Simplifying the given logarithmic equation, the expression is obtained as log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex]).
The objective is to find the resultant expression for 4 × logx -(2 × logv + 3 × logy)
According to logarithmic results,
The product of an integer constant and a logarithm term of a number is equivalent to the logarithm of the number raised to the power of the particular integer constant.
That is, b × log(a) = log([tex]a^{b}[/tex])
Hence, 4 × log(x) = log([tex]x^{4}[/tex]),
2 × log(v) = log([tex]v^{2}[/tex])
and, 3 × log(y) = log([tex]y^{3}[/tex])
So, the equation can be rewritten as log([tex]x^{4}[/tex]) - (log([tex]v^{2}[/tex]) + log([tex]y^{3}[/tex]))
The sum of the logarithms of two numbers is equivalent to the logarithm of their product.
That is, log(a) + log(b) = log(a×b)
Hence, log([tex]v^{2}[/tex]) + log([tex]y^{3}[/tex]) = log([tex]v^{2}[/tex][tex]y^{3}[/tex])
So, the equation can be rewritten as log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex])
The difference in the logarithms of two numbers is equivalent to the logarithm of their fraction.
That is, log(a) - log(b) = log(a÷b)
Hence, log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex]) = log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex])
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Which would be the result if we divide the sum of 275 and 325 by 25?
A.
25
B.
24
C.
20
D.
30
E.
40
Answer: B. 24
Step-by-step explanation:
275+325= 600
600/25 = 24
Hence, 24 is the outcome
B. 24 is your answer
x² + 16x + c = 0
What is the value of “c”
The equation can be solved as below
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.
The equation can be solved as
x² + 16x + c = 0
or, c = - x² - 16x
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Can someone help me with this, please? I really need help!
Strontium-90 (Sr-90) has a half-life of approximately 29 years. Let the initial amount of Sr-90 in a sample be 100g. If the decay function s(y)=100*0.5^y/29 expresses the amount of Sr-90 that remains in the sample after y years, in how many years will 1g of Sr-90 be left? Round up your answer to the nearest number of years
Answer: Approximately 193 years
=======================================================
Work Shown:
y = number of years
s(y) = amount of Strontium-90 (Sr-90) in grams
We plug in s(y) = 1 and solve for y to determine how long it takes for the initial 100 gram sample to decay to 1 gram.
s(y)=100*0.5^(y/29)
1=100*0.5^(y/29)
1/100 = 0.5^(y/29)
0.01 = 0.5^(y/29)
Log[ 0.01 ] = Log[ 0.5^(y/29) ] .... see note1 below
Log[ 0.01 ] = (y/29)*Log[ 0.5 ] .... see note2
(y/29)*Log[ 0.5 ] = Log[ 0.01 ]
y/29 = Log[ 0.01 ]/Log[ 0.5 ]
y = 29*Log[ 0.01 ]/Log[ 0.5 ]
y = 192.671829503468
y = 193
Footnotes
note1: if the variable is in the trees, aka exponent, then log it down. In other words, we use logs to isolate the exponent.note2: use the log rule that Log(A^B) = B*Log(A) which is the actual act of pulling down the exponent and it helps us isolate it.HELP PLEASEE ASAP HELP HELP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Place each equation with its correct group (decay or growth)
Exponential Growth Exponential Decay
V = 18,000(0.78)^t
P = 4500(1.04)^t
A = 7000(1.0575)^t
P = 50(1/2)^t
P = 45(2)^t
A = 9000(0.9)^t
The equation are
1. V = 18,000(0.78)^t is exponential decay.
2. P = 4500(1.04)^t is exponential growth.
3.A = 7000(1.0575)^t is exponential growth.
4.P = 50(1/2)^t is exponential decay.
5.P = 45(2)^t is exponential growth.
6.A = 9000(0.9)^t is exponential decay.
Given that,
We have to find which equation is exponential growth and exponential decay.
Knowing that an exponential function takes the form where a represents the function's y=a.bˣ initial value a and b represents its exponential growth or exponential decay, B should be more than 1 for exponential growth and less than 1 for exponential decay.
b>1= exponential growth.
b<1= exponential decay.
Let's now examine each equation in turn to see which one represents exponential growth and which exponential decay.
