Answers
Using the above exponent rule, the value of t in the given equality [tex]5^3/ 5^9 = 5^t[/tex] will be t = -6.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
WE need to find the value of t in the given equality 5^3/ 5^9 = 5^t
Using the above exponent rule, we get
[tex]5^{3 -9 }= 5^t\\\\5^{-6}= 5^t[/tex]
Therefore, compairing both the side we get;
t = -6.
Hence the value of t in the given equality[tex]5^3/ 5^9 = 5^t[/tex]will be t = -6.
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Related Questions
Calculate the number of 10 cm lengths of string that can be cut
from a 5m ball of string.
Answers
The string can be cut into 50 pieces of 10 cm length.
What is length in mathematics?Length is a measurement of how long an object is or the distance between two points. Length is the term used to identify the size of an object or the distance from one point to another. It can be used to determine an object's size or the distance between two points.
A measurement of length is the distance between two locations or the length of an item. The term "length" is used to describe an object's size or the separation between two points. It may be used to calculate the size of an item or the separation between two places. Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measuring systems choose a base unit for length from which all other units are derived.
Centimeters, meters, kilometers, inches, feet, and yards are some examples of conventional units used to measure length.
1 m = 100 cm
so, no. of pieces = 500/10 = 50.
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Answer: 50 pieces
Step-by-step explanation:
First, we need both of the measurements to be in the same unit.
5 m ➜ 500 cm
Next, we will use division to see how many 10 cm pieces of string can be cut.
500 cm / 10 cm = 50 pieces
Please help me please help me
Answers
Step by step
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
This means your x and y change to the opposite sign
Our point N (-1,-2) becomes ( 1, 2)
Our point K ( 3, 0) becomes ( -3, 0)
Our point P ( 1, 4) becomes ( -1, -4 )
Our point F ( -4, 2) becomes ( 4, -2)
I graphed it for you and attached
18
Kylie recorded the number of pears on a pear tree at the end of every week. The following function represents the number of pears on
the pear tree, where x represents the number of weeks.
Which statement is true?
A. The number of pears on the tree doubles each week.
B.
P(x) = 2(2+x)
O D.
The number of pears on the tree increases by 2 each week.
OC. The number of pears on the tree quadruples each week.
The number of pears on the tree increases by 4 each week.
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Answers
Based on the given function on the number of pears on the pear tree, the true statement is that The number of pears on the tree increases by 2 each week.
How to find the meaning of function?A linear regression line takes the form:
y = mx + b
y = number of pears
m = change in the number of pears per week
x = number of weeks
b = number of pears at first week
When the function is converted to a linear regression form, it takes the form:
P(x) = 2(2+x)
P(x) = 4 + 2x
This shows that the change in the number of pears per week is 2. This means that the number of pears on the tree increases by 2 each week
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Can anybody answer and simply this. (-8) × (-6)-(-5)²
Answers
Step-by-step explanation:
[tex] = - 8( - 6) - (25) \\ = 48 - 25 \\ = 23[/tex]
HOPE THIS HELPS!!
SR = 18cm, Given that SR:CD = 3:4 Find The Value of the Ratio
Answers
The value of the ratio is CD = 24 cm
How to Find The Value of the Ratio?The given parameters are
SR : CD = 3 : 4
SR = 18 cm
Substitute SR = 18 cm in the ratio SR : CD = 3 : 4
So, we have
18 cm : CD = 3 : 4
Express the ratio as a fraction
So, we have
18 cm/CD = 3/4
This gives
CD = 18 cm * 4/3
Evaluate
CD = 24 cm
Hence, the value of the ratio is CD = 24 cm
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Laura can make six flower arrangements in 25 minutes if she makes a 18 flower arrangements how many minutes will it take her
Answers
Answer:
75 flowers
Step-by-step explanation:
she needs to make 18 arrangements, so we divide 18 by 6 and get 3. 3 * 25 is 75 so the answer is 75.
Laura will arrange 18 flowers within 75 minutes of the time.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Laura can make six flower arrangements in 25 minutes if she makes 18 flower arrangements. The time will be calculated as,
Time = ( 25 x 18 ) / 6
Time = 25 x 3
Time = 75 minutes
Hence, it will take 75 minutes to arrange 18 flowers.
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Use natural logarithms to solve each equation.
ex/₂=5
Answers
3.22 approx. is the value of x in equation [tex]e^{\frac{x}{2}[/tex] = 5 solved by using natural logarithms
We have been asked to find x in [tex]e^{\frac{x}{2}[/tex] = 5 using natural logarithms
⇒ [tex]e^{\frac{x}{2}[/tex] = 5
⇒ [tex]\frac{x}{2}[/tex] = ㏑(5)
⇒ x = ㏑(25)
= 3.22 approx.
