The square root of 4096 is 64 and the square root of 529 is 23.
The square root of a number x in mathematics is a number y whose square (the outcome of multiplying the number by itself, or y·y), is equal to x.
For instance, since 4² = (-4)² = 16, 4 and -4 are the square roots of 16.The square root of x is rational if and only if x is a rational integer that can be expressed as the ratio of two perfect squares. (The square root of 2 for proof that this number is illogical; the quadratic irrational for evidence against all non-square natural numbers.) The square root function changes rational numbers into algebraic numbers, which are a superset of rational numbers.The given numbers are 4096 and 529.
Let us find the factors of 4096:
4096 = 2¹²
Therefore the square root of 4096 = √4096 = √(2¹²) = 2⁶ = 64 .
Let us find the factors of 529:
4096 = 23 × 23
Therefore the square root of 529 = √529 = √(23²) = 23 .
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Disclaimer : The question in English is :
What is the square root of 4096 and 529.?
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Find the solution set for y = 4x - 3,
given the replacement set
{(-3, 9), (-2, -11), (0, -2), (2,5)}
The solution set for y = 4x-3 is {(2,5)} from the replacement set {(-3, 9), (-2, -11), (0, -2), (2,5)}.
The provided function is an equation of line in slope-intercept form of line.
According to which, if a line has slope m and it has the Y-intercept c, then the equation of line will be,
y = mx+c,
One thing to be noted here is, if the line passes through (a,b) then it will satisfy the equation and also, it will be called a solution of the equation.
The equation is y = 4x-3,
The given replacement sets is, {(-3, 9), (-2, -11), (0, -2), (2,5)}.
We will check for each and every element of the set,
1. For (-3,9)
Putting values in,
y = 4x-3
9 = 4(-3)-3
9 ≠ -15
Not a solution.
2. For (-2,11)
Putting values in,
y = 4x-3
11 = 4(-2)-3
11 ≠ -11
Not a solution.
3. For (0,-2)
Putting values in,
y = 4x-3
-2 = 4(0)-3
-2 ≠ -3
Not a solution.
4. For (2,5)
Putting values in,
y = 4x-3
5 = 4(2)-3
5 = 5
It is a solution for the equation y = 4x -3.
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The teacher is handing out note cards to her students. She gave 84 note cards to the first
student, 76 note cards to the second student, 68 note cards to the third student, and 60 note
cards to the fourth student. What kind of sequence is this?
arithmetic
geometric
both
neither
Answer: Arithmetic
Step-by-step explanation: Because its decreasing at a constant rate of the same number 8
A new social media site is increasing its user base by approximately 6% per month.Ir the site currently has 21,740 users, what will the approximate user base be 8 months from now?
Data
• Increase: 6% per month
,• Current users: 21,740
,• Users after 8 months: ?
Procedure
As we are increasing 6%, we have to multiply the original quantity, which represents the 100%, times 100% plus the increase (6%). However, this must be done in decimals:
[tex]\frac{100\%+6\%}{100\%}=\frac{106\%}{100\%}=1.06[/tex]Then, for the first month the user base will be:
[tex]21,740\times1.06=23,044.4[/tex]Then, for the second month the user base will be:
[tex]23,044.4\times1.06=24,427.06[/tex]The third month would be:
[tex]24,427.06\times1.06=25,892.70[/tex]We could do this for eight months or we can take a shortcut:
[tex]U=U_0\times i^n[/tex]where U represents the user, U0 is the initial users, i is the increase rate, and n is the number of months.
Replacing the data we have we get:
[tex]U=21,740\times1.06^8[/tex][tex]U=34,650.26[/tex]Answer: 34,650.26 users after 8 months with a 6% increase per month.
for each problem find the instantaneous rate of change of the function at the given value ...Thank you and God Bless
Answer:
The instantaneous rate of change of the function at the given value is -2.
[tex]f^{\prime}(0)=-2[/tex]Explanation:
The instantaneous rate of change of the function at point x=a can be written as;
[tex]f^{\prime}(a)=\frac{df(a)}{dx}[/tex]For the given function;
[tex]y=2x^2-2x+2[/tex]Then the derivative of the function is;
[tex]f^{\prime}(x)=y^{\prime}=4x-2[/tex]substituting x=0, we have;
[tex]\begin{gathered} f^{\prime}(0)=4(0)-2 \\ f^{\prime}(0)=-2 \end{gathered}[/tex]Therefore, the instantaneous rate of change of the function at the given value is -2.