1. [tex]V=18000(0.78)^{t}[/tex]
The initial values a and b in this option are 18000 and 0.78 respectively. Since 0.78 is smaller than 1, this equation describes exponential decay.
2.[tex]P=44500(1.04)^{t}[/tex]
Since 1.04 is obviously more than 1, and we can see that a = 4,500 and b equals 1, we may conclude that this equation represents exponential growth.
3.[tex]A=7000(1.0575)^{t}[/tex]
Since 1.0575 is clearly more than 1 and since a equals 7000 and b equals 1.0575, this equation clearly represents exponential growth.
4.[tex]P=50(1/2)^{t}[/tex]
Given that a = 50 and b equals 1, and that 0.5 is unmistakably less than 1, it is evident that this equation describes exponential decay.
5. [tex]P=45(2)^{t}[/tex]
Since a and b are equal to 45 and 2, respectively, and 2 is obviously greater than 1, this equation represents exponential growth.
6.[tex]A=9000(0.9)^{t}[/tex]
Since 0.9 is obviously less than 1 and that an equals 9000 and b equals 0.9, this equation represents exponential decay.
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Solving Inequalities with One Variable
Show work
4+1+2≥5
Answer: The statement is true
4+1+2≥5
4+1+2 can be simplified to 7
7≥5, 7 is indeed greater than 5
Is this right? I really need to know
Yes, this is right. theta is angle C.
What are angles?In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed by two rays in the plane where they are placed. Additionally, when two planes overlap, angles are created. Dihedral angles are what they are called. When two straight lines or rays intersect at a single point, an angle is created. The vertex of an angle is the location where two points converge.
Here, angle is formed at C, A and B, but here B is 90 and the angle sign is given at C.
So, theta is angle C.
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a/ Find a polynomial U with integer coefficientsthat satisfies the given conditions: degree 5, theleading coefficient 63, and zeros are 1/3, whichhas multiplicity 2, -4, and i
Since the zeroes are 1/3 which has multiplicity 2, -4 and i, then
The factors of the polynomial are
[tex]x=\frac{1}{3}\rightarrow3x=1\rightarrow(3x-1)\rightarrow(3x-1)^2[/tex][tex]x=-4\rightarrow(x+4)[/tex][tex]x=i\rightarrow(x-i)(x+i)\rightarrow x^2-i^2\rightarrow(x^2+1)[/tex]Multiply the 3 factors
[tex]\begin{gathered} (3x-1)^2=(9x^2-6x+1) \\ U=(9x^2-6x+1)(x+4)(x^2+1) \end{gathered}[/tex]Multiply The first 2 brackets
[tex]U=(9x^3+36x^2-6x^2-24x+x+4)(x^2+1)[/tex]Add the like terms in the 1st bracket
[tex]U=(9x^3+30x^2-23x+4)(x^2+1)[/tex]Multiply the 2 brackets
[tex]U=9x^5+30x^4-23x^3+4x^2+9x^3+30x^2-23x+4[/tex]Add the like terms
[tex]U=9x^5+30x^4-14x^3+34x^2-23x+4[/tex]Since the leading coefficient is 63, multiply all terms by 7
[tex]U=63x^5+210x^4-98x^3+238x^2-161x+28[/tex]17. it is recommended that hikers' backpacks weigh no more than 20% of their body weight on overnight bikes and no more than 10% of their body weight on day hikes there are restrictions a hiker who weighs 160 pounds is planning an overnight hike. the weight of her backpack when packed with essential equipment is 15 pounds. write an inequality to show how many pounds, p, the hiker can still add to her backpack and stay within the recommended weight a hiker who weighs 180 pounds is planning a day hike. the weight of his backpack when packed with part a part b
Expressions can be represented as equations or inequalities
(a) The hiker's backpack weighs 15 lb.
(b) the hiker can add additional 19.5 pounds
The inequality that represents the additional weight is:
The hiker can add additional 19.5 pounds
(a) Long hike
The hiker's weight is given as:
, the recommended weight (x) of the backpack is calculated as:
The hiker's backpack weighs 15 lb.
