The domain of a radical function is the set of all x for which the radicand is positive. True or false?

Answers

Answer 1
Final answer:

The domain of a radical function is the set of all x for which the radicand is positive.

Explanation:

The statement in the question is almost correct. The domain of a radical function is the set of all x for which the radicand is non-negative, not just positive.

A radical function is defined as a function that contains a radical expression, which is the square root or any higher-order root of a variable or expression. The domain of a radical function is the set of all values of x that make the radicand, which is the expression inside the radical, positive.

For example, let's consider the function f(x) = √(x+3). The radicand x+3 can only be positive for values of x greater than -3. Therefore, the domain of this function is (-3, ∞).

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Related Questions

Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices
R'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?


R0, 90°
R0, 180°
R0, 270°
R0, 360°

Answers

Answer:

It should be C aka 270°

Step-by-step explanation:


Answer:

3 option is correct.

Step-by-step explanation:

Given Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices  R'(0, –2), S'(0, –4), and T'(–3, –1).

We have to tell the rule describes the transformation.

A rotation is transformation that turns a figure about a fixed point. An object and its rotation are the same shape, but the figures may turned or rotate in different directions.

Here, the coordinates shift after rotation according to the rule

(2,0) → (0,-2) i.e (x, y) → (y, -x)

As, Rotation of 270º on coordinate axes.

(x, y) → (y, -x)

which match to the given rule.

hence, 3 option is correct.

Given the function f(x)=-5x^2-x+20 find f(3)

Answers

f(x) = -5x^2 - x + 20;

f(3) = -5*3^2 - 3 + 20 = -5*9 - 3 + 20 = -45 - 3 + 20 = -28;

Answer: - 28

Step-by-step explanation:

f(x) = -5x^2 - x + 20

To find f(3), we simply put x = 3 and then simplify

f(3) = - 5(3)^2 - 3 + 20

= -5(9) - 3 + 20

= -45 - 3 + 20

= -48 +20

= -28

f(3) = -28

Identify the variables, the constant, the coefficients, and the exponents in the algebraic expression: 5x + 3y^{2} + 4. (The 2 is supposed to be little on top of the "y")

Answers

The variables are: x, y
The constant is: 4
The coefficients are: 5, 3
The exponent is: y^2

The algebraic expression 5x + 3y² + 4 has variables x and y, the constants 5, 3, and 4, the coefficients are 5 and 3 and the exponents are 1 and 2.

What is an algebraic expression?

An algebraic equation consists of terms separated by the operation of addition and subtraction.

We know in an algebraic expression a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+aⁿ,

x's are variables a's are constants and n's are exponents.

∴ In the algebraic expression 5x + 3y² + 4,

Constants are the numerical values which are 5, 3, and 4.

The variables are x and y and the exponents are the powers of the variables 2 for y and 1 for x and the coefficients are 5 and 3.

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The sum of two numbers is seventy-two. Twice one of them equals ten times the other. What are the numbers?

Answers

x+y=72
2x=10y

Solve one equation, then plug the answer into the other.

x=5y
5y+y=72
6y=72
y=12

Now that we have one answer, we can use that to solve the final answer.
x+y=72
x+12=72
x=60
the answer to the question is x=60

Mark borrowed $5,500 at 11.5 percent for five years. What is his monthly payment?


A. $131.50

B. $173.50

C. $120.95

D. $150.22

Answers

Use the formula of the present value of an annuity ordinary which is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 5500
PMT monthly payment?
R interest rate 0.115
K compounded monthly 12
N time 5years
Solve the formula for PMT
PMT=Pv÷ [(1-(1+r/k)^(-kn))÷(r/k)]
PMT=5,500÷((1−(1+0.115÷12)^(
−12×5))÷(0.115÷12))
=120.95

So the answer is C

Hope it helps!

