Sometimes we are given exponential equations with different bases on the terms. In order to solve exponential functions with different bases we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.
What is exponential equationExponential equation is an equation whose power or base number (base) and power contains a variable.
An example of an exponential equation:
32^x-3 = 81^x+5 → the exponential equation with the power contains the variable x
(2x - 5)^x = (2x - 5)^3x-4 → the exponential equation with bases and powers contains the variable x
So, in the exponential equation, it can only be the exponent that contains the variable or it can also be the base and the exponent that contain the variable. This variable is denoted by a letter, it can be from a to z. But, in general, the variable symbol that is often used in questions is the letter x.
The solution to the exponential equation is the set of all x values that satisfy the exponential equation, or we can also call it a set of solutions. So, how to solve the exponential equation varies depending on the form of the equation. The two examples of equations above are two of several forms of existing exponential equations. This means that there are still other forms of exponential equations and each equation has its own way of solving it
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write 1.1% as a decimal number
Answer:
0.011
Step-by-step explanation:
To convert a percentage into a decimal, simply divide by 100;
Some examples are:
1% = 0.01
5% = 0.05
10% = 0.1
50% = 0.5
N.B. finding a percentage of a number is multiplying by the decimal form, so, e.g. 1.1% of 1000 is:
1000 × 0.011 = 11
Answer:
0.011
Step-by-step explanation:
To convert a percentage to a decimal, you must divide the percentage by the number 100.
Therefore, 1.1% / 100 = 0.011.
(If the question was the other way around and you wanted to turn a decimal into a percentage. All you have to do is the opposite. When you have a decimal multiply it by 100 to get a percentage.)
Hope this helped you!
What is double prime called?
Double prime is called by different names as per the topics used in Mathematics :
Inches in length , second order derivative in differentiation, conjugate points, transformed coordinates etc.
As given in the question,
In Mathematics double prime is represented by ". Double prime is used to represent different types of function as per the topic.Double prime is used to represent the second derivative of the given function in differentiation.Double prime is used to represent the measure of length in inches.Double prime is also used to represent the transformed coordinates in the coordinate geometry.Sometimes double prime also represents the conjugate points.It also represents the number of arc seconds in the measure of any angle.Therefore, the double prime is known by many names such as inches in length, second order derivative, conjugate points, transformed coordinates etc.
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A movie studio keeps 240 dresses in its wardrobe for historical films. Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era.
What percent of the dresses are for films set in the 1700s or during the civil war era? Explain how you found your answer
The percent of the dresses that are for films set in the 1700s or during the civil war era is; 75%
How to find the percentage?Percentage is normally calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by the expression; Percentage = (value / total value) * 100%
Now, we are told that;
Number of movie dresses kept = 240 dresses
Fraction used for movies that take place in the 1700s = 3/5
Percentage used for movies in the civil war era = 15%
Thus;
Number of dresses in the 1700 = 3/5 * 240 = 144
Number of dresses for the civil era = 15% * 240 = 36
Thus;
Total for civil era and in the 1700s = 144 + 36 = 180
Thus;
Percentage for either period = 180/240 * 100% = 75%
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8-2 practice multiplying a polynomial by a monomial
Find each product
1. x(5x + x^2)
2. x(4x^2 + 3x + 2)
Answer:
Skills Practice. Multiplying a Polynomial by a Monomial. Find each product. 1. a(4a + 3). 2. -c(11c + 4). 4a2 + 3a. -11c2 - 4c. 3. x(2x - 5). 4. 2y( y - 4).
Step-by-step explanation:
Help me find the value of Y!
ABCD is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC is 4y-6, and the length of CD is 8y-18, find the value of y.
I know 2 lengths are equal and I know algebra but I just don't know where to start. Please explain it. Sorry there's no diagram
======================================================
Explanation:
You are correct in thinking you'll set two things equal to one another. This type of thing happens often in algebra. The question you probably have is: what two things do I set equal?
The key term is "isosceles" which tells us we have two non-parallel sides equal in this trapezoid. In other words, we ignore the parallel sides.
The non-parallel sides of a trapezoid are known as the legs.
The legs in this case are
AB = 7y-4CD = 8y-18Set those expressions equal to one another and solve for the variable y.
