The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression y = 2x⁺⁴
Applying log on both sides, we get,
log y = log (2x⁺⁴)
log y = log 2 + log x⁺⁴
log y = log 2 + 4 log x
To Check Results,
Taking exponential,
y = e^[log 2 + 4 log x]
y = e^(log 2) × e^[4 log (x)]
y = 2 × e^(log x⁴)
y = 2x⁴
Thus, the answer is verified.
Take expression y - 4x⁻¹ = 0
Applying log on both sides, we get,
log y = log (4x⁻¹)
log y = log 4 + log x⁻¹
log y = 2 log 2 - log x
To Check Results,
Taking exponential,
y = e^[2 log 2 - log x]
y = e^(2 log 2) × e^[-log (x)]
y = e^(log 4) × e^(log x⁻¹)
y = 4x⁻¹
y - 4 x⁻¹ = 0
Thus, the answer is verified.
Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.
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please help, no troll answers. will give brainliest to correct answers. option answers are
54
46
44
90
Answer:
46
Step-by-step explanation:
A right angle is always equal to 90.
You are given the angle 44 so all you need to do is 90-44 which gives you 46
Hope this helps! Have a great day :)
Answer:
<2 = 46 degrees
Step-by-step explanation:
The angle measuring 44 degrees and <2 are complementary, therefore, they add up to 90 degrees.
Let [tex]x[/tex] be <2
[tex]44 + x = 90 \text{ // Subtract 44 on both sides}\\44 + x - 44 = 90 - 44\\\to x = 46[/tex]
14-3m=4m
what is the value of m?
Answer:
2
Step-by-step explanation:
If f ( x ) = 3 x + 2 and g ( x ) = x 2 − x , find the value. f ( x ) + 1
This is a translation of one unit up of f(x), and we will get:
f(x) + 1 = 3x + 3
How to find the value of f(x) + 1?
Here we need to learn to rewrite functions:
Here we know that:
f(x) = 3x + 2
And
g(x) = x^2 - x
(we will not use g(x) in this problem)
So, f(x) +1 can be rewritten by just replacing f(x) by the equation above, so we can redefine:
h(x) = f(x) + 1
Now we replace the function f of x to get:
h(x) = 3x + 2 + 1 = 3x + 3
In this way, we conclude that:
f(x) + 1 = 3x + 3
This is a translation of one unit up of f(x).
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What is the answer to this \pi =7x-2y
Answer:
In π = 7x - 2y we first isolate y by adding 7x on both sides.
This gives us π + 7x = -2y. Divide 2 on both sides, then we are left with:
y =
Step-by-step explanation:
I just need the mathematical statement asap like rn
The number 8 is a solution to the equation 3m + 7 = 31
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
3m + 7 = 31
Subtracting 7 from both sides of the equation:
3m + 7 - 7 = 31 - 7
3m = 24
Dividing both sides of the equation by 3:
3m/3 = 24/3
m = 8
The number 8 is a solution to the equation 3m + 7 = 31
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Find the inverse of each function. Is the inverse a function?
f(x)=x²-1
In mathematics, an inverse function is one that "reverses" another function. The inverse function of F(x) = x² - 1 is ±√(x + 1).
What is the inverse function of F(x) =x²-1?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
Let the function be f(x) = x² - 1
y = x² − 1
x = y² − 1
simplifying the above equation, we get
y² = x + 1
y = ± √(x + 1)
Because there are two possible values of y for each value of x, there is no inverse function.
The inverse function of F(x) = x² - 1 is ±√(x + 1).
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In order for the parallelogram to be a rhombus, x = [?]. 32 (9x +31)°
In order for the parallelogram to be a rhombus, Then the value of x is equal to 3°.
Rhombus : A rhombus is a diamond-shaped quadrilateral that has all four sides equal. We can see rhombus-shaped figures in our day-to-day lives. Some of the real-life examples of a rhombus are shown in the below-given figure: a diamond, a kite, an earring, etc.
Since Diagonals bisect at 90°
(9x +31)° = 180° - 90° - 32°
To solve the product or quotient,
9x = 180° - 90° - 32° - 31°
We can add or subtract the values,
9x = 58° - 31°
We can divide the products,
x = (58° - 31°)/9
x = 27°/9
x = 3°
Therefore,
The value of x must be 3° in order for the parallelogram to be a rhombus.
