Which of the following is a rational number?


A. [tex]\sqrt{10}[/tex]

B.[tex]\sqrt{100}[/tex]

C.[tex]\sqrt{1000}[/tex]

D.[tex]\sqrt{100000}[/tex]

Can you please explain your answer I want to understand it

The rate at which Riya is applying the mulch to the garden is 250000:1.

It should be noted that rate is simply used to show the relationship between two things. A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the dependent variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Per unit of time is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).

From the information, Riya is applying mulch to the garden and she applied at a rate of 250000cm³ for every m² of space.

Therefore, the rate at which Riya is applying the mulch to the garden is 250000:1.

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Answer: h=1

Step-by-step explanation:

multiple 5h and -4 by 7

35h-28-1=14-8h

35h-29=14-8h

add 29 to both sides

35h=43-8h

43h=43

i think this is right...

The given equation is,

→ 7(5h - 4) - 1 = 14 - 8h

Now the required value of h will be,

→ 7(5h - 4) - 1 = 14 - 8h

→ 35h - 28 - 1 = 14 - 8h

→ 35h - 29 = 14 - 8h

→ 35h + 8h = 14 + 29

→ 43h = 43

→ h = 43/43

→ [ h = 1 ]

Hence, the value of h is 1.

Two consecutive asymptotes are θ = - π / 20 and θ = 3π / 20 and the period is π / 5.

In this question we must look for two consecutive vertical asymptotes related to a trigonometric function. A function becomes undefined when its denominator is zero. Now we proceed to simplify the expression by trigonometric formulas:

y = 4 · csc (5θ - 3π / 4)

y = 4 / sin (5θ - 3π / 4)

y = 4 / (sin 5θ · cos 3π / 4 - cos 5θ · sin 3π / 4)

y = 4 / [(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ]

The function is undefined for (- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0:

(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0

(- √2 / 2) · sin 5θ = (√2 / 2) · cos 5θ

- sin 5θ = cos 5θ

tan 5θ = - 1

5θ = - π / 4 + i · π

θ =  - π / 20 + i · π / 5

θ = (π / 5) · (- 1 / 4 + i)

There are two consecutive asymptotes:

i = 0

θ = - π / 20

i = 1

θ = 3π / 20

And the period is ΔT = 3π / 20 - (- π / 20) = π / 5.

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Answer:

Cube = 8 vertices

Pyramid=5 vertices

Step-by-step explanation:

Cube = 8 vertices

Pyramid=5 vertices

His final payment will be $271.66464 at the end of the third year.

The term "compound interest" refers to interest that is added back to the principal amount during each compounding period.

Compound interest is calculated using the formula

A = P(1+r )ⁿ,  where

P = principal balance,

r = interest rate,

n =  number of periods.

Given that a man borrows $760 at 4% and of the first year he pays back $270.

Amount owned by him at the end of the first year after repaying $270 =  (1+4%)760 - 270

= 1.04×760 - 270

= $520.4

Amount owned by him at the end of the second year after repaying $280 =  (1+4%)520.4 - 280

= 1.04×520.4 - 280

= 541.216 - 280

= $261.216

Let his final payment be x.

So, the amount owned by him at the end of the third year will be 0.

⇒ (1+4%)261.216 - x = 0

⇒ 1.04×261.216 - x = 0

⇒ 271.66464 = x

Therefore, his final payment will be $271.66464.

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Answer:

Either -8b - 24 or b = 3

Step-by-step explanation:

Answer: - 8b - 24

Distributive property

We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k

Explanation:

According to the principle of Mathematical Induction,

Let d(n) be a statement involving Natural Number n such that

d(1) is true

d(m) is true

d(m+1) is true

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all the values of n ( natural number)

Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

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Answer:

2

Step-by-step explanation:

8+14 = 22

22-5 = 17

17-7 = 10

10+3 = 13

13-7 = 6

6-4 = 2

Answer:

d) 2

Step-by-step explanation:

Answer:

the answer is the 20⁰ ok that

In the expression 2x + 5 at x = 3 Brett is wrong as the correct answer is 11.

An expression is written in the form of numbers and variables with arithmetic operations.

According to the given question we have to evaluate 2x + 5 at x = 3 and match our answer with Brett which is 41.

To obtain the value of 2x + 5 at x = 3, we have to substitute x with 3 in the given expression which is,

= 2(3) + 5

= 6 + 5.

= 11.

