The simplification of √x / √6 y³ after rationalizing all denominators is
[tex]\sqrt{6x}[/tex] [tex]y^{-3}[/tex]/ 6
Given; [tex]\frac{\sqrt{x} }{\sqrt{6} y^{3} }[/tex] , we are to simplify and also rationalize the denominators
[tex]\frac{\sqrt{x} }{\sqrt{6} y^{3} }[/tex] * [tex]\frac{{\sqrt{6} y^{3} }}{{\sqrt{6} y^{3} }}[/tex]
= [tex]{\sqrt{6} y^{3} }[/tex] * [tex]\sqrt{x}[/tex] / [tex]{\sqrt{6} y^{3} }[/tex]* [tex]{\sqrt{6} y^{3} }[/tex]
=[tex]\sqrt{6x}[/tex] * [tex]y^{3}[/tex] / [tex]\sqrt{36}[/tex]* [tex]y^{6}[/tex]
= [tex]\sqrt{6x}[/tex] * [tex]y^{3}[/tex] / 6 * [tex]y^{6}[/tex]
=[tex]\sqrt{6x}[/tex] * [tex]y^{3-6}[/tex] / 6
= [tex]\sqrt{6x}[/tex] [tex]y^{-3}[/tex] /6
The final answer to this question, is, [tex]\sqrt{6x}[/tex] [tex]y^{-3}[/tex] /6
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Suppose you invest a dollars to earn an annual interest rate of r percent (as a decimal). After t years, the value of the investment with interest compounded yearly is A(t)=a(1+r) t . The value with interest compounded continuously is A(t)=a . e rt
b. Suppose you can earn interest at some rate between 0 \% and 5 \% . Use your. knowledge of the exponential function to explain why continuous compounding does not give you much of an investment advantage.
$1.051271 is the exponential function to explain why continuous compounding does not give you much of an investment advantage.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.Simple Interest: A = P(1+rt)
P: the principal, the amount invested
A: the new balance
t: the time
r: the rate, (in decimal form)
Ex 1 - If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.
P = $1000, t = 2 years, r = 0.08.
A = 1000(1+0.08(2)) = 1000(1.16) = 1160
B) Suppose you invest $1 at 5% compounded yearly.
Suppose you invest $1 at 5% compounded continuously.
The 1st case gives you $1*(1.05)1 = $1.05
The 2nd case gives you $1*e0.05 = $1.05127
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How to solve for the value of x
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
First calculate the 3-5 Triangle
Using Pythagorean Theorum,
[tex]\sqrt{5^{2}-3^{2} } =4[/tex]
That means that the other triangle side is 2.
Using Pythagorean Theorum again,
[tex]\sqrt{3^{2}+2^{2} } =\sqrt{13}[/tex]
What value of x makes the equation -5x - (-6 - 4x) = -2(3x - 4) true?
Answer: [tex]x=\Large\boxed{\frac{2}{5} }[/tex]
Step-by-step explanation:
Given equation
[tex]-5x-(-6-4x)=-2(3x-4)[/tex]
Expand the parenthesis
[tex]-5x+6+4x=-2\times3x-2\times(-4)[/tex]
[tex]-5x+6+4x=-6x+8[/tex]
Combine like terms
[tex]-x+6=-6x+8[/tex]
Add 6x on both sides
[tex]-x+6+6x=-6x+8+6x[/tex]
[tex]5x+6=8[/tex]
Subtract 6 on both sides
[tex]5x+6-6=8-6[/tex]
[tex]5x=2[/tex]
Divide 5 on both sides
[tex]5x/5=2/5[/tex]
[tex]x=\Large\boxed{\frac{2}{5} }[/tex]
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A mountain grows by 2 centimeters every year. At this rate in how many years will the mountain grow by 1.3 meters?
well, let's keep in mind that a meter has 100 centimeters, thus 1.3 meters will be 1.3 * 100 cm, namely 130 cm.
[tex]\begin{array}{ccll} cm&year\\ \cline{1-2} 2 & 1\\ 130& x \end{array} \implies \cfrac{2}{130}~~=~~\cfrac{1}{x}\implies \cfrac{1}{65}=\cfrac{1}{x}\implies x=65[/tex]
Expand each binomial.
