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2 years ago

Is the quotient of √10 and 5 a rational number? Explain.

Mathematics

1 answer:

zhuklara [117]2 years ago

7 0

Answer:

No, it is irrational.

Step-by-step explanation:

The quotient of √10 and 5 is equal to $\frac{\sqrt{10}}{5} }$ which equals 0.6245553...

The number goes on and on forever with no determinable pattern (i.e. the decimal 0.234234234... although the decimal goes on forever, the 234 repeats over and over).

If you're still confused, check out https://www.mathsisfun.com/irrational-numbers.html I find it to be a really helpful website!

You might be interested in

The sum of the interior angles of a polygon is

Crank

Answer:

D) 15

Step-by-step explanation:

The sum of the interior angles of a polygon is given by

$(n - 2) \times 180$

We have that, the sum of the interior angles of a polygon is

26 right angles. We want to find n, the number of sides.

We substitute into the formula to get:

$(n - 2) \times 180 = 26 \times 90$

Divide through by 90

$2(n - 2) = 26$

Divide through by 2

$n - 2 = 13$

$n = 13 + 2$

$n = 15$

6 0

1 year ago

Alicia borrowed $15,000 to buy a car. She borrowed the money at 8% for 6 years. What is the interest she will pay for the loan ?

kykrilka [37]

The interest rate she would pay would be is $7,200

5 0

2 years ago

Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i

jenyasd209 [6]

Answer:

If the limit that you want to find is $\lim_{x\to \infty}\dfrac{P(x)}{Q(x)}$ then you can use the following proof.

Step-by-step explanation:

Let $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ and $Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0}$ be the given polinomials. Then

$\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}$

Observe that

$\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}$

and

$\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}$

Then

$\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}$

3 0

2 years ago

Carl bought some stock at $25 a share it increased 1 1/2 times its value. How much is the stock per share ?

jolli1 [7]

Answer: $37.50 per share

Step-by-step explanation:

Take the difference in the final price and the original price. Divide by the original price and multiply by 100.

37.5-25= 12.5

12.5/25= .50

.50*100= 50%

The other answers are $12.50 per share, and

The new stock is worth $37.50 per share.

4 0

2 years ago

Read 2 more answers

You have a budget of $48. You want to buy fruit and granola bars. Fruit costs $4 per pound, and the granola bars are $1 each. Yo

zzz [600]

1)Define the variables you will use in your model.

Let

x------->total pounds of the fruit

y-------> the total number of granola bars

TC----> total cost

Tf------> total cost of the fruit

Tg----> total cost of the granola bars

2) Write an inequality representing the total cost of your purchase. (3 points)

a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1

Tf=4*x

b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.

Tg=1*y--------> Tg=y

c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.

TC=Tf+Tg

TC=4*x+y

inequality-------> $4x+y \leq 48$

3. Write the inequality that models the number of granola bars you need to buy.

You need at least 10 granola bars

$y\geq 10$

4. Describe in words what each of your inequalities means

inequality 1

$4x+y \leq 48$

the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars

inequality 2

$y\geq 10$

5. Graph your system of inequalities.

using a graph tool

see the attached figure

6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.

Let

A-------> one point on the graph that represents a viable solution

B-------> one point on the graph that does not represent a viable solution

A(4,20)

x=4-------> total pounds of the fruit

y=20------> the total number of granola bars

check point A

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*4+20\leq 48\\ 36\leq 48$ -------> is ok

substitute the values of x and y in the inequality 2

$y\geq 10$

$20\geq 10$ --------> is ok

the point A represents a viable solution, because satisfies both inequalities

B(10,30)

x=10-------> total pounds of the fruit

y=30------> the total number of granola bars

check point B

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*10+30\leq 48\\ 70\leq 48$ -------> is not a viable solution

substitute the values of x and y in the inequality 2

$y\geq 10$

$30\geq 10$ --------> is ok

the point B is not a viable solution because does not satisfy the inequality 1

3 0

1 year ago