So, our answer is correct which is 11 and Brett is wrong.

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Answer:

1.5 meters per second

Step-by-step explanation:

90 meters divided by 60 seconds is 1.5

The formula 3x-y=5 is a linear function.

We must first examine the slope of the original function in order to determine the equation of parallel lines. We are also given the other function's intercept in this issue.

The function's slope-intercept form is y=3x-5.

In order to locate the parallel line that corresponds to the point (0,-7)

Parallel lines are those that share the same slope but have different y-intercepts, as you may have seen.

As a result, we must put in the point to solve for the y-intercept.

Thus,

y = 3x + b

-7 = 3(0) + b

-7 = b

b = -7

Thus the equation of a parallel line is y = 3x - 7

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The algebraic expression become 3n-16<8.

According to the statement

We have to find that the numerical expression.

So, For this purpose, we know that the

Algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

From the given information:

the difference between three times a number and 16 is at least 8

Then

From 1st statement it become 3n -16

And with other statement and combining

Then  the equation become

3n-16<8

Now solve the expression for the value of the n

then it becomes

3n<24

n<8.

The value becomes is 8.

So, The algebraic expression become 3n-16<8.

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Answer:

Rise/Run

or

[tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

The formula for slope is referred to rise over run,

Because the fraction consists of the rise (the change in y, going up or down) divided by the run (the change in x, going from left to the right).

A rise over run equation would be formatted like this:

Rise/Run

or

[tex]\frac{rise}{run}[/tex]

(i used to struggle with slopes, and i understand how much of a pain they are)

The inverse of function f( x ) = ( 2x - 3)² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].

A function that can reverse into another function is known as an inverse function or anti-function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.

We have the function,

f(x) = y = ( 2x - 3 )²

x = ( 2y - 3 )²

2y - 3 = ±√x

Adding 3 from each side.

2y - 3 + 3 = ±√x + 3

2y = ±√x + 3

Dividing each side of the equation by 2.

[tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex]

Hence, the inverse of function f( x ) = ( 2x - 3 )² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].

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The amount of markup on a single rose is $2.74.

The markup formula is defined as the profit per unit cost of an item and is given as,

Markup = 100 * profit/cost

We multiply by 100 because we express it as a percentage, not as a fraction.

Now it is given that,

Cost Price of a dozen roses = $2.96

Number of roses = 12

Thus, Cost Price of 1 rose = 12.96/12 = $.108

Now it is also given that, the these dozen roses are sold at $48.48

So, Selling price of 1 rose = 48.48/12 = $4.04

Thus, Profit = Selling Price - Cost Price

⇒  Profit = $4.04 - $1.08

⇒  Profit = $2.96

Thus,Amount of Markup of single rose = Profit/Cost of 1 rose

⇒ Amount of Markup of single rose = 2.96/1.08

⇒ Amount of Markup of single rose = 2.74

Thus, the amount of markup on a single rose is $2.74.

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the expression that models the situation of the total cost of a diner, less a $10 coupon divided by 4 is (x - $10)÷4

Here we have the total cost of a dinner, less a $10 coupon, divided by 4 people.

If the total cost is x, then the total cost less a $10 coupon is:

x - $10.

Now, taking the quotient (dividing the above amount by 4) we will get:

(x - $10)÷4

This is the expression that models the situation of the total cost of a dinner, less a $10 coupon divided by 4.

So the correct option is the first one.

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Answer: Be careful. There is a slight difference in the order of the questions

Answer: D

Step-by-step explanation:

:)

The sum of the three numbers 7531, 5252 and 6375 is 19158

The numbers are given as

7531, 5252, 6375

Express the numbers as a summation expression

So, we have

Sum = 7531 + 5252 + 6375

Evaluate the sum

So, we have

Sum = 19158

Hence, the sum of the three numbers 7531, 5252 and 6375 is 19158

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The equation of the line for the  point (-1, 2) is [tex]y=x+3[/tex]

It is given that line is parallel to the line y = x + 4 .    ....(2)

On comparing equation (2) with the slope intercept form which is  y = mx +c , we get  m = 1 . For parallel lines slope is same .

It is given that line passes through the point (-1, 2).

