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bogdanovich [222]
2 years ago
6

I have 3 1/2 bottles of maple syrup. I filled nine one quart bottles with syrup. How much syrup do I have left?

Mathematics
1 answer:
svetlana [45]2 years ago
3 0

Answer:

\frac{25}{4} bottle of syrup is left

Step-by-step explanation:

Total amount of syrup = \frac{31}{2}

Bottles filled with syrup = 9\frac{1}{4}

Syrup left

= \frac{31}{2} - 9\frac{1}{4}\\= \frac{31}{2} - \frac{37}{4}\\= \frac{62-37}{4}\\= \frac{25}{4}

\frac{25}{4} bottle of syrup is left

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Solve the system. -3x-y=10; y-4z=-13; x-4y+z=4
kvasek [131]

9514 1404 393

Answer:

  (x, y, z) = (-3, -1, 3)

Step-by-step explanation:

Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.

Use the last equation to write an expression for z.

  z = 4 -x +4y

Substitute this into the second equation:

  y -4(4 -x +4y) = -13

  y -16 +4x -16y = -13

  4x -15y -3 = 0

In genera form, the first equation can be written as ...

  3x +y +10 = 0

Now, the solution to these two equations can be found to be ...

  x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"

  y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation

  z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z

The solution to the system is (x, y, z) = (-3, -1, 3).

_____

<em>Additional comment</em>

Written as an augmented matrix, the system of equations is ...

  \left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]

4 0
3 years ago
The steps below show the incomplete solution to find the value of m for the equation 5m − 2m + 4 = −1 + 12: Step 1: 5m − 2m + 3
Delicious77 [7]

Given:

Consider the equation is:

5m-2m+3=-1+12

Some steps of the solution are given.

To find:

The next step of the solution.

Solution:

Step 1: The given equation is:

5m-2m+3=-1+12

Step 2: Simplifying right hand side.

5m-2m+3=11

Step 3: Simplifying left hand side.

3m+3=11

These steps are already given. So, the next step is:

Step 4: Subtracting 3 from both sides.

3m=8

Therefore, the correct option is (b).

8 0
3 years ago
Round to the nearest tenth 115 in decimal
schepotkina [342]

Answer:

it would be 115

Step-by-step explanation:

there is no decimal so that means 115. if it was 115.1 then it would be 115 because it is closer to 115. now it is different if it was .5 and up because it would round up. anything above 5 will round up

4 0
3 years ago
HELP ASAP<br> Find the 15th term or the geometric sequence 7, -21, 63,
mihalych1998 [28]
<h3><u>Answer:</u></h3>

33480783

<h2><u>Step-by-step explanation:</u></h2>

<u>Finding the Common Ratio:</u>

We know that the formula for the common ratio of a GP is:

r = aₙ / (aₙ₋₁)        <em>(Where n is any integer)</em>

<em>replacing the values, taking n=2</em>

r = -21 / 7

r = -3

<u>Solving for the 15th Term:</u>

We know that the Formula for the nth term of a GP:

G(n) = a * r ⁿ⁻¹     <em>(where a is the first term and r is the common ratio)</em>

<em>replacing the values (taking n = 15 since we need the 15th term)</em>

G(15) = 7 * (-3)¹⁴

G(15) = 33480783

Hence, the 15th term of the given GP is 33480783

5 0
3 years ago
Natara is training to run a 26-mile marathon. Each week, she increases the distance she runs on her training days. Over the firs
ValentinkaMS [17]

Answer:

Week 8

Step-by-step explanation:

For each week add 3 miles until you reach 26 miles

Week 1:5

Week 2:5+3=8

Week 3:8+3=11

Week 4:11+3=14

Week 5:14+3=17

Week 6:17+3=20

Week 7:20+3=23

Week 8:23+3=26

Hope this answers your question :)

8 0
2 years ago
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