AB = CD
7y-4 = 8y-18
-4+18 = 8y-7y
14 = y
y = 14 is the final answer
----------------------
Check:
AB = 7y-4 = 7*14-4 = 98-4 = 94CD = 8y-18 = 8*14-18 = 112-18 = 94Both legs AB and CD are 94 units long to confirm this trapezoid is indeed isosceles. The answer is confirmed.
Side note: as mentioned earlier, we completely ignore BC = 4y-6. It was probably put in there as a distraction.
How do you make a table of values for an equation?
Prior to selecting an input value range, create the table. Replace each input value with its equivalent in the supplied equation's left-hand column.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.
given
Prior to selecting an input value range, create the table.
Replace each input value with its equivalent in the supplied equation's left-hand column.
The output value can be found by analyzing the equation in the middle column.
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Use the data to complete this statement. Any non-integer answers should be entered as decimals, rounded to the tenths place. The mean of the data set is , and the sample proportion of numbers less than the mean is %.
The mean of the given data set is 21.7 and the sample proportion of numbers less than the mean is 60%.
Consider the given data set (in the image attached to this answer). We have to find the mean of the data set is, and the sample proportion of numbers. We have been told that any non-integer answers should be entered as decimals, rounded to the tenth place. The means is the average of any data set.
Here, mean = (20.5 +24.2 +18.3 + 1.3 +27+25.5 +21+19.8+27.3+18·4 + 20.5+17-6 +25.5 +23.4 +20.2)/15
Mean = 325.5/15 =21.7
The sample proportion of numbers less than
Mean = 9/100 * 15 %
Answer: 21.7 60%
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How do you find the equation of the line of best fit?
A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. For a better understanding of the idea of approximating the equation of a line of best fit and making predictions, we will look at two examples that show a scatter plot with a line of best fit.
What is a line, exactly?
Having only length and no width, a line is a one-dimensional figure. A line is created from a collection of points that are endlessly stretched in the opposing directions.
A two-dimensional plane's two points serve as its determining factors. Collinear points are two points that are located on the same line.
What is the equation for a straight line?
. A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, also known as the y-intercept, and m is the gradient.
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use pascal’s triangle to expand (3s+2)^5
The pascal’s triangle to expand (3s+2)⁵ is 243s⁵ +810s⁴ + 1080s³ + 720s² + 240s + 32.
What is the expanded form of an expression?
Expanded form, also known as expanded notation, is a method of writing numbers that allows you to see the math value of individual digits. When numbers are separated into individual place values and decimal places, a mathematical expression can be formed.
Most people are introduced to Pascal's triangle via a seemingly arbitrary set of rules. Begin with a 1 on top and 1s running down both sides of a triangle. Each new number is located between and below two other numbers, and its value is the sum of the two numbers above it. The theoretical triangle is infinite and continues indefinitely downward, but only the first six lines are shown in figure 1. More rows of Pascal's triangle are shown in the article's final figure. Another way to look at the triangle is to imagine the first line as an infinite sequence of zeros with the exception of a single 1.Add every adjacent pair of numbers and write the sum between and below them to get successive lines. Pascal's triangle is the non-zero part.
Pascal 's triangle is
1
1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
The expanded form of (3s+2)⁵ is
= 1×(3s)⁵×2⁰ + 5×(3s)⁴×2¹+ 10×(3s)³×2² +10×(3s)²×2³ + 5×(3s)¹×2⁴+ 1×(3s)⁰×2⁵
=243s⁵ +810s⁴ + 1080s³ + 720s² + 240s + 32
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Find the smallest positive integer divisible by every positive integer less than or equal to ten.
please could you explain the method to me... i'm pretty confused
Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus. Find the slope of ef and gd.
The slope of ef and gd can be found by using the formula: slope = (y2 - y1) / (x2 - x1) where ef = (x1, y1) and gd = (x2, y2) are the coordinates of the points e and g.
Isosceles Trapezoid Form A RhombusA rhombus is a quadrilateral with all sides equal in length. To prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus, we can use the following properties of an isosceles trapezoid:- The two bases (the parallel sides) are congruent.
- The two legs (the non-parallel sides) are congruent.
