e^-1.4.
To find this percentage, we can multiply the value of e^-1.4 by 100%. First, we calculate e^-1.4 approximately using a calculator:
e^-1.4 ≈ 0.24660
Multiplying by 100 to get the percentage: 0.24660 × 100% ≈ 24.7%.
Therefore, approximately 24.7% of the original Pacific halibut cohort is still alive after 7 years.
if a line on a garph is completely verticle WOULD THE SLOPE TECHNICALLY BE 0 OR UNIDENTIFIED... ONLY ANSWER IF YOU ARE CERTAIN (oops caps lock)
What is the value of x, when 10(x + 2) = 5(x + 8)?
The value of ( x ) is 4.
To find the value of ( x ) in the equation [tex]\( 10(x + 2) = 5(x + 8) \)[/tex], we'll follow these steps:
[tex]\[ 10(x + 2) = 5(x + 8) \][/tex]
[tex]\[ 10x + 20 = 5x + 40 \][/tex]
[tex]\[ 10x - 5x + 20 = 5x - 5x + 40 \][/tex]
[tex]\[ 5x + 20 = 40 \][/tex]
[tex]\[ 5x + 20 - 20 = 40 - 20 \][/tex]
[tex]\[ 5x = 20 \][/tex]
[tex]\[ \frac{5x}{5} = \frac{20}{5} \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, [tex]\( x = 4 \)[/tex] is the solution.
f(x) = sin(x^2 - 2)
find points of discontinuity, if any ...?
can someone help me please Write 243 in exponential form ...?
The exponential form of 243 is: 243 = 3⁵.
To write 243 in exponential form, you need to express it as a power of a base number.
The most common base used for this purpose is 3.
243 can be written as: 243 = 3⁵
Here's the reasoning:
[tex]\[ 3 \times 3 = 9 \][/tex]
[tex]\[ 9 \times 3 = 27 \][/tex]
[tex]\[ 27 \times 3 = 81 \][/tex]
[tex]\[ 81 \times 3 = 243 \][/tex]
So, 243 is 3 raised to the power of 5.
Therefore, 243 In exponential form is: [tex]\[ 243 = 3^5 \][/tex]
Evaluate the following expression.
153^0
distance can be represented by absolute value.true or false.?
The ponce de leon lighthouse in St.Augustine, Florida, is the second tallest brick tower in the United States.It was built in 1887 and rises 175 feet above sea level. How far from the shore is a motorboat if the angle of depression from the top of the lighthouse is 13 degree 15 minutes?
Answer:
743.41 feet.
Step-by-step explanation:
In this question it is given that height of the tower OS is 175 feet and angle of depression ∠ASB = 13°15'
angle of depression to the boat B will be equal to the angle of elevation "∠B"
Now ∠ASB = 13°15' ≈ 13° + [tex](\frac{15}{60})[/tex]°
= 13° + (0.25)°
= 13.25°
Now tan ∠B = [tex]\frac{SO}{OB}[/tex]
tan (13.25) = [tex]\frac{175}{x}[/tex]
x = [tex]\frac{175}{0.2354}[/tex]
= 743.41 feet.
Motorboat is 743.41 feet far from the shore.
f the graph of y=ax+b/x+c has a horizontal asymptote y=2 and a vertical asymptote x=-3 then a+c=?
a)-3
b)-1
c)0
d)1
E)5 ...?
Answer: 5
Step-by-step explanation:
Lim x-> a (ax+b)/x+c = a you know that a=2
Since the limit of x ->-3 equals infinity, you know that x =3.
Thus a+c = 5
Which of the following shows the correct factorization of x3 - 5x2 - 14x?
A. x(x + 7)(x + 2)
B. x(x - 7)(x - 2)
C. x(x + 7)(x - 2)
D. x(x - 7)(x + 2)
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = (− 12/5), x in Quadrant II ...?
Given that tan(x) is -12/5 in Quadrant II where sin is positive and cos is negative, we can use the Pythagorean theorem to find sin(x) and cos(x), which are then used to calculate sin(2x), cos(2x), and tan(2x).
Explanation:Given tan(x) = -12/5, x is in Quadrant II. Since tangent is negative in Quadrant II, we know that sin(x) is positive and cos(x) is negative. Using Pythagorean theorem, we can find sin(x) and cos(x). sin(x) = sqrt(1 - cos²(x)) and cos(x) = -sqrt(1-sin²(x)).
The values for sin(x) and cos(x) can then be plugged into the formulas sin2x = 2sin(x) cos(x), cos2x = cos²(x)-sin²(x) and tan2x = sin2x / cos2x to find sin(2x), cos(2x), and tan(2x).
Learn more about Trigonometric Identities here:https://brainly.com/question/3785172
#SPJ3
Which algebraic expression means “three more than a number squared”?
a) 2n+3
b) 2n-3
c) n^2+3
d) n^2-3
Option C is the correct anwser, Hope this helps :)
A = bh/2
A' = b'h/2 + bh'/2
b' = (A' - bh'/2)(2/h) can someone explain this. its steps to the derivative of bh/2.
Answer:
To find A' they used the rule of multiplication, which is:
the derivative of a product of two terms is the first term times the derivative of the second term plus the second term times the derivative of the first.
To find b' they just isolated b'
Step-by-step explanation:
Let f and g be two functions whose second derivatives are defined. Then (f · g) '' = f · g '' + f '' · g. true or false?
The statement (f · g)'' = f · g'' + f'' · g is false. The second derivative of a product of two functions is given by a different formula.
