After expanding logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]\frac{log_{10} m^3}{n^4 \\ p^-2} \\[/tex]
apply formula log a^x = x log a
[tex]= > \frac{3 log_{10} (m)}{\frac{n^4}{p^2} }\\ \\= > \frac{3 log_{10} (m) p^2}{{n^4} }[/tex]
Thus, after expanding the logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
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What type of function is this based off of these data points:
(-6,-726)
(-2,-34)
(0,0)
(2,18)
(6 ,582)
Based on the data points given, the type of function shown is a Quadratic function.
What is a quadratic function?A quadratic function is one where the values of x and y form data points that lead to a parabola being formed.
This parabola forms when the values of the data points start away from 0 and then reach zero and rise again. This is what happens with these points so the function must be a quadratic function.
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Use graphing to find the x-coordinate of the solution to each system. ) x + 2y = 6 5x - 4y = 16 A) -1 B) 4 C) 5 D) 1
The x coordinate of the solution to the system is 4
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
x + 2y = 6
5x - 4y = 16
Next, we plot the graph of x + 2y = 6 and 5x - 4y = 16 (see attachment)
From the attached graph, the point of intersection is
(x, y) = (4, 1)
Remove the y coordinate
x = 4
Hence. the x coordinate of the solution to the system is 4
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For each pair of functions, find f(g(x)) and g(f(x)) .
f(x)=3 x²+2, g(x)=2 x
The values for
[tex]f(g(x)) = 6x^3 +2 \\g(f(x)) = 6x^2 + 4[/tex]
What are the domain of the function f(x)=3 x²+2, g(x)=2 x ?[tex]Given : f(x)=3 x²+2, g(x)=2 x[/tex]
1.
[tex](f.g)(x) = f(g(x)) \\g(x) = 2x \\f(x) = 3 x^2+2 \\f(2x) = 6x^3 +2[/tex]
2.
[tex](g.f)x = g(f(x)) \\fx = 3x^2 + 2 \\g(3x^2 + 2) = 2 (3x^2 + 2) = 6x^2 + 4[/tex]
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-1/5 - (1/2 + -1/4) divided by 1/3
The answer of -1/5 - (1/2 + -1/4) divided by 1/3 is [tex]-\frac{27}{20}[/tex]
A formula is a statement containing at least two numbers/variables and at least one mathematical operation. An expression is a combination of terms combined by mathematical operations such as subtraction, addition, multiplication, and division.The terms that appear in the formula are:- Constant: A constant is a fixed number. Variables: Variables are symbols that do not have fixed values. Term: A term can be a single constant, a single variable, or a combination of variables and constants combined with multiplication or division. Coefficient: A coefficient is a number that is multiplied by a variable in an expression.We have given an expression [tex]-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))[/tex] .
On simplifying , we get
[tex]-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=-\frac{1}{5}-(\frac{1}{2} -\frac{1}{4} )\\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))= - \frac{1}{5}-(\frac{2-1}{4} )\\\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))= - \frac{1}{5}-\frac{1}{4} \\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=\frac{-4-5}{20} \\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=\frac{-9}{20}[/tex]
Now , we are asked to divide -9 /20 by 1 /3 .
On dividing, we get
[tex]\frac{\frac{-9}{20} }{\frac{1}{3} } =\frac{-9}{20} \times\frac{3}{1} \\\\=\frac{-27}{20}[/tex]
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Evaluate each expression for x=-2,0 , and 2 .
-5 x⁻²
The value of given expression for x=0 is 0, x=-2 is -1.25 and x=2 is -1.25.
Given the expression is -5x⁻².
Firstly, we will simplify the given expression -5x⁻² for x=0.
Substitute the value x=0 in given expression, we get
-5x⁻²=-5(0)⁻²
-5x⁻²=-5(0)
As we know that something multiply with 0 is zero.
So, we get
-5x⁻²=0
Now, we will simplify the given expression -5x⁻² for x=2.
