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3 years ago

A 1.8-ounce jar cinnamon costs $4.05. What is the cost per ounce?

Mathematics

2 answers:

Paha777 [63]3 years ago

6 0

$4.05/1.8 oz= $2.25 per oz

Final answer: $2.25 per oz

rodikova [14]3 years ago

3 0

Answer: The required cost per ounce of cinnamon is $2.25.

Step-by-step explanation: Given that a 1.8-ounce jar cinnamon costs $4.05.

We are to find the cost per ounce of cinnamon.

We will be using the UNITARY method to solve the problem.

We have

The cost of 1.8 ounces of cinnamon = $4.05.

Therefore, the cost of 1 ounce of cinnamon is given by

$\$\dfrac{4.05}{1.8}=\$2.25.$

Thus, the required cost per ounce of cinnamon is $2.25.

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3 years ago

What are the factors of 2x + 3x - 54? Select two options

tiny-mole [99]

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The answer: The factors are (2x-9) and (x+6).

The Problem:

Factor $2x^2+3x-54$

Step-by-step explanation:

So I'm going to do trial factors using the choices to aid me.

Factored form for this problem if it exist will be in the form:

$(mx+n)(kx+p)$ .

In general this is what it would look like if we factored any quadratic in terms of $x$ (given the quadratic is not prime but technically you could factor even over the complex numbers).

Let's look at:

$(mx+n)(kx+p)$

We want to choose $k \text{ and } m$ such that when you multiply them you get 2. Well those would have to be 2 and 1.

$(2x+n)(x+p)$

we want to choose $n \text{ and } p$ such that when you multiply them you get -54. Based on the choices we want to get with -9 and 6, or 9 and -6. We don't know the order we want to choose it in either.

For example which of these would work:

$(2x-6)(x+9)$

$(2x+6)(x-9)$

$(2x-9)(x+6)$

$(2x+9)(x-6)$

We are going to consider only the outer and inner of FOIL since we already know the first times the first is $2x^2$ and the last times the last is $-54$ .

Let's test the first one:

$(2x-6)(x+9)$

Outer: 2x(9)=18x

Inner: -6(x)=-6x

------------------------ADD!

18x-6x=12x

The first choice did not give us the middle term 3x.

Trying the second one would give us the opposite since they are in the same form as previous just the + and - are switched.

Let's look at the third one:

$(2x-9)(x+6)$

Outer: 2x(6)=12x

Inner: -9(x)=-9x

--------------------------ADD!

12x-9x=3x

This is the winner.

The answer: The factors are (2x-9) and (x+6).

7 0

3 years ago

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