The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:
To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2
These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.
The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.
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Mario traced this trapezoid. Then he cut it out and arranged the trapezoids to form a rectangle.
Pls give me a good explanation!
The calculated area of the rectangle is 70 + 7x
From the question, we have the following parameters that can be used in our computation:
Mario cuts out and arranged the trapezoids to form a rectangle.
Using the above as a guide, we have the following:
Area of rectangle = base * height
In this case, we have
base = 10 + x
Where x is the length of the missing side
Next, we have
height = 7
Substitute the known values in the above equation, so, we have the following representation
Area = 7 * (10 + x)
Evaluate
Area = 70 + 7x
Hence, the area of the rectangle is 70 + 7x
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Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. M. }1 p. M. 1, start text, space, p, point, m, point, end text, 2\text{ p. M. }2 p. M. 2, start text, space, p, point, m, point, end text, 3\text{ p. M. }3 p. M. 3, start text, space, p, point, m, point, end text, or 4\text{ p. M. }4 p. M. 4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?
The expected cost of Bob's lunch is $8.75.
To find the expected cost of Bob's lunch, we need to determine the probability that Bob and Anna will meet at Sally's Restaurant at the same time.
There are 4 possible times for Bob and Anna to choose from: 1 PM, 2 PM, 3 PM, and 4 PM. Since they are choosing randomly, the probability of them both choosing the same time is 1/4 (one out of four choices).
Now we can calculate the expected cost of Bob's lunch. If they meet successfully, Bob's lunch will cost $5. If they do not meet, Bob's lunch will cost $10. We can find the expected cost by multiplying the probability of each outcome by its corresponding cost, and then adding these products together.
Expected cost = (Probability of meeting) * (Cost if they meet) + (Probability of not meeting) * (Cost if they don't meet)
Expected cost = (1/4) * $5 + (3/4) * $10
Expected cost = $1.25 + $7.50
Expected cost = $8.75
The expected cost of Bob's lunch is $8.75.
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THIS IS 50 POINTS. This is your opportunity to show a higher level of thinking skills. The challenge is for you to create your own polynomials following the required conditions. Each of your polynomials must include all work showing how you created your final solution. Write each polynomial in two equivalent forms: standard form (ax2 + bx + c) and factored form.
1. Create a polynomial whose GCF is 2x.
2. Create a polynomial with a factor of (x + 1).
3. Create a polynomial with a factor of (2y - 3x).
4. Create a polynomial that is a difference of perfect squares.
5. Create a trinomial with a factor of (y + 4) and a GCF of 3y
A polynomial whose GCF is 2x is 2x(x² + 2x + 3), a polynomial with a factor of (x + 1) is x = (-1 ± sqrt(-3))/2, a polynomial with a factor of (2y - 3x) is -3x(2y² + 1) + 5, a polynomial that is a difference of perfect squares is (4x + 3y)(4x - 3y), and a trinomial with a factor of (y + 4) and a GCF of 3y is (3y + 4x)(y + 4).
1. To create a polynomial whose GCF is 2x, we can start by choosing two terms that have 2x as a common factor. For example, 2x³ and 4x². To make it a polynomial, we can add another term, say 6x. The polynomial in standard form is:
2x³ + 4x² + 6x
To write it in factored form, we can factor out 2x from all terms:
2x(x² + 2x + 3)
2. To create a polynomial with a factor of (x + 1), we can start by choosing two terms that multiply to x², such as x and x. To make it a trinomial with (x + 1) as a factor, we can add another term, such as 1. The polynomial in standard form is:
x² + x + 1
To write it in factored form, we can use the quadratic formula to find the roots:
x = (-1 ± sqrt(1 - 4))/2
x = (-1 ± sqrt(-3))/2
Since the roots are complex, the polynomial cannot be factored further over the real numbers.
3. To create a polynomial with a factor of (2y - 3x), we can start by multiplying two terms that have 2y and 3x as coefficients, respectively. For example, 2y² and -3x. To make it a polynomial, we can add another term, say 5. The polynomial in standard form is:
-6xy² - 3x + 5
To write it in factored form, we can factor out -3x from the first two terms:
-3x(2y² + 1) + 5
4. To create a polynomial that is a difference of perfect squares, we can start by choosing two terms that are perfect squares and have a subtraction sign between them. For example, 16x² and 9y². The polynomial in standard form is:
16x² - 9y²
To write it in factored form, we can use the difference of squares formula:
(4x + 3y)(4x - 3y)
5. To create a trinomial with a factor of (y + 4) and a GCF of 3y, we can start by multiplying two terms that have 3y as a common factor. For example, 3y and 4x. To make it a trinomial with (y + 4) as a factor, we can add another term, say 12. The polynomial in standard form is:
12y + 3y² + 12 + 4xy
To write it in factored form, we can factor out the GCF 3y from the first two terms and factor out (y + 4) from the last two terms:
3y(y + 4) + 4x(y + 4)
(3y + 4x)(y + 4)
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Which figure is a dilation of figure A?
The line passes through the same point on figure A and D.
From the figure, we have the original shape to be figure E
The center point of figure E is the origin
This means that a line drawn from the origin that passes through point A must pass through the same point on the shape
From the figure, the line passes through the same point on figure A and D.
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2 Tom Milk his cow and got 2 litres of Milk He gave Kevin 350 ml and Sold 500m to Bob. How much milk is left?
The amount of milk left is given by A = 1.150 Liters of milk = 1150 mL
Given data ,
Let the total amount of milk be = 2 Liters = 2000 mL
Now , Tom gave Kevin 350 ml and Sold 500mL to Bob
So , the remaining amount of milk is given by A
where A = total amount of milk - 350mL - 500mL
On simplifying the equation , we get
A = 2000 - 350 - 500
A = 1150 mL
Hence , the amount of milk left is 1150 mL
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70% of a class is at lunch what percentage is still studying?
Answer:
30%
Step-by-step explanation:
If there are only 2 categories:
Students at lunch and students studying, then the whole is 100%
100% - 70% = 30%
Helping in the name of Jesus.
A random number generator picks a number from 12 to 41 in a uniform manner. Round answers to 4 decimal places when possible.
a. The mean of this distribution is
b. The standard deviation is
c. The probability that the number will be exactly 36 is P(x = 36) =
d. The probability that the number will be between 21 and 23 is P(21 < x < 23) =
e. The probability that the number will be larger than 26 is P(x > 26) =
f. P(x > 16 | x < 18) =
g. Find the 49th percentile.
h. Find the minimum for the lower quartile
The mean of this distribution is 26.5. The standard deviation is 8.0623. The probability that the number will be exactly 36 is P (x = 36) = 0.0286. The probability that the number will be between 21 and 23 is P (21 < x < 23) = 0.0400. The probability that the number will be larger than 26 is P (x > 26) = 0.2857. P (x > 16 | x < 18) = undefined. The 49th percentile is 29.3700. The minimum for the lower quartile is 19.75.
a. The mean of a uniform distribution is the average of the maximum and minimum values, so in this case, the mean is:
mean = (12 + 41) / 2 = 26.5
Therefore, the mean of this distribution is 26.5.
b. The standard deviation of a uniform distribution is given by the formula:
sd = (b - a) / sqrt(12)
where a and b are the minimum and maximum values of the distribution, respectively. So in this case, the standard deviation is:
sd = (41 - 12) / sqrt(12) = 8.0623
Therefore, the standard deviation of this distribution is 8.0623.
c. Since the distribution is uniform, the probability of getting any specific value between 12 and 41 is the same. Therefore, the probability of getting exactly 36 is:
P(x = 36) = 1 / (41 - 12 + 1) = 0.0286
Rounded to four decimal places, the probability is 0.0286.
d. The probability of getting a number between 21 and 23 is:
P(21 < x < 23) = (23 - 21) / (41 - 12 + 1) = 0.0400
Rounded to four decimal places, the probability is 0.0400.
e. The probability of getting a number larger than 26 is:
P(x > 26) = (41 - 26) / (41 - 12 + 1) = 0.2857
Rounded to four decimal places, the probability is 0.2857.
f. The probability that x is greater than 16, given that it is less than 18, can be calculated using Bayes' theorem:
P(x > 16 | x < 18) = P(x > 16 and x < 18) / P(x < 18)
Since the distribution is uniform, the probability of getting a number between 16 and 18 is:
P(16 < x < 18) = (18 - 16) / (41 - 12 + 1) = 0.0400
The probability of getting a number greater than 16 and less than 18 is zero, so:
P(x > 16 and x < 18) = 0
Therefore:
P(x > 16 | x < 18) = 0 / 0.0400 = undefined
There is no valid answer for this question.
g. To find the 49th percentile, we need to find the number that 49% of the distribution falls below. Since the distribution is uniform, we can calculate this directly as:
49th percentile = 12 + 0.49 * (41 - 12) = 29.37
Rounded to four decimal places, the 49th percentile is 29.3700.
h. The lower quartile (Q1) is the 25th percentile, so we can calculate it as:
Q1 = 12 + 0.25 * (41 - 12) = 19.75
Therefore, the minimum for the lower quartile is 19.75.
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Question 5
Not yet answered
An ice-cream parlor used a scatterplot to record their total sales, in dollars, each day (s) and
the corresponding average temperature, in ºf, on that day (t). They then found a trend line of
this data to be s = 12. 75t + 32. What is the predicted total sales the ice-cream parlor makes
if the average temperature of the day is 72°f?
Marked out of
1. 00
P Flag question
O a.
$950. 00
O b. $820. 00
O c. $1,275. 00
O d. $740. 00
The predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00.
You are asked to find the predicted total sales (s) for the ice-cream parlor when the average temperature (t) is 72°F, using the trend line equation s = 12.75t + 32.
Step 1: Plug the given temperature (72°F) into the trend line equation:
s = 12.75(72) + 32
Step 2: Calculate the value of 12.75(72):
12.75 * 72 = 918
Step 3: Add 32 to the result from Step 2:
918 + 32 = 950
So, the predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00. Therefore, the correct answer is (a) $950.00.
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 the measures of the angles of a triangle are shown in the figure below solve for X
Answer:
x = 13
Step-by-step explanation:
We Know
The sum of angles of a triangle must add up to 180°
We know 2 angles, one is 60° and the other is 90°
Solve for x.
Let's solve
3x - 9 + 60 + 90 = 180
3x + 141 = 180
3x = 39
x = 13
A family spends $550 every month on food. if the family's income is $2,200 each month, what percent of the income is spent on food?
The percentage of the family's income that is spent on food is 25%.
Firstly, noting down the family's monthly spend on food ($550) and their total monthly income ($2,200).
Next, dividing the amount spent on food by the total income to find the ratio of the spend to income: $550 / $2,200.
Now, calculating this division: 550 ÷ 2,200 = 0.25.
Finally, finding the percentage, multiply the ratio (0.25) by 100: 0.25 x 100 = 25%.
So, the family spends 25% of their monthly income on food.
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PLS HELP ME FAST!!!
Write an expression for the sequence of operations described below. Subtract 5 from 7, then divide 3 by the result.Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
Answer:
3 / (7-5)
Step-by-step explanation:
"Subtract 5 from 7"
When you're subtracting from something, the reverse the order of the numbers. So, the expression here would be "7 - 5"
"Then, divide 3 by the result."
Here, you're dividing 3 by the result, so the 3 must be in the numerator (on top of the fraction), and the "result from the previous step must be in the denominator (on the bottom of the fraction). So, the expression here would be "3 / result"
Since order of operations forces division to happen before subtraction, we'll need parentheses around the first result to force the subtraction to happen first, as instructed.
So, the final expression would be "3 / (7-5)"
How many 1/4 cm cubes fit inside the prism below
55 cubes I think because in the end you have to like divide it 2 times.
Answer: 110 cubes
Step-by-step explanation:
First, we will find the volume of this prism.
V = LWH
V = (2.75 cm)(0.5 cm)(1.25 cm)
V = 1.71875 cm³
Next, we will find the volume of the cube.
V = L³
V = (0.25 cm)³
V = 0.015625 cm³
Next, we will divide the prism's volume by the cube's volume.
1.71875 cm³ / 0.015625 cm³ = 110 cubes
12 less than the product of 3 and a number, x, is at most -18
The given inequality is 3x - 12 ≤ -18. To solve for x, we can add 12 to both sides of the inequality to obtain 3x ≤ -6. Then, dividing both sides of the inequality by 3 gives x ≤ -2. Therefore, any value of x less than or equal to -2 will satisfy the inequality.
In solving the inequality, we first used the addition property of inequalities to add 12 to both sides of the inequality. This property states that if a < b, then a + c < b + c, where c is any real number. By adding 12 to both sides, we were able to isolate the variable term on one side of the inequality.
Next, we used the division property of inequalities to divide both sides of the inequality by 3. This property states that if a < b and c > 0, then a/c < b/c. By dividing both sides of the inequality by 3, we were able to solve for x.
Finally, we found that any value of x less than or equal to -2 will satisfy the inequality. This means that the solution set for the inequality is {x | x ≤ -2}. We also verified that x = -2 is a valid solution to the inequality, which confirms our solution.
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Will mark brainliest if correct
Step-by-step explanation:
See image for calculations:
(Note that interior angle + exterior angle = 180 degrees)
AND sum of exterior angles = 360 that is where the first formula comes from.
About 8 out of 10 people entering a community college need to take a refresher mathematics course. if there
are 850 entering students, how many will probably need a refresher mathematics course?
Approximately 680 out of the 850 entering students will probably need to take a refresher mathematics course which is calculated using simplified fraction.
We are given that about 8 out of 10 people entering a community college need to take a refresher mathematics course. We need to find out how many of the 850 entering students will probably need this course.
Step 1: Determine the proportion of students who need the refresher course.
The proportion is 8 out of 10, which can be written as a fraction: 8/10.
Step 2: Simplify the fraction.
Divide both the numerator (8) and the denominator (10) by their greatest common divisor, which is 2:
8 ÷ 2 = 4
10 ÷ 2 = 5
So, the simplified fraction is 4/5.
Step 3: Calculate the number of students who need the refresher course.
To find the number of students who probably need the course, multiply the total number of entering students (850) by the simplified fraction (4/5):
850 * (4/5) = (850 * 4) / 5 = 3400 / 5 = 680
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D is the centroid of PQR PA= equals 17 BD equals nine and DQ equals 14 find each missing measure
The centroid of the triangle is D and the measures of sides are solved
Given data ,
Let the triangle be represented as ΔPQR
Now , the centroid of the triangle is D
where the measure of PA = 17 units
The measure of BD = 9 units
And , the measure of side DQ = 14 units
Now , centroid of a triangle is formed when three medians of a triangle intersect
And , from the properties of centroid of triangle , we get
PA = AR
DR = DQ
AD = BD
On simplifying , we get
The measure of side AR = 17 units
PR = PA + AR = 34 units
The measure of side DR = 14 units
BR = BD + DR = 23 units
The measure of side AD = 9 units
AQ = AD + DQ = 23 units
Hence , the centroid is solved
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(7) = -1
B.
g(0) = 2
C.
g(-13) = 20
D.
g(-4) = -11
The option that can be true for the function g(x) is C; g(-13) = 20
Which statement could be true?Here we know that the function g(x) has:
The domain ---> -20 ≤ x ≤ 5
The range ---> -5 ≤ g(x) ≤ 45
And g(0) = -2
g(-9) = 6
There are two statements that could be true:
g(-13) = 20, because -13 belongs to the domain and 20 belongs to the range.
g(0) = 2 could also be true.
Now, we can see that g(-9) > g(0), then as x becomes smaller, g increases, then the option that seems to be correct is g(-13) = 20
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find cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9°. Enter c rounded to 2 decimal places. C= mi Assume LA is opposite side a, ZB is opposite side b, and ZC is opposite side c.
Cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9° and c^2 = a^2 + b^2 - 2ab*cos(C)where C is the angle opposite to side c, c comes to be ≈ 4.26 mi.
The Law of Cosines is a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them. To get side c, we can use the law of cosines, which states that c² = a² + b² - 2ab cos(C).
Plugging in the given values, we get:
c² = (2.74)² + (3.18)² - 2(2.74)(3.18)cos(41.9°)
c² ≈ 18.126
Taking the square root of both sides, we get:
c ≈ 4.26 mi
Rounding to 2 decimal places, c ≈ 4.26 mi.
Therefore, the answer is: c ≈ 4.26 mi.
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Mark invests $5,000 and earns $375 in simple interest over a 3 year period. What was the interest rate on the investment? answer is 2.5%
In May, the cost for a child is not changed. The cost for an adult is reduced by p % to $22.10. (i) Calculate p.
The cost for an adult is reduced by approximately 26.33% to $22.10.
How to solveThe original cost for an adult ticket (X) = $30
The reduced cost for an adult ticket = $22.10
We need to find the percentage decrease (p) from the original cost to the reduced cost:
p = ((Original cost - Reduced cost) / Original cost) * 100
p = (($30 - $22.10) / $30) * 100
p = ($7.90 / $30) * 100
p ≈ 26.33 %
The fee for an adult has notably decreased by approximately 26.33%, now costing a mere $22.10.
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In May, the cost for a child is not changed. The cost for an adult is reduced by p % to $22.10. If the original cost of an adult ticket is $X, (i) calculate p, given that the original cost for an adult ticket is $30.
which of the following becomes key indicator of whether or not a hypothesis can be supported? a. chi-square b. degrees of freedom c. significance level d. critical value
The significance level is the key indicator of whether or not a hypothesis can be supported. (option c)
In statistical analysis, there are several key indicators that are used to determine whether a hypothesis can be supported. One of these indicators is the significance level, which is denoted by the symbol alpha (α).
Another key indicator is the critical value, which is a value that is determined from a statistical distribution and is used to determine whether the observed data is statistically significant.
The test compares the observed frequencies of the categories to the expected frequencies, assuming that there is no association between the variables. The degrees of freedom refer to the number of categories minus one.
Therefore, to answer the original question, option (c)
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The mean of the data set below is 11. What is the value of x? Explain.
12, 9, 12.5, 13, x, 10, 11, 11, 7, 9
From the given data 11 is the mean of the data set.
What is Mean ?
In statistics, the mean (also called the average) is a measure of central tendency that represents the typical value in a data set. It is calculated by adding up all the values in the data set and dividing by the number of values.
To find the value of x in the data set, we can use the formula for the mean (also called the average). The mean is calculated by adding up all the values in the data set and dividing by the number of values. In other words:
mean = (sum of all values) : (number of values)
We are given that the mean of the data set is 11, so we can write:
11 = (12 + 9 + 12.5 + 13 + x + 10 + 11 + 11 + 7 + 9) : 10
Here, we have 10 values in the data set (including the unknown value x), so we divide the sum of all the values by 10 to find the mean.
To solve for x, we can start by simplifying the right-hand side of the equation:
110 = 75.5 + x
Next, we can isolate x by subtracting 75.5 from both sides:
x = 34.5
Therefore, the value of x that makes the mean of the data set equal to 11 is x = 34.5.
In other words, if we replace the unknown value x with 34.5, the resulting data set will have a mean of 11. This means that the sum of all the values in the data set will be 110, since:
12 + 9 + 12.5 + 13 + 34.5 + 10 + 11 + 11 + 7 + 9 = 110
And when we divide this sum by 10, we get:
110 : 10 = 11
Therefore, From the given data 11 is the mean of the data set.
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Kaylie put $900 in a savings account, earning 11% interest for 7 years. she did not make any additional deposits or withdrawals. what is the amount of interest kaylie earned?
Kaylie earned $693 in interest on her savings account.
What was the total amount of money Kaylie had in her savings account after 7 years of depositing $900 and earning 11% interest on it?Kaylie deposited $900 in a savings account and earned 11% interest on it for 7 years. After the 7-year period, Kaylie earned $693 in interest, which was compounded annually.
This brought the total amount of money in her savings account to $1,593. The power of compounding interest in savings accounts can help grow your money significantly over time.
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at a local farmers market a farmer pays $10 to rent a stall and $7 for every hour he stays there. if he pays $45 on saturday how many hours did he stay at the market
Answer: 5
Step-by-step explanation:
10 + 7h = 45
-10 -10
7h = 35
divide by 7 to both sides
h = 5
PLEASEEEEEE HELP ME!!!!!
VERY IMPORTANT!!!!
Amelie spins the following spinner, which has 10
equally sized spaces numbered 1
through 10. The numbers 1 and 7 are colored blue; the numbers 2, 4, and 6 are red; and the numbers 3, 5, 8, 9, and 10 are green. What is the probability that Amelie spins either an odd number or a red number?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
4/5
Step-by-step explanation:
In probability, if there are two events and "or" is used, we will add the probabilities of each event. Since the event that an odd number is spun does not affect whether a red number is spun, we can calculate the probability of each event separately:
Probability of spinning an odd number:
5/10 because there are 5 odd numbers possible & 10 outcomes
Probability of spinning a red number:
3/10 because there are 3 red numbers & 10 outcomes
Now add the probability of each event:
5/10 + 3/10 = 8/10 = 4/5
A bicycle mechanic wants to put a strip of plastic between the tube and tire of a 26-in. diameter bicycle tire. to the nearest inch, how long should the strip of plastic be?
The bicycle mechanic should cut a strip of plastic approximately 82 inches long to place between the tube and tire of the 26-inch diameter bicycle tire.
To calculate the length of the strip of plastic needed, we first need to determine the circumference of the tire. The formula for the circumference of a circle is C=2πr, where C is the circumference, π is approximately 3.14, and r is the radius of the circle.
In this case, the tire diameter is 26 inches, so the radius is 13 inches (half of the diameter). Therefore, the circumference of the tire is: C = 2πr = 2π(13) = 81.64 inches (rounded to two decimal places)
To ensure that the strip of plastic fits snugly between the tube and tire, it should be the same length as the circumference of the tire. Therefore, the strip of plastic should be 82 inches long (rounded to the nearest inch).
In summary, the bicycle mechanic should cut a strip of plastic that is 82 inches long to fit between the tube and tire of the 26-inch diameter bicycle tire.
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The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the
cost of each.
Answer:
Let's solve this problem using algebra. Let x be the cost of one orange and y be the cost of one apple. Then we have the system of equations:
12x + 7y = 5.36
8x + 5y = 3.68
To solve for x and y, we can use elimination. Multiplying the second equation by 3 and subtracting it from the first equation multiplied by 5, we get:
(5*12 - 7*8)x + (5*7 - 3*5)y = 26.8 - 11.04
20x = 15.76
x = 0.788
Substituting x back into one of the equations, we can solve for y:
12(0.788) + 7y = 5.36
y = 0.308
Therefore, one orange costs $0.788 and one apple costs $0.308.
Calcula dos numeros cuya suma sea 191 y su diferencia 67
The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .
You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.
We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67
Now we can solve this system of linear equations to find the values of x and y.
We can start by adding both equations:
(x + y) + (x - y) = 191 + 67
2x = 258
Then we'll divide by 2 to find the value of x:
x = 129
Now, we can plug x into Equation 1 to find the value of y:
129 + y = 191
y = 191 - 129
y = 62
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Ifj is inversely related to the cube of k, and j = 3 when k is 6, which of the following is another possible value for j and K?
(A) j = 18, k = 2
(B) j=6, k = 3
(C) j=81, k = 2
(D) j = 2, k = 81
(E) j = 3, k=2
Another possible value for j and K is (A) j = 18, k = 2
How to determine the valuesNote that in inverse variation, one of the variables increases while the other decreases.
From the information given, we have that;
j is inversely related to the cube of k,
This is represented as;
j ∝ 1/k³
Now, find the constant of variation
K = jk³
Substitute the vales
K = 3 × 6³
find the cube value
K = 648
Then, we have that;
j = 648 / 2³ = 81
For option B:
j = 648 / 3³ = 24
For option C:
j = 648 / 2³ = 81
For option D:
j = 648 / 81³ = 0.0008
For option E:
j = 648 / 2³ = 81
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Determine the equation of the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3
The equation for the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3 is:
y = (1/2)*x - 2
How to find the equation of the line?Remember that two linear equations are perpendicular if the product between the slopes is -1, here we want a line perpendicular to:
y =-2x+3
Then if the slope of our line is a, we must have that:
a*-2 = -1
a = 1/2
Then our line is something like:
y = (1/2)x + b
Now we also want our line to pass through (3, -1/2), then:
-1/2 = (1/2)*3 + b
-1/2 = 3/2 + b
-1/2 - 3/2 = b
-2 = b
The linear equation is:
y = (1/2)*x - 2
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