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3 years ago

The function f(x) = (x − 4)(x − 2) is shown.What is the range of the function?

Mathematics

1 answer:

yuradex [85]3 years ago

3 0

Answer:

The range is y ≥ -1

Step-by-step explanation:

∵ f(x) = (x - 4)(x - 2)

∴ f(x) = x² - 2x - 4x + 8

∴ f(x) = x² - 6x + 8 ⇒ quadratic function (ax² + bx + c) represented by

parabola graphically

∵ a = 1 , b = -6 , c = 8

∴ x-coordinate of its vertex = -b/2a = -(-6)/2×1 = 3

∴ f(3) = (3)² - 6(3) + 8 = -1

∵ a is positive ⇒ the curve has minimum point and it's open upward

∴ the minimum point is (3 , -1)

∴ The range is y ≥ -1 ⇒ because the minimum value is -1

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Susan threw a softball 42 years on her first try and 51 1/3 yard on her second try. How much farther did she throw the softball

Andru [333]

Answer:

28 feet farther than 1st ball.

Step-by-step explanation:

We have been given that Susan threw a softball 42 yards on her first try and $51\frac{1}{3}$ yard on her second try.

To find second ball is how much farther from the 1st ball, we will subtract 42 yards from $51\frac{1}{3}$ yards.

$\text{The second ball is farther from 1st ball}=51\frac{1}{3}\text{ yards}-42\text{ yards}$

$\text{The second ball is farther from 1st ball}=\frac{154}{3}\text{ yards}-42\text{ yards}$

Let us have a common denominator.

$\text{The second ball is farther from 1st ball}=\frac{154}{3}\text{ yards}-\frac{42*3}{3}\text{ yards}$

$\text{The second ball is farther from 1st ball}=\frac{154}{3}\text{ yards}-\frac{126}{3}\text{ yards}$

$\text{The second ball is farther from 1st ball}=\frac{154-126}{3}\text{ yards}$

$\text{The second ball is farther from 1st ball}=\frac{28}{3}\text{ yards}$

$\text{1 yard}=3\text{ feet}$

$\frac{28}{3}\text{ yards}=\frac{28}{3}\times 3\text{ feet}$

$\frac{28}{3}\text{ yards}=28\text{ feet}$

Therefore, Susan thrown the second ball 28 feet farther from the 1st ball.

7 0

3 years ago

Please answer correctly !!!!!!!!!!!!!! Will Mark Brianliest !!!!!!!!!!!!!!!!!!!

alexgriva [62]

Answer:

x = 30

Step-by-step explanation:

well from the theorem we have

$\frac{15}{3}=\frac{x}{6}$

yes i know you could say that the right way is

$\frac{3}{15}=\frac{6}{x}$

well if you notice they are the same only that in my way the x is in the numerator which means it will be far easier to know it's value :)

$\frac{15}{3}=\frac{x}{6}\\\\5=\frac{x}{6}\\\\6[5]=6[\frac{x}{6}]\\\\30=x$

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163 puzzles and 173 action figures is the answer

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