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2 years ago

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

Mathematics

2 answers:

tia_tia [17]2 years ago

8 0

Answer:

the answer is - The range of the function is all real numbers greater than or equal to 0.

Step-by-step explanation:

UNO [17]2 years ago

4 0

Answer:

The domain of the graph is all real numbers less than or equal to 0

Step-by-step explanation:

we have the function

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

we know that

The radicand must be positive

$-x \geq 0$

Solve for x

Multiply by -1 both sides

$x\leq 0$

The domain is the interval ------> (-∞,0]

All real numbers less than or equal to zero

The range of the function is the interval -----> [0,∞)

$f(x)\geq 0$

see the attached figure to better understand the problem

All real numbers greater than or equal to zero

Verify each statement

case 1) The domain of the graph is all real numbers

The statement is false

Because, the domain is all real numbers less than or equal to zero

case 2) The range of the graph is all real numbers

The statement is false

Because, the range is all real numbers greater than or equal to zero

case 3) The domain of the graph is all real numbers less than or equal to 0

The statement is true

case 4) The range of the graph is all real numbers less than or equal to 0

The statement is false

Because, the range is all real numbers greater than or equal to zero

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Sierra is selling bracelets to raise money for the Language Club at school. Each bracelet with yellow beads sells for $5. Each b

matrenka [14]

Answer:

Correct answer is:

$5y+6r=660\\y=2r+8$

Step-by-step explanation:

Given that Number of bracelets with yellow beads is represented by $y$

Each bracelet with yellow beads is sold for $5.

Total money raised by bracelets with yellow beads = Number of bracelets sold $\times$ Money raised by sale of one such bracelet = $5y$

Also Given that Number of bracelets with Orange beads is represented by $r$

Each bracelet with orange beads is sold for $6.

Total money raised by bracelets with orange beads = Number of bracelets sold $\times$ Money raised by sale of one such bracelet = $6r$

Given that total money raised by sale of both type of bracelets is $660.

so, the first equation becomes:

$5y+6r=660 ....... (1)$

It is also given that "The number of bracelets with yellow beads that Sierra sold is 8 more than twice the number of bracelets with orange beads"

$\Rightarrow r =2r+8 ...... (2)$

So, by equation (1) and (2), the system of equations is:

$5y+6r=660\\y=2r+8$

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1 year ago

Given: FH ⊥ GH; KJ ⊥ GJ Prove: ΔFHG ~ ΔKJG Identify the steps that complete the proof. ♣ = ♦ = ♠ =

Feliz [49]

1 is all right angles are congruent 2 angles fgh is congruent to angle kgj 3 aa similarity theorem just took the test this are correct

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2 years ago

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Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1

astra-53 [7]

Answer:

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

Step-by-step explanation:

This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:

$x^{2} - 24 = 1$

Given that resulting expression is a second order polynomial of the form $x^{2} - a^{2}$ , there are two real and distinct solutions. Roots of the expression are:

$x_{1} = -5$ and $x_{2} = 5$ .

Now, it is also required to determine which part of the interval $(x_{1}, x_{2})$ is equal to a number greater than zero (positive). That is:

$x^{2} - 24 > 0$

$x^{2} > 24$

$x < -4.899$ and $x > 4.899$ .

Therefore, exists two sub-intervals: $[-5, -4.899]$ and $\left[4.899,5\right]$ . Besides, $x^{2} - 24 > y = 1$ in each sub-interval. The definite integral of the region between the two curves over the x-axis is:

$A = \int\limits^{-4.899}_{-5} [{1 - (x^{2}-24)]} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} [{1 - (x^{2}-24)]} \, dx$

$A = \int\limits^{-4.899}_{-5} {25-x^{2}} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} {25-x^{2}} \, dx$

$A = 25\cdot x \right \left|\limits_{-5}^{-4.899} -\frac{1}{3}\cdot x^{3}\left|\limits_{-5}^{-4.899} + x\left|\limits_{-4.899}^{4.899} + 25\cdot x \right \left|\limits_{4.899}^{5} -\frac{1}{3}\cdot x^{3}\left|\limits_{4.899}^{5}$

$A = 2.525 -2.474+9.798 + 2.525 - 2.474$

$A = 9.9\,units^{2}$

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

4 0

1 year ago

Events M and N are independent events. In this scenario, if P(M) = 0.46 and P(M and N) = 0.138, then P(N) = .

Oksi-84 [34.3K]

Answer:

P(N)=0.3

Step-by-step explanation:

Given: P(M)= 0.46, P(M and N)=0.138

Using P(M) ×P(N)= P(M and N)

⇒0.46×P(N)= 0.138

⇒P(N)= $\frac{0.138}{0.46}$

⇒P(N)=0.3

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2 years ago

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Peter mixes 4 1/2 cups of orange juice, 1 1/3 cups of ginger ale, and 6 1/3 cups of strawberry lemonade to make some punch. What

ella [17]

Just add them all:(FYI, I first converted all the mixed fraction to improper)
11/3+19/3= 30/3+9/2
Now take out the LCM,
60/6+27/6= 87/6
Hence, the total number of cups that peter makes is 87/6

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1 year ago

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