(x²+x)⁴
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. The expression be (x²+x)⁴ is expanded as x⁸ + 4x⁷ + 6x⁶ + 4x⁵ + x⁴.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
By using binomial expansion theorem, we get
x⁸ + 4x⁷ + 6x⁶ + 4x⁵ + x⁴
The expression be (x²+x)⁴ is expanded as x⁸ + 4x⁷ + 6x⁶ + 4x⁵ + x⁴.
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Part 2: What the answers to the worksheet
The rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).
Given that, a rotation and reflection composition is equivalent to other compositions.
What are rotation and reflection?Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape.
Rotation rule:
Rotation of a point through 180°, about the origin when a point A (x, y) is rotated about the origin O through 180° in the anticlockwise or clockwise direction, it takes a new position A' (-x, -y).
Reflection rule:
A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.
Therefore, the rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).
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A package of a 8 count AA batteries cost 6.40. A package of 20 count AA batteries cost 15.80. Which statement about the unit prices is true?
Write an equation in slope-intercept form of the line
The linear equation in the slope-intercept form is:
y = (-1/3)*x + 4
How to write the linear equation?Remember that if a line passes through two points (a, b) and (c, d), then the slope is given by:
slope = (d - b)/(c - a)
By looking at the graph, we can see that the points (0,4) and (3, 3), then the slope will be:
s = (3 - 4)/(3 - 0) = -1/3
And we can see that the y-intercept is y = 4 (because the line passes through the point (0,4))
Then the linear equation in the slope-intercept form is:
y = (-1/3)*x + 4
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For any two integers a and b, a + b>a - b
The statement is True. Any two integers a, b will satisfy the condition which is: a + b > a - b
In the given question, we have been asked whether the statement a + b > a - b is True or not. For this, we know that the sum of any two Integer is always greater than the difference between them. This can be explained with the help of an example. Suppose a = 2, and b = 1.
Putting values of a, b in the condition, we get:
=> a + b > a - b => 2 + 1 > 2 - 1
=> 3 > 1
Hence, the statement a + b > a - b is True.
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Macario works part time at a clothing store in the mall. He is paid $9 per hour plus 12% commission on the items he sells in the store. Write an equation in slope-intercept form to represent Macario's hourly wage y.
The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s
What is a slope-intercept function?
A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that represents Macario's hourly wage y is shown thus:
y=9x+0.12s
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Determine if each statement is true or false. Justify your answer.
(log x)² = log x²
The given logarithmic representation i.e., (log x)² = log x² is true only for x = 1 and 100 and for rest it is not valid.
Given that, (log x)² = log x², let's proceed to simplify this in order to reach at the conclusion part.
(log x)² = log x²
(log x)² = 2log x
(log x)² - 2log x = 0
log x(log x - 2) = 0
⇒log x = 0 or log x - 2 = 0
Now, put log x = 0
⇒ x = 1
Now, put log x - 2 = 0
log x = 2
log x = 10²
x = 100
Hence, we got two values for x one is 1 and other is 100. Now, putting one by one in (log x)² = log x² in order to reach at the conclusion.
Put x = 1 in (log x)² = log x², we get
(log 1)² = log 1²
0 = 0²
0 = 0
⇒ true for x = 1
Now, put x = 100 in (log x)² = log x² , we get
(log 100)² = log 100²
2² = 2log 100
4 = 2 x 2
4 = 4
⇒ true for x = 100
So, (log x)² = log x² is true only when x = 1 and 100 for rest it is false.
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Can anyone help me calculate the value of y
Based on the fact that this is an equilateral triangle, the value of y can be found to be 5.
What is the value of y?The figure given is an equilateral triangle which means that the lengths of all the sides are equal.
As DC is equal to 20, it means that all the other sides should be 20 as well.
This means that the value of y is:
20 = 15 + y
y = 20 - 15
y = 5
In conclusion, y is 5.