- The diagonals of the trapezoid bisect each other.
Using these properties, we can see that:- The midpoints of the legs are congruent, since the legs are congruent.
- The midpoints of the bases are congruent, since the bases are congruent.
- The segments joining the midpoints of the legs and the bases are congruent, since they are both the same distance from the midpoint of the bisected diagonal.
Therefore, the segments joining the midpoints of the sides of an isosceles trapezoid are congruent, and since they are congruent they form a rhombus.The slope of ef and gd can be found by using the formula: slope = (y2 - y1) / (x2 - x1) where ef = (x1, y1) and gd = (x2, y2) are the coordinates of the points e and g.
Since the slope of the line perpendicular to the diagonals of a rhombus is always opposite reciprocal, the slope of ef and gd are opposite reciprocal, which means:the slope of ef = -1/slope of gd.
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What are the rules for substitution?
The rules for substitution are, first simplify the given equation, solve one of the equations for any unknown value, substitute the step 2 solution in another equation, solve the new equation, and finally solve the equation to find the second variable.
The substitution method is the algebraic method to solve different linear equations. In this method, the value of one variable from either of the equation is substituted in the other equation.
The following steps of rules are used to solve an equation by substitution method:
Step 1. Simplify the given equation by removing the parenthesis.
Step 2. Solve one of the equations for any unknown value.
Step 3. Substitute the step 2 solution in the other equation.
Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.
Step 4. Finally, solve the final equation for the second variable.
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HELP PLS RIGJT NOW solve systems of linear Equations
Answer: (5, -2)
Step-by-step explanation:
They give you two equations with two variables. You can solve this using elimination or substitution. However, it seems as though the problem wants you to do it through elimination. On the right, you have the equation
6x + 10y = 10
+ -6x - 24y = 18
After add these equations, you get -14y = 28. By dividing both sides by -14, you get y = -2. You can plug y = -2 back into either one of the original equations, and solve for x.
x = 5.
So your answer is (5, -2)
How do you describe the end behavior of the graph if the degree is odd and the leading coefficient is positive?
The end behavior of a graph with an odd degree and a positive leading coefficient is that the graph will tend to increase infinity as x approaches positive infinity and decrease to negative infinity as x approaches negative infinity.
This end behavior of a graph is due to the fact that when the degree is odd, the leading coefficient acts as a multiplier for the highest degree term, making its contribution to the graph’s y-value the largest and most dominant. For example, if the equation of the graph is y = 4x^3 + x^2 – 7x + 5, then the end behavior of the graph will be increasing to positive infinity as x approaches positive infinity and decreasing to negative infinity as x approaches negative infinity. To calculate this, we can use the equation y = 4x^3. When x = 1000, y = 4,000,000,000. As x increases, y will continue to increase to positive infinity. When x = -1000, y = -4,000,000,000. As x decreases, y will continue to decrease to negative infinity.
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graph the direct variation y=-=1.5x. using the graph find the value of x when y=-3,4,5 and 6
The graph of function y = -1.5x, for x = -3, 4, 5, and 6 is shown.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
y = -1.5x.
Substitute the value of x = -3, 4, 5, and 6.
x = -3
y = -1.5(-3)
y = 4.5
Similarly,
x = 4 ;y = -6
x = 5 ;y = -7.5
x = 6 ;y = -9
Thus, the graph for the value of has been shown,
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How many times would you expect to roll a 5 if you rolled a fair die 300 times? Round your answer, if needed.
A.
0.167
B.
50
C.
17
D.
33
The number of times you would expect to roll a 5 if you rolled a fair die 300 times is B. 50.
We should note that that a fair die has a six sided cube and the number that is on the die faces start from 1 to 6 .
Since each of the die faces consists of a probability of 1/6 now let find the number of times to roll a die.
Expected number of times = 300 × 1/6
Expected number of times = 50
Therefore we can conclude that the expected number of time to rolled the die is B. 50 times.
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If f(x)=4-x^2 and g(x)=6, which expression is equal to (g-f)(3)
The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = 4 - x² and g(x) = 6
The function (g - f)(x) will be given as,
(g - f)(x) = 6 - 4 + x²
(g - f)(x) = 2 + x²
The value of the function (g - f)(x) at x = 3 will be give as,
(g - f)(x) = 2 + (3)²
(g - f)(x) = 2 + 9
(g - f)(x) = 11
The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.
