Using the change of base formula the evaluated value of [tex]log_{3} 33[/tex] is 3.184
Change of base formula is used to change the base of logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.
According to the change of base formula :
[tex]log_{a} b = \frac{log_{x} b}{log_{x} a}[/tex]
where base x is base 10
According to the question, we have to find the value of [tex]log_{3} 33[/tex]
Thus applying change of base formula we get
[tex]log_{3} 33 = \frac{log_{10} 33}{log_{10} 3}[/tex]
calculating the value of log from the calculator we get,
[tex]log_{3} 33 = \frac{1.519}{0.477}\\log_{3} 33 = 3.184[/tex]
Thus using the change of base formula the evaluated value of [tex]log_{3} 33[/tex] is 3.184
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Write each equation in logarithmic form. 2⁻³=0.125
[tex]log_{2} ( 0.125) = -3[/tex] is exponential equation in logarithmic form.
How can you tell whether an exponential function is growing or deteriorating?
As the exponential's base is greater than 1, which occurs when those numbers increase, we are seeing exponential growth. When the exponential's base is between 1 and 0, and those numbers decrease, we have exponential decay.Convert the exponential equation to a logarithmic equation using the logarithm base (2) of the right side ( 0.125) equals the exponent
( -3 )
[tex]log_{2} ( 0.125) = -3[/tex]
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Tarini took a math quiz. For each incorrect question, she lost 2 points. If Tarini got 5 questions incorrect, how many points did she lose? Represent your answer as an integer.
Answer: She lost 10 points
Step-by-step explanation:
She loses 2 points per the wrong answer. Therefore, do 2 times 5. That gives you ten.
An integer is just a positive whole number btw!
I hope this helps!
evaluate the expression for the given value of the variable
please show work [tex]|-4b-8|+|-1-b^2|+2b; with b=-3[/tex]
The value of the expression when b = -3 is 24
What are functions?Functions can be defined as expression, rules or law that explains the relationship between two variables:
A dependent variablesAn independent variableIt is also important to note that the absolute value of a number is the distance of the number from zero irrespective of its direction in a number line.
Absolute value of a number must take a positive sign.
It is denoted with the symbol '| | '
Given the expression;
| -4b - 8 | + | -1 - b²| + 2b
Substitute the value of b as -3
We have;
|-4(-3) - 8| + |-1 - (-3)²| + 2(-3)
expand the bracket
|-12-8| + |-1 - 9| - 6
Take the absolute values
20 + 10 - 6
24
Thus, the value of the expression when b = -3 is 24
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Use this Distant vs time graph to answer the questions:
1. What measurement is represented on the x-axis and what unit is it measured in?
2. What measurement is represented on the y-axis and what unit is it measured in?
3. Hours 0-4 (Section A) the person is traveling away from their starting location. How far do they travel in those 4 hours? Remember to include units.
4. What is their rate of change (speed) in Section A? Remember to include units.
5. What is happening in Section B (Hours 4-6)?
6. What is the rate of change (speed) in Section B? Remember to include units
7. How far did this person travel in Section C (Hours 6-7)? Remember to include units.
8. What is their rate of change (speed) in Section D (Hours 7-10)? Remember to include units.
9. During which section was the person moving at the highest speed? What was their speed? Defend your answer.
10. During which section did the person travel the farthest? How far did they travel?
11. BONUS: Write a short (paragraph) scenario that tells the story about where the data on the graph came from. You can be as creative as you want!
Using the piecewise function graphed in this problem, we have that:
1. The x-axis represents the time in hours.
2. The y-axis represents the distance in miles.
3. The person traveled 30 miles in those 4 hours.
4. The person traveled at a rate of 7.5 miles per hour in Section A.
5. In section B, the person remained stopped 30 miles from her starting point for 2 hours.
6. The velocity for Section B was of 0 miles per hour.
7. The person traveled 30 miles in Section C.
8. 8. The speed in Section D was of 20 miles per hour.
9. The person was moving at the highest speed in Section C, at a rate of 30 miles per hour.
10. The farthest distance traveled was of 60 miles in Section D.
11. A person had an appointment 30 miles away from their home, and due to slow traffic had to leave early. Then the appointment lasted 2 hours, then the person went to another place 30 miles away to do something then came back home.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
From the graph, the function has four different definitions, in intervals, A, B, C and D.