Substitute the value x=2 in given expression, we get
-5x⁻²=-5(2)⁻²
Now, we will square the expression to simplify it, we get
-5x⁻²=-5(4)⁻¹
Further, we will divide it above expression by 1 to remove negative sign, we get
-5x⁻²=-5/4
-5x⁻²=-1.25
Furthermore, we will simplify the given expression for x=-2.
Substitute the value x=-2 in given expression, we get
-5x⁻²=-5(-2)⁻²
Now, we will square the given expression, we get
-5x⁻²=-5(4)⁻¹
Further, we will divide it above expression by 1 to remove negative sign, we get
-5x⁻²=-5/4
-5x⁻²=-1.25
Hence, the value of expression -5x⁻² for x=0, 2 and -2 is 0, -1.25 and -1.25.
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A rectangular brick wall is 7 m wide and 1 m
tall.
Use Pythagoras' theorem to work out the
distance between diagonally opposite corners.
Give your answer in metres (m) to 1 d.p.
The diagonal of the given brick using the Pythagorean Theorem is 5√2.
The Pythagorean Theorem is what?The three sides of a right triangle in Euclidean geometry have a basic relationship known as the Pythagorean theorem, also referred to as Pythagoras' theorem.This statement implies that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.A Pythagorean triple is made up of three positive integers a, b, and c if and only if their sum, a2 + b2, is equal to their sum, c2.Such a triple is frequently written as (a, b, c), and a well-known example is (3, 4, 5).So, let the diagonal be 'x'.
Pythagorean formula: x² = b² + h²
Now,
x² = b² + h²x² = 7² + 1²x² = 49 + 1x² = 50x = √50x = √5 × 5 × 2x = 5√2Therefore, the diagonal of the given brick using the Pythagorean Theorem is 5√2.
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For each annual rate of change, find the corresponding growth or decay factor. -75 %
For each annual rate of change , the corresponding growth or decay factor is - 0.75 .
Given : annual rate of change = - 75 % .
To find : corresponding growth or decay factor .
For an exponential growth function ,
y = a ( [tex]1 + r^{t}[/tex] ) ,
( 1 + r ) is the growth factor and
for an exponential decay function y = a ( [tex]1 - r ^{t}[/tex] ) ,
( 1 - r ) is the decay factor .
According to question ,
( - 75 ) / 100 = - 0 .75
Hence , for each annual rate of change , the corresponding growth or decay factor is - 0.75 .
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For questions 4-7, find the measures of the angles in the picture below.
(Questions shown in image)
Answer:
Measures of each angle are as follows:
4. ∠BXC = 20°
5. ∠FXE = 85°
6. ∠GXD = 75°
7. ∠BXF = 75°
Step-by-step explanation:
#4
∠BXC is opposite ∠EXD and so it is the same as ∠EXD = 20°
#5
∠FXE is opposite ∠CXG and so it is the same as ∠CXG = 85°
#6
Angles ∠CXG, ∠GXD and ∠EXD line on a straight line so the sum of these angles must be 180°
∴ m∠CXG + m∠GXD + m∠EXD = 180°
Substituting known values for ∠CXG and ∠EXD we get
85 + ∠GXD + 20 = 180°
105 + m∠GXD = 180°
m∠GXD = 180-105 = 75°
#7
∠BXF is opposite ∠GXD which we computed in #6 to be 75°
So m∠BXF = m∠GXD = 75°
The population of a community, , is modeled by this exponential function, where x represents the number of years since the population started being recorded. what is the approximate population 3 years after the population started being recorded?
The approximate population 3 years after the population started being recorded is 2584.
What is an exponential function:
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Given that,
The population of a community is modeled by this exponential function, where x represents the number of years since the population started being recorded:
p(x) = 2,400(1.025)×
Plug x = 3 years in the above function.