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For each annual rate of change, find the corresponding growth or decay factor. -55 %
The decay factor for the annual rate of change of - 55 % is 0.45.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = - 55 % = - 55 / 100 = - 0.55
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (- 0.55)
B = 1 - 0.55
B = 0.45
Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.45.
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Please help me please help me please help me please
Name a line that passes through point D
Answer:
BC
Step-by-step explanation:
its easy d will keep going as shown the arrow so when its pass c it will be in between makinn it BC (i cant explain well but thats the answer)
Find each real root. ³√-27
The average temperature in the mountains is 61° in April. The average temperature in that same spot is −2° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
61 + |−2| = 63°, −2° is the farthest from 0°
61 − |−2| = 59°, −2° is the farthest from 0°
61 + |−2| = 63°, 61° is the farthest from 0°
61 − |−2| = 59°, 61° is the farthest from 0°
The location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
From the question, we are to determine how much warmer the location is in April than in December
From the given information,
Average temperature in April = 61°
and
Average temperature in December = -2°
To determine how much warmer the location is, we will add the absolute values of the temperatures
That is,
61 + |-2|
= 61 + 2
= 63°
61° the temperature that is farthest from 0
Hence, the location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
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-3 + (1 1/2) + (2 1/2)
What is 33% written as a fraction?
thirty-three over one thousand
3 over ten
8 over twenty-five
thirty-three over one hundred
Solve each equation. 2 e ³x=16
The solution of the exponential equation 2e³x = 16 is x = 0.398.
What are defined as the exponential equation?Exponential equations are those in which the variables appear as exponents.
Exponential equations, for example, take the form a∧x = b∧y.Should use property of equality of the exponential functions to solve exponential calculations with the same base.If b is not a positive number, then b∧x = b∧y if but only if x = y. Throughout other words, is if bases are exactly the same, the exponents must also be the same as well.If the bases are not the same, accomplish the exponential equations using logarithms.Now, for the stated equation 2 e³x=16;
Divide both side by 2
=> e³x = 8
=> x = 8/ e³
As, we are aware of the exponential function 'e' that is the value of e = 2.72...
Substitute the value of the exponent 'e' in the obtained expression.
=> x = 8/ (2.72)³
=> x = 8/20.132
=> x = 0.398
Therefore, the obtained value of x for the given exponential function is 0.398.
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find the vertex y= -2x^2
The vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the vertex of the function?The equation of the function is given as
y = -2x^2
A quadratic function is represented as
y = a(x - h)^2 + k
Where the vertex is
vertex = (h, k)
This means that the equation y = -2x^2 can be rewritten as
y = -2(x - 0)^2 + 0
When the equations are compared, we have
vertex = (h, k) = (0, 0)
Hence, the vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)
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Solve. Check for extraneous solutions. √x²+3 =x+1
x = 1 is not an extraneous solution.
✓(x² + 3) = x + 1
Taking square on both the sides of the equation, we get
(✓(x² + 3))² = (x + 1)²
x² + 3 = (x + 1)²
Using the identity (a+b)²= a² + b² + 2ab on the right hand side of the equation, we get
x² + 3 = x² + (1)² + 2(x)(1)
x² + 3 = x² + 1 + 2x
2x = 2
x = 1
Confirming the value is extraneous solution or not
Putting the root x = 1 in the original equation ✓(x² + 3) = x + 1, we get
✓(1² + 3) = 1 + 1
✓4 = 2
2 = 2
⇒ LHS = RHS
∴ x = 1 is not an extraneous solution.
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i need help asap please help me
Answer: yo wassup picture isn't straight cant see
Step-by-step explanation:
The lines represented by y=-5x+10and5y=x+15 are
The lines represented by y = -5x + 10 and 5y = x + 15 are; Perpendicular
How to interpret slopes of lines?
We are given the equation of two lines as;
Line 1; y = -5x + 10
Line 2; 5y = x + 15
Now, the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, for the equation in line 1, we know that;
slope = -5 while the y-intercept is 10
For line 2, the equation can be rewritten as;
y = ¹/₅x + 3
Slope = 1/5
y-intercept = 3
Now, we know that when two lines are perpendicular, it means that their slopes are negative reciprocals of each other.