From the axis of the graph, we have that:
1. The x-axis represents the time in hours.
2. The y-axis represents the distance in miles.
Considering that the graph has points (0,0) and (4,30), we have that:
3. The person traveled 30 miles in those 4 hours.
The velocity is given by distance divided by time, hence:
30/4 = 7.5.
4. The person traveled at a rate of 7.5 miles per hour in Section A.
In Section B, the person remains at the same position, hence:
5. In section B, the person remained stopped 30 miles from her starting point for 2 hours.
The distance was of 0, hence:
6. The velocity for Section B was of 0 miles per hour.
In Section C, from the y-axis of the graph, the distance traveled was:
60 - 30 = 30 miles.
7. The person traveled 30 miles in Section C.
For Section D, the person traveled 60 miles in 10 - 7 = 3 hours, hence:
60/3 = 20.
8. The speed in Section D was of 20 miles per hour.
10. The farthest distance traveled was of 60 miles in Section D.
In Section C, the person traveled 30 miles in one hour = 30 miles per hour, hence:
9. The person was moving at the highest speed in Section C, at a rate of 30 miles per hour.
For item 11, a situation that can be modeled is:
A person had an appointment 30 miles away from their home, and due to slow traffic had to leave early. Then the appointment lasted 2 hours, then the person went to another place 30 miles away to do something then came back home.
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11. Intervals. Given the intervals I₁ = (2.5, 5.5], 1₂ =[3, 6], 1,=[5.5, 7] and I₁ = (5.5, 10]. Find
(a) I, or 1₂ or 1₂ =
(c) I, and I, =
(b)
(d)
I, and I₂ =
I, and I₁ =
12. Intervals.
1) Given the interval (1.5, 3.5). Find (a) the middle point:
13. Equations. Solve the following equations:
(b) the width (length):
2) Find the interval for which the middle and the width are equal to 2 and 6, respectively:
The interval of I₁ or I₂ or I₄ is (2.5 ,10].
The interval of I₁ and I₂ is [3 , 5.5] .
The interval of I₁ and I₃ is [5.5]
The interval of I₁ and I₄ is (5.6 , 7]
In arithmetic, a (real) interval could be a set of real numbers that contains all real numbers lying between any 2 numbers of the set.For instance, the set of numbers x satisfying zero zero x ≤ one is associate degree interval that contains zero, 1, and every one numbers in between.(a) because the all 3 intervals square measure connected by or which suggests they're going to all embrace the quantity lying from interval one to three and is given by (2.5 ,10].
(b) because the interval square measure connected by and which suggests the common numbers lying in interval one and a couple of and is given by [3 , 5.5] .
(c) because the interval square measure connected by and which suggests the common numbers lying in interval one and three and is given by [5.5]
(d)As the interval square measure connected by and which suggests the common numbers lying in interval one and four and is given by (5.6 , 7] .
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The complete question is given below :
Given the intervals I₁ = (2.5, 5.5], I₂ =[3, 6], I₃=[5.5, 7] and I₄ = (5.5, 10]. Find
(a) I₁ or I₂ or I₄
(b) I₁ and I₂
(c) I₁ and I₃
(d) I₁ and I₄
Joseph buys a subway pass for $55. Every time he rides the subway, money is deducted from the value of the pass. He rode the subway 5 times and $40 was deducted from the value of the pass. How much was deducted from Joseph's account for each ticket? Write a mathematical expression to represent this situation; then find the answer.
The amount deducted from Joseph's account for each ticket is $8
The mathematical expression representing the situation is:15=55-5x
What is the total amount deducted from the subway pass?