Answer:

C option is correct

Step-by-step explanation:

Given: payment borrowed (P)= $5,500

            rate (r)=11.5 or 0.115

           Time(t)= 5 years

           Compound monthly(k)=12

To find : Monthly payment (M)

Formula used :  [tex]M= P/(\frac{1-(1+\frac{r}{k})^{-kn}}{\frac{r}{k}})[/tex]

 Solution :     [tex]M= 5500/(\frac{1-(1+\frac{0.115}{12})^{-60}}{\frac{0.115}{12}})[/tex]

                by solving we get, M =$120.95

therefore, option C is correct

                 


What is the perimeter of a polygon with vertices at (-6,-1) (-3,-4) (6,5) and (3,8) ​?

Answers

The formula of the distance between 2 points states that the distance AB between points A(a, b) and B(c, d) is found as follows:

                    [tex]\displaystyle{ AB= \sqrt{(a-c)^2+(b-d)^2} [/tex].


Let the points of the polygon be A(-6,-1), B(-3,-4), C(6,5) and D(3,8). Then, the perimeter of the polygon ABCD is
                             
                                                   AB+BC+CD+DA.

We can find each of AB, BC, CD, DA by the Distance Formula as follows:


[tex]\displaystyle{ AB= \sqrt{(-6+3)^2+(-1+4)^2}=\sqrt{9+9}=\sqrt{2\cdot9}=3\sqrt{2}[/tex].

[tex]\displaystyle{ AB= \sqrt{(6+3)^2+(5+4)^2}=\sqrt{81+81}=\sqrt{2\cdot81}=9\sqrt{2}[/tex].

[tex]\displaystyle{ AB= \sqrt{(6-3)^2+(5-8)^2}=\sqrt{9+9}=3\sqrt{2}[/tex].

[tex]\displaystyle{ AB= \sqrt{(-6-3)^2+(-1-8)^2}=\sqrt{81+81}=9\sqrt{2}[/tex].


Thus, the perimeter of the polygon is 

           [tex]9\sqrt{2}+9\sqrt{2}+3\sqrt{2}+3\sqrt{2}=24\sqrt{2}[/tex] (units).


Answer: [tex]24\sqrt{2}[/tex] units

Suppose we did an experiment to gather data on the number of​ un-popped kernels of microwave popcorn. Half of the students in your class took home a​ bag, put it in the freezer​ overnight, and popped it the next day. The other half took the​ bag, left it on their kitchen counter​ overnight, and popped it the next day. Each group counted the number of​ un-popped kernels. Are these data paired or​ independent

Answers

This would be an example of independent data as the bags of popcorn were subjected to different conditions. In one case the bag was placed into the freezer, and in the second case it was left at room temperature. Considering that the conditions of both bags were different, we must view this data as independent.

The data collected on the number of un-popped kernels of popcorn, where one group's bags were frozen and the other's were left at room temperature, are considered independent. This is because each bag was only subjected to one condition and was not measured in both conditions, which would be necessary for paired data.

In the question provided, students collected data on the number of un-popped kernels of microwave popcorn where one group froze the popcorn while the other left it at room temperature. To determine whether the data are paired or independent, we need to understand the nature of the experiment setup.

Since every student’s popcorn was subject to a unique condition (frozen or room temperature) and they're not measured in both conditions, we can deduce that the data here are independent. This means that the outcome of one does not influence the outcome of the other.

In comparison to a scenario where the same item or subject is tested under two different conditions the popcorn experiment does not meet this criterion; that would be an example of paired data. An unpaired test such as the unpaired t-test may be appropriate here if we want to assess the effects of freezing on the number of un-popped kernels compared to leaving them at room temperature. Each bag of popcorn represents an independent sample from the population of all popcorn bags.

Bill takes the commuter train to work every day. during the morning commute, a train arrives every 25 min. if bill arrives at the station at a random time for the morning commute, what is the probability that he will have to wait at least 5 min for a train?

Answers

The probability is 80% or .8. Bill could have to wait anywhere from 0-25 minutes, and only 5 of those would mean he waits less than 5 minutes. So 20/25 = .8 = 80%.

A high-speed bullet train travel 900 feet in 5 seconds at this rate how far would it travel in 1 minute

Answers

Since there are 60 seconds in one minute, we can form the equation:
[tex]900 \div 5 = x \div 60[/tex]
From here, we can cross multiply.
[tex]5x = 54000[/tex]
[tex]x = 10800[/tex]
The train would travel 10,800 feet in one minute.

