To find the product of the expression (a-3/7) divided by (3-a/21), multiply (a-3/7) by the reciprocal of (3-a/21), yielding the simplified expression ((21a - 9)/ (21a - 7)) valid for all values of 'a' except when 'a' equals 8/3.
Explanation:The student is asking for the product of the expression (a-3/7) divided by (3-a/21). To simplify this expression, we need to apply the division of fractions rule, which states that to divide by a fraction, you multiply by its reciprocal. The reciprocal of (3-a/21) is (21/(3a-1)). So our new expression is (a-3/7) × (21/(3a-1)).
We can multiply the numerators and denominators separately: (a-3/7) × 21 = (a× 21 - 3× 3) and 7 × (3a-1) = 21a-7. Simplified, we get ((21a - 9)/ (21a - 7)) as the product.
However, we should also check if the expression is defined for all values of 'a' as there may be values for which the denominator becomes zero. Specifically, we need 'a' to not be such that (3a-1) equals 7, which simplifies to a = 8/3. So for all values of 'a' except when 'a' equals 8/3, the product of the given expression is ((21a - 9)/ (21a - 7)).
Figure ABCD is a trapezoid with point A (0, −4). What rule would rotate the figure 270° clockwise?
Answer-
The rule (x, y) → (-y, x) would rotate the figure 270° clockwise and after rotation the coordinate of A will be (4, 0)
Solution-
ABCD is a trapezoid with vertex A at (0, -4)
The trapezoid ABCD is rotated 270°.
While rotating a point with coordinate (x, y) 270° clockwise, its new coordinate will be (-y, x)
So applying the rule, new coordinate of A will be (4, 0)
Therefore, the rule (x, y) → (-y, x) would rotate the figure 270° clockwise and after rotation the coordinate of A will be (4, 0)
the 400ths power of number is 9^1000 what is the number
Wich is bigger two thirds of 30 or one fifth of 25?
the length of a rectangle is 6 units shorter than 1/4 of the width x. Write an expression for the perimeter of the rectangle.
what is the improper fraction of 7/2
The normal body temperature of a camel is 37° C this temperature varies by up to three degrees C throughout the day write and solve an absolute value inequality that represents the range of normal body temperatures in degrees celsius of a camel throughout the day
Is the number of calories you have burned since midnight at any time during the say a function\?
A tank initially contains 200 gallons of brine, with 50 pounds of salt in solution. brine containing 2 pounds of salt per gallon is entering the tank at the rate of 4 gallons per minute and is is flowing out at the same rate. if the mixture in the tank is kept uniform by constant stirring, find the amount of salt in the tank at the end of 40 minutes. the amount of salt in the tank at the
Final answer:
The amount of salt in the tank at the end of 40 minutes is still 50 pounds.
Explanation:
To find the amount of salt in the tank at the end of 40 minutes, we need to calculate the change in the amount of salt in the tank over that time period.
The tank contains 200 gallons of brine with 50 pounds of salt in solution. Brine containing 2 pounds of salt per gallon is entering and exiting the tank at a rate of 4 gallons per minute.
Since the rate of flow in and out of the tank is the same, the amount of salt in the tank remains constant. Therefore, the amount of salt in the tank at the end of 40 minutes is still 50 pounds.
A city's sales tax is 0.07write this decimal as a fraction and tell how many cents of tax are on each dollar
without using a calculator order the numbers from least to greatest square root of 200, 15, and 14
To order the numbers from least to greatest, estimate their square roots: 14 < 14.14 < 15.
Explanation:To order the numbers from least to greatest, we need to compare their square roots. Without using a calculator, we can estimate the square roots to determine the order.
The square root of 200 is approximately 14.14.The square root of 15 is approximately 3.87.The square root of 14 is approximately 3.74.Therefore, the order from least to greatest is 14 < 14.14 < 15.
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Chris said that it is 31 days until his birthday. how many hours until his birthday? minutes? second?
4 1
__ / ( - __ )
5 15
I hope you got satisfied
What is -9/10 - 7.1?