On the premise that Joseph's subway pass was deducted each time he passes through the subway and that $40 was deducted in all for his number of passes, the total cost of $40 can be modeled into an equation as shown below:
amount left after the deductions=55-40
amount left after the deductions=15
15=total amount paid-(number of passes*cost per subway pass)
total amount paid=55
number of passes=5
cost per subway=x
15=55-5x
5x=55-15
5x=40
x=40/5
x=$8
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17/60/17/3+(5/2-21/3*5/7)*(13*5/26+1/2)
[tex] \implies - \frac{149}{20} \\ [/tex]
Step-by-step explanation:[tex] \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21}{3} \times \frac{5}{7} )( \frac{13 \times 5}{26} + \frac{1}{2} )\\[/tex]
According to the Bodmas rule,
B stands for BracketO stands for orderD stands for DivisionM stands for MultiplicationA stands for AdditionS stands for SubtractionAccording to the question,
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21}{3} \times \frac{5}{7} )( \frac{13 \times 5}{26} + \frac{1}{2} ) \\[/tex]
[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21 \times 5}{3 \times 7} )( \frac{65}{26} + \frac{1}{2}) \\ [/tex]
[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{105}{21} )( \frac{65}{26} + \frac{1}{2}) \\ [/tex]
[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{(21 \times 5 )- (2 \times 105)}{42} )( \frac{(1 \times 65 ) + (13 \times 1)}{26} ) \\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{105 - 210}{42})( \frac{65 + 13}{26} ) \\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {105}{42})( \frac{78}{26} ) \\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {105 \times 78}{42 \times 26})\\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {8190}{1092})\\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} - \frac {8190}{1092}\\ [/tex]
[tex] \implies \frac{17}{60} \times \frac{3}{17} - \frac{8190}{1092} \\ [/tex]
[tex] \implies \frac{17 \times 3}{60 \times 17} - \frac{8190}{1092} \\ [/tex]
[tex] \implies \frac{51}{1020} - \frac{8190}{1092} \\ [/tex]
[tex] \implies \: \frac{(91 \times51) -(85 \times 8190) }{92820} \\ [/tex]
[tex] \implies \: \frac{4641 -696150 }{92820} \\[/tex]
[tex] \implies \: - \frac{691509 }{92820} \\[/tex]
[tex] \implies \: - \frac{691509 \div 4641 }{92820 \div 4641} \\[/tex]
[tex] \implies - \frac{149}{20} \\ [/tex]
Appropriate tools o bought 4 stamps each week for 3 weeks. he wants to put amps on each page of his album. how many pages will niko use? tell how you can use tools to help solve the problem. choose a tool to represent the problem. explain why you chose that tool. solve the problem. explain how you used the tool you chose
ud7e7urfueitsisurwo6krwowi5ai6woaowi5
Solve each equation. Check your answers.
log 6 x-3=-4
log (6x) - 3 = -4 => x = 0.167, by 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,
log (6x) - 3 = -4 => log (6x) = -1
Since the base of the logarithm taken generally is 10, raising both the sides by 10:
[tex]10^{log_{10}(6x)}=10^{-1}[/tex]
=> 6x = [tex]\frac{1}{10}[/tex]
=> x = [tex]\frac{1}{60} = 0.167[/tex] (approx.)
Hence, log (6x) - 3 = -4 => x = 0.167, by properties of logarithm.
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ASAPPP!!!
PLSSS RQQ ANSWER JUST FOR THE LAST QUESTION AT THE VERY BOTTOM!!!
Based on the probability of getting a yellow on one spin, the number of yellows expected from 420 spins is 210 yellows
How many yellows are expected?The number of yellows you can expect are:
= Number of spins x Probability of getting yellow
Solving gives:
= 420 x 1/2
= 420 / 2
= 210 yellows
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983,512 × 1=
A. 983,512
B. 983,513
The value of 983,512 × 1 will be 983,512 by using the multiplicative identity of multiplication.
We are given the expression:
983,512 × 1
We need to find the result after multiplication.
Multiplication is one of the basic operations of mathematics that is used to simplify the expression.
Here, we will use the property of multiplicative identity as the number is multiplied by 1.
By using this, we get that the result will be the same number as anything multiplied by 1 will always give the same number.
So, we get that:
= 983,512
Therefore, we get that, the value of 983,512 × 1 will be 983,512 by using the multiplicative identity of multiplication.
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A manufacturer of candies has daily costs of T(x)=2x2−3200x+6800. T is the total cost in dollars and x is the number of units produced. How many units need to be produced to have minimum cost?
The units that need to be produced to have minimum cost is 800 units.
How to calculate the units?From the information, the manufacturer of candies has daily costs of T(x)=2x² - 3200x+6800.
Therefore, we will differentiate with respect to x. This will be:
T(x)=2x² - 3200x+6800.
4x - 3200
4x - 3200 = 0
4x = 3200
Divide
x = 3200/4
x = 800
Therefore, the units that need to be produced to have minimum cost is 800 units.
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E and F are sets of real numbers defined as follows.
E={v I v≤v3}
F={v I v>6}
Write E∪F and E∩F using interval notation.
If the set is empty, write ∅.
The union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F = ∅ (null sets) is in interval notation.
What is set?
A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have:
E and F are sets of real numbers defined as follows. E={v | v ≤ 3} F={v | v > 6}
E ∪ F = (-∞, 3] or (6, ∞)
E ∩ F = ∅ (null sets)
Thus, the union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F = ∅ (null sets) is in interval notation.
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If 0²/₃=0 , why is 0⁻²/₃ undefined?
0²/₃ = 0 but 0⁻²/₃ is undefined because 1/0 is undefined.
Consider 0²/₃. So here, 0 has a positive power though a rational at that.
Any positive powers of 0 is considered as 0 itself. This expression also means that the square of the cubic root of zero. We know that cubic root of 0 is 0 and 0² = 0 itself. So we can conclude that 0²/₃ = 0.
Now consider 0⁻²/₃ .
We have [tex]a^{-b}=\frac{1}{a^b}[/tex].
So here, 0⁻²/₃ = [tex]\frac{1}{0^{\frac{2}{3}} }[/tex]
From the previous case, 0²/₃ = 0
So we get 0⁻²/₃ = 1/0, which is undefined.
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Mr yuan wants to use his credit to pay off the full amount that another customers balance does Mr,Yuan have enough money to pay it off.
If Mr. yuan wants to use his credit to pay off the full amount that another customer's balance, then he can pay off for Wenner.
Customer Balance ($)
Girardi -85.23
Lewis 20.44
Stein 116.33
Yuan 13.50
Wenner -9.85
As he got the balance of -9.85 and Mr. yuan got the balance of 13.50. About the above problem is based on financial literacy which is the ability to understand and make full of our financial skills. Some of the basics of financial literacy which we can have practical applications are such as budgeting, banking, handling credit and debt, and investing. Financial literacy is essential just to avoid higher levels of debt and to have enough income for retirement.
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Es urgente por favooor
Tres compañeros se reparten un premio que han ganado en un
concurso. Carlos se lleva 1/3 del premio, Luisa los 2/5 del premio y
Carmen, el resto, que son 62’40 €.
a) ¿A cuánto ascendía el premio?
b) ¿Cuánto corresponde a Carlos y a Luisa?
Angle 1 and Angle 2 are a Linear pair.
M angle 1 =x-20 and M angle 2 =x+28
Find the measure of each angle.
Angle 1 = ? Angle 2 = ?
Answer:
Answer: ∠1 = 109° ∠2 = 71°
Step-by-step explanation:
If the two angles form a linear pair, then their sum is 180°
∠1 + ∠2 = 180°
(5x + 9) + (3x + 11) = 180
8x + 20 = 180
8x = 160
x = 20
∠1 = 5x + 9
= 5(20) + 9
= 100 + 9
= 109
∠2 = 3x + 11
= 3(20) + 11
= 60 + 11
= 71
CHECK:
∠1 + ∠2 = 180°
109° + 71° = 180°
180° = 180°
Step-by-step explanation:
hope it helps
A random sample of 49 people are selected from a population and it is found that 12 people in the sample are over six feet tall. what is the best point estimate of the proportion of people in the population who are over 6 feet tall? write your answer as a decimal using the appropriate rounding rule.
If a random sample of 49 people is selected from a population and it is found that 12 people in the sample are over six feet tall, then the best point estimate of the proportion of people in the population who are over six feet tall is 0.24
The point estimate is a term used in mathematics to calculate a single value as an approximate of a parameter of a population.
Point estimate can be given the formula:
point estimate = Number of successes / Total number of samples
In this case, the total number of samples = 49
number of people over six feet tall (successes) = 12
Therefore,
proportion of people over six feet tall = 12 / 49
proportion of people over six feet tall = 0.2448
Decimal can be rounded to two decimal places, if the third digit is less than 5, round the second digit down. On the other hand, if the third digit is more than 5, round the second digit up.