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^{\frac{x}{2}[/tex] = 5
numbers like 2%, 3%, 4% and 6% are often used to represent the grade of a road. such a number tells how steep a road is. 3% grade means that for every horizontal distance of 100 ft, the road rises or descends 3 feet. in each of the following cases, find the road grade to two decimal places.
Answers
(a) Grade = 2.86%
(b) Grade = 5.85%
What is the horizontal distance?The projectile's horizontal range is the distance it travels while in flight. Since there is no acceleration in the horizontal direction, the greatest distance traveled in the horizontal direction is what this definition means.Vertical distance is the distance following the direction of gravity, and horizontal distance is the distance along the ground surface. The distance between a building and the observer is an example of a horizontal distance, and the building's height is an example of a vertical distance.Anything that forms a 90-degree angle (right angle) with the horizontal or the horizon is referred to as vertical because it is the opposite of the horizontal. The line that spans from left to right is therefore considered horizontal.By the angle's tangent, multiply the object's height. Let's assume, for the purposes of this illustration, that the item is 150 feet tall. The product of 150 and 1.732 is 86.603. 86.603 feet separate you from the thing horizontally.Find the road grade to two decimal places:
Grade in terms of percentage = (rise/run) * 100%
(a) Grade = (40/1400) * 100% = 2.86%
(b) Grade = 5.85%
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Given P(-3, 9), Q(8,-2), R(-8, 8), and S(0, y). Find y such that PQ || RS.
Answer: y
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the PQ line
[tex]P(\stackrel{x_1}{-3}~,~\stackrel{y_1}{9})\qquad Q(\stackrel{x_2}{8}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{-11}{8 +3}\implies -1[/tex]
if indeed RS || PQ, then their slopes are exactly the same, thus
[tex]R(\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad S(\stackrel{x_2}{0}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-8)}}} \implies \cfrac{y -8}{0 +8}~~ = ~~\stackrel{\stackrel{slope}{\downarrow }}{-1} \\\\\\ \cfrac{y-8}{8}=-1\implies y-8=-8\implies \boxed{y=0}[/tex]
When a number is decreased by 10% of itself, the result is 81, what is the number?
Answers
The number is 90.
What is the number?
Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %. Percentages are a measure of frequency.
When the number is decreased, the number becomes smaller. This means that the original number is larger than 81.
The equation that can be used to represent the information in the question is:
(1 - percentage decrease) initial number = 81
(1 - 0.1)x = 81
0.9x = 81
x = 81 / 0.9
x = 90
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Simplify the expression to a polynomial in standard form
(x+6)(3x² + 4x − 3)
Answers
Answer:
3x^3 -8*x^2 + 8*x + 3
Step-by-step explanation:
The standard form for a plolynomial is:
a*x^n + b*x^(n-1) + c*x^(n - 2) ........
We have:
(x-1)(3x^2-5x-3)
this is equal to:
3*x^3 - 5*x^2 + 3*x - 3*x^2 +5*x + 3
where the thing that i did is distribute the multiplication
this is equal to:
3x^3 -8*x^2 + 8*x + 3
Solve the following radical equations.
√(x+3) = 4√x-2
Answers
The solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.
The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
Eliminate the radical on the both sides by squaring on both sides-
Both sides must be raised to the second power.
√(x+3) ²=(4√x-2 )²
After squaring we get
x+3=16(x-2)
Solving the equation-
We get rearranged equation as :
x+3=16x-32
15x=35 x=35/15 which further reduces to 7/3 .
Check if the solution is correct by putting it in original equation-
putting x=7/3 in the equation √(x+3) = 4√x-2
we get √16/3=√16/3
Therefore, the solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.
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Simplify each expression.
ln e
Answers
ln (e) = 1, by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]
In case of natural logarithm, b = e, i.e., [tex]log_e(a)=x[/tex] = ln (a) = x
In the given expression, a = e
Hence, ln (e) = x
By properties of logarithms, we get that: ln (e) = 1.
Hence, ln (e) = 1, by the properties of logarithm.
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Expand each binomial.
(x+4)⁸
Answers
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (x+4)⁸ is expanded as x⁸ + 32x⁷ + 448x⁶ + 3584x⁵ + 17920x⁴ + 57344x³ + 114688x² + 131072x + 65536
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.
Let the expression be (x + 4)⁸
Use the binomial expansion theorem to find each term. The binomial theorem states
(a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0nnCk⋅(an-kbk).