[tex]f^{\prime}(0)=-2[/tex]The graph shows the function f(x).
f(x)
Which equation represents f(x)?
a.f(x) = -√√x
b. f(x) = -√√x-1
c. f(x)=√√/-x-1
d. f(x)=√x
Answer:
The correct option is 3.
Step-by-step explanation:
The parent cube root function is
From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.
If the parent cube root function is reflected across the y-axis, then x is replaced by -x.
Now, the graph of new function sifts 1 unit down. So, the required function is
The graph shows the function .
From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).
Check the above function by these points.
At x=-8,
At x=0,
At x=8,
All these points satisfy by the abobe function. It means the above function is correct.
Therefore the correct option is 3.
Air pressure decreases exponentially with increases in elevation. The air pressure, y, (in atm units) at a given elevation, x, (in meters) can bemodeled using equation y = e where k is the decay constant.At an elevation of 5486 m where the air pressure is 0.5 atm, what is the value of k?O A k=In( 5486)0.5B. k =In(0.5)548654860.5D. k = - In ( 3956
Take natural log on both side of the equation to simplify it,
[tex]\begin{gathered} \ln y=\ln (e^{-kx}) \\ \ln y=(-kx)\ln e \\ \ln y=-kx \\ k=\frac{-\ln y}{x} \end{gathered}[/tex]S
Consider the figure. If <7 and <11 are supplementary then lines
Solution
- The two angles, <7 and <11 are supplementary. This implies that the line q is a transversal line upon which angles <7 and <11 are drawn.
- In order for line q to be the transversal and <7 and <7 to be supplementary, it implies that the lines r and s are parallel.
Final Answer
The answer is "r and s"
True or False. 8 (12 + 3) is equivalent to 120
Use the order of operations and the distributive property to solve this expression. Work starting from the parenthesis.
8(12 + 3) = 120
8(15) = 120
120 = 120
The equation is true.
Answer:
True because you must do parentheses first so 12+3=15x8=120 so it is equivalent
(3s)/(s^2 - 16) (s-4)/(s^2)
Answer: =111e3t(33cosh11−−√t+711−−√sinh11−−√t)
Step-by-step explanation:
Solve the equation algebraically
-3(h+6)-7=5
Write your answer as an internet or reduced fraction.
H=
Answer:
h = -10
Step-by-step explanation:
-3(h+6) - 7 = 5
-3h - 18 - 7 = 5
-3h - 25 = 5
+25 +25
-----------------------
-3h = 30
÷-3 ÷-3
-----------------------
h = -10
I hope this helps!
Simplify.3(x + 4)12 x3 x + 127x3(x+4)
We need to apply "Distributive Property" in order to get rid of the grouping symbols in the algebraic expression.
Such means to multiply 3 by each of the terms inside the parenthesis. That is:
3 times x and then 3 time 4:
3 times x remains as "3 x" since we don't know the value of "x", and 3 times 4 becomes 12:
3 (x+4) = 3 x + 12
Which seems to be the second option you listed.
I am having a hard time understanding explicit formulas with arithmetic sequences. The current sequence I am working with is:2, 8, 14, 20, 26The common difference is 6. I don't know how to come up with the explicit formula when given the sequence.
Solution
we are given the sequence
[tex]2,8,14,20,26,..[/tex]The first term = 2
Common difference = 6
The sequence is an arithmetic progression
The nth term is given as
[tex]\begin{gathered} a_n=a+(n-1)d \\ a=2 \\ d=6 \\ a_n=2+(n-1)(6) \\ a_n=2+6n-6 \\ a_n=6n-4 \end{gathered}[/tex]Therefore, the answer is
[tex]a_{n}=6n-4[/tex]Which sequences are geometric? Select three options.
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ..
(i) –2.7, –9, –30, –100, ... case of a geometric sequence
(ii) –1, 2.5, –6.25, 15.625, ... case of a geometric sequence
(iii) 9.1, 9.2, 9.3, 9.4, ... not a case of a geometric sequence
(iv) 8, 0.8, 0.08, 0.008, ... case of a geometric sequence
(v) 4, –4, –12, –20, .. not a case of a geometric sequence
What is a geometric sequence?
A geometric sequence is one in which the ratio of two succeeding terms is fixed. The common ratio is what's known as this ratio.
Checking each sequence one by one right now.
