When is the product of the square root of a prime number and a nonzero rational number a rational number?

Answer:

The height h it will travel in t minutes

Height h = 6 + 20(t)

Oh=20t + 6

Step-by-step explanation:

A hot air balloon starts at a height of 6 feet above the ground and then rises at a rate of 20 feet each minute.

Initial height h0 = 6 feet

Then it travel 29 feet each minute

Rate = 20 feet/ minute

The height h it will travel in t minutes

Height h = 6 + 20(t)

The required number is 4.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The sum of a number and six is ten.

let the number be x.

So, x + 6 = 10

Now, solving for x

x = 10 - 6

x = 4

Hence, the value of x is 4.

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ2

Answer:

Algebraic expression = x+3=2x-6

Step-by-step explanation:

Let the unknown number be x ;

[tex]x+3 =2x-6[/tex]

Further explanation

[tex]x+3=2x-6\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}x+3-3=2x-6-3\\\\Simplify\\x=2x-9\\\\Collect\:like\:terms\\x-2x =-9\\\\Simplify\\-x =-9\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{-9}{-1}\\\\x =9[/tex]

Answer:

900   + 20 + 7

Answer:

[tex]900+20+7[/tex]

Step-by-step explanation:

Write 927 as a mathematical expression in expanded form.

So we see the number 927. It has hundreds, tens, ones. So the only thing we have to do it separate the number by hundreds, tens, ones. So now, let's start!

Hundreds: [tex]900[/tex]

Tens: [tex]20[/tex]

Ones: [tex]7[/tex]

We have 900, 20, and 7. Let's try adding them up to make 927.

[tex]900+20+7[/tex]

[tex]=927[/tex]

This is how we do 927 in expanded form.

Hope this Helps!

Answer:

(1,2), (2,4), (3,6), (4,1), ( 5,3), (6,5)

Step-by-step explanation:

Given the first two solutions of the n-Queens problem for n = 6

The solution requires that no two queens share the same row, column, or diagonal and each variable lies in the domain [1,6] (6 rows).while finding a solution we must ensure that no two queens are not placed on the same row and in the same diagonal

hence the first two solutions can be expressed as :

(1,2), (2,4), (3,6),(4,1),( 5,3), (6,5)

Answers:

The term "root" is another way of saying "zero of a function"

============================================

Explanation:

To find the roots, we need to solve f(x) = 0 for x

f(x) = 0

5x/(x^2 - 25) = 0

5x = 0*(x^2-25)

5x = 0

x = 0/5

x = 0

Plugging x = 0 into f(x) leads to f(x) = 0.

The root is x = 0 meaning the x intercept is at 0 on the x axis number line. This is the origin (0,0).

---------------

To find the vertical asymptotes, set the denominator equal to 0 and solve for x

x^2 - 25 = 0

x^2 - 5^2 = 0

(x-5)(x+5) = 0 ... difference of squares rule

x-5 = 0 or x+5 = 0

x = 5 or x = -5

If either x = 5 or x = -5, then then the denominator x^2-25 is zero

We cannot divide by zero, so these values are excluded from the domain, and this produces the vertical asymptotes.

--------------

The horizontal asymptote is y = 0 because the degree of the numerator is 1, while the degree of the denominator is 2. The denominator's degree is larger, which leads to y = 0. The rules for finding the horizontal asymptote are

For those rules above, m and n are the degrees of the numerator and denominator respectively. The a,b refers to the leading coefficients of the numerator and denominator.

The asymptotes and zero of the function are ±5 and 0 respectively

Given the function below;

[tex]f(x)=\frac{5x}{x^2-25}[/tex]The vertical asymptotes occur at the point where the function goes large that is the denominator is zero.

If the denominator is zero, hence;

x^2 - 25 = 0

x^2 = 25

x = ±√25

x = ±5

Hence the asymptotes of the function is ±5

For the zero of the function;

[tex]\frac{5x}{x^2-25}=0\\5x = 0\\x = 0\\[/tex]

Hence the zero of the function is 0

Learn more on asymptotes here: https://brainly.com/question/25827382

Answer:

7x.

