The value of x for the equation log₄64=x is 3.
What is the significance of logarithmic functions?Due of their connection to exponential functions, logarithmic functions are crucial. Exponential equations and the characteristics of exponential functions may both be investigated using logarithms. Additionally, they will be of great service in calculus, where they will be used to determine the slope of specific functions and the region enclosed by particular curves. They also have useful uses in economics.
Given,
log₄64=x
It can be expressed as -
64 = 4ˣ
4³ = 4ˣ
As base is same,
x = 3
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i need help on this i don’t understand it really
Answer:
Point G
Step-by-step explanation:
It is point G because since you mirrored it and flipped it, you need to flip figure one and if you move it to where figure two is, in the same place, the new point R is where point G is, so G corresponds to R
Question 4 of 5
Meredith is trying to estimate √51 She uses this table of values:
7. 4² 7. 5²
Square 7. 02 07. 12 7. 22 7. 3²
Value 49. 0 50. 41 51. 84 53. 29 54. 76 56. 25
Square 7. 62 7. 72 7. 82 7. 92 8. 02
Value 57. 76 59. 29 60. 84 62. 41 64. 0
4
What should she do next to find √51 to the nearest hundredth?
OA. She should find the average of 7. 1 and 7. 2.
B. She should find the squares of numbers between 7. 2 and 7. 3.
OC. She should find the squares of numbers between 7. 1 and 7. 2.
O D. She should estimate that √51 is 7. 20.
SUBMIT
She needs to locate the squares of the integers between 7.1 and 7.2 in order to estimate √51.
What is the square root of a number?Finding an integer's square root is the inverse of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root of a number can be discovered by looking for a number that, when squared, produces the original value. It follows that a× a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number.
In the question given to us,
look at the table, we know
(7.1)² = 50.41 and (7.2)² = 51.84
So, (7.1) < √51 < 7.2 { estimate }
They should therefore determine the squares of the numbers between 7.1 and 7.2.
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The complete question is :
Meredith is trying to estimate √51 She uses this table of values:
What should she do next to find √51 to the nearest hundredth?
A. She should find the average of 7. 1 and 7. 2.
B. She should find the squares of numbers between 7. 2 and 7. 3.
C. She should find the squares of numbers between 7. 1 and 7. 2.
D. She should estimate that √51 is 7. 20.
Find the inverse of each function. Is the inverse a function? f(x)=∛x-5
The inverse function is written as [tex]f^{-1}(x)[/tex] =x³+15x²+75x+125 and the inverse is a function.
The inverse of a function is defined as the opposite function . Ideally we use a function to map the dependent variable y based on the independent variable x. Inverse function is the relation which defines the value of x depending on a particular value of y.
For an inverse function the domain of the function changes to the range and vice-versa.
Mathematically for a function defined as y=g(x) where g(x) is a polynomial of x . We solve the equation for x in terms of y.
Given function is g(x)=∛x-5
Therefore it can be written as
y= ∛x-5
or, y+5=∛x
Cubing both sides we get:
(y+5)³=(∛x)³
or, y³+15y²+75y+125=x
or, x=y³+15y²+75y+125
So the inverse function can be written as:
[tex]f^{-1}(x)[/tex]=x³+15x²+75x+125 and the inverse function exists.
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Which of these strategies would eliminate a variable in the system of equations? \begin{cases} -7x + 2y = 5 \\\\ 3x - 5y = -5 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ −7x+2y=5 3x−5y=−5
One strategy to eliminate a variable is by multiplying the first equation by 5 and the second equation by 2 and then adding the resulting equations or by multiplying the first equation by 3 and the second equation by 7 and then adding the resulting equations
Solving system of EquationsFrom the question, we are to determine the strategies that would eliminate a variable in the given system of equations
The given system of equations is
-7x + 2y = 5
3x - 5y = -5
We can eliminate the variable y multiplying the first equation by 5 and the second equation by 2
That is,
5 × [-7x + 2y = 5
2 × [3x - 5y = -5
--------------------------
-35x + 10y = 25
6x - 10y = -10
------------------------
-29x = 15
Also,
We can eliminate the variable x by multiplying the first equation by 3 and the second equation by 7
That is,
3 × [-7x + 2y = 5
7 × [3x - 5y = -5
-------------------------
-21x + 6y = 15
21x - 35y = -35
---------------------
-29y = -20
Hence, one strategy is by multiplying the first equation by 5 and the second equation by 2 and then simplify by adding
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A student wants to save $ 8000 for college in five years. How much should be put into an account that pays 5.2% annual interest compounded continuously?
