Answers
Answer:
h(x) = 4·log₃(x) +2
Step-by-step explanation:
Part A:h(x) = f(x) +g(x)
h(x) = (log₃(x) +3) +(log₃(x³) -1)
h(x) = log₃(x) +3·log₃(x) +2
h(x) = 4·log₃(x) +2 . . . . . "simplest" form
h(x) = log₃(9x⁴) . . . . . . . as a single logarithm
__
Part B:No system of equations is given. Perhaps you want to find x for f(x) = g(x).
log₃(x) +3 = log₃(x³) -1
log₃(x) +3 = 3·log₃(x) -1
4 = 2·log₃(x) . . . . . . . . . . . add 1-log₃(x)
2 = log₃(x) . . . . . . . . . . . . divide by 2
3² = x = 9 . . . . . . . . . . . . . take the antilog
The solution to f(x) = g(x) is x = 9.
_____
Additional comment
The relevant rules of logarithms are ...
a = log₃(b) ⇔ 3^a = b
log(a^b) = b·log(a)
log(ab) = log(a) +log(b)
Related Questions
Help pwease
A gym is offering a deal to new members. Customers can sign up by paying a
registration fee of $250 and a monthly fee of $42. How much will this membership
cost a member by the end of the year?
Answers
Answer:
Since there are 12 months in a year, the answer is 42 * 12 + 250 = $754.
Because he will pay 250$ for registration and 42$ for every month
The year equals= 12 months
So 42$*12 = 504$ plus the registration cost 504+250= 754$
What is the quotient of 480 divided by -60
Answers
should be the answer
The quotient when 480 is divided by -60 is 8.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
The numbers given are 480 and -60.
Both are in opposite signs, that is one negative and other positive.
So the quotient will be negative.
Now divide 480 by 60.
Since both of the numbers contain 0 at the end, cancel it.
Then it becomes 48 divided by 6.
48 / 6 = 8
Hence the quotient is 8.
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The difference of twice a number and 7 is 20. Find the number.
Answers
Answer:
twice the difference gives 2(difference). 7 = 14 20 = 40
Step-by-step explanation:
Roselyn is driving to visit her family, who live 150 kilometers away. Her average speed is 60 kilometers per hour. The car's tank has 20 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 kilometers per liter. Fuel costs 0.60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answers
Roselyn can drive a distance until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.Roselyn can travel 120 km before running out
Distance travelled with 20 l of petrol in solution and final answer.
Roselyn's average speed is 60 kilometers per hour, and she needs to travel 150 kilometers to reach her family's place. Therefore, she will require a total of 150/60 = 2.5 hours to complete the journey.
The car's fuel efficiency is 6 kilometers per liter, meaning it consumes 1/6 liters of fuel per kilometer. To determine the total fuel required, we multiply the fuel consumption rate by the total distance: 150 * (1/6) = 25 liters of fuel.
Since the car's tank has 20 liters of fuel at the beginning of the drive, Roselyn will need an additional 25 - 20 = 5 liters of fuel to complete the journey.
As fuel costs 0.60 dollars per liter, Roselyn will need to spend a total of 5 * 0.60 = 3 dollars to purchase the necessary fuel.
Therefore, Roselyn can drive until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.
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Could anyone explain this question in detail?
Answers
Answer:
h and k are simply variables that stand in for the x and y of a point. Math books could have easily have used x1, x2 y1 y2, etc, but h and k is the convention.
anyway, this is a guess n check question. Substitute the x value of the point for h, and y value for k, and whichever one gives you a true equation is the right one.
Answer:
Step-by-step explanation:
y = a(x-h)²+k is the “vertex-form equation” for a vertical parabola with vertex (h,k).
Since a>0, the parabola opens upwards. (If a<0, it opens downwards. If a=0, it is not a parabola at all.)
The parabola y = a(x-h)²+2k is the same shape as the first equation, but it is shifted vertically by k units.
Since (2,4) is a point on the first parabola, (2,4+k) is a point on the second parabola.
You ask 150 people about their pets. The results show that 9/25 of the people own a dog. Of the people who own a dog. 1/6 of them also own a cat. How many people own a dog and a cat?
Answers
Answer: 9
Step-by-step explanation:
In order to find the people out of the 150, we first multiply 9/25 and 150 together. This will give us the people who DO own a dog. This brings us to 54.
Now, if we multiply 54 by 1/6 we get the answer of 9, because 1/6 of the dog owners own a cat as well. We have now reached the desired amount.
what is 1,256 rounded to the nearest hundredth
Answers
Answer:
1,300
Step-by-step explanation:
1256, if something is more than 5 then it goes up but if it's 4 or lower it goes down so 1256 rounded up to the nearest hundredth is 1300.