Step-by-step explanation:

Seven times a number = 7x.

An algebraic expression for the given statement is 7x.

The given statement is seven times a number.

We need to write an algebraic expression for the given statement.

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

Given that, use the variable x to represent the unknown number.

Now, seven times a number=7x

Therefore, an algebraic expression for the given statement is 7x.

To learn more about an algebraic expression visit:

https://brainly.com/question/19245500.

#SPJ2

Answer:

  1/2 liter

Step-by-step explanation:

If she starts with 1 1/2 liters and removes 1/4 liter, the remaining amount is ...

  (1 1/2) -(1/4) = 1 2/4 -1/4 = 1 1/4 . . . liters.

The brother drinks 2/5 of that, so drinks ...

  (2/5)(1 1/4 L) = (2/5)(5/4 L) = 2/4 L = 1/2 L

Rosanne's brother drinks 1/2 L of the lemonade.

Answer:

plane EHV

Step-by-step explanation:

To find the other name of plane T, we have to find any three non-collinear points on the plane T.

It means we have to find any three points which lie on the plane T but in a single straight line.

From the given figure it is clear that points E, H and V lie on plane T and they are not collinear.

Therefore, the other name of plane T is plane EHV.

Note: There are many other possible names of plane T, EHV is one of them.

Answer:

Week 3.

Step-by-step explanation:

Add up the hours for each week.

Week 3 is the highest at 36 hours.

Answer:

week 3

Step-by-step explanation:

week 3. it totals for 36 hours in this week

Answer:

A

Step-by-step explanation:

The average is over the months not added each month

Answer:  4n-3

================================================

Explanation:

day 1 = 1 sold

day 2 = 5 sold

day 3 = 9 sold

day 4 = 13 sold

Each time we're going up by 4. This is effectively the slope of the line since it represents the rate of change. The starting amount sold (1) is the y intercept

So we go from y = mx+b to y = 4x+1

Afterward, replace x with n to get 4n+1

On day n = 0, we have 4n+1 = 4(0)+1 = 1 sold. While this is correct, it doesn't really help to start with day 0 and it's better to start with day 1 instead.

What we can do is replace n with (n-1) and then simplify

4(n-1)+1 = 4n-4+1 = 4n-3

Now plugging in n = 1 leads to 4n-3 = 4(1)-3 = 1

Plugging in n = 2 leads to 4n-3 = 4(2)-3 = 5

and so on.

Answer: One fourth of the entire trip.

Step-by-step explanation:

The initial distance is D.

" He fell asleep halfway home."

Then he fells asleep when the distance between his actual position and his house was half of D, or:

D/2.

"He didn't wake up until he still had half as far to go as he had already

gone while asleep."

So he wakes up when his actual position is a fourth of the initial distance:

(D/2)/2 = D/4.

Then if the entire trip has a distance D, and he was sleeping between:

D/2 - D/4 = 2D/4 - D/4 = D/4.

in a trip of a distance D, he was asleep a distance of D/4.

Then, returning to the question:

How much of the entire trip home was Samuel asleep?

This is equal to the quotient between the distance that he travels asleep and the total distance:

r = (D/4)/D = 1/4.

Then he was asleep in 1/4 of the entire trip.

Excuse me, is this I ready because you know you can get  reported right... just try your best, it's not a real grade! :)

& possibly delete this question because a bot can track and report this to your school. People at my school did that and got in 3 days detention...