- What formula should you use?
$6208.86 amount should be put into an account that pays 5.2% annual interest compounded.
Compound interest is interest calculated on the principal and the interest accrued in previous periods. Compound interest is interest based on principal and interest accumulated over a period of time.A general formula for the number of times capital is compounded in his year. If the interest is compounded annually, the amounts is given by [tex]A=P(1+\frac{r}{100})^t[/tex] ...(1) where "A" represents the new principal , "P" represents the original or initial amount , "r" is the annual rate , "t" represents the number of years .
It is given that a student wants to save $ 8000 for college in five years having interest 5.2% annual interest compounded .
Putting [tex]A=\$8000 , \ r= 5.2\% , \ t=5 \ years[/tex] in equation (1) , we get
[tex]8000=P(1+\frac{5.2}{100} )^5\\\\8000=P(1+0.052)^5\\\\8000=P(1.052)^5\\\\8000=1.28848P\\\\P=\$6208.86[/tex]
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If f(x)=2x-3x^2 what is f(2)
f(2) is -8
According to the question,
Given that,
f(x)=2x-3x^2
Substitute x = 2 into f(x) = 2x-3x^2
f(2)=2x-3x^2
f(2)=2x2 - 3x [tex]2^{2}[/tex]
f(2)= 4 - 3 x 4
f(2)= 4 - 12
f(2)= - 8
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
Example of an Equation:
4y + 2 = 18
4×2 + 3x − 28 = 0
9m = 49.5
Equation Types
Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:
Linear equations
Quadratic equations
Cubic equations
Quartic equations
Differential equations
Parametric equations
Equation of a line
The standard form of the equation of a line is A x + By + C = 0. The slope-intercept form of an equation is y = mx + b, where m is the slope of the line and b is the y-intercept. However, there are various types of equations to represent lines.
Equation of x-axis
Generally, we say that the equation of the x-axis equation is of the form y = 0. However, we can also write the x-axis equation as x = c where c is constant.
The x-axis comprises all the real values of x, although the value of y is equal to 0 on the complete x-axis.
Thus, x can be recognised as constant and y as 0.
In the coordinate system representation, we can represent any point on the x-axis as (c, 0), where c is any real number.
Therefore, the x-axis formula will be x= c + y
Here,
c = constant
y = 0
The x-axis formula is x = c, where c is constant.
Equation in One Variable
The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.
17 – 9 = 8
x + 4 = 4y + 22z
4x2 + 3x – 7 = 0
The three examples above represent equations that propose equality (could be true or not) between two expressions.
The first equation does not contain any variable.
The second equation has three different variables, such as x, y and z. Thus, it is a multivariate equation.
The third equation contains only one variable, i.e. x.
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I NEED HELP ASAP!!!
Which of the following expressions represents “the difference between a number and eleven”?
11 – n
-11 n
n + 11
n – 11
All of the following represent the same concept except _____.
a number minus five
five more than a number
the sum of a number and five
a number increased by five
thank you!!
The expressions represents “the difference between a number and eleven” is (n - 11) while, for the second case, the one statement which does not represent the same concept, among the four options provided is "a number minus five".
As per question statement, we are provided with two separate questions, first one requiring us to determine the expressions represents “the difference between a number and eleven”, while the second one requiring us to determine the one statement which does not represent the same concept, among the four options provided.
Considering the first case, the statement “the difference between a number and eleven”, considering the number to be "n" can be mathematically expressed as [tex](n - 11)\\[/tex]. Hence, the correct answer is [tex](n - 11)\\\\[/tex].