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The area of the curved surface of a cylindrical jar is 1,584 square centimeters. The height of the jar is 28 centimeters. a) What is the circumference of the jar? b) What is the radius of the jar?
please help this is due soon
The circumference of the jar is 56.57cm.
The radius of the jar is 9 cm.
What is the circumference of the jar?A cylinder is a three-dimensional object. It is a prism with a circular base.
The curved surface area of a cylinder = 2πrh
Where:
π = 3.14r = h = 281584 = 2 x 3.14 x 28 x r
r = 1584 / (2 x 3.14 x 28)
r = 9 cm
Circumference = 3.14 x diameter
diameter = 2 x radius
3.14 x 2 x 9 = 56.57cm
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S = a + b + c
Solve for b.
[tex]s=a+b+c[/tex] solve for b
Flip:
[tex]a+b+c=s[/tex]
Add -a to both sides:
[tex]a+b+c+-a=s+-a[/tex]
[tex]b+c=-a+s[/tex]
Add -c to both sides:
[tex]b+c+-c=-a+s+-c[/tex]
[tex]\fbox{b = -a - c + s}[/tex]
Answer:
S - c - a = b or b = S - c - a ( same answer just written differently)
Step-by-step explanation:
S = a + b + c move the unwanted exponents to the other side
S = a + b + c / - c
S - c = a +b / - a
S - c - a = b
how many different digits are used in the hexadecimal number system?
Answer:16
Step-by-step explanation:
what number should be added to 8000 to make it a perfect square
Answer:
100 should be added as 8100 is square root of 90 ...
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
4
Step-by-step explanation:
For this question, the x represent the question mark.
8 + (-4) = x
Since positive plus negative equals negative, we subtract.
8 - 4 = x
x = 4
HELLPPPP ME RIGHT AWAY PLEASE?
Answer: 3 = 12 , 4 = 2 , 2 = 22
Step-by-step explanation: Since t represents the number of tickets purchased, we need to plug that into our equation.
d = -10t + 42
d = -10(3) + 42
We know that d is the balance of the bank account, so if we plug in the number of tickets purchased, we will solve to get the balance of the bank account.
d = -10(3) + 42
d = -30 + 42
d = 12
In this equation, If we purchase 3 tickets, the balance of the bank account would be 12 dollars.
Let's do the last 2 equations using d = -10t + 42.
d = -10(4) + 42
d = -40 + 42
d = 2
In this equation, If we purchase 4 tickets, the balance of the bank account would be 2 dollars.
d = -10(2) + 42
d = -20 + 42
d = 22
In this equation, If we purchase 2 tickets, the balance of the bank account would be 22 dollars.
what is the diameter of the semi circle whose perimeter is 54
Perimeter of a semi circle = ñr + d(2r),ñ=22/7,r=?, d=2r
54=22/7 × r +2r
54=3.142r +2r
54=5.142r
r=54/5.142
r=10.5
d=2r
d=2×10.5017
d=21.00cm
Which expression is equivalent to the given expression?
A.
B.
C.
D.
Answer:
I believe the answer is D
Answer:
D. (2x +1)(x -6)
Step-by-step explanation:
You want the expression that is equivalent to 2x² -11x -6.
ChoicesThere are a couple of ways to go at this. One way is to eliminate the answers that make no sense: A and C. We say these are nonsense because they have an overall factor of 2. The coefficient -11 is not a multiple of 2, so there cannot be such a factor.
If you were to examine the remaining choices (after eliminating A and C), you would find the x-term of the product to be ...
B: 2x(-2) +3(x) = -4x +3x = -x
D: 2x(-6) +1x = -12x +x = -11x . . . . . the expression we're looking for
FactorsIf you were to factor this equation, you would look for factors of 2·(-6) = -12 that have a sum of -11. Of course, those are -12 and 1. This means we can rewrite the equation as ...
2x² -11x -6 = 2x² -12x +x -6
= 2x(x -6) +1(x -6) . . . . . . . factor by grouping (pairs of terms)
= (2x +1)(x -6) . . . . . . . . . . matches choice D.