Divide 30 by 1/2 and add 10 what is the answer?

Answers

30 divided by 1/2= 60

60 + 10= 70
30 divided by 2= 15+10 Answer= 25 I know that's not right

Which of the following shows the proper steps to construct a perpendicular bisector of a segment through any point?

Answers

I hope you already can see which is the correct one. Hope this help 

Define the function g(x) in terms of f(x)

Answers

Function g(x) is a transformation of f(x) 3 units down and 6 units left

Hope this helps!

A computer company can sell 130 boxes of printer paper each week at a price of $9 per box. For each $1 increase in the price, it will sell 10 fewer boxes per week. What price per box will provide the maximum revenue for the computer company?

$9

$10

$11

$12

Answers

$11 because you take ten off for every extra dollar above nine. If you do 9*130 you get $1170. If you do $10 you subtract ten from the 130 boxes of printer paper each week so that would be 130-10=120 then you multiply 120*10=$1200.  If you do $11 you subtract twenty from the 130 boxes because that's two extra dollars, 130-20=110. 110*11= $1210. If you do twenty you have to subtract 30 boxes, 130-30=100. 100*12= 1200. Therefore, $11 per box would be the highest revenue for the company.
Final answer:

The maximum revenue for the computer company is achieved at the price of $11 per box which is calculated based on the decrease in quantity sold with every $1 increase in price.

Explanation:

To find the price per box that will provide the maximum revenue for the computer company, we need to analyze how changes in price affect the number of boxes sold and the revenue generated. The company sells 130 boxes of printer paper each week at $9 per box. For each $1 increase in price, it will sell 10 fewer boxes.

Let's define the revenue function as R(p) where p is the price per box. The initial revenue is 130 boxes × $9. For each $1 increase, the revenue function becomes (130 - 10(p - 9)) × p. We need to find the value of p that maximizes this revenue function.

Let's calculate:

At $9: R($9) = 130 × $9 = $1170At $10: R($10) = (130 - 10(1)) × $10 = 120 × $10 = $1200At $11: R($11) = (130 - 10(2)) × $11 = 110 × $11 = $1210At $12: R($12) = (130 - 10(3)) × $12 = 100 × $12 = $1200

We can see that the revenue is maximum at $11 per box. So, the price per box that will provide the maximum revenue for the computer company is $11.

Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN△LMN?

Answers

Answer:

Step-by-step explanation:

Final answer:

The area of the triangle inside the rectangle is calculated by using the formula for the area of a triangle, 1/2 * base* height. Given the base is the length of the rectangle and the height is the breadth of the rectangle, we substitute these measurements into the formula to determine the area. Area of triangle LMN is 15.6 square cm.

Explanation:

To determine the area of the triangle inside the rectangle, we first need to understand the relationship between these two shapes. Given the base of the triangle, LN, is the same as the length of the rectangle, 6.5 cm, and the triangle is between the parallel lines of the rectangle, we can infer that the height of the triangle is the same as the breadth of the rectangle, which is 4.8 cm.

Now, the area of a triangle is given by the formula 1/2 * base * height.

Substituting the given measurements into this formula, we get

= 1/2 * 6.5 cm (base) * 4.8 cm (height)

= 0.5 * 6.5 cm (base) * 4.8 cm (height)

= 15.6 square cm

This will give us the area of the triangle LMN.

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The complete question is given below:

Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN?

The length of rectangle and triangle are same, 6.5 cm. The breadth of rectangle is 4.8 cm. The triangle lies between the parallel lines of rectangle with base LN.

Find the difference between the product of 21.33 and 2.04 and the sum of 1.115, 3.18, 22.0613, and 12.2384.        A. 5.1318   B. 38.5947   C. 4.9185   D. 43.5132  

Answers

first the product of 21.33 and 2.04= 43.5132
and the sum of 1.115+3.18+22.0613+12.2384=38.5947
now the difference both answers = 43.5132-38.5947 = 4.9185( C)
option C is correct

To find the difference, first find the product of 21.33 and 2.04, then find the sum of 1.115, 3.18, 22.0613, and 12.2384, and finally subtract the sum from the product. The correct answer is 4.9185.