Answer:

The  points are

        [tex]t_1 =  0.7433[/tex]

        [tex]t_2 = -0.299[/tex]

Step-by-step explanation:

From the question we are told that

   The  first equation is  [tex]x(t) = 3t^3 -2t^2-2t -4[/tex]

     The second equation is  [tex]y(t) =  3t^2 -2t -2[/tex]

Now differentiating the first and second equation

        [tex]\frac{dx(t)}{dt} =  9t^2 -4t-2[/tex]

and

      [tex]\frac{dy(t)}{dt} =  6t-2[/tex]

Now

     [tex]\frac{dy(t)}{dx(t)}  =  \frac{\frac{dy(t)}{dt} }{\frac{dx(t)}{dt} } = \frac{9t^2 -4t-2}{6t-2}[/tex]

at critical point

     [tex]\frac{dy(t)}{dx(t)}  = 0[/tex]

=>   \frac{9t^2 -4t-2}{6t-2}=0[/tex]

=>   [tex]9t^2 - 4t-2 = 0[/tex]

solving using quadratic formula we have that

     [tex]t_1 =  0.7433[/tex]

and [tex]t_2 = -0.299[/tex]

Answer: no

Step-by-step explanation:

Answer:

-36

Step-by-step explanation:

4(1 - 25) + 70 - 10

PEMDAS

Parentheses first

4( -24) + 70 -10

Then multiply and divide

-96 + 70-10

Then add and subtract

-36

Answer:

1009479

Step-by-step explanation:

637,391 + 372,088 = 1009479

Answer:

the answers 1009479

Step-by-step explanation:

Answer:

(3/2)x - 14

Step-by-step explanation:

If two lines are perpendicular, their slopes are mathematically negative reciprocals of one another.

Here the given line is y = (-2/3)x; the slope is -2/3, and the negative reciprocal of that is 3/2.  The desired line will have this slope 3/2.

Using the slope-intercept form of the equation of a straight line, y = mx + b, we write out

-8 = (3/2)(4) + b, obtaining -8 = 6 + b, or b = -14.

The desired equation is (3/2)x - 14.

Answer:

In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers avoid going down blind alleys and learn how to modify conjectures to produce provable theorems.

Step-by-step explanation:

Answer:

The answer is B: $29.35x + $17.45y

Answer:

The radius of [tex]x^{2}+y^{2}-18\cdot x - 14\cdot y +124 = 0[/tex] is [tex]\sqrt{6}[/tex].

Step-by-step explanation:

The given expression must be converted into the standard form of a circle, which is described by:

[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Location of center, dimensionless.

[tex]r[/tex] - Radius, dimensionless.

The expression is modified algebraically as follows:

1) [tex]x^{2}+y^{2}-18\cdot x - 14\cdot y +124 = 0[/tex] Given

2) [tex](x^{2}-18\cdot x)+(y^{2}-14\cdot y)+124 = 0[/tex] Commutative and associative properties.

3) [tex](x^{2}-18\cdot x+81)+(y^{2}-14\cdot y +49)+124 = 81+49[/tex] Commutative and associative properties/Compatibility with addition

4) [tex](x-9)^{2}+(y-7)^{2} + 124 = 130[/tex] Perfect square binomial/Definition of sum

5) [tex](x-9)^{2}+(y-7)^{2} = 6[/tex] Compatibility with addition/Existence of additive inverse/Modulative property/Result

Given that [tex]r^{2} = 6[/tex], the radius of the circle is [tex]\sqrt{6}[/tex].

Answer:

(a)

L is not reflexive, L is anti-reflexive  

L is not symmetric.

L is not anti-symmetric

L is transitive.  

(b)

D is reflexive

D is not symmetric.

D is anti-symmetric

D is transitive.

Step-by-step explanation:

a)

Given that;

domain of the given  relation L is the set of all real numbers

For x , y ∈ R , xLy if x less than y.

relation L, where xLy if x less than y, For x, y ∈ R

so For every x ∈ R, it is then false that x less than x.  

That is (x, x) does not belongs to L.

∴ L is not reflexive, L is anti-reflexive.

For every x,y ∈ R, if (x,y) ∈ L (i.e. x < y), then (y, x) does not belongs to L, since it is false that y < x.

∴ L is not symmetric.