(i) –2.7, –9, –30, –100, ...
r=(-9/2.7)=3.33
=(-30/9)=3.33
=(-100/9)=3.33
⇒This is a case of a geometric sequence
(ii) –1, 2.5, –6.25, 15.625, ...
r=(2.5/-1)=2.5
=(-6.25/2.5)=2.5
=(15.625/-6.25)= 2.5
⇒This is a case of a geometric sequence
(iii) 9.1, 9.2, 9.3, 9.4, ...
since the ratio between terms is not the same.
⇒This is not a case of a geometric sequence
(iv) 8, 0.8, 0.08, 0.008, ...
since the ratio between terms is the same.
⇒This is a case of a geometric sequence
(v) 4, –4, –12, –20, ..
since the ratio between terms is not the same.
⇒This is not a case of a geometric sequence
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Answer:
option 1,2,4,5 are correct answers
Step-by-step explanation:
what is the means proportional between 4 and 81
Given
4
18
Procedure
The mean proportional, or geometric mean, of two positive The mean proportional, or geometric mean, of two positive
[tex]\frac{a}{x}=\frac{x}{b}[/tex]When solving
[tex]\begin{gathered} x=\sqrt[]{a\cdot b} \\ x=\sqrt[]{4\cdot81} \\ x=\sqrt[]{324} \\ x=18 \end{gathered}[/tex]The answer would be 18
Please help
12x2+20-3x−5
Factor out the GCF from the entire expression
I WILL FIRST GROUP THE LIKE TERMS AND SIMPLIFY THEM BEFORE FACTORISING
IT IS VITAL TO SIMPLIFY LIKE TERMS BEFORE FACTORISING.
[tex]12 {x}^{2} - 3x + 20 - 5 \\ = 12 {x}^{2} - 3x + 15[/tex]
THE GCF IN THE EXPRESSION IS 3 MEANING WE WILL DIVIDE EACH AND EVERY TERM IN THE P
EXPRESSION BY 3
[tex] = 3(4 {x}^{2} - x + 5)[/tex]
HOPE THIS HELPS.
Simplify −6g(3g + 2).
−18g^2 + 2
−18g^2 − 12g
−18g + 2
−18g − 12g
Answer:
B. −18g^2 − 12g
Step-by-step explanation:
Hope this helps!
Please tell me if its incorrect
Simplify the expression below by applying the zero exponent rule. (5-8)^0 = Answer
Zero Exponent Rule:
[tex]\begin{gathered} a^0=1 \\ a\neq0 \end{gathered}[/tex]Thus, anything to the power of 0 is "1", except 0.
Let's simplify the expression shown:
[tex]\begin{gathered} (5-8)^0 \\ =(-3)^0 \\ =1 \end{gathered}[/tex]Answer1Write the equation of a line that is parallel to the line whose equation is y = 1/3x +6 and passes through the point(-3,5).
Answer:
y = 1/3 x + 6
Explanation:
The slope of two parallel lines is the same; thereofre the equation of the line we are seeking looks like
[tex]y=\frac{1}{3}x+b[/tex]where b is a constant hitherto unknown.
Now, we know from point (-3, 5) that when when x = -3, y = 5; therefore,
[tex]5=\frac{1}{3}(-3)+b[/tex]the above simplifies to
[tex]5=-1+b[/tex][tex]\therefore b=6[/tex]Hence, the equation of the line is
[tex]y=\frac{1}{3}x+6[/tex]Find the sum and product of the roots of the equation 4x^2-12=3x
Given the equation:
[tex]4x^2-12=3x\text{ ----- equation 1}[/tex]Required: sum and product of the roots of the equation
solution:
For a quadratic equation of the form
[tex]ax^2\text{ + bx + c = 0 ------ equation 2}[/tex]the sum of the roots is expressed as
[tex]\text{sum of roots = -}\frac{b}{a}[/tex]the product of the roots is expressed as
[tex]\text{product of roots = }\frac{c}{a}[/tex]The given quadratic equation can be rewritten in the form as in equation 2 to be
[tex]4x^2-3x-12\text{ = 0 ----- equation 3}[/tex]In comparison to equation 2,
[tex]\begin{gathered} a\text{ = 4} \\ b\text{ = -3} \\ c\text{ =-12} \end{gathered}[/tex]Thus,
Sum of roots:
[tex]\begin{gathered} \text{sum of roots = -}\frac{b}{a} \\ =-\frac{-3}{4} \\ =\frac{3}{4} \end{gathered}[/tex]thus, the sum of the roots is
[tex]\frac{3}{4}[/tex]Products of roots:
[tex]\begin{gathered} \text{product of roots = }\frac{c}{a} \\ =\frac{-12}{4} \\ =-3 \end{gathered}[/tex]thus, the product of the roots is
[tex]-3[/tex]
What are two ways you can find 17-8? Explain.
