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3 years ago

Find the range of the function. f(x)=10-x^2

Mathematics

1 answer:

Ratling [72]3 years ago

5 0

Answer:

range = x ≤ 10

Step-by-step explanation:

Given in the question the function

f(x)=10-x^2

The range of a function is the complete set of all possible resulting values of the dependent variable F(x) after we have substituted the domain which is the values of x.

domain = set of all integers

range = x ≤ 10

f(x)=10-x²

since any negative value of x will be positive with squared so we will start from 0

f(0) = 10-0² = 10

f(1) = 10 - 1² = 9 = f(-1) = 10 -(-1)²

....and so on.

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16x² -9 = 4×² + (4x²+9)

lesya [120]

For this case we must solve the following equation:

$16x ^ 2-9 = 4x ^ 2 + (4x ^ 2 + 9)$

We remove the parentheses on the right side:

$16x ^ 2-9 = 4x ^ 2 + 4x ^ 2 + 9$

We add similar terms on the right side:

$16x ^ 2-9 = 8x ^ 2 + 9$

We subtract $8x ^ 2$ from both sides of the equation:

$16x ^ 2-8x ^ 2-9 = 9\\8x ^ 2-9 = 9$

We add 9 to both sides of the equation:

$8x ^ 2 = 9 + 9\\8x ^ 2 = 18$

We divide by 8 on both sides of the equation:

$x ^ 2 = \frac {18} {8}\\x ^ 2 = \frac {9} {4}$

We apply square root to both sides of the equation:

$x = \pm \sqrt {\frac {9} {4}}$

We have two roots:

$x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}$

Answer:

$x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}$

4 0

4 years ago

Apply the distributive property to factor out the greatest common factor.<br> 12 + 20 =

Yakvenalex [24]

Answer:

Step-by-step explanation:

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6 0

3 years ago

What is the length of the hypotenuse of the triangle if Side A = 11 and Side B = 5? What is the length of Side C?

dusya [7]

Answer:

34mx32

Step-by-step explanation:

3 0

3 years ago

Jeff bought a new cell phone for $500 and 4 accessories, 10 points

Elina [12.6K]

Answer:

Purchase amount = $642

Step-by-step explanation:

Given that:

Jeff has bought:

cell phone = $500

4 Accessories = 4 * $25

4 acessories = $100

Total = $500 + $100 = $600

As the sale tax is 7% so

Sale tax = 7% (600)

Sale Tax = 0.07(600)

Sale Tax = $42

So the purchase amount will be Total + Sale Tax

Purchase amount = $600 + $42 = $642

i hope it will help you!

7 0

4 years ago

Whats the probably of drawing one blue marble from a bag which contains 4 red marbles 6 green marbles 1 whit marble and 3 blue a

zalisa [80]

Answer:

$\dfrac{3}{14}$

Step-by-step explanation:

Total number of marbles :

4 + 6 + 1 + 3 = 14

Total number of blue marbles = 3

P(getting a blue marble) =

$\dfrac{number\:of\: blue\: marbles}{total\: number\: of\:marbles}$

= $\dfrac{3}{14}$

3 0

3 years ago