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Which of the following may fall under the category of collateral? Answer choices: a high salary, a credit card balance of $12,000, an antique vase valued at $125,000, or a previous loan that was repaid in full
The option B , that is , an antique vase valued at $125,000 can be categorized as collateral asset.
What is a collateral asset ?
An asset that a borrower pledges to a lender as a guarantee that the loan will be repaid is known as collateral asset.
We know that the assets that a lender accepts as security for a loan are referred to as collateral. That meant lenders are protected by the collateral in this way. To put it another way, if the borrower stops making loan payments, the lender may be able to sell the collateral to collect some or all of its losses.
So , let's check which of the given option falls under category of collateral.
A.
This is not collateral asset because for a credit card there is no security money given to bank. We only need to pay a maintenance charge and nothing else.
B.
This is a collateral asset.
For an antique vase whose value is $125000 , if the person has purchased this by taking a loan then he would have paid some security money as deposits. If any case he is not able to pay the loan by time the property or the asset becomes collateral which meant the lender may sell the asset to some or all of his losses.
C.
This is not collateral asset because if the loan is repaid in full there will be no extra charges liable on the asset and it can't be categorized as collateral.
Therefore , the option B , that is , an antique vase valued at $125,000 can be categorized as collateral asset.
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1. He is spending more money than he makes.
2. He has to cut back on other expenses.
3. It is a listing of what an individual owns minus what they owe.
4. an antique vase valued at $125,000
5. capital
Explanation: I took the same quick check and got 100%, hope this helps!
Which of these numbers lies between 4 and 4.5 on a number line? A √13 B √17 C √22 D √28
Therefore √17 will lie between 4 and 4.5 on the number line .
In basic mathematics, real numbers are shown as a graphic of a graduated straight line called a number line. Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.
According to one standard, positive numbers always fall on the right side of zero, whereas negative numbers always fall on the left. The line also contains arrowheads at both ends, signifying that it continues in both the positive and negative directions indefinitely.
Let us find the decimal values of the given numbers.
13 lies between 9 and 16 , therefore √13 lies between 3 and 4 on the number line .
17 lies between 16 and 25 , therefore √17 lies between 4 and 5 on the number line .
22 lies between 16 and 25 , therefore √22 lies between 4 and 5 on the number line .
28 lies between 25 and 36 , therefore √28 lies between 5 and 6 on the number line.
Therefore √17 will lie between 4 and 4.5 on the number line as 4.5² = 20.25.
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What is logbase 3√81
Answer:
log3(sqrt(81)) = 2
Step-by-step explanation:
the quotient of a number x and five is half the difference of the number and four write an equation that represents the statement
Answer:
x/5 - 4
Step-by-step explanation:
Here are the first 7 terms of a quadratic sequence.
(a) Find an expression, in terms of n, for the nth term of this sequence.
6 11 18 27 38 51
A committee of four is to be selected from a group of sixteen people. How many different committees are possible, given the following conditions?
(a) There is no distinction between the responsibilities of the members
(b) One person is the chair, and the rest are general members.
(c) One person is the chair, one person is the secretary, one person is responsible for refreshments, and one person cleans up after meetings.
permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
The factorial function (symbol: !) just means to multiply a series of descending natural numbers.
a) The number of four people committees that can be selected from a group of 16 people is:
no. of committees are possible = 16!/ 4!
(16x15x14x13)/(1x2x3x4)=1820
b)Given that
One person is the chair, and the rest are general members
n! / (n − r)!
where n is the number of things to choose from,
Pick a chairman:: 16 ways
Pick 3 others:: 15C3 = 455 ways
Ans: 16×455 = 7200
c)
Each committee has a chair, a secretary, a refreshment person and a cleanup person.
The number of combinations of assignments within each committee is: 4x3x2x1=24.
The total number of committees with each committee member’s responsibility is: 1820x24=43680.
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Divide. Rationalize all denominators. √3x⁵ / 8 x²
The value of the expression [tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex] after rationalizing the denominator is [tex]\frac{\sqrt{3}(x^{3})}{8}[/tex]..
