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Alika [10]
2 years ago
5

Manny is making 12 quarts of orange juice from concentrate and water. The number of quarts of water is 3 times the number of qua

rts of concentrate. How many quarts of concentrate and how many quarts of water does Manny need?
Mathematics
1 answer:
trasher [3.6K]2 years ago
8 0

Answer: There are 3 quarts of concentrate and 9 quarts of water.

Step-by-step explanation:

Since we have given that

Ratio of number of quarts of water to number of quarts of concentrate is

3:1

Number of quarts of orange juice from concentrate and water = 12 quarts

So, the number of quarts of concentrate would be

\dfrac{1}{4}\times 12\\\\=\dfrac{12}{4}\\\\=3\ quarts

the number of quarts of water would be

\dfrac{3}{4}\times 12\\\\=3\times 3\\\\=9\ quarts

Hence, there are 3 quarts of concentrate and 9 quarts of water.

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each equation with the operation yo
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The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

9 ± √89 /4 = 2x² - 9x - 1.

4 ± √22 /2 = 2x² - 8x - 3.

Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5.                                                  x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4.     24 can also be written as 4 × 6 and √4 = 2. So                                                                                     x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3.                                                   x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So                                                                              x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3.                                                    x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4.     88 can also be written as 4 × 22 and √4 = 2. So                                                                             x = 8 ± 2√22 / 2×2 = 4± √22/2.

2x² - 9x - 1, here a = 2, b = -9, c = -1.                                                     x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4.                                          x = 9 ± √89 / 4.

2x² - 9x + 6, here a = 2, b = -9, c = 6.                                                    x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4.                                                                             x = 9 ± √33 / 4

To match we solve the monomials.

1. -15u^3 + 5u^3

Adding

-15u^3 + 5u^3=-10u^3

2.  10u^3 +(-5u^3)

Adding

10u^3-5u^3=5u^3

3. 10u^3 + 5u^3

Adding

10u^3 + 5u^3=15u^3

4.  5u^3+ (-10u^3)

Adding

5u^3-10u^3 =-5u^3

Two separate ways to find the answers.

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Add some of them or all of them to your sum of 47.75, if either or exceeds the limit then that is what left out.
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There are two jobs you can apply for. the first job pays $22,000 the first year, with raises of $4,000 each year thereafter. the
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We let the number of years that the two jobs will have the same payment be denoted as t. Equating the wages of these two jobs after t - 1 years will give us an equation of,
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The value of t from the generated equation is 3. Therefore, after 3 years the jobs will be paying the same wages.
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2 years ago
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The price of an article is Rs 1200 and a customer pays Rs 1380 with VAT. Find the rate of VAT​
garik1379 [7]

Answer:

15%

Step-by-step explanation:

vat amount

= 1380 - 1200

=180

finding the rate of vat

= 1380/1200 *100

= 115%

NB : the 115% shows that 1200 8 115% = 1380 , this give total amount including vat , we only want vat hence we have to deduct the 100% which indicates the amount of article)

hence 115 - 100 = <u>15%</u>

15% * 1200= 180

8 0
2 years ago
Kelly hiked in the woods it took her 1/14 hour to walk 1/4 mile after she snacked she walked another 1/6 mile in 1/16 hour
mariarad [96]

General Idea:

The relationship between rate(R), distance(D) and time(T) given below:

R= \frac{D}{T}

Applying the concept:

We need to make use of the formula to find Kelly's walking rate before and after her snack

Kelly \; Walking \; Rate \; before \; Snack:\\Distance \div Time = \frac{1}{4}  \div \frac{1}{14}  =  \frac{1}{4}  \times \frac{14}{1}  = \frac{14}{4}  = \frac{7}{2}  =  3 \frac{1}{2} \;   miles \; per \; hour\\\\Kelly \; Walking \; Rate \; after \; Snack:\\Distance \div Time = \frac{1}{6}  \div \frac{1}{16}  =  \frac{1}{6}  \times \frac{16}{1}  = \frac{16}{6}  = \frac{8}{3}  =  2 \frac{2}{3} \;   miles \; per \; hour\\\\

Option A isn't correct because before snack Kelly walking rate is not 4/14 miles per hour.

Option B is <u>Correct,</u> Kelly walking rate after snack is 2 2/3 miles per hour.

Option C isn't correct because it doesn't took Kelly 2 hours longer to walk 1/6 mile than it did for her to walk 1/4 mile.  It took 1/112 hour longer.

\frac{1}{14}  - \frac{1}{16}  = \frac{1 \cdot 8}{14 \cdot 8}  - \frac{1 \cdot 7}{16 \cdot 7}  =  \frac{8}{112} - \frac{7}{112}  = \frac{1}{112}

Option D isn't correct because 2 2/3 miles per hour is slower than 3 1/2 miles per hour.

Conclusion:

Option B is <u>Correct,</u> Kelly walking rate after snack is 2 2/3 miles per hour.

3 0
2 years ago
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