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3 years ago

For which value of x must the expression √37x be further simplified?

Mathematics

1 answer:

vekshin13 years ago

5 0

Answer:

37x

Step-by-step explanation:

Since it has a square root you can square it to get rid of it so your final answer is 37x

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Two dice are tossed together. What is the probability of getting an odd number on the second die and a total of five?

wolverine [178]

Probability = (number of ways to succeed) / (total possible outcomes) .

The total possible results of rolling two dice is

(6 on the first cube) x (6 on the second one) = 36 possibilities.

How many are successful ? I need you to clarify something first.
You said that the 'second die' shows an odd number. When a pair
of dice is rolled, the problem usually doesn't distinguish between them.
And in fact, you said that they're "tossed together" (like a spinach and
arugula salad ?) so I would understand that they would lose their identity
unless they were, say, painted different colors, and we wouldn't know
which one is the second one.

Oh well, I'll just work it both ways:

First way:
Two identical dice are tossed.
The total is 5 and ONE cube shows an odd number.

How can that happen ?

1 ... 4
4 ... 1
3 ... 2
2 ... 3

Four possibilities. Probability = 4/36 = 1/9 = 11.1% .

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

Second way:
A black and a white cube are tossed together.
The total is 5 and the white cube shows an odd number.

How can that happen:

B ... W
4 .... 1
2 .... 3

Only two possibilities. Probability = 2/36 = 1/18 = 5.6% .

3 0

3 years ago

The sum of two numbers is 26. The larger number is 5 more than twice the smaller. What are

babymother [125]

Answer:

Step-by-step explanation:

Let n = the smaller of the two numbers, and since the other number is 5 more than twice the smaller number n, then ...

Let 2n + 5 = the second and larger number.

Since the sum of the two unknown numbers is 26, then we can write the following equation to be solved for n as follows:

n + (2n + 5) = 26

n + 2n + 5 = 26

Collecting like-terms on the left, we get:

3n + 5 = 26

3n + 5 - 5 = 26 - 5

3n + 0 = 21

3n = 21

(3n)/3 = 21/3

(3/3)n = 21/3

(1)n = 7

n = 7

Therefore, ...

2n + 5 = 2(7) + 5

= 14 + 5

= 19

CHECK:

n + (2n + 5) = 26

7 + (19) = 26

7 + 19 = 26

26 = 26

Therefore, the two desired numbers whose sum is 26 are indeed 7 and 19.

7 0

2 years ago

Read 2 more answers

5. David Read's the problem:

vladimir1956 [14]

Answer:

No, David's answer does not seem reasonable.

Let x= original purchase amount

25x = $10.25, so solve for x by dividing both sides by .25, and you get x = $41.

If the shirt was $18, the shorts must have been $41-$18 = $23 NOT $41.

Step-by-step explanation:

7 0

3 years ago

Solve these recurrence relations together with the initial conditions given. a) an= an−1+6an−2 for n ≥ 2, a0= 3, a1= 6 b) an= 7a

8_murik_8 [283]

Answer:

a) 3/5·((-2)^n + 4·3^n)
b) 3·2^n - 5^n
c) 3·2^n + 4^n
d) 4 - 3 n
e) 2 + 3·(-1)^n
f) (-3)^n·(3 - 2n)
g) ((-2 - √19)^n·(-6 + √19) + (-2 + √19)^n·(6 + √19))/√19

Step-by-step explanation:

These homogeneous recurrence relations of degree 2 have one of two solutions. Problems a, b, c, e, g have one solution; problems d and f have a slightly different solution. The solution method is similar, up to a point.

If there is a solution of the form $a[n]=r^n$ , then it will satisfy ...

$r^n=c_1\cdot r^{n-1}+c_2\cdot r^{n-2}$

Rearranging and dividing by $r^{n-2}$ , we get the quadratic ...

$r^2-c_1r-c_2=0$

The quadratic formula tells us values of r that satisfy this are ...

$r=\dfrac{c_1\pm\sqrt{c_1^2+4c_2}}{2}$

We can call these values of r by the names r₁ and r₂.

Then, for some coefficients p and q, the solution to the recurrence relation is ...

$a[n]=pr_1^n+qr_2^n$

We can find p and q by solving the initial condition equations:

$\left[\begin{array}{cc}1&1\\r_1&r_2\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]$

These have the solution ...

$p=\dfrac{a[0]r_2-a[1]}{r_2-r_1}\\\\q=\dfrac{a[1]-a[0]r_1}{r_2-r_1}$

_____

Using these formulas on the first recurrence relation, we get ...

$c_1=1,\ c_2=6,\ a[0]=3,\ a[1]=6\\\\r_1=\dfrac{1+\sqrt{1^2+4\cdot 6}}{2}=3,\ r_2=\dfrac{1-\sqrt{1^2+4\cdot 6}}{2}=-2\\\\p=\dfrac{3(-2)-6}{-5}=\dfrac{12}{5},\ q=\dfrac{6-3(3)}{-5}=\dfrac{3}{5}\\\\a[n]=\dfrac{3}{5}(-2)^n+\dfrac{12}{5}3^n$

The rest of (b), (c), (e), (g) are solved in exactly the same way. A spreadsheet or graphing calculator can ease the process of finding the roots and coefficients for the given recurrence constants. (It's a matter of plugging in the numbers and doing the arithmetic.)

_____

For problems (d) and (f), the quadratic has one root with multiplicity 2. So, the formulas for p and q don't work and we must do something different. The generic solution in this case is ...

$a[n]=(p+qn)r^n$

The initial condition equations are now ...

$\left[\begin{array}{cc}1&0\\r&r\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]$

and the solutions for p and q are ...

$p=a[0]\\\\q=\dfrac{a[1]-a[0]r}{r}$

Using these formulas on problem (d), we get ...

$c_1=2,\ c_2=-1,\ a[0]=4,\ a[1]=1\\\\r=\dfrac{2+\sqrt{2^2+4(-1)}}{2}=1\\\\p=4,\ q=\dfrac{1-4(1)}{1}=-3\\\\a[n]=4-3n$

And for problem (f), we get ...

$c_1=-6,\ c_2=-9,\ a[0]=3,\ a[1]=-3\\\\r=\dfrac{-6+\sqrt{6^2+4(-9)}}{2}=-3\\\\p=3,\ q=\dfrac{-3-3(-3)}{-3}=-2\\\\a[n]=(3-2n)(-3)^n$

_____

<em>Comment on problem g</em>

Yes, the bases of the exponential terms are conjugate irrational numbers. When the terms are evaluated, they do resolve to rational numbers.

6 0

3 years ago

What is the goal in solving an equation?

Lelechka [254]

Your answer is, get the variable by itself.

The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation.

<h3><u>What is an equation?</u></h3>

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

<h3><u>3 types of equations</u></h3>

slope-intercept form

point-slope form

standard form

Thus, <u>option a</u> is your answer.

Learn more about equations here

https://brainly.in/question/5052814

4 0

3 years ago