Answer: 1300
1256, if something is more than 5 then it goes up but if it's 4 or lower it goes down so 1256 rounded up to the nearest hundredth is 1300
Step-by-step explanation:
I WILL GIVE 5 STARS
Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Answers
Part A: The average rate of change of each section are,
Section A = 8, Section B = 32.
Part B: There are 4 times greater is the average rate of change of Section B than Section A.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and divi
The function is given by,
⇒ f (x) = 4 (2)x
Section A is from x = 1 to x = 2.
Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16
Again, section B is from x = 3 to x = 4.
Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64
Part A:
In section A, the average rate of change is = 8
And in section B, the average rate of change is = 32
Part B:
Therefore, the average rate of change of section B is greater than section A is,
⇒ 32 / 8 = 4
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Help please!!!! I’ll give brainilest
Answers
So the correct ans is ‘D’
Multiply each pair of numbers -4.25x(-1.25)=
Answers
The decimal 0.004 7 is equivalent to what percent
Answers
Answer:
the answer is 0.4
Step-by-step explanation:
Answer:
100 = 0.0046%
100 is equivalent to 0.0046
Need help on finding g .
Answers
The numeric values for this problem are given as follows:
g(-1) = -2.g(2) = 0.g(3) = 0.5.How to obtain the numeric values of the function?The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.
For x between -2 and 2, the function is defined as follows:
g(x) = -(x - 1)² + 2.
Hence the numeric value at x = -1 is given as follows:
g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.
For x at x = 2 and greater, the function is given as follows:
g(x) = 0.5x - 1.
Hence the numeric values at x = 2 and x = 3 are given as follows:
g(2) = 0.5(2) - 1 = 0.g(3) = 0.5(3) - 1 = 0.5.A similar problem, also featuring numeric values of a function, is given at brainly.com/question/28367050
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When we are choosing a random sample and we do not place chosen units back into the population, we are
Answers
The Lakers won 35 games and lost 47 games. At this rate, how many games should they win, in a 96-game season?
Answers
Answer:
37 games if you were to round percents
y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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What happens when you add and subtract like fractions
Answers
Answer:hey must have the same denominator (the bottom value). If the denominators are already the same then it is just a matter of either adding or subtracting the numerators (the top value). If the denominators are different then a common denominator needs to be found.
Step-by-step explanation:
ess spent
7x minutes on the computer. Her sister spent
5x+10 minutes on the computer, which was the same amount of time Jess spent. How many minutes was Jess on the computer?
Answers
Answer:
Step-by-step explanation:
If Jess spent 7x minutes on the computer, we see that there is a variable X which is the amount of minutes Jess spent on the computer multiplied by 7.
Jess' sister spent an equal amount of time on the computer so right away we can say that 7x=5x+10
To get the variable X by itself, we have to subtract 5x from both sides of the equation leaving us with 2x=10
Lastly, we have to isolate the X variable to determine its value. We do that by dividing X by its coefficient 2 across both sides.
X=5
By plugging X in to the original equations: 7(5)=5(5)+10 - both sides equal thirty-five and so this equation is true.
So therefore, Jess spent thirty-five minutes on the computer.
A closet in Shivani's house is 2 yards by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $38.00 per square yard?
Answers
The amount it would cost to put a new floor in the closet is $76.00
Calculating how much it would cost to put a new floor in the closetFrom the question, we are to calculate how much it would cost to put a new floor in the closet
From the given information,
A closet in the house is 2 yards by 1 yard.
To determine how much it would cost to put a new floor in the closet,
First,
We calculate the area of the closet
Area of the closet = 2 yard × 1 yard
Area of the closet = 2 square yards
Now,
From the given information,
The flooring costs $38.00 per square yard
Thus,
The amount it would cost to put a new floor in the closet is
2 × $38.00
= $76.00
Hence,
The amount it would cost is $76.00
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Ramesh dan syarika ans. Ramesh takes a medical and health insurance policy with a deductible of RM1 500 per year and co-insurance of 20% of covered medical expenses. Ramesh went to the hospital for the first time for knee treatment and the medical cost was RM700, the medical cost for the second and third treatments was RM2 000 and RM1 700 respectively. The three treatments were in the same year. How much medical expenses should be borne by Ramesh and the insurance company?
Answers
Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.
1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.
2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.
3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.
4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.
5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.
6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.
7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.
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2/5 × 1/6 , but the answer as a fraction
11 points
Answers
Answer:
1/15
Step-by-step explanation:
2/5*1/6
Make the denominator the same
12/30*5/30
2/30
Simplify
1/15
Answer:
The exact form is 1/15 and the decimal form is 0.06.
