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3 years ago

What is the value of the exponential expression 36 1/2

Mathematics

2 answers:

miss Akunina [59]3 years ago

5 0

Answer:

The value of the given exponential expression $36^{\frac{1}{2}}\:$ is 6.

Step-by-step explanation:

Given: the exponential expression $36^{\frac{1}{2}}\:$

We have to find the value of the given exponential expression $36^{\frac{1}{2}}\:$

Consider the given exponential expression $36^{\frac{1}{2}}\:$

We know $\sqrt{x}=x^{\frac{1}{2}}$

Thus, $36^{\frac{1}{2}}=\sqrt{36}$

Factor the number 36 as $36=6^2$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

we have,

$\sqrt{6^2}=6$

Thus, the value of the given exponential expression $36^{\frac{1}{2}}\:$ is 6.

garik1379 [7]3 years ago

4 0

For this case we have an exponential expression of the form:
$36^{ \frac{1}{2}}$
We can rewrite the exponential expression using power properties.
We have then:
$\sqrt{36}$
From here, we take the square root of 36.
We have then:
$\sqrt{36} = 6$
Answer:
The exponential function is given by:
$36^{ \frac{1}{2}}=6$

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Hunter-Best [27]

Answer:

m∠J = 45° , m∠I = 45° and m∠M = 90°

And the ΔJIM is an isosceles right angled triangle.

Step-by-step explanation:

(a). In ΔJIM,

∠J = 2x + 15,

∠I = 5x - 30, and

∠M = 6x

Now, using angle sum property of a triangle that sum of all the angles in a triangle is 180°

⇒ ∠J + ∠I + ∠M = 180°

⇒ 2x + 15 + 5x - 30 + 6x = 180°

⇒ 13x -15 = 180°

⇒ 13x = 195

⇒ x = 15

Therefore, m∠J = 45° , ∠I = 45° and m ∠M = 90°

(b). Now, ΔJIM is a right angled triangle right angled at M.

Also, ∠J = ∠I = 45°

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So, ΔJIM is an isosceles triangle because its two sides are equal.

Hence, ΔJIM is a right angled isosceles triangle right angled at M.

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3 years ago

Determine if the situation described in each row can be represented by 9x+3=21 or by 3x+9=21. Select the correct answer in each

grin007 [14]

Selina gave 2 stickers to each of her friends.

Robert bought 4 bottles of paint.

<h3>What is a numerical expression?</h3>

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Selina had 21 stickers. She gave the same amount of stickers to each of her 9 friends and had 3 stickers left over.

This can be represented as,

9x + 3 = 21.

9x = 18.

x = 2.

So, she gave 2 stickers to each of her friends.

Robert went to an art supply store.

He got a pack of paintbrushes for $9 and some bottles of paint for $3 each.

His total came out to $21, before tax.

3x + 9 = 21.

3x = 12.

x = 4.

Robert bought 4 bottles of paint.

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1 year ago

Javier teaches yoga classes at his community center. In a 60-minute class last night, he taught 30 poses. Today, he has a 30-min

Hatshy [7]

Answer:

Step-by-step explanation

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2 years ago

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Mario had 9 green 810 Brown 6 Orange and 9 blue m&m's what is the fractions of M&M's that are orange? Help please

Ipatiy [6.2K]

Hey You!

Let's add up the total about of M&M's.

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3 years ago

Solve the equation uding the most direct method: 3x(x+6)=-10?

Tanzania [10]

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

<h3>Distribute</h3>

Use the distributive property to distribute 3x into the term (x + 6):

$3x(x+6)=-10$

$3x^2+18x=-10$

<h3>Rearrange</h3>

To create a quadratic equation, add 10 to both sides of the equation:

$3x^2+18x+10=-10+10$

$3x^2+18x+10=0$

<h3>Use the Quadratic Formula</h3>

The quadratic formula is defined as:

$\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

a = 3
b = 18
c = 10

Set up the quadratic formula:

$\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}$

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

$\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}$

Simplify the radicand:

$\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}$

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

$\sqrt{4\times51}$

Then, using the Product Property of Square Roots, break this into two radicands:

$\sqrt{4} \times \sqrt{51}$

Since 4 is a perfect square, it can be evaluated:

$2 \times \sqrt{51}$

To simplify further for easier reading, remove the multiplication symbol:

$2\sqrt{51}$

Then, substitute for the quadratic formula:

$\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}$

This gives us a combined root, which we should separate to make things easier on ourselves.

<h3>Separate the Roots</h3>

Separate the roots at the plus-minus symbol:

$\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}$

$\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}$

Then, simplify the numerator of the roots by factoring 2 out:

$\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}$

$\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}$

Then, simplify the fraction by reducing 2/6 to 1/3:

$\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}$

$\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}$

The final answer to this problem is:

$\displaystyle x=\frac{-9 + \sqrt{51}}{3}$

$\displaystyle x=\frac{-9 - \sqrt{51}}{3}$

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2 years ago