Answer:
use logarithms
Step-by-step explanation:
Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.
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You will note that this approach works well enough for ...
a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents
(x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs
but doesn't do anything to help you solve ...
x +3 = b^(x -6)
There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.
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Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.
In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.
To solve an expression with variables in the exponents, you apply the rules of exponents.
Explanation:When solving an expression with variables in the exponents, you need to apply the rules of exponents. Here are the key rules:
For example, (27x^3)(4x^2) can be simplified to 108x^5.
what is the solution to this equation? 4x^2+98=0
Follow below steps;
The equation to solve is 4x² + 98 = 0.
1. Subtract 98 from both sides to get 4x² = -98.
2. Divide by 4 to obtain x² = -24.5.
3. Take the square root, remembering that √(-1) = i, so x = ±√24.5i.
if *(pic below)* complete the following statement
f(6)=___
If 1 inch = 2.5 centimeters, how many centimeters are there in 40 inches
Final answer:
To convert 40 inches to centimeters, multiply the number of inches (40) by the conversion factor (2.54 cm/inch), which equals 101.6 centimeters.
Explanation:
To calculate how many centimeters are in 40 inches, we use the conversion factor that 1 inch is exactly equal to 2.54 centimeters. Knowing this, we can simply multiply the number of inches by the conversion factor to get the measurement in centimeters.
Determine the number of inches to be converted (in this case, 40 inches).
Multiply the number of inches by the conversion factor (2.54 cm for every 1 inch).
Calculation: 40 inches × 2.54 cm/inch = 101.6 centimeters.
Therefore, there are 101.6 centimeters in 40 inches.
True or false a positive slope goes up as you move from left to right along the x-axis.
8 bits is enough to represent 256 different numbers. how many total bits do you need to represent 512
How do I do proofs? What’s the next step
A group of 156 tourists had enough food for a stay of 125 days in a mountain. however just before they left, n tourists left the group, this meant that the group had enough food to lengthen their stay for another 70 days. how many left the group?
please show your steps.
There are 15 tennis balls in a box, of which 9 have not previously been used. three of the balls are randomly chosen, played with, and then returned to the box. later, another 3 balls are randomly chosen from the box. find the probability that none of these balls has ever been used
Final answer:
The probability that none of the balls have been previously used is 20.96%.
Explanation:
To find the probability that none of the three balls selected have ever been used, we first calculate the probability of selecting a ball that has not been used each time.
Initially, there are 15 balls in total, out of which 9 have not been used. So, the probability of selecting a ball that has not been used on the first draw is 9/15.
After the first draw, the number of balls in the box remains the same, but the number of unused balls decreases to 8. So, the probability of selecting a ball that has not been used on the second draw is 8/15.
Similarly, for the third draw, the probability of selecting a ball that has not been used is 7/15.
Since the balls are chosen randomly and returned to the box after each draw, the probabilities are independent. Therefore, to find the probability that none of the balls have ever been used, we multiply the probabilities of each draw:
(9/15) x (8/15) x (7/15) = 0.2096, or approximately 20.96%.
8 tens 5 hundredths = thousandths
What is the difference of squares of twenty and thirteen
HELP!!!!!!!! PLZ!!!!!!!!WILL GIVE BRAINLIEST!!!!!!!! :)
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week.
1.)Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work.
2.)Graph the inequalities.
3.)What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain.
4.)What is the maximum amount of money Lia can earn in 1 week? Explain.
What is p% of 200p3?
The solution of p% of 200p³ is,
⇒ p% of 200p³ = 2p⁴
We have to given that,
An expression to solve,
⇒ p% of 200p³
Now, We can simplify by applying percentage as,
⇒ p% of 200p³
⇒ p/100 × 200p³
⇒ p × p³ × 200/100
⇒ p⁴ × 2
⇒ 2p⁴
Therefore, The solution of p% of 200p³ is,
⇒ p% of 200p³ = 2p⁴
Learn more about the percent visit:
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△ABC is mapped to △A′B′C′ using each of the given rules.
Which rules would result in △ABC being congruent to or not congruent to △A′B′C′ ?
Drag and drop each rule into the boxes to classify it as Congruent or Not Congruent.
Congruent Non Congruent
Choices to go to either congruent or non congruent
(x,y)----(x+5,y) (x,y)---(5x,5y) (x,y)-----(0.5x, 0.5y) (x,y)-----(x,-y) (x,y)------(-x,-y)
Answer:
(x,y)→(x+5,y) will be congruent; (x,y)→(5x,5y) will not be congruent; (x,y)→(0.5x, 0.5y) will not be congruent; (x,y)→(x,-y) will be congruent; (x,y)→(-x,-y) will be congruent.
Step-by-step explanation:
The types of translations that result in congruent images are translations or slides; reflections; and rotations.
Translations will add to the x- and y-coordinates; this is why the first transformation is congruent.
Reflections will negate one or more of the coordinates; this is why the fourth and fifth transformations are congruent.
The remaining two are dilations; these are stretches or shrinks that occur when the coordinates are multiplied by a number other than 1. These change the size of the figure, which is why they are not congruent.
Answer: Just took the test these are the correct anwsers
Step-by-step explanation:
how do you condense logX times log2
solve 18x-17y=-8 this is linear equations slope intercept form
A bank charges $5.00 per month plus $.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month.
Felicia put $8500 into a CD that pays 2.8% interest compounded semiannual. According to the rule of 72, approximately how long will it take for her money to double ?
You arrive in my class 45 seconds after leaving math which is 90 meters away
You traveled the 90 meters in 45 seconds at a speed of 2 meters per second.