So now what weare supposed to do is
Subtract 15 from both sides
(b) Day hike
The hiker's weight is given as:
The hiker is embarking on a day hike (i.e. short hike), the recommended weight (x) is calculated as:
The hiker's backpack weighs 7.5 lb.
So, the additional weight the hiker can add is represented as:
Subtract 7.5 from both sides
Hence, the hiker can add additional 19.5 pounds
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Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-7,-2); y= -3x + 1
the equation of line which passes through point (-7,-2) and is parallel to the graph of the given equation is y = -3x +23.
What is Algebraic expression ?
Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables..
Here, the given equation is :
y = -3x + 1
which passes through point (-7,-2)
Let us first find the slope of line m which is parallel to the liney = -3x + 1 using point-intercept equation of line that is given by :
y = mx + c....(1)
y = -3x + 1
comparing above equation with equation (1) we get
m = -3
Now, the slope of line parallel to line y = -3x + 1 will have same slope that is m = -3
Now, Let us find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-(-2)) = -3(x-(-7))
(y+2) = -3x-21
y = -3x -21 -2
y = -3x +23
Therefore, the equation of line which passes through point (-7,-2) is y = -3x +23.
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if i had 90 days and i did two months how many days do i have with the school breaks in it to ???
Answer:
Nothing cause your an special and you should know
Step-by-step explanation:
duh
4(x−3)−7x≥6 Responses
Answer:
x ≤ -6
Step-by-step explanation:
4(x-3) -7x ≥ 6 Distribute the 4
4x - 12 -7x ≥ 6 Combine like terms
-3x - 12 ≥ 6 Add 12 to both sides
-3x ≥ 18 Divide both sides by -3 Remember to flip the inequality sign
x ≤ -6
NEED HELP!!! TIMED!!!
An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval 0 <= x <= 1?
The exponential grows at half the rate of the quadratic.
The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic.
The exponential grows at four times the rate of the quadratic.
The statement which is true of the growth rate of the functions over the interval 0 ≤ x ≤ 1 is that: B. The exponential grows at the same rate as the quadratic.
What is the rate of change?The rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity.
Mathematically, the rate of change can be calculated by using this formula;
[tex]Rate = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Rate = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
From the given interval and graph (see attachment), the data point for the exponential function would be as follows:
Point (x₁, x₂) = (0, 1)Point (y₁, y₂) = (1, 2)Next, we would calculate the rate of change of the exponential function over the given interval:
Rate of change = (2 - 1)/(1 - 0)
Rate of change = 1/1
Rate of change = 1.
From the given interval and graph (see attachment), the data point for the quadratic function would be as follows:
Point (x₁, x₂) = (0, 1)Point (y₁, y₂) = (0, 1)Next, we would calculate the rate of change of the quadratic function over the given interval:
Rate of change = (1 - 0)/(1 - 0)
Rate of change = 1/1
Rate of change = 1.
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For i = √-1, (1 + 2i)² = ?
The value of given expression is F(x) = (-3 +4√-1)
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given i = √-1
F(x) = ( 1 + 2i)²
F(x) = ( 1 + 4i² + 4i)
F(x) = ( 1 - 4 + 4√-1)
F(x) = ( -3 + 4√-1)
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The cost of a family membership at a local gym is $20 for a parking permit plus $15 for each member of the family. express this cost as a function of the number of people in a family, x, using one car.
(A) f(x) = 20x + 15
(B) f(x) = 35x
(C) f(x) = 15x + 20
(D) f(x) = 20x + 1
(E) f(x) = 15x + 1
PLEASE ANSWER ASAP! I WILL GIVE YOU BRAINLIEST IF CORRECT!
Answer:
its C cause when it said permit plus $15 for each member in the family they mention by C
Two parrel lines cut by a transversal find each angle mesure
The angles formed between the parallel lines and the common transversal are;
7. [tex] \displaystyle{m \angle ABC = 92^{ \circ} }[/tex]
8. [tex] \displaystyle{m \angle MPQ = 125^{ \circ} }[/tex]
9. [tex] \displaystyle{m \angle MNP = 56^{\circ} }[/tex]
10. [tex] \displaystyle{m \angle WXZ = 130^{ \circ} }[/tex]
Corresponding angles
1 and 5, 2 and 6, 4 and 8, 3 and 7
Alternate interior angles
4 and 6, 3 and 5
Alternate exterior angles
1 and 7, 2 and 8
Same side exterior angles
1 and 8, 2 and 7
Same side interior angles
4 and 5, 6 and 3
What are parallel lines on a coordinate plane?Parallel lines on a coordinate plane are lines that have the same slope.