P(3) = 2400(1.025)³
P(3) = 2400x1.0768
P(3) = 2584.53 ≈ 2584 people
Therefore,
The approximate population 3 years after the population started being recorded is 2584 people.
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A quadratic function is shown on the graph.
an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
The range of the quadratic function is {y |0 ≤ y < 9}
What is the range of a function?The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?From the question, we have the following parameters:
The parabola opens upwardVertex = (0, 0)Closed circle point = (-2, 4)Open circle point = (3, 9)Write out the vertex
So, we have
Vertex = (0, 0)
Remove the x value
y = 0
From the question, we have
The parabola opens upward
This means that the vertex is a minimum
So, the range is
y ≥ 0
Rewrite as
0 ≤ y
Recall that:
Closed circle point = (-2, 4)
Open circle point = (3, 9)
Remove the x values
Closed circle point = 4
Open circle point = 9
Remove the smaller y value
Open circle point = 9
This means that the highest value of y is at open circle point = 9
This is represented as
y < 9
So, we have
0 ≤ y and y < 9
Combine both
0 ≤ y < 9
Rewrite properly as
{y |0 ≤ y < 9}
Hence, the range of the quadratic function is {y |0 ≤ y < 9}
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{y |0 ≤ y < 9}
The person above need the shine, im just making it simple
A university class has 21 students: 11 are history majors, 4 are psychology majors, and 6 are art majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a psychology major and the second student is an art major?
The probability that the first student selected is a psychology major and the second student is an art major is 0.057.
How to calculate the probability?Probability for psychology = 4/21
Probability for art major = 6/21
Therefore, the probability that the first student selected is a psychology major and the second student is an art major will be:
= P(Psychology) × P(art)
= 4/21 × 6/20
= 24/420
= 0.057
Therefore, the probability that the first student selected is a psychology major and the second student is an art major is 0.057.
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This figure is a step in which construction?
Find the inverse of each function. Is the inverse a function? y=10-2 x²
The inverse of the function y= 10 - 2x² is y =√ (10 - x) / 2. .
Inverse Variation:
A connection between two variables is said to have inverse variation when one of the variables rises while the other falls.
When two variables, let's say X and Y, are coupled in such a way that raising X results in a drop in Y and vice versa, this is known as indirect or inverse variation.
All we have to do to find the inverse of a function is switch the variables x and y.
x = 10 - 2y²
Now, solve for y as follows:
2y² = 10 - x
y² = (10 - x)/2
y = √ (10 - x) / 2
Therefore, the inverse of the function y=10 - 2x² is y = √ (10 - x) / 2.
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2. The population of a city grows at a rate of 5% per year. The population in 1990 was
400,000. In what year would we predict the population to reach 1,000,000?
The year in which we predict the population to reach 1,000,000 based on annual growth rate of 5% is 2009
How many years would population will be 1,000,000?
The year that the population of the city would reach 1,000,000 can be determined by first of all computing the number of years beginning from 1990 that it would take the population size of 400,000 to reach 1,000,000
FV=PV*(1+G)^n
FV=future population size=1,000,000
PV=present population size=400,000
g=population growth rate per year=5%
N=number of years it takes population to become 1,000,000=unknown
1,000,000=400,000*(1+5%)^N
1,000,000/400,000=(1+5%)^N
2.50=(1.05)^N
take log of both sides
ln(2.50)=N*ln(1.05)
N=ln(2.50)/ln(1.05)
N=19(rounded to the nearest whole number)
number of years before population reach 1m=1990+19
number of years before population reach 1m=2009
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first to answer will get brainliest
Reflexive Property of congruence justifies the statement
∠K ≅ ∠K
The Reflexive Property of congruence states that any geometric figure is congruent to itself. The figures are being the reflection of itself. They have the line segments of same length, an angle has the same angle measure and the figure has same shape and size as itself.
If two triangles have a common side or a common angle, then Reflexive Property of congruence is used to prove that the two triangles are congruent.