Step-by-step explanation:
I used an app. It should be correct!
How many pounds are in 1.2 tons
Answers
Answer: 2,400
Step-by-step explanation: Multiply the mass value by 2000
Answer:
2400 pounds
Step-by-step explanation:
1 ton is 2000 pounds
So we can multiply the number of tons by 2000 to get the answer.
1.2 * 2000 = 2400 pounds
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
1 and 2, please and thank you!
Answers
In your own words, please describe the difference between the regression equation hat and the regression equation.
Please see the picture
Answers
While the regression equation represents the overall relationship between x and y, the regression equation with the hat symbol represents the specific predicted value of y based on a given value of x.
Describe Regression Equation?A regression equation is a mathematical formula that describes the relationship between two or more variables in a data set. It is used in regression analysis, which is a statistical method used to model and analyze the relationship between a dependent variable (the variable we are trying to predict) and one or more independent variables (the variables that we use to predict the dependent variable).
The regression equation takes the form of:
y = a + bx
where y is the dependent variable, x is the independent variable, a is the intercept (the value of y when x is zero), and b is the slope (the change in y for each unit change in x).
The regression equation is derived using a technique called least squares regression, which minimizes the sum of the squared differences between the observed values of the dependent variable and the values predicted by the equation.
The regression equation can be used to predict the value of the dependent variable for a given value of the independent variable. It can also be used to test hypotheses about the relationship between the variables and to estimate the strength and direction of the relationship.
In summary, a regression equation is a mathematical formula that describes the relationship between two or more variables in a data set. It is used to model and analyze the relationship between a dependent variable and one or more independent variables, and can be used to make predictions and test hypotheses about the relationship.
The regression equation, \(\mathrm{y = \beta_1 + \beta_1x}\) , is a mathematical formula used to model the relationship between two variables, x and y. The regression equation predicts the value of the dependent variable (y) based on the value of the independent variable (x).
The hat symbol in the regression equation, often denoted as y-hat, represents the predicted value of y based on the regression equation. In other words, given a particular value of x, y-hat is the predicted value of y based on the estimated coefficients of the regression equation.
So, while the regression equation represents the overall relationship between x and y, the regression equation with the hat symbol represents the specific predicted value of y based on a given value of x.
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A rectangular field is 5cm wide and 4cm long requires 260m of fencing. find y
Answers
Answer:
50 + x + 50 + x = 260, or
100 + 2x = 260, or
50 + x = 130,
Step-by-step explanation:
Match the following.
1. fractions that may be expressed differently, but still have the same value
mixed
number
2. consists of an integer and a proper fraction
denominator
3. a fraction with a numerator that is larger than or equal to the denominator
proper fraction
4. the bottom part of a fraction; represents the whole
equivalent fractions
5. the top part of a fraction; represents part of the whole
improper fraction
6. a fraction with a numerator that is less than the denominator
numerator
Answers
Answers:
the answers are...
1.) equivalent fractions
2.) mixed number
3.) improper fraction
4.) denominator
5.) numerator
6.) proper fraction
look at the screenshot!!
hope this helps :)
Answer:
1. Fractions that may be expressed differently, but still have the same value
→Equivalent fractions
2. Consists of an integer and a proper fraction
→Mixed number
3. A fraction with a numerator that is larger than or equal to the denominator
→Improper fraction
4. The bottom part of a fraction; represents the whole
→Denominator
5. The top part of a fraction; represents part of the whole
→Numerator
6. A fraction with a numerator that is less than the denominator
→Proper fraction
What is the equation of the line in slope intercept form?
Answers
Answer:
y = x + 60
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line
m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1
the line crosses the y- axis at (0, 60 ) ⇒ c = 60
y = x + 60 ← equation of line
At lunch a waiter had seven customers and two of them didn’t leave a tip.If he got seven each from the ones who did tip how much money did he earn?
Answers
Answer:
$35
Step-by-step explanation:
7 customers - 2 who didn't tip = 5 who did tip
$7 from those who did tip * 5 ppl who tipped = $35 earned
What number is ten more than 100? Write an equation.
Answers
Answer:
10+100=110
Step-by-step explanation:
easy as pie
Answer:
110?
Step-by-step explanation:
If its 10 more (more being addition) than 100 then it should be 110
Nine more than the product of a number and 3 is equal to 6
Answers
Answer:
x = - 3
Step-by-step explanation:
9 more than the product of a number and three is equal 6.
9 + (x · 3) = 6
9 + 3x = 6
3x = -9 + 6
3x = - 3
x = - 3
Answer:
3x + 9 =6
Step-by-step explanation:
What are the numbers and called in a number line ??
Answers
Answer:
numbers
Step-by-step explanation:
numbers