7. According to corresponding angle theorem, we have;
4•x° = (3•x + 23)°
Which gives;
4•x = (3•x + 23)
4•x - 3•x = 23
x = 23
[tex] \displaystyle{m \angle ABC = 4 \cdot x^{ \circ} = (4 \times 23)^{ \circ} = 92^{ \circ} }[/tex]
8. 5•x° = (3•x + 50)°
5•x - 3•x = 50
2•x = 50
x = 50 ÷ 2 = 25
[tex] \displaystyle{m \angle MPQ = (3 \cdot x + 50)^{ \circ} = (3 \times 25 + 50)^{ \circ} = 125^{ \circ} }[/tex]
9. According to alternate interior angles theorem we have;
2•a° = (a + 28)°
2•a° - a° = 28°
a = 28
[tex] \displaystyle{m \angle MNP = (a + 28)^{\circ} = (28 + 28)^{ \circ} = 56^{\circ} }[/tex]
10. 5•y = 2•y + 78°
5•y - 2•y = 78°
3•y = 78°
y = 78° ÷ 3 = 26°
y = 26°
[tex] \displaystyle{m \angle WXZ = 5•y = 5 \times 26^{\circ} = 130^{ \circ} }[/tex]
Corresponding angles
The corresponding angles are;
1 and 5, 2 and 6, 4 and 8, 3 and 7
Alternate interior angles
The alternate interior angles are;
4 and 6, 3 and 5
Alternate exterior angles
The alternate exterior angles are;
1 and 7, 2 and 8
Same side exterior angles
The same side exterior angles are;
1 and 8, 2 and 7
Same side interior angles
The same side interior angles are;
4 and 5, 6 and 3
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how did you get the answer for 1.13-0.46
help me....
Answer: 0.67 Just subtract
Step-by-step explanation:
I'm confused about what you are asking But ill assume you want to subtract?
1.13 minus 0.46 is 0.67
Answer:
0.67
Step-by-step explanation:
just get the answer taking out
please help me with this!!!!
Answer:
x int = (5,0)
y int = (0,-2)
Step-by-step explanation:
To solve for x int set y as zero
4x - 10(0) = 20
4x - 0 = 20
4x = 20 divide by 4 to get x alone
x = 5
To solve for y set x as zero
4(0) - 10y = 20
0 - 10y = 20
- 10y = 20 divide by -10 to get y alone
y = -2
write an equation for the line, in point slope form that passes through the following points
(3,4)
(6,10)
The linear equation in the slope-point form is:
(y - 4) = 2*(x - 3)
How to get the equation for the line?
For a line with a slope M that passes through a point (a, b), the point-slope form is:
(y - b) = M*(x - a)
And if the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
M = (y₂ - y₁)/(x₂ - x₁)
In this case the line passes through (3,4) and (6,10) is:
M = (10 - 4)/(6 - 3) = 6/3 = 2
And using the point (3, 4), we can write:
(y - 4) = 2*(x - 3)
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VAT is set at 15%, how do you calculate the amount of VAT if the price of an article is R345
51.75 is the amount of VAT.
How does the VAT work?
VAT, or value-added tax, is a tax that must be paid on purchases made within the borders of EU member states. The end consumer of the commodity or service is always responsible for paying the tax.In the United States, there is no VAT. However, even though the US doesn't have a VAT, consumers are still required to pay federal excise taxes when buying goods like cigarettes, alcohol, and fuel. Several states and towns also levy sales taxes.= 15% of VAT on Rs 345
= 345 * 15%
= 345 * 15/100
= 51.75
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Under her cell phone plan, Nora pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill at $42 per month. Write and solve an equation which can be used to determine g, the number of gigabytes of data Nora can use while staying within her budget.
Answer:
Step-by-step explanation:
the answer is 1.3 gigabytes
Answer:the equation which can be used to determine the number of gigabytes is 35.5 + 5x = 42 and the solution is x = 1.3
Step-by-step explanation:
Anyone help this is 1 grade homework
Answer:
(What's a number story?) Sam had 10 coins. Then, he gave 3 to his sister. How much money does he have left?