Since the given angle is K, therefore by the Reflexive Property of congruence we could say that the angle K is congruence to angle K.
⇒ ∠K ≅ ∠K
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the value of y varies directly with x if x=3 then y=21
When y= 105 then x= 15.
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
given:
At x=3, y=21
at y= 105 , x=?
So, creating proportionality
105/x= 21/3
105/x = 7
x= 105/7
x=15
Hence, when y= 105 then x= 15.
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The question attached here is incomplete.
The complete question is
The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?
Show each step of the solution. 12x<9(2x-3)+9
Answer:solve for x
x>3
Step-by-step explanation: 12x<9(2x−3)+9
Use the distributive property to multiply 9 by 2x−3.
12x<18x−27+9
Add −27 and 9 to get −18.
12x<18x−18
Subtract 18x from both sides.
12x−18x<−18
Combine 12x and −18x to get −6x.
−6x<−18
Divide both sides by −6. Since −6 is negative, the inequality direction is changed.
x>
−6
−18
Divide −18 by −6 to get 3.
x>3
If a rectangle has sides
5x + 7 and 2x + 2. What is the perimeter of the rectangle in terms of x in simplest
form?
Answer:
14x+18
Step-by-step explanation:
2(5x+7) + 2(2x+2)
10x+14+4x+4
14x+18
HI please help!!!!!!!!!!!
he started with 90 dollars and spent $3.50 each day
36. PHYSIOLOGY If you know how tall you were at the age of 2, you canestimate your adult height (in inches). Girls can use the expression 25+ 1.17h where h is the height (in inches) at the age of 2. Boys can use the expression 22.7 + 1.37h. Estimate the adult height of each person to the nearest inch.
a. A girl who was 34 inches tall at age 2 b. A boy who was 33 inches tall at age 2
Answer: The adult height of a girl who was 34 inches tall at age 2 is = 64.98 inches.
The adult height of a boy who was 33 inches tall at age 2 is = 67.91 inches.
Step-by-step explanation:
Given data,
PHYSIOLOGY If you know how tall you were at the age of 2, you can estimate your adult height (in inches).
Girls can use the expression 25+ 1.17h
where, h is the height (in inches) at the age of 2.
and, Boys can use the expression 22.7 + 1.37h.
So,
Let adult height of boys is represented by = y and
Let adult height of girls is represented by = x
From the equation,
adult height of girls expression is x = 25+ 1.17h
adult height of boys expression is y = 22.7 + 1.37h
First we can solve option a,
We have been asked to find the adult height of a girl who was 34 inches tall at age 2.
x = 25+ 1.17h
where, h = 34 inches
x = 25 + 1.17 (34)
x = 25 + 39.78
x = 64.98 inches
Therefore,
The adult height of a girl who was 34 inches tall at age 2 is = 64.98 inches.
First we can solve option b,
We have been asked to find the adult height of a boy who was 33 inches tall at age 2.
y = 22.7 + 1.37h
where, h = 33 inches
y = 22.7 + 1.37(33)
y = 22.7 + 45.21
y = 67.91 inches
Therefore,
The adult height of a boy who was 33 inches tall at age 2 is = 67.91 inches.
So,
The adult height of a girl who was 34 inches tall at age 2 is = 64.98 inches.
The adult height of a boy who was 33 inches tall at age 2 is = 67.91 inches.
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find the square root 0.36
A. 0.06
B. 0.18
C. 0.006
D. 0.6
Answer C please, thank you
Answer:
the 1st value represents x, the independent value
the 2nd value represents y, the dependent value
I think that is what it is asking
It is a vague question
Answer:
GradeHours StudiedStep-by-step explanation:
You want to know the meaning of the first and second values in the ordered pairs that represent the relation shown in the diagram.
Ordered pairThe ordered pairs representing a relation are understood to be ...