Coming to the second case, considering the number to be "n",
Option (A) is "a number minus five" which when mathematically stated becomes [tex](n-5)[/tex]
Option (B) is "five more than a number" which when mathematically stated becomes [tex](n+5)[/tex]
Option (C) is "the sum of a number and five" which when mathematically stated becomes [tex](n+5)[/tex]
And, option (D) is "a number increased by five" which when mathematically stated becomes [tex](n+5)[/tex].
That is, Option (B), (C) and (D) all belong to the same concept. Hence, the one statement which does not represent the same concept, among the four options provided is "a number minus five".
Expressions: Expressions in mathematics, are mathematical statements that have two or more terms, consisting of numbers or variables, or both, and being connected by operators in between.To learn more about Expressions, click on the link below.
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1-39. Estimate the areas of Montana and California using the grid below. Which state has the greatest
area? Compare the area of Montana to the area of California. Explain how you estimated the area of
each state.
California has the greatest area of each state.
What does a math area mean?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.So, we know that
Montana = 5 * 9 = 45 grids
California = 15 + 16 + 14 + 6 = 51 grids
45 < 51
California has the greatest area .
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a jogger begins her workout by jogging to a park, a distance of 12 miles. she then jogs home at the same speed, but along a different route. this return trip is 18 miles, and her time is one hour longer. find her jogging speed.
The jogging speed of the jogger is 6 miles/hour.
Given that:-
Distance from home to park = 12 miles
Distance from park tp home from a different route = 18 miles
It is also given that the time taken to reach home from park is 1 hour longer than the number of hours taken to reach park from home.
We have to find the speed of the jogger.
Let the time taken by jogger to reach park from home be t hours.
Hence, according to the data given in the question,
Time taken by jogger to reach home from park is (t+2) hours.
We know that,
Speed = distance/time
We know that the speed of jogger in each route is same.
Hence, we can write,
12/t = 18/(t+1)
2/t = 3/(t+1)
2(t+1) = 3t
2t+2 = 3t
t = 2 hours.
Hence, speed of the jogger = 12/2 = 6 = 18/(2+1) = 18/3.
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Radio signals travel at a rate of 3 × 108 meters per second. How many seconds would it take for
a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height
of 4.2 x 107 meters? (Hint: Time is distance divided by rate.)
01.26 x 1016 seconds
01.26 x 1015 seconds
01.4 x 10¹ seconds
01.4 x 10-¹ seconds
Answer:
0.14*10⁻¹ seconds
Step-by-step explanation:
3 × 10⁸ = 30*10⁷
Then:
4.2*10⁷ / 30*10⁷ = 4.2/30 = 0.14
0.14 = 1.4*10⁻¹ seconds
For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=1 when x=-1.5
After direct variation y = 2 when x = -3.
What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ 1/-1.5That is y = kx ⇒ y = 1/-1.5 × xWhen x = -3:
1/-1.5 × -3 ⇒ y = 2Therefore, y = 2 when x = -3.
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A 2-gallon container of laundry detergent costs $14.64. What is the price per quart?
Answer:
Step-by-step explanation:
$1.20 dollars
Evaluate each logarithm.
log₁/₅625
We need to know about logarithm to solve this problem. The answer of the given algorithm is -4.
Logarithm is the exponent that a base needs to be raised to get a certain number. There are a few rules of algorithm, log a + log b can be written as log ab, log a- log b can be written as log a/log b. When a number whose logarithm is being calculated is raised to a power, the power can be multiplied to the log itself. In this question we have to find the logarithm of 625 with base 1/5. To find the logarithm of this number we need to first write 625 in terms of 1/5, the log of number same as base is equal to 1.
[tex]log_{\frac{1}{5} } 625=-log_{\frac{1}{5} } (\frac{1}{5} )^{4} =-4log_{\frac{1}{5} } \frac{1}{5} =-4[/tex]
Therefore we found out the logarithm of 625 with base 1/5 to be -4.
