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2 years ago

Given y = (2x + 3)2, what is the standard form of the given quadratic equation.

Mathematics

1 answer:

alexandr402 [8]2 years ago

8 0

Answer:

$y=4x^2+12x+9$

Step-by-step explanation:

Perform the square of the binomial, combine like terms, and then write the remaining expression in decreasing order of powers of x:

$y=(2x+3)^2\\y=(2x+3)\,(2x+3)\\y=4x^2+6x+6x+9\\y=4x^2+12x+9$

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Emma is making a recipe that needs 2 1/2 cups of sugar. Each

IrinaVladis [17]

The given partial fraction divided by the fraction of sugar in a scoop is

equal to multiplying the partial fraction by the reciprocal of the fraction.

The number of scoops of sugar needed is 10 scoops.

Reasons:

The amount of sugar the recipe Emma is making needs = 2 1/2 cups

Amount of sugar in each scoop of sugar = 1/4 cups

Required:

The amount of scoops Emma needs to add for the entire recipe

Solution:

The amount of sugar needed = 2 1/2 cups

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Therefore;

$\displaystyle Number \ of \ scoops = \mathbf{\frac{Cups \ of \ sugar \ needed}{Cups \ of \ of \ sugar \ per \ scoop}}$

Which gives;

$\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}}$

$\displaystyle 2 \frac{1}{2} = \frac{5}{2}$

$\displaystyle \frac{ \frac{5}{2}}{\frac{1}{4} } = \mathbf{ \frac{5}{2} \times \frac{4}{1} = \frac{20}{2 }} = 10$

Therefore;

$\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}} = 10 \, scoops$

The number of scoops she needs for the entire recipe is 10 scoops

Learn more about division by fractions here:

brainly.com/question/20591763

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