Therefore,
proportion of people over six feet tall = 0.2448 = 0.24
Thus the point estimate of the proportion of people in the population who are over 6 feet tall is calculated to be 0.24
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The distance between two numbers on the number line is 8. If one of the numbers is 5, what are the two
possibilities for the other number?
smaller possible number =
larger possible number =
Answer:
(adding/subtracting 8 from 5)
smaller number is -3
larger number is 13
or it could be -4 and 14
since the question says the distance is 8
Which of these describes the location of the ordered pair (0.8, −1.2)?
A: Quadrant I
B: X-axis
C: y-axis
D: Quadrant IV
A Gallup poll asked americans how many hours of sleep they usually get. The difference between the percent of adults who slept s’more than the recommended amount of time and the percent who slept less than the recommended amount of time is 3%. In total, these groups make up 25% of the population. What percent of the population sleeps more than the recommended number of hours, and what percent sleeps less?
The percent of the population sleeps more than the recommended number of hours will be 30%.
How to illustrate the information?From the information, it should be noted that the difference between the percent of adults who slept more than the recommended amount of time and the percent who slept less than the recommended amount of time is 3%.
It should be noted that this was 25% of the population.
Therefore, the percent of the population sleeps more than the recommended number of hours will be:
= 27% + 3%
= 30%
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Suppose a line perpendicular to a pair of parallel lines intersects the lines at the points (a, 4) and (0,6). If the distance between the parallel lines is √5 , find the value of a and the equations of the parallel lines.
There are two possibilities: (i) Perpendicular line: y = 2 · x + 6, Parallel lines: y = - (1 / 2) · x + 7 / 2, y = - (1 / 2) · x + 6, (ii) Perpendicular line: y = - 2 · x + 6, Parallel lines: y = (1 / 2) · x + 7 / 2, y = (1 / 2) · x + 6.
How to determine the equations of a line and the two lines perpendicular to the former
The missing coordinate of one of the points of intersection can be found by using the least distance between the two parallel lines and the Pythagorean theorem:
(a - 0)² + (4 - 6)² = 5
a² + (- 2)² = 5
a² + 4 = 5
a² = 1
a = ± 1
There are two possibilities: (x₁, y₁) = (- 1, 4), (x₂, y₂) = (1, 4). Now we proceed to find the equations associated to each case:
(x₁, y₁) = (- 1, 4), (x₃, y₃) = (0, 6)
The equation of the perpendicular line is:
Slope
m = (6 - 4) / [0 - (- 1)]
m = 2
Equation of the line
y - 4 = 2 · (x + 1)
y - 4 = 2 · x + 2
y = 2 · x + 6
The slope of the two parallel lines is:
m' = - 1 / m
m' = - 1 / 2
First parallel line
y - 4 = (- 1 / 2) · (x + 1)
y - 4 = - (1 / 2) · x - 1 / 2
y = - (1 / 2) · x + 7 / 2
Second parallel line
y - 6 = - (1 / 2) · x
y = - (1 / 2) · x + 6
(x₂, y₂) = (1, 4), (x₃, y₃) = (0, 6)
The equation of the perpendicular line is:
Slope
m = (6 - 4) / (0 - 1)
m = - 2
Equation of the line
y - 4 = - 2 · (x - 1)
y - 4 = - 2 · x + 2
y = - 2 · x + 6
The slope of the two parallel lines:
m' = - 1 / m
m' = 1 / 2
First parallel line
y - 4 = (1 / 2) · (x - 1)
y - 4 = (1 / 2) · x - 1 / 2
y = (1 / 2) · x + 7 / 2
Second parallel line
y - 6 = (1 / 2) · x
y = (1 / 2) · x + 6
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What is the length of the long leg in the right triangle shown below? O A. 6 B. 3 C. 643 D. 6√2 30* N 60°
Answer:
c.) 6√3
Step-by-step explanation:
This can be solved using both sine and cosine rule.