Putting [tex]y_1=2,\ x_1=-1[/tex] and m = 1 in equation (1) , we get

     [tex]y-2=1(x-(-1))\\y-2=x+1\\y=x+3[/tex]

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For Vertical asymptotes at x=0 and x=3 , horizontal asymptote at y=0 , a zero at -4, the rational function will be - (x+4) / (x)(x-3)

Asymptote, a line or curve that serves as the boundary of another line or curve in mathematics. An example of an asymptotic curve is a descending curve that approaches but does not reach the horizontal axis, which is the asymptote of the curve.

Given,

Vertical asymptotes at x=0 and x=3 , it means that these both factors are included in the denominator.

horizontal asymptote at y=0, it means means highest degrees in both numerator and denominator is 0.

zero at -4, it means we have this as factor in numerator.

The required rational function will be -

(x+4) / (x)(x-3)

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The values of "x" and "y" in the given matrix equation is 5 and 3 respectively.

A matrix equation is an equation in which a matrix acts as a variable.

The given system of equation;

x + 2y = 11

x + 4y = 17

[1    2 ] =  [11]

[1   4  ]  =  [17]

determinate of the equation, Δ

Δ = [1    2 ]

      [1   4  ]  

Δ = (4 x 1) - (2 x 1) = 2

Δx =  [11    2 ]

        [17   4  ]  

Δx  = (4 x 11) - (17 x 2) = 10

Δy =  [1    11 ]

        [1   17  ]  

Δy = (17 x 1) - (11 x 1) = 6

x = Δx/Δ

x = 10/2 = 5

y = Δy/Δ

y = 6/2 = 3

Thus, the values of "x" and "y" in the given matrix equation is 5 and 3 respectively.

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a) The line segment PQ has a length of √85 (approx. 9.219).

b) The coordinates of the midpoint of the line segment PQ is (4, 0.5).

Herein we find a line segment whose endpoints are known: P(x, y) = (3, 5), Q(x, y) = (5, - 4), and we are asked to determine the length of the line segment and the coordinates of the midpoint as well. a) First, we determine the vector between the points P and Q by sum of vectors:

PQ = Q(x, y) - P(x, y)

PQ = (5, - 4) - (3, 5)

PQ = (2, - 9)

And its magnitude is determined by using the Pythagorean theorem:

PQ = √[2² + (- 9)²]

PQ = √85

b) The coordinates of the midpoint is found by using the following formula:

M(x, y) = 0.5 · P(x, y) + 0.5 · Q(x, y)

M(x, y) = 0.5 · (3, 5) + 0.5 · (5, - 4)

M(x, y) = (1.5, 2.5) + (2.5, - 2)

M(x, y) = (4, 0.5)

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The marginal distribution of males is 13 %

A two-way frequency table shows the frequencies (or "counts") of two categorical variables.

For example, the following two-way table displays the results of a study in which 100 participants were asked which sport they preferred: baseball, basketball, or football.

The rows represent the respondent's gender, while the columns show which sport they chose:

There are two variables in this example: Sports and Gender.

A marginal distribution is simply the sum of the distributions of these separate variables. The marginal distributions in a two-way table are shown in the table margins: Marginal distributions are valuable because, while we frequently collect data for two variables (such as Sports and Gender), we may have particular questions regarding only one variable.

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Answer: Aiza have left from her lifeguarding job = $ 700

Step-by-step explanation:

Given that,

Aiza made $55 a day lifeguarding in the summer.

She worked six days a week for five weeks.

For two weeks of the summer she went on vacation.

She spent approximately $68 a day each for two weeks.

Aiza earning per day = $55

Aiza worked for six days in a week.

Aiza worked for five weeks.

Total earning for weeks

                          = $ 55(6)

                          = $ 330 / week

Total earning for 5 weeks

                           = $ 330(5)

                           = $ 1650

Aiza spent per day for vacation = $ 68

Aiza was an vacation for two weeks.

Total expenditure for two weeks,

Number of days in each week = 7 days

                                                   = 2(7)($ 68)

                                                   = $ 952

Aiza have left with = Total earning - Total expenditure

                               = $ 1650 - $ 952

                               = $ 700

Therefore, Aiza have left from her lifeguarding job = $ 700

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1. The constant term of the polynomial is: 8.

2. The exponent of the third term is 1.

A term of a polynomial can include any of the following:

Any of the above is referred to as a term of a polynomial.

Given the polynomial, -y^4 + 2y² + 3y + 8, the polynomial has 4 terms, -y^4, 2y², 3y, and 8.

Thus:

1. The constant term of the polynomial is: 8.

2. The exponent of the third term is 1.

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