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A right circular cylindrical metallic rod is 16 inches tall. The radius of the base is 4 inches. What is the surface area of this metallic rod, in terms of π? the choices are 150π 140π 145π and 160π
Answer:
160π
Step-by-step explanation:
The surface area of a right circular cylinder can be calculated using the following equation:
[tex]\boxed{\mathrm{Surface \ area = }2 \pi rh + 2 \pi r^2}[/tex] ,
where h is the height and r is the radius of the base of the cylinder.
We are told that the rod is 16 inches tall, therefore h = 16. We are also told that the radius of the base is 4 inches, therefore r = 4. Using this information along with the formula above, we can calculate the surface area of the metallic rod:
Surface area = [tex](2 \times \pi \times 4 \times 16) + (2 \times \pi \times (4)^2)[/tex]
= [tex]128\pi + 32\pi[/tex]
= [tex]\bf 160\pi[/tex]
Therefore the surface area of the metallic rod is 160π.
Answer:
[tex]144\pi \: or \: 145\pi[/tex]
SA to cylinder is
[tex]2\pi \: rh + \pi \: r {}^{2} [/tex]
=2
[tex] 2 \times \pi \times r \\ \times h + \pi \times r {}^{2} [/tex]
2
[tex]2\pi \times 4 \times 16 + \pi \times 4 \times 4[/tex]
answer =
[tex]144\pi \: to \: 145\pi[/tex]
answer quick thank you
Answer:
b = a² - 6
Step-by-step explanation:
a = [tex]\sqrt{b+6}[/tex] ← square both sides to clear the radical
a² = b + 6 ( subtract 6 from both sides )
a² - 6 = b
a)find the value of 2x+y when x=4 and y=3
Answer:
11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
Plug in x and y values into the equation
2(4) + (3)Multiply
8 + 3Add
11
Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (g ⁰ h)(a)
For the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (a) will be 5 a² + 3.
We are given the functions:
g (x) = 5 x - 2
h (x) = x² + 1
We first need to find the composite function g o h (x).
So, we get that:
g o h (x) = g ( h (x) )
g o h (x) = 5 ( x² + 1 ) - 2
g o h (x) = 5 x ² + 5 - 2
g o h (x) = 5 x² + 3
Now, we need to find the value of the composite function for x = a. So, we get that:
g o h (x = a) = 5 (a)² + 3
g o h (a) = 5 a² + 3
Therefore, for the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (a) will be 5 a² + 3.
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Solve each equation. ln 5 x=4
The solution for the equation ln 5 x=4 is 10.92.
What is an equation ?
ln 5 x=4
5 x = [tex]e^{4}[/tex]
x = 10.92
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.
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How do you message ppl?
20 points!!!
Answer:
You can't. You must be a trusted helper.
Answer:
just message them by messaging them
Work out 3/4-1/3 in fraction form
Answer:
[tex]\frac5{12}[/tex]
Step-by-step explanation:
[tex]\frac34 - \frac13\\\\\to \frac34 \times \frac33 - \frac13 \times \frac44\\\\\to \frac9{12} - \frac4{12}\\\\\to \frac{9 - 4}{12} \to \frac5{12}[/tex]
y = - x + 1 + 4
t
2 3
X
|
0
- |
-21
-3
y
Answer:
1+4=5 23×21=44 44-3=41
Step-by-step explanation:
ANSWER= LOL
what is the answer to this ? 5b+3.79
Answer:
5
Step-by-step explanation:
5b+3.79
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n−1 .
5b^1-1
Subtract 1 from 1.
5b^0
For any term t except 0, t^0 = 1
5×1
For any term t, t×1=t and 1t=t.
5
The length of a rectangle is 15 inches more than twice the width. if the perimeter is 54 inches, find the dimensions (p = 2l + 2w)
Answer:
length = 23 inches , width = 4 inches
Step-by-step explanation:
let width be w then length l = 2w + 15
the perimeter P is calculated as
P = 2l + 2w
given P = 54 , then
2(2w + 15) + 2w = 54
4w + 30 + 2w = 54
6w + 30 = 54 ( subtract 30 from both sides )
6w = 24 ( divide both sides by 6 )
w = 4
l = 2w + 15 = 2(4) + 15 = 8 + 15 = 23
the length is 23 inches and width is 4 inches
What is the perimeter of this rectangle in simplest form.