To find the difference between the product of 21.33 and 2.04 and the sum of 1.115, 3.18, 22.0613, and 12.2384, follow these steps:

Calculate the product of 21.33 and 2.04:
21.33 × 2.04 = 43.5132Calculate the sum of 1.115, 3.18, 22.0613, and 12.2384:
1.115 + 3.18 + 22.0613 + 12.2384 = 38.5947Subtract the sum from the product:
43.5132 - 38.5947 = 4.9185

The difference is 4.9185, which corresponds to option C in the given choices.

Martha is cycling at a speed of 20 kilometers per hour. how long will it take her to cover a distance of 60 kilometers?

Answers

60 / 20 = 3  ---->  Only 3 hours
Martha was cycling 20 kilometers per hour and she needed to go 60 kilometers
60/2= 3 hours

Please help not really sure what to do here.

Answers

All you have to do is add all lengths together so it should be 'F'
I'm pretty sure it's F because it said minimum but I might be wrong sry

Which equation represents the value of x?

Answers

remember Pythagorean theorem

if we have a right triangle with legs a and b and hytponuse c then

[tex]a^2+b^2=c^2[/tex]


we are given a right triangle with legs x and y and hypotohuse 10

so therfor

[tex]x^2+y^2=10^2[/tex]

[tex]x^2+y^2=100

solve for x

minus y² from both sides

[tex]x^2=100-y^2[/tex]

sqare root both sides

[tex]x=\sqrt{100-y^2}[/tex]

the answer is the 4th option

An equation represents the value of x is x=√100-y².Therefore, option D is the correct answer.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given triangle ABC, AB=x units, BC=y units and AC=10 units

By using Pythagoras's theorem, we get

10²=x²+y²

x²=100-y²

x=√100-y²

Therefore, option D is the correct answer.

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The sum of two positive numbers is 42. What is the smalles possible value of the sum of their squares?

Answers

Okie, it is not too hard.
Set these numbers a and b, notice a, b positive.
We have a+b=42.
You can see the next on my photo

Or you can use the formula of Cauchy

A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company.

|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000.
|x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.

Answers

 the equation that represents the salaries is |x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000

What happens when you multiply a positive number by a positive number less than 1?

Answers

you are given the percentage of the whole integer that is the number less then one, for example 37 * 0.15 = 5.55, because 15% of 37 is 5.55

The coordinates of the vertices of quadrilateral RSTU are R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4) . Which statement correctly describes whether quadrilateral RSTU is a rectangle?

Answers

Answer:

For k12- the answer is Quadrilateral RSTU is not a rectangle because it has no right angles.


Step-by-step explanation:


Solution: A quadrilateral RSTU whose vertices are  R(−4, 1) , S(4, −1) , T(3, −6) , and U(−5, −4).

RS = [tex]\sqrt{(4+4)^{2}+(-1-1)^{2}} =\sqrt{64+4}= \sqrt{68}[/tex]

ST= [tex]\sqrt{(4-3)^{2}+(-1+6)^{2}}= \sqrt{1+25} =\sqrt{26}[/tex]

TU=[tex]\sqrt{(3+5)^{2}+(-6+4)^{2}}= \sqrt{64+4}= \sqrt{68}[/tex]

UR =[tex]\sqrt{(-5+4)^{2}+(-4-1)^{2}}= \sqrt{1+25} =\sqrt{26}[/tex]

→RS=TU, and ST=UR⇒ Opposite sides are equal.

Slope of RS = [tex]\frac{-1-1}{4+4} = \frac{-2}{8}=  \frac{-1}{4}[/tex]

Slope of TS= [tex]\frac{-6+1}{3-4} =\frac{-5}{-1}=5[/tex]

Slope of RS × Slope of TS = -1/4 × 5 = -5/4 ≠ -1, So lines are not perpendicular.

∴ quadrilateral RSTU  is not a rectangle.

98,464 rounded to the nearest ten thousand is

Answers

Rounded to the nearest 10,000, your answer is 100,000
In 98,464 the 8 is larger than four so the 9 gets rounded up. Since 9 is right before 10 your answer will be 100,00.