(first value, second value) = (input value, output value)
= (value at arrow tail, value at arrow head)
The diagram labels the ends of the arrows as "Grade" and "Hours Studied." That tells you the values mean ...
first value: Grade
second value: Hours Studied
Determine if 0.131331333133331333331... is rational or irrational and give a reason for your answer.
A road race is 13 1 2 miles long. there are water stations every 3 4 mile including at the finish line. how many water stations are there in all?
By solving the improper fractions, there are 18 water stations in all.
This problem can be solved by two methods:
Method 1 :
First of all, calculate 13²/₃ miles in fraction. The value is 13.5 miles. Then calculate 3/4 mile in fraction. The value is .75 miles.
Now divide 13.5 miles by 0.75 miles.
13.5 ÷ 0.75 = 18
So, 18 water stations are there in all.
Method 2 :
Convert 13 ¹/₂ miles into an improper fraction from 27/2 miles.
Now, again divide 27/2 miles by 3/4.
27/2 ÷ 3/4 = ²⁷/₂ ₓ ⁴/₃ = 18
So, 18 water stations are there in all.
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Mario walks 9 blocks from his home to a resturant. He then walks back toward home for 5 blocks, where he stops at a bookstore. How many blocks is Mario from his home?
Answer:
4
Step-by-step explanation:
9 - 5 = 4
What is each logarithm expanded?
a. log₃ 250/37
We need to know about logarithm to solve this problem. The logarithm expanded is [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]
Logarithm is the power to which a base should be raised to get a given number. Expanding logarithm is writing logarithms usisng addition, subtraction, simplifying the logarithm. In logarithm, log ab can be written as log a+ log b and log a/b can be written as log a -log b, [tex]log_{a} b[/tex] can be written as log b/log a. We will be using these rules to expand the given logarithm. In the given logarithm we have the base of the log as 3 and we have logarithm of fraction, which we can expand.
[tex]log_{3} \frac{250}{37} =log_{3} 250 - log_{3} 37=\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]
So we found the expansion of the given algorithm using the rules for expansion of algorithm to be [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex].
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what would the area a large rectangle has side lengths of 8 centimeters and 7 centimeters. a small square with side lengths of 4 centimeters is cut out of the large rectangle.
Answer:
40 cm^2
Step-by-step explanation:
Area of rectangle = length * width.
Area of square = length^2
To find the area of the given shape, we must subtract the area of the square from the area of the rectangle.
Area of the given rectangle = 8 * 7 = 56 cm^2
Area of the given square = 4^2 = 16 cm^2
56 - 16 = 40 cm^2
Help me out please I would really appreciate it.
Answer:
-55
Step-by-step explanation:
The pattern here is subtracting by 2 higher than the previous term.
As you can see
1 -2 = -1
-1 - 4= -5
-5 - 6 = -11
etc.
Continuing until the eighth term gets you - 41 - 14 = -55
What is the volume of a cone (in cubic inches) of radius 2 inches and height 6 inches? Use 3.14 for π. Round your answer to the nearest hundredth. (1 point) a 12.56 b 25.12 c 37.68 d 75.3
Given the radius and height, the volume of the cone to the nearest hundredth is 25.12 in³.
Option b)25.12 in³ is the correct answer.
What is the volume of the cone with the given radius and height?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3)πr²h
Given the data in the question;
Radius r = 2inHeight h = 6inConstant pi π = 3.14Volume V = ?Plug the given values into the volume formula above and simplify.
V = (1/3)πr²h
V = (1/3) × 3.14 × (2in)² × 6in
V = (1/3) × 3.14 × 2in² × 6in
V = (1/3) × 3.14 × 4in² × 6in
V = 25.12 in³
Given the radius and height, the volume of the cone to the nearest hundredth is 25.12 in³.
Option b)25.12 in³ is the correct answer.
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(11a^4 - 2a^2 - 12a^3) - (9a^2 - a^3) - (12a^4 + 10a^3 + 11a^2) please simplify
Answer:
-a^2*(a^2+21a+22)
best I can do