The statement (f · g)'' = f · g'' + f'' · g is false.
The second derivative of a product of two functions, f(x) and g(x), is given by (f · g)'' = f''g + 2f'g' + fg''.
To see why the given statement is false, consider the example where f(x) = x and g(x) = x^2. The left-hand side is 0, but the right-hand side is not zero, so the statement does not hold true.
Learn more about Functions here:https://brainly.com/question/21145944
#SPJ2
6375/10000 in simplest form
What is the value of the expression when a = 5 and b = 2?
a + 2b −3
6
9
11
24
48 is how many percent of 70
Mrs.ulrich has 3 times as many markers as colored pencils.the total number of markers and colored pencils is 84.how many markers does mrs.ulrich have
What type of polynomial is 2x2-6x+4? ...?
find the next 3 terms in the sequence 1, 1, 2, 3, 5, 8, . . .
A.) 9,10,11
B.) 11.14.17
C.) 13,21,34
D.)14,26,50
What is the value of f(-2)
To calculate the value of f(-2), a function definition f(x) is required. The information provided does not include this, making it impossible to determine the value of f(-2) without further details.
Explanation:In the context given, it appears that the question f(-2) refers to finding the value of a function f when the variable is -2. However, the provided information does not include a function or formula for f(x) that can be evaluated at x = -2. The details given seem to be related to various mathematical and scientific principles such as lens formula, chemical reactions, and quadratic equations, but none of these can be directly linked to a function f(x) to evaluate f(-2). To answer the question about the value of f(-2), the explicit function definition f(x) is necessary. Without this definition, it is impossible to determine the value of f(-2).
The value of f(2) for the function f(x) = 2x^2+1 is 9. This is calculated by substituting '2' into the function, squaring it, multiplying by 2, and then adding 1.
To find the value of f(2) for the function f(x) = 2x^2+1, you simply substitute '2' for every instance of 'x' in the function's formula. Here's the step-by-step calculation:
Replace 'x' with '2': 2(2)^2 + 1
Multiply '2' by '4': 8 + 1
Add '1' to '8': 9
Therefore, the value of f(2) is 9.
The probable question maybe:
What is the value of f(2) if f(x) = 2x^2+1?
A box contains 13 transistors, 3 of which are defective. if 3 are selected at random, find the probability that
a. All are defective
b. None are defective
a. Probability all defective: [tex]\( \frac{1}{286} \)[/tex]. b. Probability none defective: [tex]\( \frac{60}{143} \)[/tex].
To solve this problem, we can use the concept of probability.
a. Probability that all selected transistors are defective:
When selecting the first transistor, the probability of choosing a defective one is [tex]\( \frac{3}{13} \)[/tex], as there are 3 defective transistors out of 13 total.
After the first defective transistor is chosen, there are 2 defective transistors left out of 12 total transistors.
So, the probability of choosing a second defective transistor given that the first one was defective is [tex]\( \frac{2}{12} \).[/tex]
Similarly, for the third selection, the probability of choosing a defective transistor given that the first two were defective is [tex]\( \frac{1}{11} \)[/tex].
To find the probability that all three selected transistors are defective, we multiply the individual probabilities:
P(All defective) = [tex]\frac{3}{13} \times \frac{2}{12} \times \frac{1}{11}[/tex]
P(All defective) = [tex]\frac{3 \times 2 \times 1}{13 \times 12 \times 11}[/tex]
P(All defective) = [tex]\frac{6}{1716}[/tex]
P(All defective) = [tex]\frac{1}{286}[/tex]
So, the probability that all selected transistors are defective is [tex]\( \frac{1}{286} \).[/tex]
b. Probability that none of the selected transistors are defective:
This is essentially the complement of the event that all selected transistors are defective. Since there are 3 defective transistors out of 13, the remaining 10 transistors are not defective.
So, to find the probability that none are defective, we select 3 out of the 10 non-defective transistors.
P(None defective) = Number of ways to choose 3 non-defective transistors/Total number of ways to choose 3 transistors
P(None defective) = [tex]\frac{{\binom{10}{3}}}{{\binom{13}{3}}}[/tex]
P(None defective) = [tex]\frac{{120}}{{286}}[/tex]
P(None defective) = [tex]\frac{{60}}{{143}}[/tex]
So, the probability that none of the selected transistors are defective is [tex]\( \frac{{60}}{{143}} \).[/tex]
jake goes to the grocery store and buys 3 apple, 2 cans of soup, and 1 box of cereal. the apples cost $0.89 each; the soup costs $2.98 per can; and the box of cereal costs $4.99.
Answer:
c=(3 x 0.89)+(2.98)+4.99
Step-by-step explanation:
A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.
Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
Answer:
5
Step-by-step explanation:
Which relationship is always true for the angles r, x, y, and z of triangle ABC?
x + z = y
180 degrees − x = r
x + y + z = 180 degrees
x + y + z = 90 degrees
Answer with explanation:
In the problem , given about triangle, four angles are given , r,x ,y and z.
→→One of the three, must be exterior angle of triangle ABC, and other three, must be interior angles of Δ ABC.
So, two properties of triangle that we will use in this problem
1. Angle sum property of triangle: the sum of three angles of triangle is 180°.
2.Exterior angle property: Exterior angle of a triangle is equal to sum of two interior opposite angles.
So, if x, y and z are interior angles , and r is exterior angle
then
Option 3: x + y + z = 180° is always true.
either, r= y + z
and ,r +x=180°