8∑k=08!(8−k)!k!⋅(x)8−k⋅(4)k∑k=088!(8-k)!k!⋅(x)8-k⋅(4)k
Expand the summation
8!/(8−0)!0!.(x)⁸⁻⁰⋅(4)⁰+8!/(8−1)!1!(x)⁸⁻¹⋅(4)¹+…+8!/(8−8)!8!(x)⁸⁻⁸⋅(4)⁸
Simplify the exponents for each term of the expansion.
1⋅(x)⁸⋅(4)⁰+8⋅(x)⁷⋅(4)1+…+1⋅(x)⁰⋅(4)⁸¹⋅(x)⁸⋅(4)⁰+8⋅(x)⁷⋅(4)¹+…+1⋅(x)⁰⋅(4)⁸
Simplify the polynomial equation, we get
x⁸ + 32x⁷ + 448x⁶ + 3584x⁵ + 17920x⁴ + 57344x³ + 114688x² + 131072x + 65536
Therefore, by expanding the binomial equation, we get
(x + 4)⁸ = x⁸ + 32x⁷ + 448x⁶ + 3584x⁵ + 17920x⁴ + 57344x³ + 114688x² + 131072x + 65536
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help me please!!! will mark brainliest!!
Answers
Answer:
2
Step-by-step explanation:
(0,2) is the y-intercept
a. An undefined term is a term that has been given no formal definition. In geometry, there are three undefined terms that form the basis for the subject. What are those three undefined terms? Do your best to define those terms.
Answers
The three undefined terms that form the basis for geometry are:
- Point
- Line
- Plane
What is undefined?The term undefined is often used to refer to an expression that is not assigned an interpretation or a value.
The main three undefined terms of geometry are:
- Point
In geometry, a point has no dimension.
A point is represented by a dot.
The point has no length, width, or thickness.
A dot can be very tiny or very large.
- Line
A line is a straight one-dimensional figure that has a length but does not have a thickness, and it extends endlessly in both directions.
A line is made of a set of points that is extended in opposite directions infinitely.
- Plane
A plane, in geometry, prolongs infinitely in two dimensions.
It has zero thickness, zero curvature, infinite width, and infinite length.
It is also known as a two-dimensional surface.
Thus,
The three undefined terms that form the basis for geometry are:
- Point
- Line
- Plane
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You are given that f(x)=x²+4 and g(x)=3 x-1 .
a. What are the domain and range of f(x) and g(x) ?
Answers
The domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .
Domain : The set of all the possible values of x is called domain of the function .
Range : The set of all the possible values of y is called the range of the function .
Given : f ( x ) = [tex]x^{2}[/tex] + 4 , g ( x ) = 3 x - 1 .
To find : Domain and Range of functions .
f ( x ) = [tex]x^{2}[/tex] + 4
Domain = R ( real nos. )
Range = y ≥ 4 .
g ( x ) = 3 x - 1
Domain = R ( real nos. )
Range = R ( real nos. )
Therefore , the domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .
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does anyone know how to do this question?
Answers
The diameter of the given sphere is; 39.5 cm
What is the Volume of the Sphere?
The formula for Volume of Sphere is;
V = 4/3 πr³
where;
V is volume
r is radius
We are given; V = 32250 cm³
Thus;
4/3 πr³ = 32250
Make r the subject of the formula to get;
r = ∛((32250 * 3/4)/π)
r = ∛7699.12
r = 19.75 cm
Now, radius * 2 = diameter
Thus; diameter = 2 * 19.75 = 39.5 cm
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You are ready to spend your Christmas money! You go to your
favorite store and buy some jewelry. They are running a sale where
everything is $10! You got $130 for Christmas and don't have any
more than that to spend.
Write an inequality to represent how many pieces of jewelry (j)
you can buy.
Answers
Answer:
[tex]10j \leqslant 130[/tex]
[tex]j \leqslant 13[/tex]
I need an example of a multi step equation, solved, showing every possibility.
PLEASE lots of points and will give brainliest!!!
Answers
Answer:
Step-by-step explanation:cevap çok basit cevap eşittir cevap yani çok basit
Answer:
3^x=x^(x/3)
3^(3*x)=x^(3*x/3)
3^(3x)=x^x
(3^3)^x=x^x
27^x=x^x
27^(x*1/x)=x^(x*1/x)
27^(x/x)=x^(x/x)
27^1=x^1
x=27
Step-by-step explanation:
What is the common difference in this recursive equation?
GIVING BRAINLIEST
look at the picture i attached :)
Answers
The common difference for the recursive equation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5 is 5.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The recursive equation:
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5
and [tex]a_{1}[/tex] = -3
We can find the consecutive term using the recursive equation.
[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + 5 = -3 + 5 = 2
[tex]a_{3} =a_{2}[/tex] + 5 = 2 + 5 = 7
The sequence we get is:
-3, 2, 7, 12,....
The common difference means the differences in between two consecutive terms.
2 - (-3) = 5
7 - 2 = 5
12 - 7 = 5
Thus the common difference is 5.
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Johnny signs up for a cell phone plan that his
parents require him to pay. His bill each
month is $37.28. What impact will his cell
phone bill have on his savings account over
the next 6 months?
Answers
Answer:
He has to pay $223.68 after 6 months
Step-by-step explanation:
I don't know if I understood you right but I think you meant how much does he have to pay in 6 months. That would be 37.28x6=223.68
The number below is not correctly written in scientific notation.
281 × 104
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
2.81 × 10?
Write the new exponent value in the blank below.
Answers
Answer:
Step-by-step explanation:
30.466666.999
2.81*10^4
the number of times you move the decimal adds to the exponent
Solve each equation.
2y+1=25
Answers
Solution of this polynomial equation is y = 12
What is a polynomial ?In mathematics, simply polynomial or polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2y+52 x + 1 =253x² + 5x+19(x-3)³According to question,
2y+1=25
=> 2y +1 -1 = 25-1
=> 2y = 24
=> y = 12
Thus solution for given equation is y=12.
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Can I have answer to this question please?
Answers
Given the data in the table, the slope, y-intercept and equation of the table are 1/3, (0,-2), and y = (1/3)x - 2 respectively.
What is the slope, y-intercept and slope-intercept form?Given that;
x y
-3 -3
0 -2
3 -1
6 0
9 1
Slope m = rise/run = (y₂ - y₁)/(x₂-x₁)
Using the, the points (-3,-3) and (0,-2) from the table
x₁ = -3y₁ = -3x₂ = 0y₂ = -2Slope m = rise/run = (y₂ - y₁)/(x₂-x₁)
Slope m = rise/run = ((-2) - (-3)) / ( 0 - (-3) )
Slope m = 1/3
To determine the y-intercept b, use the formula for equation of line.
y = mx + b
Substitute in Point( -3,-3 ) and m = 1/3 and solve for b
y = mx + b
-3 = (1/3)(-3) + b
-3 = -3/3 + b
-3 = -1 + b
b = -3 + 1
b = -2
Hence the y-intercept in point form is (0,-2)
The equation of the line in slope-intercept form will be;
y = mx + b
y = (1/3)x + (-2)
y = (1/3)x - 2
Given the data in the table, the slope, y-intercept and equation of the table are 1/3, (0,-2), and y = (1/3)x - 2 respectively.
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i will give 25 points A large company receives about 189 calls an hour. If the receptionist works a 45 hour week, about how many calls will she answer?
Answers
The receptionist will answer 8505 calls
Find the value of the missing angle. Remember the figure is not drawn to scale.
Answers
Answer:
Step-by-step explanation:
hey Can u help me answer this question ? The way you use your money reveals your true priorities. Knowing that, how could having budget categories help you prioritize your money ?
in 2012 the total value of exports from the United States was $2,210,585,000,000 that year sports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012
Answers
The required value of sports imports of the United States in 2012 is $2,745,240,000,000.
.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
the total value of exports from the United States in 2012 = $2,210,585,000,000
Now it is also given that,
the total value of exports from the United States in 2012 = $837,965,000,000 more than half of the US imports
Therefore, we can write
the total value of exports from the United States in 2012 = $837,965,000,000 + imports/2
Putting the value of exports we get,
2,210,585,000,000 = 837,965,000,000 + imports/2
Taking alike terms together we get,
Imports/ 2 = 2,210,585,000,000 - 837,965,000,000
Solving we get,
Imports/ 2 = 1,372,620,000,000
Multiplying by 2 both the side by 2 we get,
Imports = 2,745,240,000,000
Thus, the value of imports of the United States in 2012 = $2,745,240,000,000
Thus, the required value of imports of the United States in 2012 is $2,745,240,000,000.
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The correct question is :
in 2012 the total value of exports from the United States was $2,210,585,000,000 that year exports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012
PLEASE HELP!THIS IS DUE TODAY!I REALLY NEED ANSWERS!