Addition fact: I think it's that you have to take the amount of money he has left (Which is 7), and add it to 3 to make 10.
Hope this helps!
please help!! I really need help please help
Answer:
Step-by-step explanation:
Second answer: Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
Third answer: The transitive property of equality formula is given as follows: If x = y and y = z, then x = z. Where x, y and z belongs to the same category elements. For example, if “x” represents the measurement of a line segment, then y and z should represent the measurement of the line segment.
Fourth answer: Congruent segments are segments that have the same length. ≅ Points that lie on the same line are called collinear.
how many hundreds multiplied by 4 will fit into 2018
We need to know numbers that multiplied by 4 are not greater than 2018.
For example, the number 100 (one hundred), when multiplied by 4 gives 400.
It obviously fits into 2018.
The number 900 by 4 gives 3600
Mr.peters has 80 sheets of colored paper.Seven of his students need the paper for a project.how many sheets does each student get? How many sheets are leftover?
Answer:
each student gets 1 sheet. There are 73 sheets left.
Step-by-step explanation:
Each student only needs 1 sheet and so you just do 80-7 and you get 73
pleaseeeee answer Separatrix Separation
The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances.
We have to explain the separatrix separation.
When in motion, a pendulum can either swing from side to side or rotate continuously. The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances. But when the pendulum is pushed at a nearly constant rate, the math breaks down.
A pendulum in motion has two possible motions: a continuous circle or a side-to-side swing. The separatrix—the point at which it switches from one kind of motion to another—can be estimated in the majority of straight forward circumstances. However, the mathematics breaks down when the pendulum is pushed at a nearly constant velocity.
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please help with this (percentages)
the delivery times for a distributing site are normally distributed with an unknown population mean and standard deviation. if a random sample of 25 deliveries is taken to estimate the mean delivery time, what t-score should be used to find a 98% confidence interval estimate for the population mean?
The t-statistic is the t-value at the intersection of the row for DF = 25 and the 0.025 (one-tail) column is 2.06
How to calculate confidence interval for population mean for small sample?If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
The number of degrees of freedom will be n - k
The confidence level in the confidence interval
The parameters given in the question is;
The number of pizza orders in the sample is n
The sample size = 26
The number of samples used in the estimate, k = 1 group of 26 randomly sampled.
The level of confidence that the interval contains the population mean = 95%
Therefore, the significance level;
α = 1 - 95% = 1 - 95/100
= 0.05
Here α-level for the upper and lower limit of the interval are;
α/2 = 0.05/2 = 0.025 long
The degrees of freedom, DF = n - k
DF = 26 - 1 = 25
The t-statistic is the t-value at the intersection of the row for DF = 25 and the 0.025 (one-tail) column (0.025 two-tail column);
[tex]t_{\alpha/2, DF} = 2.06[/tex]
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\frac{5}{8}-\frac{1}{8} 8 5 − 8 1
After solving the given fractions, the resultant fraction is 1/2.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The terms with a numerator and a denominator are called fractions.So, 5/8 - 1/8:
Now, solve as follows:
5/8 - 1/8(5 - 1)/84/81/2
Therefore, after solving the given fractions, the resultant fraction is 1/2.
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The correct question is given below:
Solve: 5/8 - 1/8
The width of stamp M is 43 inches, and the length is 75 inches. The dimensions of stamp M are 76 times the dimensions of stamp P. What is the length of stamp P, in inches? A:6/5 B:8/7 C:14/9 D:49/3
If the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.
Given that the width of stamp M is 43 inches, length is 75 inches and the dimensions of stamp M are 76 times the dimensions of stamp P.
We are required to find the length of stamp P in inches.
Suppose the length of stamp P be x.
According to question, the length of stamp will be 76x.So,
75=76x
x=75/76
Hence if the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.
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Answer:
the answer is A, 6/5
Conrad has 6 more marbles than Rory has. Let r represent the number of marbles that Rory has. Select the expression that represents the number of marbles that Conrad has.
Answer:
Conrad = r + 6
Step-by-step explanation:
