14. What is the product of -3x and 5x2 + x?

Mary bought 4 gallons of milk for $10.00. Jill bought 2.5 gallons for $6.00.

RoseWind [281]

Step-by-step explanation:

In order to find the better buy, we must find the cheaper unit price or price per gallon. To find the price per gallon, divide the cost by the number of gallons.

Mary

Mary bought 4 gallons for $11.

The price is $11 and the gallons are 4.

Jill

Jill bought 2.5 gallons for $7.25

The price is $7.25 and the gallons are 2.5

Better buy

Mary paid $2.75 per gallon and Jill paid $2.90 per gallon. 2.75 is less than 2.90, so Mary had the better buy.

3 0

2 years ago

What is 9%+278.045 or 278.045+9%

rodikova [14]

The answer to this equation would be 278.135

3 0

3 years ago

Describe how to transform:

Anna71 [15]

Answer:

$x^\frac{35}{6}$

Step-by-step explanation:

The expression to transform is:

$(\sqrt[6]{x^5})^7$

Let's work first on the inside of the parenthesis.

Recall that the n-root of an expression can be written as a fractional exponent of the expression as follows:

$\sqrt[n]{a} = a^{\frac{1}{n}}$

Therefore $\sqrt[6]{a} = a^{\frac{1}{6}}$

Now let's replace $a$ with $x^{5}$ which is the algebraic form we are given inside the 6th root:

$\sqrt[6]{x^5} = (x^5)^{\frac{1}{6}}$

Now use the property that tells us how to proceed when we have "exponent of an exponent":

$(a^n)^m= a^{n*m}$

Therefore we get: $(x^5)^{\frac{1}{6}}=x^{\frac{5}{6}}}$

Finally remember that this expression was raised to the power 7, therefore:

$[tex](\sqrt[6]{x^5})^7=(x^\frac{5}{6})^7=x^\frac{35}{6}$ [/tex]

An use again the property for the exponent of a exponent:

8 0

3 years ago

The number 6458 rounded to the nearest thousand

Murrr4er [49]

Answer:

6500

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Determine whether each equation below does or does not represent a proportional relationship. support your answer using either a

Triss [41]

Answer:

As the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship.
As the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship.

Step-by-step explanation:

Solving equation A: y = x 

Let us consider the given equation A:

y = x

Putting x = 1 in y = x

y = x

y = 1 ∵ x = 1

Hence, (1, 1) is the ordered pair of y = x

Putting x = 2 in y = x

y = x

y = 2 ∵ x = 2

Hence, (2, 2) is the ordered pair of y = x

Putting x = 3 in y = x

y = x

y = 3 ∵ x = 3

Hence, (3, 3) is the ordered pair of y = x

Putting x = 4 in y = x

y = x

y = 4 ∵ x = 4

Hence, (4, 4) is the ordered pair of y = x

Putting x = 5 in y = x

y = x

y = 5 ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y x

1 1

2 2

3 3

4 4

5 5

As from the table, lets take the ratio of every point i.e. y/x

For (1, 1), the ratio will be y/x ⇒ 1/1 = 1
For (2, 2), the ratio will be y/x ⇒ 2/2 = 1
For (3, 3), the ratio will be y/x ⇒ 3/3 = 1
For (4, 4), the ratio will be y/x ⇒ 4/4 = 1
For (5, 5), the ratio will be y/x ⇒ 5/5 = 1

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

Solving equation A: y = x +2

Let us consider the given equation A:

y = x + 2

Putting x = 1 in y = x + 2

y = x + 2

y = 1 + 2 ⇒ 3 ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

Putting x = 2 in y = x + 2

y = x + 2

y = 2 +2 ⇒ 4 ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

Putting x = 3 in y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5 ∵ x = 3

Hence, (3, 5) is the ordered pair of y = x + 2

Putting x = 4 in y = x + 2

y = x + 2

y = 4 + 2 ⇒ 6 ∵ x = 4

Hence, (4, 6) is the ordered pair of y = x + 2

Putting x = 5 in y = x + 2

y = x + 2

y = 5 +2 ⇒ 7 ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y x + 2

1 3

2 4

3 5

4 6

5 7

As from the table, lets take the ratio of every point i.e. y/x

For (1, 3), the ratio will be y/x ⇒ 3/1 = 3
For (2, 4), the ratio will be y/x ⇒ 4/2 = 2
For (3, 5), the ratio will be y/x ⇒ 5/3 = 5/3
For (4, 6), the ratio will be y/x ⇒ 6/4 = 3/2
For (5, 7), the ratio will be y/x ⇒ 7/5 = 7/5

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

Keywords: equation, graph

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6 0

3 years ago