A composite number can be written as the product of prime numbers
frank finished his history assignment 1/5 hours then he completed his math assignment in 2/3 hours what is the total amount of time Frank's been doing these two assignments write your answer in simplest fraction form
The total amount of time Frank's been doing these two assignments will be 13 / 15 hours.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Frank finished his history assignment in 1/5 hours then he completed his math assignment in 2/3 hours.
Then the total amount of time Frank's been doing these two assignments will be
⇒ 1/5 + 2/3
⇒ (3 + 2 x 5) / 15
⇒ 13 / 15 hours
The total amount of time Frank's been doing these two assignments will be 13 / 15 hours.
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What is 681,542 rounded to the nearest hundred thousand.
Antonio is ready to move out of his parent's house and live on his own. He found a great apartment that has all utilities included. His job as an assistant plumber requires him to have a car, but his hours are flexible enough to give him time on the weekends to have fun with his friends. What is the best way Antonio's budget can be modified to help him save enough for the $200 down payment and make the $500 monthly rental payment? Monthly Budget Old Budget New Budget Income Wages $1500 $1500 Expenses Food Cell Phone Savings Entertainment Car Expenses . $250 $175 $200 $200 $300 . $____ $____ $____ $____ $____ Net Income $375 $____ a. Antonio could keep his budget the same and hope he gets a raise at work. b. Antonio could reduce his monthly entertainment expenses by $100 to help pay the monthly rent. He could take $200 out of savings once for the deposit. c. Antonio could live at his parent’s house for one more month and save his net income. After one month of living at home, he would have enough additional money for the deposit and one year’s rent at the apartment. d. Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit.
Answer:
d. Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit.
Step-by-step explanation:
As you can see, Antonio´s expenses add up to a total of $1,125 a month
Expenses:
Food $250
Cellphone $175
Savings $200
Entertainment $200
Car $300
Total: $1175
So he has $375 each month free to pay for the rent, he is $125 short of making it to the $500 monthly rent, so he only has to cut expenses for $125 dollars, by reducing his food expenses $75 and his entertainment expenses $50 he makes the $125 that he is lacking and is able to afford the $500 monthly rent.
a painter works 37.5 hours one week. If she worked 5 days, how many hours did she work on average per day?
Graph a line passing through the point left (−3,6) and having the slope one third. Give the slope-intercept form of the equation of the line if possible.
The equation of the line passing through the point (-3,6) with a slope of a third is y = 1/3x + 7. The graph of this line can be drawn by plotting the y-intercept at (0,7) and using the slope to plot other points.
Explanation:The provided point through which the line passes is (-3,6) and the slope is a third. The general slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept. That is, it represents the point where the line intersects the y-axis.
Let's use this information to find the equation of the line. We know that y = mx + b. We can substitute the slope (m=1/3) and the point (-3, 6) into this equation: 6 =(1/3)(-3) + b.
Solving this for b gives us b = 6 + 1 = 7. Therefore, the equation of the line in slope-intercept form is y = 1/3x + 7.
To graph the line, you can start by plotting the y-intercept at (0,7) on the y-axis, then rise 1 unit and run 3 units (since the slope = rise/run = 1/3) from the y-intercept point to plot the second point. Connect these points to draw the line.
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the point (4,7) is on the graph of y=x^2+c. what is the value of c?
The value of c in the equation y = x² + c, given the point (4,7) lies on the graph, is found to be -9 after substituting the point's coordinates into the equation and solving for c.
To find the value of c in the equation y = x² + c, where the point (4,7) is on the graph, we substitute the x and y values from the point into the equation. This gives us:
7 = 4² + c
7 = 16 + c
Now, we subtract 16 from both sides to solve for c:
c = 7 - 16
c = -9
Therefore, the value of c is -9.
0.8 is 10 times as great as wich decimal?
Estimate the quotient 24 3/7÷3 7/13
12-5x-4kx=y solve for x
the mantle layer of earth begins about 70 kilometers underneath the surface. The layer called the outer core begins about 2970 kilometers underneath the surface. Write an interger for the position of each layer relative to the surface
In the 2011 new york marathon 29867 men finished the race, and 16928 women finished the race. Each finisher was given a t-shirt. About how many men's shirts were given away? About how many women's shirts were given away? Explain how you found your answers.