Answers
The solutions to the equations are:
A. b = ac² (dark green); b = 2
B. v = m - k (light blue); v = 5
C. p/q = r/s; q = 8
D. m = 3n/4 (red); m = 6
E. x = y(w + z) (light green); x = 10
F. d1 = 2m - d2 (dark blue); d1 = 7
G. s = 8r/9 (purple); s = 4
H. w = [tex]\sqrt{\frac{x - y}{v} }[/tex] (orange); w = 3
I. x = [tex]\frac{y - y_1 }{m} + x_1[/tex] (pink); x = 1
J. c = 5a - 7 (brown); c = 9
How to Solve and Evaluate Equations?To solve for a variable in an equation, we need to isolate the variable to one side of the equation.
A. a = b/c²
a(c²) = b/c²(c²) [multiplication property of equality]
ac² = b
b = ac² (dark green)
Substitute a = 1/8 and c = 4 into the equation
b = (1/8)(4²)
b = (1/8)(16)
b = 2
B. m - v = k
m - v - m = k - m [subtraction property]
-v = k - m
v = -k + m
v = m - k (light blue)
Substitute k = -7 and m = -2 into the equation
v = -2 - (-7)
v = -2 + 7
v = 5
C. p/q = r/s
Cross multiply
qr = ps
qr/r = ps/r [division property]
q = ps/r (yellow)
Substitute k = -7 and m = -2 into the equation
q = (14)(-4)/-7
q = 8
D. 4m + 2n = 5n
4m + 2n -2n = 5n - 2n [subtraction property]
4m = 3n
4m/4 = 3n/4 [division property]
m = 3n/4 (red)
Substitute n = 8 into the equation
m = 3(8)/4
m = 6
E. w = x/y - z
w + z = x/y - z + z [addition property]
w + z = x/y
y(w + z) = x/y(y) [multiplication property]
y(w + z) = x
x = y(w + z) (light green)
Substitute w = -8, y = -5, and z = 6 into the equation
x = -5(-8 + 6)
x = -5(-2)
x = 10
F. m = 1/2(d1 + d2)
2m = d1 + d2 [multiplication property]
2m - d2 = d1 [subtraction property]
d1 = 2m - d2 (dark blue)
Substitute m = 10 and d2 = 13 into the equation
d1 = 2(10) - 13
d1 = 20 - 13
d1 = 7
G. 2r = 5s/2 - s/4
2r = (10s - s)/4
2r = 9s/4
2r(4) = 9s/4(4) [multiplication property]
8r = 9s
8r/9 = 9s/9 [division property]
8r/9 = s
s = 8r/9 (purple)
Substitute r = 9/2 into the equation
s = 8/9(9/2)
s = 4
H. vw² + y = x
vw² + y - y = x - y
vw² = x - y
vw²/v = (x - y)/v
w² = (x - y)/v
w = [tex]\sqrt{\frac{x - y}{v} }[/tex] (orange)
Substitute v = 5, x = 38, y = -7 into the equation
w = [tex]\sqrt{\frac{38 - (-7)}{5} }[/tex]
w = √9
w = 3
I. [tex]y - y_1 = m(x - x_1)[/tex]
[tex]\frac{y - y_1 }{m} = x - x_1\\\\\frac{y - y_1 }{m} + x_1 = x[/tex]
x = [tex]\frac{y - y_1 }{m} + x_1[/tex] (pink)
Substitute x1 = 9, y = 19, y1 = -5, and m = -3 into the equation
x = (19 - (-5))/-3 + 9
x = -8 + 9
x = 1
J. 2a + 3c = 17a - 21
2a - 17a = -3c - 21
-15a = -3c - 21
-15a + 21 = -3c
-15a/-3 + 21/-3 = -3c/-3
5a - 7 = c
c = 5a - 7 (brown)
Substitute a = 16/5 into the equation
c = 5(16/5) - 7
c = 16 - 7
c = 9
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If x^2 + x = 1
what is (x^5 + 8)/ x+1
Answers
The value given expression of (x⁵ + 8)/(x + 1) is (x⁶ + 8x).
What is termed as indices/index?In mathematics, an index (indices) is the power but rather exponent raised to the a number or variable. In number 2⁴, for example, 4 is the index of 2. Indexes is the plural form of index. We encounter constants and variables in algebra. A constant is just a value that cannot be altered. A variable quantity, on the other hand, can be assigned such a number or have its value changed.The given expression is-
(x⁵ + 8)/(x + 1) .......equation 1
It is stated that;
x² + x = 1
Taking x common;
x(x + 1) = 1
Bring x on the other side.
(x + 1) = 1/x
Put the value of (x + 1) in equation 1.
= (x⁵ + 8)/(x + 1)
= (x⁵ + 8)/[1/x]
Simplifying;
= (x⁵ + 8)x
Multiplying x on both values;
= x⁵x + 8x
= x⁶ + 8x
Thus, the value of the given expression is (x⁶ + 8x).
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