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garik1379 [7]
3 years ago
8

What number must you add to complete the square x^2+4x=15

Mathematics
1 answer:
Andrew [12]3 years ago
6 0
Since we want it in the form: (x - a)², let's first expand (x - a)² and then equate for the coefficients.

(x - a)² = x² - 2ax + a²
x² + 4x - 15 = x² - 2ax + a²

Now, let's focus on the middle term.
4x = -2ax
4 = -2a
a = -2

Thus, we know that a = -2
Then, we can say (x + 2)² = x² + 4x - 15
x² + 4x + 4 = x² + 4x - 15
Thus, 19 units are needed in order to complete the square to produce:
(x + 2)²
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A farm packages eggs into cartons that hold two dozen eggs each. Last week, 5,398 eggs were collected. How many cartons will the
Sonbull [250]

Answer:

225

Step-by-step explanation:

We're told that each carton holds two dozen eggs, or 24 eggs. To find out how many cartons the farm will need, we divide the total amount of eggs by the amount of eggs that fit in each carton. So:

\frac{5398}{24} = 224.916667

Since the number is a decimal, you need to round up to make sure every egg is in a carton. So, your answer is 225.

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2 years ago
Examine this system of linear<br> equations.<br> y – 3x=-2,<br> y = 4
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Answer:

2, 4

Step-by-step explanation:

Ok so for this you have to substitute. y=4 so you put a 4 where the y is. This becomes

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Now divide -3 from both sides. Which becomes

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4 0
3 years ago
Read 2 more answers
Vincent and Jean are two cooks who work in a village. Each of them can either bake cakes or make pizzas. Every ingredient is rea
babymother [125]

Answer:

a) Jean b) Jean c) Vincent d) Jean              

Step-by-step explanation:

We are given the following information in the question.

Vincent can bake 10 cakes or make 5 pizzas

Jean can bake 12 cake or make 8 pizzas.

a) Absolute advantage of baking cake

Jean has the absolute advantage of baking cake as he can bake more cakes as compared to Vincent.

b) Absolute advantage of making pizza

Jean has the absolute advantage of making pizza as he can make more pizzas as compared to Vincent.

In order to find comparative advantage, we find the opportunity cost which can be defined as:

\text{Opportunity Cost} = \displaystyle\frac{\text{What one sacrifices}}{\text{What one gains}}

c) Comparative advantage in baking cakes

Opportunity cost of Vincent for baking cakes = \frac{5}{10} = \frac{1}{2}

Opportunity cost of Jean for baking cakes = \frac{8}{12} = \frac{2}{3}

The less is the opportunity cost the better, hence, Vincent has comparative advantage in baking cakes.

d) Comparative advantage in making pizzas

Opportunity cost of Vincent for making pizzas = \frac{10}{5} = 2

Opportunity cost of Jean for making pizzas = \frac{12}{8} = \frac{3}{2}

The less is the opportunity cost the better, hence, Jean has comparative advantage in making pizzas.

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3 years ago
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Answer:

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