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a cube root or a square root, from the fraction's denominator to its numerator (numerator).
Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex]
Now, let [tex]y=\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex]
[tex]y=\frac{\sqrt{3} x^{2}(x^{3})}{8x^{2}}[/tex]
Using the exponent rule [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]y=\frac{\sqrt{3}(x^{3})}{8}[/tex]
The value of the expression when rationalized [tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex] is [tex]\frac{\sqrt{3}(x^{3})}{8}[/tex].
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Make g the subject of the formula w = 7 - Vg
Answer:Isolate the g
w = 7 - √g
Do the opposite of PEMDAS, first subtract 7 from both sides
w (-7) = -√g + 7 (-7)
w - 7 = -√g
multiply -1 (as -√g is the same as -1√g) to both sides
-1(w - 7) = √g
-1w + 7 = √g
to get rid of the square root, you must square both sides
Note: -1w is the same as -w
Note: you are squaring all the terms on the other side, not just one.
(-w + 7)² = (√g)²
g = (-w + 7)²
g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or g = (-w + 7)² )
Use the FOIL method (First, Outside, Inside, Last)
(-w)(-w) = w²
(-w)(7) = -7w
(7)(-w) = -7w
(7)(7) = 49
g = w² - 7w - 7w + 49
simplify (combine all like terms)
g =w² - 7w - 7w + 49
g = w² - 14w + 49
g = w² - 14w + 49 is your answer
hope this helps
Step-by-step explanation:
4. The simple interest on a savings account is directly proportional to the amount of the investment.
A savings account with $6,000 earns $75.00 after 1 year. Find a mathematical model that gives the
interest Nafter 1 year in terms of the amount invested P, then calculate the simple interest after
saving an amount of $10,500.
The points E(-8,1)(−8,1), F(1,1)(1,1), and G(-3,8)(−3,8) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.
Applying the distance formula, the perimeter of triangle EFG to the nearest tenth is: 25.7 units
What is the Perimeter of a Triangle?The perimeter of triangle EFG with the following points is the sum of all its three sides = EF + FG + EG.
Find the length of each sides of triangle EFG using the distance formula, d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]:
Given:
E(-8,1)
F(1,1)
G(-3,8)
Using the distance formula:
EF = √[(1−(−8))² + (1−1)²]
EF = √81
EF = 9 units
FG = √[(−3−1)² + (8−1)²]
FG = √65
FG ≈ 8.1 units
EG = √[(−3−(−8))² + (8−1)²]
EG = √74
EG ≈ 8.6 units
The perimeter of triangle EFG = 8.1 units + 9 units + 8.6 units ≈ 25.7 units
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m∠WYX = (2x − 7)° and m∠WYZ = (3x + 2)°. If ∠WYX and ∠WYZ are complementary,
what is the measure of each angle?
A) m∠WYX = 67°; m∠WYZ = 113°
B) m∠WYX = 27°; m∠WYZ = 63°
C) m∠WYX = 31°; m∠WYZ = 59°
D) m∠WYX = 63°; m∠WYZ = 117°
The values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C
What are complementary angles?Complementary angles are defined as angles that sum up to 90 degrees.
Example:
If x and y are complementary angles, then;
x + y = 90°
From the information given, we have the angles;
m∠WYX = (2x − 7)° m∠WYZ = (3x + 2)since they are complementary, then;
2x - 7 + 3x + 2 = 90
collect like terms
2x + 3x = 90 + 5
Add like terms
5x = 95
Make 'x' the subject of formula
x = 95/5
x = 19
But;
m∠WYX = (2x − 7) = ( 2(19) - 7) = 38 - 7 = 31°
m∠WYZ = (3x + 2)° = (3(19) + 2) = 57 + 2 = 59°
Thus, the values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C
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please answer with work
The numeric values to the functions are given as follows:
10. 34.
11. 42.
12. 7.5.