1st method:
[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(60) = \dfrac{long \ leg}{12}[/tex]
[tex]\sf long \ leg= 12sin(60)[/tex]
[tex]\sf long \ leg= 6\sqrt{3}[/tex]
2nd method:
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\sf cos(30) = \dfrac{long \ leg}{12}[/tex]
[tex]\sf long \ leg= 12cos(30)[/tex]
[tex]\sf long \ leg=6\sqrt{3}[/tex]
please help!!!! give 100 points
Answer:
m<1=75 degree m<2=105degree
m<3=75 degree m<4=105 degree
Answer:
m∠1 = 75°
m∠2 = 105°
m∠3 = 75°
m∠4 = 105°
Step-by-step explanation:
Angles on a straight line sum to 180°
⇒ m∠1 + m∠2 = 180°
Given:
m∠2 - m∠1 = 30°⇒ m∠2 - m∠1 + m∠1 = 30° + m∠1
⇒ m∠2 = 30° + m∠1
Substitute the found expression for m∠2 into the first equation and solve for m∠1:
⇒ m∠1 + m∠2 = 180°
⇒ m∠1 + 30° + m∠1 = 180°
⇒ m∠1 + 30° + m∠1 - 30° = 180° - 30°
⇒ m∠1 + m∠1 = 150°
⇒ m∠1 = 150° ÷ 2
⇒ m∠1 = 75°
As angles on a straight line sum to 180°, subtract m∠1 from 180° to find m∠2:
⇒ m∠2 = 180° - m∠1
⇒ m∠2 = 180° - 75°
⇒ m∠2 = 105°
Vertical Angles Theorem: When two straight lines intersect, the opposite vertical angles are the same (congruent).
⇒ m∠3 = m∠1 = 75°
⇒ m∠4 = m∠2 = 105°
ppppppllllllssss hhhhheeeeellllppppp
The expression 9x²y⁻³, for x = 5 and y = 3 simplifies to 25/3.
What is an improper fraction?A fraction in which the numerator is greater than the denominator is called an improper fraction.A fraction is called a proper fraction when the denominator is greater than the numerator.
Given an expression with exponents 9x²y⁻³, for x = 5 and y = 3.
In this, we have to replace the variables x and y with their numerical value in the given expression.
So, 9x²y⁻³, for x = 5 and y = 3 is,
= 9(5)²(3)⁻³
= 9(5)²/(3)³.
= 9.(25)/27.
= 1.(25)/3.
= 25/3.
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What is the slope and y-intercept of the line 3x - 2y = 12?
Answer:
Slope: (3/2)
y-intercept: (0, -6)
Step-by-step explanation:
3x - 2y = 12
-3x -3x
-2y = -3x + 12
÷-2 ÷-2 ÷-2
---------------------
y = (3/2)x - 6
Slope: (3/2)
y-intercept: (0, -6)
I hope this helps!
Choose the correct term to complete each sentence.
(Radical functions/Inverse functions) are of the form f(x)=n√x
Radical functions are of the form f(x)=n√x.
If we want to find the inverse of a radical function, we will need to restrict the domain of the answer because the range of the original function is limited. Determine the range of the original function. Replace f(x) with y, then solve for x.
MORE: Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol. Radical equation - An equation containing radical expressions with variables in the radicands.
To reverse that operation, you can find the square root of that power: In this case, the sign asks you to find which factor can be multiplied by itself twice to equal the expression inside the radical. (The expression inside the radical is also called the radicand.)
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What is the value of X in the equation3/2{4x-1}-3x=5/4-{x+2}?
Answer:
x = 3/16
Step-by-step explanation:
Answer: x = 3/4 or X = - 1/8
Step-by-step explanation:
A certain population grows exponentially. The population grows from 3500 people to 6425 people in 8 years. What is the growth rate of the population?
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6425\\ P=\textit{initial amount}\dotfill &3500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &8\\ \end{cases}[/tex]
[tex]6425=3500(1 + \frac{r}{100})^{8} \implies \cfrac{6425}{3500}=\left( \cfrac{100+r}{100} \right)^8\implies \cfrac{257}{140}=\left( \cfrac{100+r}{100} \right)^8 \\\\\\ \sqrt[8]{\cfrac{257}{140}}=\cfrac{100+r}{100}\implies 100\sqrt[8]{\cfrac{257}{140}}=100+r \\\\\\ 100\sqrt[8]{\cfrac{257}{140}}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{7.89}\approx r \end{array}}[/tex]
The area of the square is 1 square unit. Two small triangles can be put
together to make a square or to make a medium triangle.
Answer:
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