The number of t-shirts given to men is 29867 and the number of t-shirts given to women is 16928.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Given that,
Each male finisher has given a t-shirt
So,
Number of men finishers = number of t shirt
Since,
number of t-shirts given to man = 29867
Similarly,
Each women's finisher has given a t-shirt
So,
Number of women's finishers = number of t-shirts
So,
number of t-shirts given to women = 16928
Hence "The number of t-shirts given to men is 29867 and the number of t-shirts given to women is 16928".
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Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
Final answer:
Larry's new solution has an approximate salt concentration of 11.33%. This was calculated by adding the initial mass of salt in the solution (10.5 g) to the extra salt added (15 g), resulting in a new total mass of salt (25.5 g), then dividing by the total mass of the new solution (225 g), and finally multiplying by 100%.
Explanation:
To find the percent of salt in Larry's new solution, we first need to calculate the total mass of the solution and how much of that mass is salt. Initially, we have 210 grams of a 5% salt solution. To find out how much salt that is, we use the percentage:
210 g × 0.05 = 10.5 g of salt
Now, Larry adds 15 grams of salt to this solution, so we add that amount to the initial salt mass:
10.5 g + 15 g = 25.5 g of salt
The total mass of the new solution is the sum of the mass of the original solution and the added salt:
210 g + 15 g = 225 g
Finally, to find the mass/mass percent concentration of the new solution, we divide the total mass of salt by the total mass of the solution and multiply by 100%:
((25.5 g / 225 g) × 100% = 11.33%
So, the percent of salt in Larry's new solution is approximately 11.33%.
Best way to work out planet torrid take 6 years to complete one orbit , planet monde blanc takes 9 years in the year 2035 both planets are lined up perfectly.
How many years will it be before the two worlds are line up again ?
alyssa received 30,000 from an inheritance and invests in a certificate of deposit paying 5% annual interest and the rest in apple inc. offering an annual return of 11%. if the annual income from her income from her investment is 2220.00, how much did alyssa invest in each?
A birds nest is 12 feet above the ground. A moles den is 12 inches below the ground. What is the difference in height of these 2 positions?
Final answer:
The difference in height between the bird's nest and the mole's den is 132 inches.
Explanation:
To find the difference in height between the bird's nest and the mole's den, we need to convert the measurements to the same units. The nest is 12 feet above the ground, which is equivalent to 12 x 12 = 144 inches above the ground. The mole's den is 12 inches below the ground. To find the difference, we subtract the depth of the mole's den from the height of the bird's nest: 144 - 12 = 132 inches.
Final answer:
To find the difference in height between the bird's nest and the mole's den, convert the measurements to the same unit and calculate the total difference.
Explanation:
To find the difference in height between the bird's nest and the mole's den, we need to convert the measurements to the same unit. Since the bird's nest is 12 feet above the ground and the mole's den is 12 inches below the ground, we can convert both measurements to inches. There are 12 inches in a foot, so the bird's nest is 12 x 12 = 144 inches above the ground. The difference in height is then 144 inches + 12 inches (negative sign since it's below the ground) = 156 inches.
A line can be defined in general form by the equation Ax+By = C where A, B and C are constants. You may assume that both A and B are non-zero. Then the slope of the line is , its x intercept is , and its y intercept is . Of course your answers will depend on A, B, and C. Remember that mathematics, and WeBWorK, are case sensitive, so make sure to use upper case letters A, B and C.
Final answer:
The slope of a line in general form can be found by rearranging the equation to solve for y. The x-intercept is obtained by setting y = 0 and solving for x, while the y-intercept is obtained by setting x = 0 and solving for y.
Explanation:
The slope of a line defined in general form by the equation Ax+By = C can be found by rearranging the equation to solve for y, resulting in y = (-A/B)x + (C/B). The coefficient of x, -A/B, represents the slope of the line. The x-intercept can be found by setting y = 0 and solving for x, resulting in x = C/A. Similarly, the y-intercept can be found by setting x = 0 and solving for y, resulting in y = C/B.