To plot the points in item 13, to plot the points, we follow the procedure described below:
Plot A(a,b) on the first quadrant.Plot B(-a,b) on the second quadrant, reflecting point A over the y-axis.Plot C(-a,-b) on the third quadrant, reflecting point B over the x-axis.Plot D(a,-b) on the third quadrant, reflecting point A over the x-axis.How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For item 10, we want to find the numeric value of -9x - 2 at x = -4, hence:
-9(-4) - 2 = 36 - 2 = 34.
For item 11, we want to find the numeric value of 24 - 8x at x = -2.25, hence:
24 - 8(-2.25) = 24 + 18 = 42.
For item 12, we want to find the numeric value of 15x + 9 at x = -0.1, hence:
15(-0.1) + 9 = -1.5 + 9 = 7.5.
For item 13, we have that (a,b) is positive, hence the following procedure is used to plot all points:
Plot A(a,b) on the first quadrant.Plot B(-a,b) on the second quadrant, reflecting point A over the y-axis.Plot C(-a,-b) on the third quadrant, reflecting point B over the x-axis.Plot D(a,-b) on the third quadrant, reflecting point A over the x-axis.More can be learned about the numeric values of a function at brainly.com/question/28367050
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If $15,000 is invested at 6. 5% annual interest compounded annually, how long would it take for the account balance to reach $50,000? Round your answer to the nearest tenth
The account balance invested at 6. 5% annual interest compounded annually will take 19.1 years to reach $50,000.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded annually, and t is the time in number of year
Using this formula, find t, the time it will take the account to reach $50,000 when
B = $15,000
r = 6.5% = 0.065
n = 1
B = P(1 + r/n)^t
$50,000 = $15,000(1 + 0.065/1)^t
(1 + 0.065)^t = $50,000/$15,000
1.065^t = 10/3
t = 19.1 years
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Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.5(1/4) x
4x you had 0.5x are the y -intercept.
How can you tell whether an exponential function is growing or deteriorating?
As the exponential's base is greater than 1, which occurs when those numbers increase, we are seeing exponential growth. When the exponential's base is between 1 and 0, and those numbers decrease, we have exponential decay.You can obviously plot it but if you can also conside that in your function you have 4x
; this tells you that as
x increases (gets bigger) certainly
4x will increase as well (you can consider
4²= 16 and 4³ = 64
). It is true that you have to multiply by
0.5
but nevertheless the entire function will grow anyway!
Graphically:
graph{0.5*(4^x) [-14.24, 14.24, -7.12, 7.12]}
If you want, try to think at the case where instead of having
4x you had 0.5x .
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I need help with this, can someone help me?
Answer: 5y^2
Step-by-step explanation: hope this helps
Answer: it is the third option
Explanation: as any number with a negative power will be the reciprocal
----> y^-2 = 1/y^2
----> 5 x 1/y^2
----> 5/y^2
i hope this helps
Marsha pays $30 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 8 months of having the membership?
|−30| − 8 = $22
−8|30| = −$240
8|−30| = $240
|−30| − |8| = $22
The total amount subtracted from her account after 8 months of having the membership is given by −8|30| = −$240
What is the number operation symbol of the amount subtracted from her account?
The amount subtracted from Marsha's account per month would be negative since it reduces the account balance after the car wash membership fee has been paid, in other words, the total amount subtracted for 8 months is determined as the negative $30 per month multiplied by 8 months
total amount subtracted for 8 months=-30*8
total amount subtracted for 8 months=-$240
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Answer:
I think it is b
Step-by-step explanation:
The formula for finding the volume of a cube is V = s³, where
s is the length of one side. What is the volume, in cubic units, of
a cube with side length 3 units? Round to the nearest
hundredth when necessary.
The volume of the cube is determined as 27 unit³.
What is defined as the volume of the cube?A cube's volume is the total number of cubic units it occupies in three dimensions. A cube is a three-dimensional shape with six faces, twelve edges, and eight vertices. As a result, the volume of a cube is defined as the space enclosed by it's own six faces.We can calculate the volume of such a square box simply by measuring the length of one of its sides. The volume of a square box is equal to a cube of the length of its side.The volume is calculated using the formula V = s³, in which "s" is the length of a square box's side.
The cube's side length is 3 units.
The volume of a cube = 3³ unit³.
= 3×3×3
= 27
Thus, the volume of the cube is estimated as 27 unit³.