Slopes of lines 1 and 2 are negative reciprocals of each other and thus they are perpendicular.
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5x - 2x + 5 = 2x + 26
solving for x when d is on both sides
answer :
so this is the answer of the value of x
The solution of the linear equation is x = 21.
How to solve the linear equation for x?
Here we have the linear equation:
5x - 2x + 5 = 2x + 26
To solve this for x, move all the terms with x to the left side and all the others to the right side:
5x - 2x - 2x = 26 - 5
5x - 4x = 21
x = 21
The solution of the linear equation is x = 21.
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X-2/5 + 1/2x-3=1 pls solve this
Answer:
44/15
Step-by-step explanation:
[tex]x-\frac{2}{5}+\frac{1}{2}x-3=1 \\ \\ \frac{3}{2}x-\frac{17}{5}=1 \\ \\ \frac{3}{2}x=\frac{22}{5} \\ \\ x=\frac{44}{15}[/tex]
A scout leader is going to pair a new member with one of the fifteen troop members. five of the boys love to go camping ten like to fish three enjoy archery twelve like to go hiking and one boy enjoys carving.what is the probability the new boy will be paired with a boy who does not love camping
The probability of the new boy being paired up with a boy who does not love camping is 2/3 or 66.66%
Total no. of troop members = 15
No. of boys who love camping = 5
No. of boys who love fishing = 10
No. of boys who love archery = 3
No. of boys who love hiking = 12
The boy who enjoys carving = 1
Boys who do not like camping = 1 - 5/15 = 10/15 = 2/3*100 = 66.66%
So, the probability that the new boy will be paired up with a boy who does not love camping is 66.66% or 2/3.
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Write each logarithmic expression as a single logarithm.
log 3+4 log x
The single logarithm of log 3 + 4 log x is = log (3x^4).
What is a logarithmic function?
A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1
Write the given logarithmic expression in a single logarithm. log 3 + 4 log x
Given logarithmic expression is log 3 + 4 log x
Applying given properties of logarithmic function;
log a + log b = log (ab)
2 log a = log a²
Now, log 3 + 4 log x = log 3 + log x^4
= log (3x^4)
Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).
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In the diagram, AngleTRV ≅ AngleVRW.
2 lines intersect. A line with points T, R, W intersects a line with points S, R, V at point R.
What is the measure of AngleSRT?
mAngleSRT =
degrees
The value of the angle SRT using the given parameters is; ∡SRT = 90°
How to find the angle at a point of Intersection?
Collinear points are the points that lie on the same straight line or in a single line. Thus, the points T and W are collinear.
We are told that ∡TRV ≅ ∡VRW. That congruency statement can only be possible if both angles are 90°.
From the above, it means that we can say that;
∡TRV = ∡VRW = 90°
Now since the two lines intersect each other at point R, we can say that;
∡SRT = ∡VRW because they are both vertically opposite angles.
Thus;
∡SRT = 90°
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Answer: 90
Step-by-step explanation:RIGHT ON EDGE 2023
What property was used in step 1 to arrive at step 2? Step 1: 5 (x minus 7) = 55. Step What property was used in step 1 to arrive at step 2? Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18. distributive property addition property of equality subtraction property of equality division property of equality2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18. distributive property addition property of equality subtraction property of equality division property of equalityWhat property was used in step 1 to arrive at step 2? Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18. distributive property addition property of equality subtraction property of equality division property of equalityv
The property which was used in step 1 to arrive at step 2 is: A. distributive property.
What is the distribution property?The distributive property states that when the sum of two (2) or more addends are multiplied by a number, the same output is produced as when each addend is multiplied respectively by the number, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
x(y + z) = xy + xz.
By applying the distributive property of multiplication to step 1, we have:
5(x - 7) = 55.
5x - 35 = 55
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Complete Question:
What property was used in step 1 to arrive at step 2?
Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.
distributive property
addition property of equality
subtraction property of equality
division property of equality
Answer:
A.) Distributive property.
Step-by-step explanation: