The real number resulting from the expression x-y/xy is positive when x is negative and y is positive. This is determined by following the rules of signs in arithmetic where subtracting a positive number from a negative results in a negative and dividing a negative number by another negative results in a positive.
Explanation:The given expression in question is x-y/xy. To understand the sign of the resulting real number we have to discern the signs of x, y and the result of subtraction, x-y.
As mentioned, x is less than 0 and hence negative and y is greater than 0, thus positive. So when you subtract a positive number y from the negative number x, the result will obviously be negative. This is due to the 'rules of signs' in arithmetic.
Then, for the division, when you divide this negative result by the multiplication of x (which is negative) and y (which is positive), the answer will be positive. This is again because of the 'rules of signs' for division - a negative number divided by a negative number yields a positive number.
So, the sign of the result of the real number expression x-y/xy is positive when x<0 and y>0.
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Bobby will buy coffe and hot chocolate for his co-workers each cup of coffe costs $2.25 and each cup of hot chocolate costs $1.50 .he pays a total of $15.75 for 8 cups
( please answer me as quickly as possible)
Final answer:
Bobby can buy 5 cups of coffee at $2.25 each and 3 cups of hot chocolate at $1.50 each to meet his budget of $15.75 for 8 cups in total. We find this by solving a system of equations.
Explanation:
Bobby wants to buy a total of 8 cups of coffee and hot chocolate for his co-workers with a budget of $15.75. Since each cup of coffee costs $2.25 and each cup of hot chocolate costs $1.50, we need to find out how many cups of each he can buy.
Let's denote the number of cups of coffee as C and the number of cups of hot chocolate as H.
The total cost for coffee will be $2.25 × C and for hot chocolate $1.50 × H.
The total amount spent is $15.75, and the total number of cups is 8, so we have two equations: 2.25C + 1.50H = 15.75 and C + H = 8.
We can solve this system of equations using substitution or elimination. For simplicity, we'll use substitution.
From C + H = 8, we can express H in terms of C: H = 8 - C.
Substitute H in the cost equation: 2.25C + 1.50(8 - C) = 15.75.
Simplify and solve for C: 2.25C + 12 - 1.50C = 15.75, which simplifies to 0.75C = 3.75, and therefore C = 5.
Now, plug C = 5 into H = 8 - C to find H: H = 3.
Bobby can buy 5 cups of coffee and 3 cups of hot chocolate.
At first public inquiry showed there were 637000 women motorcyclists in the US up from 437000 just 8 years ago before it. Find the percent of increase in the number of women motorcyclists during these 8 years
The percent of increase in the number of women motorcyclists over the 8-year period is approximately 45.77%, calculated by finding the difference between the final and initial number of motorcyclists, dividing by the initial number, and converting the ratio to a percentage.
Explanation:To calculate the percent of increase in the number of women motorcyclists over the 8-year period provided, follow these steps:
Determine the initial and final values. Initial value: 437,000; Final value: 637,000.
Calculate the increase by subtracting the initial value from the final value: 637,000 - 437,000 = 200,000.
Divide the increase by the initial value to find the increase ratio: 200,000 / 437,000 ≈ 0.4577.
Multiply the increase ratio by 100 to convert it to a percentage: 0.4577 * 100 ≈ 45.77%.
Therefore, the percent of increase in the number of women motorcyclists during these 8 years is approximately 45.77%.
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(x + 2)4 = x4 + 8x3 +... Use the Binomial Theorem to complete the binomial expansion. Enter only the next three terms; use the ^ key for exponents, example: 10x^2+20x+30.
A rectangle has a length of x inches and a width 2 inches less than the length. If the dimensions were tripled what would be the area of the new rectangle in terms o x
simplify the ratio
60 cents: $2
The ratio 60 cents: $2 simplifies to 3:10 after converting dollars to cents and dividing both terms by the greatest common divisor, which is 20.
To simplify the ratio 60 cents: $2, we need to first express both quantities in the same units. Since 1 dollar is equal to 100 cents, $2 is equivalent to 200 cents. Thus, the ratio becomes 60 cents : 200 cents.
Next, we simplify the ratio by dividing both sides by the greatest common divisor. In this case, both 60 and 200 are divisible by 20, which is the greatest common divisor. So we divide both sides by 20:
[tex]\frac{60}{20}[/tex] = 3
[tex]\frac{200}{20}[/tex] = 10
Therefore, the simplified ratio is 3:10.
Sanjay’s dog weighs 46 pounds on earth. multiply the dog’s earth weight by 0.38 to find how much it would weigh on mars, and by 2.36 to find how much it would weigh on jupiter. how much less would the dog weigh on mars than on jupiter
Factors of 14 least to greatest
Can anyone show me steps on how to solve this equation.. I will upvote!
5x+7=4x+10
Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents. ( 4 x 3 y −2 ) 3 (4x3y-2)3
1.For f(x)= 5x+1 : Find(-4).
a.-19 b.1 c.-21 d. 21
2. Write in Standard form an equation of the line passing through the given point with the given slope.
slope=-8 ; (-2,-2)
a.8x+y=-18 b.-8x+y=-18 c. 8x-y=-18 d.8x+y=18
1.a. -19 at x = -4 for f(x) = 5x + 1.
2.a. 8x + y = -18 the standard form of the equation.
What is a line ?A line has no definite length it can extend in both the directions indefinitely.
According to the given question a functions f(x) = 5x + 1 is given and we have to find the value of this function when x = -4.
Given f(x) = 5x + 1
f(-4) = 5(-4) + 1
f(-4) = -20 + 1
f(-4) = -19.
In the second question we have to write an equation of the line passing through the point (-2,-2) with slope -8.
We know equation of a line in slope intercept form is y = mx + b.
∴ -2 = (-8)(-2) + b
-2 = 16 + b
b = - 18.
So, y = -8x -18 OR 8x + y = -18.
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What is 110.079 to the nearest hunderdths?
Which of the following relations are functions?
A. {(a,b),(b,a),(c,c),(e,d)}
B. {(c,e),(c,d),(c,b)}
C. {(b,b),(c,d),(d,c),(c,a)}
D. {(a,b),(b,c),(c,d),(d,e)}
x^2-14x-4=0, solve by completing the square
The solution of the equation found by completing the square are;
x = 7 - √(53) and 7 + √(53)
What is the completing the square method?Completing the square method involves writing the quadratic expression of the form a·x² + b·x + c as (x + d)² + e, where d and e are constants.
Moving the constant to one side of the equation, we get;
x² - 14·x = 4
We complete the square on the left side of the equation by adding and subtracting the square of the half the coefficient of x term inside the parenthesis. Therefore, we add and subtract (-14/2)² = 49, as follows;
(x² - 14·x + 49) - 49 = 4
Therefore; (x - 7)² - 49 = 4
The -49 is moved to the right side of the equation to get;
(x - 7)² = 4 + 49 = 53
Taking the square root of both sides, we get;
x - 7 = ± √(53)
Therefore; x = 7 ± √(53)
The solution is; x = 7 + √(53) and 7 - √(53)
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What is the value of the sum 5 + 10 + 15 + ... + 95 + 100? ...?
A number n is at least 7
The inequality would be equal to n ≥ 7.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We are given that the phrase as;
"A number n is at least 7"
Therefore, the inequality would be;
n ≥ 7
Or
n = 7
Thus, the inequality would be equal to n ≥ 7.
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Use the prime factoriations of 24 and 28 to find their greatest common factor
Tim is buying packages of paper plates and cups. He wants to have equal amounts of each, but plates come 24 per pack, and cups come 16 per pack. What is the least amount of plates and cups Tim will have to buy to get the same number of each?
8
16
24
48
!!!!!!!!!!!!!!!!!!!!!!HELP ASAP!!!!!!!!!!!!!!!!!!!!
Jayden used the following steps to simplify the given expression.
-3 + 2(2 + x + 3)
Step 1: = -3 + 2(x + 2 + 3)
Step 2: = -3 + 2(x + 5)
Step 3: = -3 + 2x + 10
Step 4: = 2x + (-3) + 10
Step 5: = 2x + 7
What property of real numbers was used in step 3?
A)distributive property
B)associative property of addition
C)commutative property of addition
D)associative property of multiplication
Answer:
Option A -distributive property
Step-by-step explanation:
Given : expression -3 + 2(2 + x + 3)
Step 1: = -3 + 2(x + 2 + 3)
Step 2: = -3 + 2(x + 5)
Step 3: = -3 + 2x + 10
Step 4: = 2x + (-3) + 10
Step 5: = 2x + 7
In step 3 distributive property is applied i.e. c(a+b)=ca+cb
in step 2- 2(x+5) when we apply distributive property it became
2x+10
Therefore, option A is correct
A dilation on a rectangle has a scale factor of 4. what is the effect on the perimeter of the rectangle ? ...?
The dilation of a rectangle with a scale factor of 4 will result in each side of the rectangle being multiplied by 4, thus the perimeter will also be quadrupled.
Explanation:When a rectangle undergoes a dilation with a scale factor of 4, the lengths of all sides of the rectangle are multiplied by 4. Since perimeter is the sum of all the side lengths of a rectangle, the perimeter will also be affected by the scale factor. Therefore, if the original perimeter of the rectangle is P, the new perimeter after dilation will be 4 × P.
Using the property of dilations, the new dimensions of the rectangle will be proportional to the original dimensions. For example, if the original length l and width w of the rectangle are scaled by a factor of 4, the new dimensions will be 4l and 4w respectively. Subsequently, the new perimeter will be 2(4l + 4w) which is the same as saying 4 × (2l + 2w), proving the perimeter is scaled by the same factor of 4.
The amount of weight that Sam loses is directly proportional to the number of hours he spends exercising. If Sam loses a pound of weight for each 3 hrs of exercise, how many hours must he spend exercising to lose 25 lbs?
A) 25 hrs
B) 50 hrs
C) 75 hrs
D) 80 hrs
Answer:
The answer is C. 75 hours.
Step-by-step explanation:
In order to determine the hours, we have to know about direct proportionality.
The direct proportionality happens when two variables increase at the same time and their rate is a constant. It means that if one variable is increased, so the other variable will be increased too.
I have attached an image that shows a graph of two variables with direct proportionality.
In this case, we can get the constant of both variables: losing weight and the spending time.
[tex]k=\frac{Weight}{Time}=\frac{1}{3} =0.33[/tex]
Then we need to know how many hours Sam will spend to lose 25 lbs:
[tex]\frac{25}{T}=k=0.33\\ T=\frac{25}{0.33}\\ T=75.76[/tex] hours.
Finally, Sam needs to spend 75 hours to lose 25 lbs.
Which mathematical property is demonstrated?
5 + 3w + 2 = 5 + 2 + 3w
associative property of addition
commutative property of multiplication
associative property of multiplication
commutative property of addition
Answer:
commutative property of addition
Step-by-step explanation:
Verify the identity.
tan(x+(pi/2)) = -cot x
Write the expression 4 log x − 6 log (x + 2) as a single logarithm
To write the expression 4 log x − 6 log (x + 2) as a single logarithm, apply the properties of logarithms.
Explanation:To write the expression 4 log x − 6 log (x + 2) as a single logarithm, we can make use of the following logarithmic properties:
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log(xy) = log(x) + log(y)The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log(x)The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log(x) - log(y)Using these properties, we can simplify the given expression as follows:
4 log x − 6 log (x + 2) = log(x^4) - log((x + 2)^6)
Therefore, the expression can be written as the single logarithm log(x^4) - log((x + 2)^6).
Help Please
A group of 9 friends go bowling.How many different possibilities are there for the order in which they play if the youngest person is to bowl first.
Please explain your answer. Thanks ...?
write an equation in slope intercept form with a slope 3/2 and y-intercept -2
what number is 82% of 230
Solve (x + 2 < 5) (x - 7 > -6).
Please help
Juan charges $3.50 per hour for babysitting. Write a rule to describe the amount of money (M) earned is a function of the number of hours (h) spent baby-sitting. HELP PLEASE
a boat travels 66 miles in 2 hours. what is its rate in feet per minute?
The rate of the boat that travels 66 miles in 2 hours is approximately 2904 feet per minute.
Given:
Distance traveled = 66 miles
Time taken = 2 hours
We know that:
1 mile = 5280 feet
66 miles = 66 [tex]\times[/tex] 5280
348,480 feet
Next, we'll convert the time from hours to minutes.
1 hour = 60 minutes,
2 hours = 120 minutes
Now, we can calculate the rate in feet per minute:
Rate (feet per minute) = [tex]\dfrac{ Distance \ in\ feet}{Time\ in\ minutes}[/tex]
Rate = [tex]\dfrac{348480}{120}[/tex]
Rate ≈ 2904 feet per minute
So, the rate of the boat is approximately 2904 feet per minute.
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Another math help ^_^