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which quadrant does the point (2, 3) lie?A I B IIC III D III
The quadrant of the given point (2,3) is given A I ( that is first quadrant ).
As given in the question,
Given point is equal to :
Point ( 2, 3 )
Conditions of the quadrant in the coordinate plane is given by :
Let ( x ,y ) be the coordinates in the coordinate plane.
In the first quadrant : ( x , y ) both x and y are positive.
In the second quadrant : ( -x , y ) x is negative and y is positive.
In the third quadrant : ( -x , -y ) x is negative and y is negative.
In the fourth quadrant : ( x , -y ) x is positive and y is negative.
Here in the given point ( 2,3 ) both x and y are positive.
Given point lies in the first quadrant.
Therefore, the quadrant of the given point (2,3) is equal to A I ( that is first quadrant ).
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What is the exponential form of 12?
Exponential form of 12 is 2. 2. 3. It is based on the prime factorization of the number.
Exponential form is a mathematical operation written as [tex]a^{n}[/tex] involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times.
[tex]a^{n}[/tex] = a × a × a.... n times
In order to write the exponential form we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. The exponential form is an easier way of writing repeated multiplication involving base and exponents.
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Breanna bikes 84 miles in 6 hours at a constant rate. The formula d = rt gives the relationship between distance (d), rate (r), and time (t). At what rate was Breanna biking?
Breanna was biking at a constant rate of 14 miles per hour.
What does rate means?A rate can be defined as the speed at which something happens or changes or the amount or number of times it happens or changes in a particular period.
The formula that describes the relationship between distance (d), rate (r), and time (t) is d = rt.
Now, we will solve for r. From d = rt. Our r will equals to:
= d/t.
Now we compute the rate at which Breanna was biking.
= 84 miles/6 hours
= 14.
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Y=3/4x+3 I’m so confused on how to graph the and solve it please helpp
In Y=3/4x+3 the Slope is 3/4, the Y-intercept is (0,-3) and the usual form is 3x4y=12. , which does not have a conic section. as opposed to asymptotes.
How to draw a graph ?
Use the slope and y-intercept, or two points, to graph the line. 3 / 4 of a slope; y-intercept: (0,-3) Write in formal language. 3 x-4 y=12 Discover the negative reciprocal of the original line's slope.
[tex]$$m_{\text {perpendicular }}=-\frac{4}{3}$$[/tex]
In order to identify the periods during which the equation is increasing or decreasing, graph it. Continued Growth There are no asymptotes since the equation Y=3/4x+3 is not a reasonable expression. There are no asymptotes. Any conic section's form is not compatible with the equation. Not a Conic Section.This subject can't be explored any further. Please double-check the supplied phrase or select a different subject.
[tex]$$y={3}/{4} x-3$$[/tex][tex]$$y={3}/{4} x+3$$[/tex]
Identify the y-intercept = b , y = mx + b. Plot the y-intercept. The focus will be (0, b). Calculate the slope=m of the equation y = mx + b. Create a single step utilizing the rise and run from the slope. Connect those two places with your line.
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How many solutions does -3=2x²-8x+8 have
The quadratic equation has two solutions, x1 = 3.44 and x2 = 0.56
What are Quadratic equations?Quadratic equations are the ones with degree 2. The standard form of a quadratic equation with variable x is ax2 + bx + c = 0, where a ≠ 0. These equations can be solved by splitting the factorisation, completing the square, or by quadratic formula method.
2x²-8x+8 = -3
2x²-8x+8+3 = 0
2x²-8x+11=0
Using the quadratic formula
x = (- b ± √(b² - 4ac)) / 2a
where a = 2
b = -8
c = 11
x = (-(-8) ± √(11² - 4(2)(11))) / 2(2)
x = (8 ± √(121 - 88)) / 4
x = (8 ± √(33))/4
x 1 = (8 + √(33))/4
x1 = (8 + √(33))/4
x1 = (8 + 5.75)/4
x1 = 13.75 / 4
x1 = 3.44
x2 = (8 - √(33))/4
x2 = (8 - 5.75)/4
x2 = 2.25/4
x2 = 0.56
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