Speed = Distance / Time
Given:
Distance = 90 metersTime = 45 secondsWe can now calculate the speed:
Speed = 90 meters / 45 seconds
= 2 meters/second
This means you traveled at a speed of 2 meters per second to get from your math class to the next class.
Complete Question:
You arrive in my class 45 seconds after leaving math which is 90 meters away. Find speed.
Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant? The equation __ models the scenario. Hans will plant ___ snapdragons.
Answer:
the equation: x=45-y . models the scenario
Hans will plant: 16 . snapdragons
Step-by-step explanation:
did it on edge 2021
Please help I really need it.
use the profit function to calculate Wacky widget company's break even point rounded to the nearest widget. 0=90w-(57w+5000)
Which angle is the included angle for DE¯¯¯¯¯ and FE¯¯¯¯¯ ?
∠D
∠E
∠F
Answer: ∠E
Step-by-step explanation:
The included angle for [tex]\overline{DE}[/tex] and [tex]\overline{FE}[/tex] is [tex]\angle{E}[/tex].
The included angle for any two lines or line segments is represented by the common vertex point.
For example : The included angle for [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex] is [tex]\angle{B}[/tex] [Since B is the common end point in [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex] ]
Similarly, the included angle for [tex]\overline{DE}[/tex] and [tex]\overline{FE}[/tex] is [tex]\angle{E}[/tex] (Since E is the common vertex in [tex]\overline{DE}[/tex] and [tex]\overline{FE}[/tex] )
You are asked to distribute 10 balls into three groups: 2 balls, 3 balls, and 5 balls. (a) if the 10 balls are indistinguishable, how many different arrangements can you have
Explain why the graph shown may be misleading. (please help)
What type of endorsement is illustrated by the following example: Tom Ash 7609-25-26-3 A) Restrictive endorsement B) Full endorsement C) Blank endorsement D) Signature endorsement
The answer is letter c which is blank endorsement. It is a sign by the maker of an instrument, for instance a check, which allows any holder of the instrument to declare a claim for payment. Since no payee is stated, such an endorsement fundamentally turns the instrument into a bearer security.
The example given 'Tom Ash 7609-25-26-3' indicates a blank endorsement, which is when the original holder of a negotiable instrument signs their name without naming a new payee or providing other instructions, making the instrument payable to the bearer.
Explanation:The type of endorsement illustrated by 'Tom Ash 7609-25-26-3' is a blank endorsement. In a blank endorsement, the holder of a negotiable instrument, such as a check, simply signs their name on the back of the instrument without specifying the new payee or any other instructions. This means that the instrument becomes payable to the bearer and can be transferred merely by delivery. The other types of endorsements include restrictive, full, and signature endorsements, but since there are no additional instructions or named endorsee next to the signature, it does not qualify as any of those.
On the average, actively managed mutual funds have an expense ratio of about __________ .
a. 5 percent
b. 3 percent
c. 2.5 percent
d. 1.5 percent
A die is rolled 13 times. what is the probability of at least two 2's appearing? (round your answer to four decimal places.)
Which of the following is the linear parent function
Answer:
Option C is correct linear parent function.
Step-by-step explanation:
We need to choose from the option as a linear parent function.
We will look each option and explain each one.
Option A: [tex]f(x)=|x|[/tex]
Here we have absolute sign on x. It is parent function of absolute function.
Option B: [tex]f(x)=x^2[/tex]
Here we have square on x. It is parent function of quadratic or parabola.
Option C: [tex]f(x)=x[/tex]
It is parent function of linear because exponent of x is 1 and coefficient of x is 1.
Option D: [tex]f(x)=2x[/tex]
It is linear function but not parent because coefficient of x is not 1.
Hence, Option C is correct linear parent function.
JIMMMMMM
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y ≥ −3x + 3
y is less than 3 over 2 times x minus 6
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (−6, 3) included in the solution area for the system? Justify your answer mathematically. (4 points)
Answer:
The point (-6,3) is not included in the solution area for the system.
Step-by-step explanation:
The given inequities are
[tex]y\geq -3x+3[/tex] .... (1)
[tex]y<\frac{3}{2}x-3[/tex] .... (2)
Part A: The related equations are
[tex]y=-3x+3[/tex]
[tex]y=\frac{3}{2}x-3[/tex]
Put x=0 in the above equation to find the y-intercept and put y=0, to find the x-intercept.
[tex]y=-3(0)+3=3[/tex]
The y-intercept of first equation is 3.
[tex]0=-3x+3\Rightarrow x=1[/tex]
The y-intercept of first equation is 1.
[tex]y=\frac{3}{2}(0)-3=-3[/tex]
The y-intercept of second equation is -3.
[tex]0=\frac{3}{2}x-3\Rightarrow 2[/tex]
The y-intercept of first equation is 2.
The related line of inequality (1) is a solid line because the sign of inequality is ≥ and the related line of inequality (2) is a dotted line because the sign of inequality is <.
Shaded portion of first inequality is above the related line and the shaded portion of second inequality is below the related line.
The solution area is shown in the below graph.
Part B: The point (−6, 3) is not included in the solution area for the system.
Check the given inequalities by the point (-6,3).
[tex]3\geq -3(6)+3[/tex]
[tex]3\geq -18+3[/tex]
[tex]3\geq -15[/tex]
This statement is false.
Therefore the point (-6,3) is not included in the solution area for the system.
prime numbers divided by 4 remainder 1 proven true
What is 41.925 as a mixed number in simplest form?