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14 days ago

Which statement is true about the function f(x)= StartRoot negative x EndRoot?

Mathematics

2 answers:

Leona [4.1K]14 days ago

8 0

Answer:

The correct statement is that the range of the function consists of all real numbers equal to or greater than zero.

Step-by-step explanation:

Leona [4.1K]14 days ago

4 0

Answer:

The domain includes all real numbers less than or equal to zero.

Step-by-step explanation:

Given the function:

$f(x)=\sqrt{-x}$

The radicand (expression under the square root) must be non-negative:

$-x \geq 0$

Solving for x:

Multiplying both sides by -1 reverses inequality:

$x\leq 0$

Thus, the domain is (-∞, 0].

All real numbers up to and including zero.

The function's range corresponds to [0, ∞).

$f(x)\geq 0$

Refer to the included diagram for clearer visualization.

All real numbers from zero upward.

Evaluating each statement:

Case 1) The domain is all real numbers.

This is incorrect because the domain is constrained to values less than or equal to zero.

Case 2) The range is all real numbers.

This is also false since the output values are zero or positive only.

Case 3) The domain consists of all real numbers less than or equal to zero.

This is correct.

Case 4) The range is all real numbers less than or equal to zero.

This is false as the range is from zero upwards.

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Kevin drew a triangle with angle measures of 30 degrees and 40 degrees and side measures of 5 cm, 7cm, and 8 cm. Explain, using

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He created a scalene triangle.
A scalene triangle has sides and angles that do not measure alike.

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2 days ago

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Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books. If two

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There are 2 beginner, 6 intermediate, and 3 advanced books, totaling 11.

P(advanced) = 3/11
replaced
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P(both) = 3/11 * 2/11 = 6/121 <=

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4 days ago

What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

Inessa [3907]

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format $y/x=k$ or $y=kx$

For this question, we have

the point $(5,12)$ lies on the direct variation line

therefore

Determine the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

The equation is

$y=\frac{12}{5}x$

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point $(0,0)$

$x=0\ y=0$

Insert the values of x and y into the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is valid

thus

the point $(0,0)$ lies on the direct variation line

case B) point $(2.5,6)$

$x=2.5\ y=6$

Insert the values of x and y into the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is valid

thus

the point $(2.5,6)$ lies on the direct variation line

case C) point $(3,10)$

$x=3\ y=10$

Insert the values of x and y into the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not valid

thus

the point $(3,10)$ does not lie on the direct variation line

case D) point $(7.5,18)$

$x=7.5\ y=18$

Insert the values of x and y into the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is valid

thus

the point $(7.5,18)$ lies on the direct variation line

case E) point $(12.5,24)$

$x=12.5\ y=24$

Insert the values of x and y into the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not valid

thus

the point $(12.5,24)$ does not lie on the direct variation line

case F) point $(15,36)$

$x=15\ y=36$

Insert the values of x and y into the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is valid

thus

the point $(15,36)$ lies on the direct variation line

ultimately

the solution is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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1 day ago

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The budget of a university organizations is split evenly among its various committees . if they have a budget of P 60.000 repres

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Response:

m(n) = 60000

Amount = 60000/n

Step-by-step breakdown:

Provided

Budget = 60000

Solving part (a) as a function mn

To achieve this, simply substitute m(n) for the budget amount.

This results in;

m(n) = 60000

Solving part (b) for the amount each committee is allocated.

Given that the budget will be evenly split.

Amount = m(n)/n

Replace m(n) with 60000

Amount = 60000/n

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11 days ago

Ten liters of pure water are added to a 50-liter pot of soup that is 50% broth. Fill in the missing parts of the table.

Zina [3914]

Answer:

c= 25

d= 60

Step-by-step explanation:

C: This is because 25+0 is simply 25. Essentially, you are not adding anything, so it remains unchanged!:)

D: 50 + 10 = 60. That’s straightforward addition!

Hope this helps!

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5 days ago

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