Jordan bought 9 pounds of fruit. He paid $2.39 a pound for 5 pounds. He paid $1.99 a pound for the rest. How much did Jordan spend on fruit? (please let me know how you did it)

Answers

5 pounds worth cost 2.39

9 - 5 = 4

the last 4 pounds cost 1.99

so you get this equation: 5(2.39) + 4(1.99)

5 x 2.39 = 11.95
4 x 1.99 = 7.96
11.95 + 7.96 = 19.91

Jordan spends $19.91

hope this helps
so he bought 9 lbs of fruit

he paid 2.39 a lb for 5 lbs.....thats 2.39 * 5 = 11.95
and now he has (9 - 5) = 4 lbs remaining...that he paid 1.99 per lb....thats is (1.99 * 4) = 7.96

for a total of : 11.95 + 7.96 = 19.91 <==

u can basically set it up like this : total cost = 2.39(5) + 1.99(4)

HELP ME!!!!!!!!!!!!!!!1 translate each sentence into an equation

1- 7 berries are 5 less than twice the number of berries Mickey had for lunch.

2- Negative 4 times the difference of a number 7 is 12

Answers

7 - 5 x m
-4 x 3
i believe these are correct if this isnt is there any other information? 

Point P is the incenter of triangle ABC, PZ = 7 units, and PA = 12 units.



The radius of the incircle centered at point P is ? units.

Answers

what is the answer?????

Answer:

The answer is 7 units

Step-by-step explanation:

I don't know but I got it right

I think you dont need to calculate anything they gave us the answer when they said PZ=7

What is the value of the expression “two less than six times the difference of a number and five” when n = 9?

Answers

I assume the number is 9 here, so your equation would be

(6(9-5))-2
which is equal to 24-2, which is 22.

Answer:

22

Step-by-step explanation:

The value of expression is 22.

Step-by-step explanation:

Given the statement “two less than six times the difference of a number and five” when n = 9. we have to find the value of expression formed by the above statement.

Difference of a number n and 5 gives (n-5)

Now, we have to write two less than 6 times the difference, we get the expression  6(n-5)-2

Here, the number n is 9

∴Value of expression is 6(9-5)-2=6(4)-2=24-2=22

Hence, the value of expression is 22.

A student solved the problem below by first dividing 20 by 10. What mistake did the student make?

A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?

Answers

50 percent. hope this helps <3

Answer:

Sample Response: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.

The base of a box is a rectangle. The width of the box is half its length. The height of the box is 0.5m. Find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.

Answers

Answer:


Step-by-step explanation:

We assume the box is open-top.


If the width of the box is represented by w, then its length is 2w. The area of the base is then w·2w = 2w².


The combined area of the sides is the product of the perimeter of the base, 2(w+2w) = 6w and the height, 0.5, so is 3w.

Since the base area is 1.08 m² less than the lateral area, we have

... 2w² = 3w -1.08

... 2w² -3w +1.08 = 0 . . . . rearrange to standard form

... w² -1.5w +0.54 = 0 . . . make the leading coefficient 1 (divide by 2)

... (w -0.9)(w -0.6) = 0 . . . factor

The width of the box may be either 0.6 meters or 0.9 meters.

The volume is the product of width, length, and height

V = w·2w·0.5 = w²

V = 0.36 m³ . . . or . . . 0.81 m³. . . . . . (there are two possible answers)

what are the roots of x in -10x^2 + 12x - 9=0

Answers

The "roots" of a function are the values of x for which y is zero. To solve this, be must use the quadratic formula, where a= -10, b=12, and c=-9
Quadratic formula:
x= [-b +/- √(b²-4ac)] ÷ 2a
Plugging in a, b, and c:
x= (-12 +/- √144 - 4(-10)(-9)) ÷ -20
 x= (-12 +/- √(144 + 360)) ÷ -20
x = (-12 +/- 6√14) ÷ -20
x  = (-12 + 6√14)/-20 or (-12 - 6√14)/ -20
x = 3/5 +/- 3√(14) / 10

Answer:

k=-11

Step-by-step explanation:

Correct for plato

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