The two ways to find solution of the expression (17-8) are by direct arithmetic method and indirect simplification method.
In arithmetic method, the first step is to determine whether the numbers are rational or irrational, so as to simplify the solution process. If numbers are rational, then they are checked for the sign determining their position on number line and then the calculations are performed. Here, 17 is positive rational number and -8 is negative rational number. Hence, 17-8 is equalized to 9. In indirect simplification method, the numbers to be subtracted are broken down to simpler terms which can be easily subtracted and reduced to get the answer. In the subtraction of 17-8, we break 8 in the form of (7+1). Then the expression becomes 17 - (7+1). Now, this expression can easily be solved to get the answer. Therefore, 17 - (7+1) = 10 - 1 = 9.
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Which is an algebraic expression for five more than z
The algebraic expression for 5 more than z is Z + 5.
Given,
5 more than z.
We need to find the algebraic expression.
What are the different algebraic expressions?
We have,
Examples:
- 3 more than M = M + 3
- 3 less than M = M - 3
- 3 times M = 3 x M
- 3 times M less than 2 = 3M - 2
- 3 times M more than 2 = 3M + 2
Find the algebraic expression for 5 more than Z.
We have,
5 more than Z = Z + 5
Thus the algebraic expression for 5 more than z is Z + 5.
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helpppp me out please will give brainiest to first right answer
Answer:
-490
Step-by-step explanation:
:]
Find the domain of the rational expression: 3x+21
all real numbers except 4
all real numbers except -7
all real numbers except 0
all real numbers except -21
Answer: The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Domain: (−∞,∞)
Range: (−∞,∞)
Hope this helps! :)
Please Help, thank you.
The interval notation for the change in temperature are-
Increasing temperature; (1, 3) ∪ (6, 8).Decreasing temperature; (0, 1) ∪ (3, 6).What is termed as the interval notation?An interval is represented on a number line using interval notation. In those other words, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two particular given numbers.For the given function;
Increasing temperature; It is the temperature in which the graph is increasing or we can say that for as the vale of x increases the value of y also increases. Thus, the interval notations are-
Increasing temperature; (1, 3) ∪ (6, 8).
Decreasing temperature: It is the temperature in which the graph is decreasing or we can say that for as the vale of x increases the value of y also decreases. Thus, the interval notations are-
Decreasing temperature; (0, 1) ∪ (3, 6).
Thus, the interval notations for the function are found.
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Which is closest to X, the distance between the base of the lighthouse and the boat
we have
then, we use the trigonometric tangent identity:
[tex]\begin{gathered} \tan 25=\frac{22}{x} \\ x=\frac{22}{\tan 25} \\ x=47.2 \end{gathered}[/tex]answer: x = 47.2
Consider the equation below.
log4(x+3)= log2 (2+x)
Which system of equations can represent the equation?
Answer:
x=2log(2)−3log(4)log(4)−log(2)
Step-by-step explanation:
I hope this matches one of your answers
The decimal form is -4
Solve for X.
X =?]
5X - 16 x + 10
Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1. The factors of the expression are______and_____
The factors of the expression are 2.5 and 11/5.
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions. Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3.
Given Data
Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1.
Algebraic expression:
The factors of the expression are:
10 = 5y -1
11 = 5y
y = 11/5
y = 2.5
The factors of the expression are 2.5 and 11/5.
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Shavon and Jesiah are having a race. Shavon can run 100 meters in 30 seconds. Jesiah can run 120 meters in 40 seconds. Who is running faster in meters per second, and by how much?
Shavon is running faster by 0.33 meter.
How to calculate the value?From the information, Shavon and Jesiah are having a race and Shavon can run 100 meters in 30 seconds. The speed will be:
= Distance / Time
= 100 / 30
= 3.33 meter per second
Jesiah can run 120 meters in 40 seconds. The speed will be:
= Distance / Time
= 120 / 40
= 3 meters per second.
Shavon runs faster. This is illustrated as:
= 3.33 - 3
= 0.33 meter
She's 0.33 meters faster.
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Please help me with this question my son keeps getting this wrong, please help I have attached the image of the problem from his math paper.
The terms in the given expression are
[tex]8x^3y^2,4x^2y^3,40xy^3[/tex]The common factor in all the three time is
[tex]4xy^2[/tex]Take the common factor outside the brackets and write the remaining inside the brackets.
[tex]4xy^2(2x^2-xy+10y)[/tex]