Answers
Step 2. Substitution
Step 3. Combine like terms
Step 4. Additive Property of Equality
Step 5. Subtraction Property of Equality
Step 6. Division Property of Equality
Related Questions
use analytic methods to find the extreme values of f(x)= (1/x) + lnx on the interval 0.5 ≤ x ≤ 4 and where they occur
Answers
At the extreme values, f'(x) = 0
f'(x) = -1/x^2 + 1/x = 0
(x - 1)/x^2 = 0
x - 1 = 0
x = 1
f(1) = 1/1 + ln 1 = 1
Therefore, the extereme value is 1 and occurs at x = 1.
Solve the system by the elimination method. Check your work. 2a + 3b = 6 5a + 2b - 4 = 0
Answers
2a + 3b = 6
5a + 2b - 4 = 0
multiply thru the top equation by 2
Multiply thru the bottom equation by 3
4a + 6b = 12
15a+ 6b = 12
Subtract and solve for "a":
11a = 0
a = 0
Solve for "b" using 2a + 3b = 6
2*0 + 3b = 6
b = 2
Answer:
Step-by-step explanation:
a=0
b=2
answer (0,2)
What is the ratio of the area of the inner square to the area of the outer square?
(a−b)²+b²/a²
a²−b²/a²
(a−b)²/(a+b)²
(ab)²/(a+b)²
Answers
(a−b)²+b²/a²
proof
if A is the area of the
inner squared, so A= c², and c²= (a−b)²+b²
so the side of the outer must be a-b +b=a, its area is a²
Answer: I just did the quiz in Plato the answer will be option A or (a-b) 2+b2/a2
Step-by-step explanation:
round 1,647 to the nearest thousand
Answers
Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.
0
1
2
7
Answers
Answer:
I believe the answer is (C.2)
Step-by-step explanation:
The answer isn’t 1. I took the test and ‘B’ is incorrect
Final answer:
C: 2
To find the average rate of change of the function f(x) from x = 0 to x = 1, we compute (f(1) - f(0)) / (1 - 0), which results in (3 - 1) / 1 = 2. The average rate of change is therefore 2.
Explanation:
To calculate the average rate of change for the function f(x) = −x⁴ + 4x³ − 2x² + x + 1 from x = 0 to x = 1, we use the formula:
Average rate of change = ∆f/∆x = (f(x_2) - f(x_1)) / (x_2 - x_1)
First, we need to find the values of f(x) at x = 0 and x = 1:
f(0) = −(0)⁴ + 4(0)³ − 2(0)² + (0) + 1 = 1f(1) = −(1)⁴ + 4(1)³ − 2(1)² + (1) + 1 = 3Using these values, we calculate the average rate of change:
Average rate of change = (3 - 1) / (1 - 0) = 2 / 1 = 2
Therefore, the average rate of change of the function from x = 0 to x = 1 is 2.
carla looks from the top of a diving board, and lines up a ball floating on the surface of the water with the bottom of the opposite corner of the pool. calculate the total distance across the surface of the pool. explain your reasoning
Answers
Below is the solution:
12/x = 10/9
10x/ 20 = 108/10
x = 10.8
9 + 10.8 = 19.8 ft
(1) Which fraction is a multiple of 1/6
A) 7/16
B) 11/12
C) 4/6
D) 6/9
(2) which fraction is a multiple of 1/8
A) 14/18
B) 7/16
C) 8/9
D) 5/8
(3) which fraction is NOT a multiple of 1/10
A) 10/3
B) 8/10
C) 3/10
D) 10/10
(4) which fraction is NOT a multiple of 1/12
A) 5/12
B) 11/12
C) 2/10
D) 3/13
Answers
___________
1) [C]: 4/6 ;
___________
2) [D]: 5/8 ;
___________
3) [A]: 10/3 ;
___________
4) Both: [C]: 2/10; and: [D]: 3/13; are NOT multiples of 1/12
_______________________
Kayla notices that she can buy snacks and candy in bulk at the grocery store. The snacks she wants to buy cost $1.29 per kilogram.
Answers
Leslie can determine which option will give her more yogurt by comparing the weights of the two options.
Explanation:To determine which option will give Leslie more yogurt, she needs to compare the weights of the two options. First, she needs to convert the weight of the first option from pounds to ounces. Since 1 pound is equal to 16 ounces, the 2 pound container is equal to 32 ounces. Next, she can compare the weights of the two options. The first option is 32 ounces and the second option is 5 containers of 6 ounces each, which is a total of 30 ounces. Therefore, the first option will give Leslie more yogurt.
What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?
Answers
f(x) = 5(2)^x
f(1) = 5(2)^1
f(1) = 10
So the point (1,10) is on this curve
Do the same for x = 5
f(x) = 5(2)^x
f(5) = 5(2)^5
f(5) = 160
The point (5,160) is also on the curve
Use the slope formula now
m = (y2-y1)/(x2-x1)
m = (160-10)/(5-1)
m = 150/4
m = 37.5
The average rate of change is 37.5
as the fish-and-game warden of your township, you are responsible for stocking the town pond with fish before fishing season. the average depth of the pond is 20 feet. you plan to start the season with one fish per 1000 cubic feet. you intend to have at least 25% of the opening day's fish population left at the end of the season.what is the maximum number of licenses the town can sell if the average seasonal catch is 20 fish per license?
...?
Answers
= 1,332,000 ft^2
Average depth of 20 ft =
1,332,400 / 20 = 2,664,000 ft^3
2,664,000 ft^3 / 1 fish/1,000 ft^3 = 26,640 fishes
26,640 x 75 % = 19,980 catchable fishes
19,980 /20 = 999 licenses
hope this helps
At a gas station, the price of a regular gas was $3.80 per gallon on monday. the price increased to $3.85 per gallon on tuesday. round the price per gallon for each day to the nearest tenth of a dollar.
Answers
Tuesday' gas, $3.85 rounded to the nearest tenth of a dollar would be $3.90
Hope this helps!! and if you ever need anything else just ask! :)
Answer:
A round number is less accurate, but easier to use, because you get rid of certain decimals.
There are some rules to do this:
If we want to round a number to the nearest tenth, we have to look what's the unit after it, if that unit is more than 5, we round the tenth to the upper number. For example, 10.66 would be rounded to 10.7.If we want to round a number, and the next digit is lower that 5, we just maintain the same digit. For example, 10.44 would be rounded to 10.4However, there's a specific case, if we want to round a number to the tenth, and the following digit is 5, we could round up or round down the tenth digit. If the digit we want to round is pair, then we maintain the same digit, if it's odd, we can round to the upper digit. For example, 10.65 would be rounded to 10.6, and 10.75 would be rounded to 10.8Therefore, according to these rules, the round number would be $3.8 and $3.8
A number decreased by 10 is greater than -5.
How can I write this in an inequality?
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simplified:
x>5
Helpppppppp I'm really bad in math
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What you could do is multiply each side by 12.
Then it will become 6x + 2x = 24
Combine like terms: 8x = 24
Now divide each side by 8
The answer is x = 3
Write an equation of the direct variation that includes the point (9, –12).
(A.) y = 1 1/3x (B.) y = - 1/12x (C.) y = 1 1/3x (D.) -3/4x ...?
Answers
The equation of direct variation for the point (9, -12) would be y = -1 1/3x. The constant of variation, 'k', is found by dividing 'y' by 'x'. Therefore, 'k' is -12/9, which simplifies to -1 1/3.
Explanation:In a direct variation, the equation can be represented in the form y = kx, where 'k' is the constant of variation. Here, 'k' can be found by dividing 'y' by 'x'. So, in the given point (9, -12), 'k' would be -12/9, which simplifies to -4/3 or -1 1/3. Therefore, the equation of the direct variation that includes the point (9, -12) would be y = -1 1/3x. The provided options don't include this equation, so it might be a mistake in the question options. Remember, the correct equation should always have 'y' and 'x' directly vary, and 'k' have the same sign as the given 'y' value.
Learn more about Direct Variation here:https://brainly.com/question/9775007
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Kumbu saleh traded primarily in
Answers
Hope this will help.
If Harrisen makes $10 an hour, how much will he make in a 40 hour work week?
$30
$50
$40
$400
Answers
For 40 hour, it would be: $10 * 40 = $400
So, option D is your answer.
Hope this helps!
three randomly selected households are surveyed. the numbers of people in the households are 1,3,8 assume that samples of size n =2 are randomly selelcted with replacement from the population of 1,3,8. Listed below are the nine different sampls
1,1 1,3 1,8 3,1 3,3 3,8 8,1 8,3 8,8
find the variance of each of the nine samples then summerize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values
s^2 Probability
3.3
1
6.3
49
Answers
The variances for the samples were calculated, and then the probability of each distinct variance value was found. The results were summarized in a table showing the probability distribution of the variances.
Explanation:The variance of a sample is calculated using the formula:
s^2 = Σ ( xi - X_bar )^2 / (n - 1).
Where 'xi' represents each value in the sample, 'X_bar' is the mean of the sample and 'n' is the number of values in the sample. Let's calculate the variance for each of these samples:
Next, find the probability of each distinct variance value by counting the number of times it occurs and dividing by the total number of samples (9 in this case). The sampling distribution of the variances with probabilities looks something like this:
Variance = 0 : Probability = 3/9 = 0.33Variance = 2 : Probability = 2/9 = 0.22Variance = 25 : Probability = 2/9 = 0.22Variance = 49 : Probability = 2/9 = 0.22Learn more about Variance and Probability here:https://brainly.com/question/31698743
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To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.
Answers
Answer:0.075
Step-by-step explanation:
What is 0.98 rounded to the nearest thousandth?
Answers
it may also be asking for 0.980, which is equal but shows the thousandth place
The number 0.98 already has a zero in the thousandths place and no further digits; hence it remains as 0.980 when rounded to the nearest thousandth.
The given number, 0.98, when rounded to the nearest thousandth, does not change because it has a zero in the thousandths place. To round a number to the nearest thousandth, you look at the digit in the ten-thousandths place. If this digit is 5 or greater, you round up.
If it is less than 5, you keep the digit in the thousandths place as it is. Since 0.98 has a zero in the thousandths place already and there are no further digits, it remains as 0.980 when rounded to the nearest thousandth.
Help solve x+6=4y
2x-8y=-12
Answers
x = -6+4 + , y E R
1.3 yrs = ? hrs ...?
Answers
1 year = 365.25 days
1.3 years = x days
________________
1.3 years = 1.3 * 365.25 days = 474.825 days
________________
________________
1 day = 24 h
474.825 days = x hours
________________
474.825 days = 474.825 * 24 hours = 11395.8
6 sweets cost 24p altogether how much do 5 sweets cost
Answers
To calculate the cost of 5 sweets when 6 sweets cost 24p, divide the total cost by the number of sweets to determine the cost of one sweet, then multiply by 5. The cost for 5 sweets is 20p.
To find out how much 5 sweets cost when 6 sweets cost 24p altogether, we first need to calculate the cost of one sweet. We divide the total cost by the number of sweets to get the cost per sweet. Here's how it's done:
Find the cost of one sweet by dividing the total cost of 6 sweets (24p) by 6: Cost per sweet = 24p / 6 = 4p.Now, multiply the cost per sweet by the number of sweets you want to find the cost for, which in this case is 5: Cost for 5 sweets = 4p / sweet × 5 sweets = 20p.Therefore, 5 sweets would cost 20p.
When sam breathes in, his chest expands, causing air to fill his lungs. which structure causes his chest to expand?
Answers
In the Math Club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the Math Club at a statewide math contest?
Answers
34 In All. 14 boys (14/34) 11 Seniors, - 4 so we don't double count. (14/34) + (7/34)
There are in total 34 children: 20 girls + 14 boys = 34 children
There are in total 11 seniors: 7 senior girls + 4 senior boys = 11 senior children
When we have two events that do not occur together, so only one of the events can happen (there is OR in a sentence), then we use the addition rule and add up probabilities of the events. We have two events not occurring together:
1. The probability of selecting a boy is 14/34 (because there are 14 boys among 34 children).
2. The probability of selecting a senior is 11/34 (because there are 11 seniors among 34 children).
Now, we just need to add them up. However, we have already counted 4 senior boys in the probability of the first event and thus, must subtract the probability of selecting a senior boys (4/34):
14/34 + 11/34 - 4/34 = (14+11-4)/34 = 21/34
Plot 4/3 and 26/3 on the number line.
Answers
4/3 = 1.3333
26/3 = 8.6666
so, on a number line, you'd just plot 4/3 a little past 1, and plot 26/3 a little over half past 8.
original price $18 markup 15%
Answers
appleseed a tech company spends a fixed cost of $1500 to manufacture the wristbands for their new appleseed watch plus $100 per unit manufactured solution
Answers
The y-intercept is 1500. It represents the fixed cost to manufacture the wristbands.
a. The slope is 100. It shows the cost per wristband.
b. The y-intercept is 1500. It shows the fixed cost for manufacturing the wristbands.
Given that,
The fixed cost of $1,500 for manufacturing the wristbands. And, there is $100 per unit.Based on the above information, we can conclude that
a. The slope is 100. It shows the cost per wristband.
b. The y-intercept is 1500. It shows the fixed cost for manufacturing the wristbands.
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What is the sum of square root -2 and squareroot -18
Answers
1.414i + 4.234i = 5.657i
The 'i' is included because the sqrt of a negative number is imaginary.
The sum of the square roots of -2 and -18 is [tex]\( 4\sqrt{2}i \)[/tex], where i is the imaginary unit.
The sum of the square roots of -2 and -18 involves complex numbers because both -2 and -18 are negative.
The square root of a negative number is not a real number, but it can be expressed using imaginary units.
The square root of -2 can be represented as [tex]\( \sqrt{-2} = \sqrt{2}i \),[/tex] where i is the imaginary unit, defined as [tex]\( i = \sqrt{-1} \).[/tex]
Similarly, the square root of -18 can be written as [tex]\( \sqrt{-18} = \sqrt{18}i \).[/tex]
Now, to find the sum of these square roots:
[tex]\[ \sqrt{-2} + \sqrt{-18} = \sqrt{2}i + \sqrt{18}i \][/tex]
[tex]\[ = \sqrt{2}i + \sqrt{2 \times 9}i \][/tex]
[tex]\[ = \sqrt{2}i + 3\sqrt{2}i \]\\\\ = (\sqrt{2} + 3\sqrt{2})i \][/tex]
[tex]\[ = 4\sqrt{2}i \][/tex]
So, the sum of[tex]\( \sqrt{-2} \) and \( \sqrt{-18} \)[/tex] is [tex]\( 4\sqrt{2}i \).[/tex]
Help me please !
Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistical analysis in your letter.
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To solve a three-variable system of equations, you can use a combination of the elimination and substitution mehtods.
True or False ...?
Answers
This is the best way to solve these kinds of equations, as you get rid of the unnecessary variables.
Final answer:
True, a combination of the elimination and substitution methods can solve a three-variable system of equations.
Explanation:
The statement is True. We can use a combination of the elimination and substitution methods to solve a three-variable system of equations. In the elimination method, we aim to eliminate one variable by adding or subtracting the equations, allowing us to solve for the remaining variables. This method works well when the coefficients of one variable are opposites in two equations.
In the substitution method, we solve one equation for one variable and substitute this expression into the other equations. This allows us to solve for the remaining variables. This method is more straightforward when one equation can be easily solved for one variable.