For every x ∈ R, we can say  its  false that x less than x. That is (x, x) does not belongs to L.

∴ L is not anti-symmetric.

For every x,y,z ∈ R, if (x, y) ∈ L(i.e. x < y) and (y, z) ∈ L(i.e. y < z), then (x, z) ∈ L, since it is true that x<z when x<y and y<z.

∴ L is transitive.  

b)

Also lets consider a relation D, where xDy if there is an integer n such that y = xn, For x, y ∈ Z.

Now

For every x ∈ Z, it is true that x = x × 1. That is (x, x) belongs to D.

∴ D is reflexive,

For every x,y ∈ Z, if (x,y) ∈ P (i.e. y=x × n), then (y, x).

if (x,y) ∈ D, then there exist an integer n such that y=x × n.

Then x = y × (1/n).

Thus, (y,x) does not belongs to D, since 1/n is not an integer, but it is a real number.

∴ D is not symmetric.

For every x,y ∈ Z, if (x,y) ∈ D (i.e. y=x × n), then (y, x) also belongs to D only when x=y. where n=1.

∴ D is anti-symmetric.

For every x,y,z ∈ Z, if (x,y) ∈ D (i.e. x × n1= y), and (y,z) ∈ D (i.e. y × n2 = z), then (x,z)∈ D.

if (x,y) ∈ D, then there exist an integer n1 such that y=x × n1.

if (y,z) ∈ D, then there exist an integer n2 such that z=y × n2.

Thenz = (x × n1) × n2 ⇒ z=x × (n1 × n2).  

where (n1 × n2) is an integer. Thus (x,z) ∈ Z

∴ D is transitive.

Step-by-step explanation:

42x=252

x=252/4

x=6

well hope that helps

Answer: Answer is the steps

Step-by-step explanation:

Step 1:  Richie rewrite the equation as 24x + 18(x-2) =216

Step 2: Richie  applied the distributive property to eliminate the parentheses  and got the equation  24x + 18x - 32 = 216

Step 3: Richie combine like terms  to get the equation 42x -36 =216

Step 4: Richie added 36 to both sides to get the new equation 42x = 252  

Richie was not done solving for x so in

Step 5: Richie should have divided both sides by 42 to get  the final answer

x = 6.

Answer:

FG = 18

Step-by-step explanation:

to find the length FG

FG + 31 = 49

FG = 49 - 31

FG = 18

Answer:

  1.2144xx

Step-by-step explanation:

The multiplier of value for the first year was (1 +38%) = 1.38.

The multiplier of value for the second year was (1 -12%) = 0.88.

Then the multiplier of value for the two years was ...

  1.38×0.88 = 1.2144

The value of the stock after 2 years was ...

  1.2144xx

_____

Comment on the variable

We have used the variable given in the problem statement (xx). If you intend something different, replace xx with the variable you intend.

Answer: -32, -11, 5, 31, 33

Answer:

-32, -11, 5, 31, 33

Step-by-step explanation:

The smallest one is -32. I know this because it's:

The next one is -11. -11 is the next smallest because it's:

The third one is 5. It's the third greatest because it's:

The fourth one is 31. It's the fourth greatest because it's:

The last one is 33. It's the greatest because it's:

Answer:

2501/50

Decimal:50.02

Step-by-step explanation:

5 × 10 + 2× 1/100

5 × 10 = 50

2 × 1/100 = 1/50

50 + 1/50

50×50. 1

_____ + ___

50. 50

50 × 50 + 1 = 2501 meaning 2501 over 50 is your answer

Answer:

100

Step-by-step explanation:

Hope this helped! ;)

Answer:

The digit in the ones spot will come out to be 4.

Step-by-step explanation:

Since the  are both an even number of ten, and you're subtracting 6, their both gonna come out to have a 4 in the ones spot in the number answer.

Well 50 is just 10 x 5 so...

if you solve 10 + 6 = 16 then you can do 50 + 6 = 56