The perimeter of the rectangle in it simplest form is 8x - 10.
How to find the perimeter of a rectangle?The perimeter of a rectangle can be found as follows:
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
length = 3x - 7
width = x + 2
perimeter of a rectangle = 2(3x - 7 + x + 2)
perimeter of a rectangle = 2(3x + x - 7 + 2)
perimeter of a rectangle = 2(4x - 5)
perimeter of a rectangle = 8x - 10
Therefore, the perimeter of the rectangle in it simplest form is 8x - 10.
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What is the slope of the line that passes through the points (-4, 2) and (-5, 0)? Write your answer in simplest form.
The slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.
How to Find the Slope of a Line that Passes through two Points?The slope of a line (m) = change in y/change in x = y2 - y1/x2 - x1 or rise/run of the line.
Given the following points on the line:
(-4, 2) = (x1, y1)
(-5, 0) = (x2, y2)
Substitute the values into m = y2 - y1/x2 - x1:
Slope (m) of the line = (0 - 2) / (-5 - (-4))
Slope (m) of the line = (-2) / (-5 + 4)
Slope (m) of the line = -2/-1
Slope (m) of the line = 2
Thus, the slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.
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Solve the compound inequality.
2x-4 > 8 or 3x-1 < -10
Responses
-3 < x < 6
x < 6 or x < -3
x > 6 or x < -3
x > 2 or x < -3
Step-by-step explanation:
2x-4 > 8 or 3x-1 < -10
Grouping the like terms
2x > 8 +4 or 3x < -10 +1
2x > 12 or 3x < -9
2x > 12 3x < -9
2 2 3 3
x > 6 or x < -3
Mrs. Saunders can clean the windows of her house in 3 hours. Her daughter can clean the windows in 6 hours. How long will it take them to clean the windows if they work together?
Answer:4.5 hours, 4 hours and 30 minutes, 4 and a half hours
Step-by-step explanation: you are averaging, so you add all of the numbers together and divide that by the number of numbers.
3+6=9, 9 divided by 2=4.5
Answer:
2hours
Step-by-step explanation:
let windows = x
Mrs. Saunders can clean one-third of the windows in an hour = x/3
daughter can clean one-sixth of the windows in an hour = x/6
so,
x/3+x/6 = 1
thus, x = 2
mother and daughter together can clean the windows in 2 hours
12,345.6789 to nearest whole number
After rounding off the whole number it becomes 12,346.
According to the statement
We have to find that the value of the whole number.
So, For this purpose, we know that the
The whole numbers are the numbers without fractions and it is a collection of positive integers and zero.
From the given information:
The given number is a 12,345.6789
Then
We know that the
Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers etc.
The number
12,345.6789
Its round off to the
12,346
Because when the number greater than 5 comes after the point then while rounding off we increased the number by 1.
So, After rounding off the whole number it becomes 12,346.
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Calculate the possible values for missing value (2, 19) (32, y) given the distance of 34
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{y})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{d}{34}=\sqrt{(32-2)^2 + (y-19)^2}\implies 34^2=(32-2)^2 + (y-19)^2 \\\\\\ 1156=30^2 +(y-19)^2\implies 1156=900 + (y-19)^2\implies 256=(y-19)^2 \\\\\\ \pm\sqrt{256}=\pm\sqrt{(y-19)^2}\implies \pm 16=\pm (y-19)\implies \mp 16 =y - 19 \\\\\\ \mp 16 + 19 = y\implies y= \begin{cases} 3\\ 35 \end{cases}[/tex]
what is the solution to this system of equations?
y = x - 2
y = - 0.5x + 4
Answer:
(4, 2 )
Step-by-step explanation:
y = x - 2 → (1)
y = - 0.5x + 4 → (2)
substitute y = x - 2 into (2)
x - 2 = - 0.5x + 4 ( add 0.5x to both sides )
1.5x - 2 = 4 ( add 2 to both sides )
1.5x = 6 ( divide both sides by 1.5 )
x = 4
substitute x = 4 into (1)
y = 4 - 2 = 2
solution is (4, 2 )