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Which expression is not equivalent to Negative 3 x minus one-half + 4 y?
The expression that is not equivalent is - 2x -0.5 + 6 y + 3 x
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Given the expression -3x - 0.5 + 4y
We are to get the equation equivalent to the expression
2y - 5x - 0.5 + 2y + 2x
4y -3x - 0.5
Hence, the equations are equal
For the expression -2 x -0.5 + 6 y + 3 x
This is equivalent to x + 6y - 0.5
Hence , the expression that is not equivalent is -2 x -0.5 + 6 y + 3 x
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Find the amount in a continuously compounded account for the given conditions.principal: $ 400 annual interest rate: 7.6% time: 1.5 years
The amount in a continuously compounded account is $448.30.
Given that the given conditions are the annual interest rate is $400, time is 7.6% and time is 1.5 years.
Continuous compounding means that the account balance is continuously profitable and transfers that interest back to the balance so that it is also profitable.
To find the amount in a continuously compounded account we will use the formula [tex]A=Pe^{rt}[/tex].
[tex]A=400\times e^{(0.076)(1.5)}[/tex]
Now, we will simplify the above expression, we get
[tex]A=400\times e^{0.114}[/tex]
Now, we will evaluate the value of e that is [tex]e^{0.114}[/tex] is 1.120752, we get
A=400×1.120752
A=448.30
Hence, the amount in a continuously compounded account for the given conditions principal: $ 400 annual, interest rate: 7.6%, time: 1.5 years is $448.30.
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Evaluate the following.
||-2|-|3-12||
Answer:
7
Step-by-step explanation:
You want the value of the expression ||-2|-|3-12||.
EvaluationInner groups are evaluated first:
||-2|-|3-12|| = |2 -|-9||
= |2 -9|
= |-7| = 7
The value of the expression is 7.
__
Additional comment
The absolute value function changes negative signs to positive:
|-2| = 2
It has no effect on positive signs.
|2| = 2
Evaluate the following expression
Find 2x - 3y - z if x = -2, y = 3, and z = -2
Answer:
-11
Step-by-step explanation:
2x - 3y - z
2(-2) - 3(3) - (-2)
-4 -9 +2
-13+2
-11
Answer:
-11
Step-by-step explanation:
What we are solving for: 2x - 3y - z
x = -2
y = 3
z = -2
We can just plug in the variables.
[tex](2*-2) - (3*3) - (-2)[/tex]
[tex]-4-9+2[/tex]
Therefore, the answer is -11.
Hope this helped!!
When a distribution is skewed, the _______ is used to measure the center and the _______ is used to measure variation.
When a distribution is skewed, the median is used to measure the center and the interquartile range is used to measure variation.
The fundamental characteristics of mean for skewed data distribution:
A skewed distribution's mean will always lag behind the distribution's tail.The median is bigger than the mean when the data set is skewed to the right, which causes the mean to be located toward the right of the distribution.Additionally, if the data set has a leftward skew, the mean will be less than the median and will be located nearer the left of the distribution.Therefore, a skewed data set's center cannot be found using the mean.
In a skewed data collection, the median always stays quite near to the center. The best way to measure the center is hence to use the median.
Additionally, the mean and median of a normal distribution are equal, and both are used to locate the middle of the data set.
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Which function correctly describes the zeros given?
0,−1,2
A) F(x)= x(x+1)(x-2)
B) F(x)= x(x-1)(x+2)
C) F(x)= (x+1)(x-2)
D) None of these
Using the factored form of a polynomial for the given zeros, we can see that option A is the correct one, the function is:
F(x) = x*(x + 1)*(x - 2)
Which function correctly describes the zeros given?For a polynomial with the zeros:
x₁, x₂, x₃, ..., xₙ
The polynomial can be written as:
y = (x - x₁)*(x - x₂)*...*(x - xₙ)
In this case, the zeros are:
0, -1, and 2
Then we can write the polynomial as:
y = (x - 0)*(x + 1)*(x - 2)
If we simplify this, we get:y = x*(x + 1)*(x - 2)Which is the one we can see in option A, so we conclude that option A is the correct one.F(x) = x*(x + 1)*(x - 2)
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