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Zinaida [17]
3 years ago
13

At the movies, you order 3 boxes of popcorn and a bottle of water. The cost of the bottle of water Is $1.75. Your total is $9.25

. Write and solve an equation to find the cost of one box of popcorn.
Mathematics
1 answer:
Phoenix [80]3 years ago
8 0
If popcorn is p and water is w the equation can be written as

3p + w = 9.25

because there was 3 boxes of popcorn and one water (hence the coefficients) and the total is 9.25

then plug in 1.75 for w the price of water:

3p+ 1.75 = 9.25

you can move stuff around algebraically now (subtract 1.75 on both sides and divide by three on both aides) to get the cost of one box of popcorn (p).

The answer is 2.50
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Use the binomial expansion and approximation to find √3​
belka [17]

According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...

An acceptable result cannot be found manually for it requires a <em>high</em> number of elements, with the help of a solver we find that the <em>approximate</em> value of √3 is 1.732.  

<h3>How to approximate the value of a irrational number by binomial theorem</h3>

Binomial theorem offers a formula to find the <em>analytical</em> form of the power of a binomial of the form (a + b)ⁿ:

(a + b)^{n} = \sum \limits_{k = 0}^{n} \left(\begin{array}{c}n\\k\end{array}\right)\cdot a^{n-k} \cdot b^{k}     (1)

Where:

  • a, b - Constants of the binomial.
  • n - Grade of the power binomial.
  • k - Index of the k-th element of the power binomial.

If we know that a = 1, b = 2 and n = 1 / 2, then an approximate expression for the square root is:

√3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...

To learn more on binomial expansions: brainly.com/question/12249986

#SPJ1

8 0
1 year ago
What is the answer to 1.1x + 1.2x - 5.4 = -10
lord [1]
1.1x+1.2x-5.4=-10

11/10x+12/10x-54/10=10

11x/2.5+2^2-1*3/5x-3^3/5=-10

(11x)+2(2*3x)+2(-3^3)/2*5=-10

11x+2(6x)+2(-27)/2*5=-10

11x+2*6x-2*27/2*5=-10

11x+12x-54/2*5=-10

23x-54/2*5=-10

23x-54=-100

23x=-46

23x/23=-46/23

x=-2*23/23

x=-2
8 0
3 years ago
Read 2 more answers
Solve the following system of equations graphically on the set of axes below.
eimsori [14]

Answer:

  (x, y) = (3, 5)

Step-by-step explanation:

To solve these equations graphically, you plot each one, then identify the coordinates of the point of intersection.

The first equation can be graphed using the y-intercept of -1 and the slope of 2.

The second equation has a y-intercept of 18/3 = 6, and a slope of -1/3. The x-intercept of 18 is off the chart, so the slope and intercept are a good way to plot this line, too.

__

The slope is the "rise" divided by the "run". A slope of 2 means the line goes up 2 units for each unit to the right. A slope of -1/3 means the line goes down 1 unit for each 3 units to the right.

The solution is (x, y) = (3, 5).

8 0
2 years ago
What is the length of DE?
miskamm [114]

Answer:

11

Step-by-step explanation:

If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.

AC *CB = CD CE

4 * (10-4) = CD * 8

4 * 6 = 8 *CD

24 = 8 CD

Divide each side by 8

24/8 = CD

3 = CD

We want the length DE

DE = CD + CE

     = 3 + 8

DE = 11

5 0
2 years ago
The recycling and reuse industry employs approximately 1,025,000 more workers than the waste management industry. Together they
NARA [144]

Answer:

Step-by-step explanation:

The recycling and reuse industry employs approximately 1,025,000 more workers than the waste management industry. This means that

Number of workers employed by The recycling and reuse industry = the number of workers employed by the waste management industry + 1,025,000

Let y = the number of workers employed by the waste management industry. Therefore

x = y + 1,025,000 - - - - - - 1

Since total = 1,275,000

x + y = 1,275,000 - - - - - - -2

Substituting equation 1 into equation 2, it becomes

y + 1,025,000 + y = 1,275,000

2y = 1,275,000 - 1,025,000

y = 250000/2 = 125000

x = y + 1,025,000 = 125000 + 1,025,000 = 1150000

The recycling and reuse industry employs 1150000 workers

The waste management industry employs 125000 workers

7 0
3 years ago
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