Evaluate 16^1/2 x 2^-3<br> Give your answer as a fraction in its simplest form.

Double number line 3t+15=45

Reika [66]

Answer:

t=-10 or t=20

Step-by-step explanation:

We want to solve the equation:

$|3t - 15| = 45$

We use the definition of the absolute value function to get:

$- (3t - 15) = 45 \: or \: (3t - 15) = 45$

Divide through the first equation by -1 to get:

$3t - 15 = - 45 \: or \: 3t - 15 =45$

We now add 15 to both sides of the equation to get:

$3t = - 45 + 15 \: or \: 3t =45 + 15$

$3t = - 30 \: or \: 3t =60$

Divide through by 3

$t = - 10 \: or \: t = 20$

4 0

3 years ago

3+<img src="https://tex.z-dn.net/?f=3%2B%5Csqrt%7B2%7D%2F4%5Csqrt%7B2%7D%2B2" id="TexFormula1" title="3+\sqrt{2}/4\sqrt{2}+2" al

tester [92]

This is the answer unless the 2/4 is meaning divide the two if thats the case the answer is 48+√2 over 8

8 0

1 year ago

Simplify the expression and rewrite in rational exponent form.

Dahasolnce [82]

Answer:

$4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$

Step-by-step explanation:

The given expression: $4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}$

Step 1: Change radical to fractional exponent.

Formula for fractional exponent: $\sqrt[n]{a}=a^{\frac{1}{n}}$

The power to which the base is raised becomes the numerator and the root becomes the denominator.

$\Rightarrow 4 x^{\frac{3}{5}} \cdot y^{4} \cdot x^{\frac{1}{2}} \cdot y^{\frac{5}{3}}$

Step 2: Apply law of exponent for a product $a^{m} \times a^{n}=a^{m+n}$

Multiply powers with same base.

$\Rightarrow 4 x^{\frac{3}{5}+\frac{1}{2}} \cdot y^{4+\frac{5}{8}}$

Take LCM for the fractions in the power.

$\Rightarrow 4 x^{\frac{6}{10}+\frac{5}{10}} \cdot y^{\frac{12}{3}+\frac{5}{3}}$

$\Rightarrow 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$

Hence the simplified form of $4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$ .

5 0

3 years ago

Solve the following problems using Pythagoras. Include a diagram . a. How long must a ladder be to reach 12 ft up the wall, if t

RUDIKE [14]

The length of ladder used is 12.25 ft.

<h3>What is Pythagoras theorem?</h3>

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Solution:

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse^2 = Base^2 + Height^2

16^2 = B^2 + 8^2

B^2 = 256 - 64

B = √192 = 13.856 units

Therefore, the measure of the third side of a triangle is 13.856 units.

given:

base= 2.5 ft,

perpendicular= 12 ft

Using Pythagoras theorem,

H² = B² + P²

H² = 2.5² + 12²

H² = 6.25+ 144

H= 12.25 ft

Learn more about Pythagoras theorem here: brainly.com/question/343682

#SPJ2

6 0

2 years ago

Read 2 more answers

Find the arc length, x, when<br> r= 8 and 0 = 5 radians.

lys-0071 [83]

Answer:

Arc Length = 40

Step-by-step explanation:

Arc Length Formula: S = rΘ

R = radius

Θ = Radians

<u>Step 1: Identify the radius and the radian angle</u>

R = 8

Θ = 5 radians

<u>Step 2: Plug into the equation</u>

S = (8)(5)

<u>Step 3: Solve</u>

S = 40

Answer: Arc Length = 40

7 0

3 years ago

Evaluate 16^1/2 x 2^-3 Give your answer as a fraction in its simplest form.