All categories

2 years ago

5/16x20/30 Cancel and simplify

Mathematics

1 answer:

nikitadnepr [17]2 years ago

5 0

Answer: 5/24

Step-by-step explanation:

First:

Reduce fractions where possible.

Then your initial equation becomes:

5/16 * 2/3

Second:

Applying the fractions formula for multiplication,

5*2 and 16*3 = 10/48

Simplifying 10/48, the answer is

5/24

You might be interested in

I don’t know what it is<br> 15 ft. x 8 ft=

alexdok [17]

Answer:

The answer is 120 sq. ft.

3 0

2 years ago

Please help me! Need answer quick!

aksik [14]

Let h = height of triangle

h^2 + 12^2 = 15^2

h^2 + 144 = 225

h^2 = 225 - 144

h^2 = 81

sqrt{h^2} = sqrt{81}

h = 9 cm

For part B, we need to find surface area because it represents the perimeter of this 3-D figure. The formula needed is SA = B + LA.

1. First find the lateral area.

LA = perimeter of triangle • height

LA = ph

p = 15 + 15 + 24

p = 30 + 24

p = 54 cm

LA = (54)(9)

LA = 486 cm^2

2. We now find the base of each triangle. This is found by finding the area of each triangle and multiplying by 2.

A = (1/2)bh

A = (1/2)(24)(9)

A = 108 cm^2

A = 2•108 cm^2

A = 216 cm^2 = our B in the surface area formula.

SA = B + LA

SA = 216 cm^2 + 486 cm^2

SA = 702 cm^2

The amount of cardboard needed is 702 cm^2.

6 0

3 years ago

Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

3 years ago

In the expression a=k over b, what is k ?

andreyandreev [35.5K]

Answer: k=ab

Step-by-step explanation:

a= $\frac{k}{b}$

ab=k

8 0

2 years ago

Please help :((

yanalaym [24]

Answer:

C = 2 * π * R = 2 * π * 14 = <u>87.9646 cm</u>

Step-by-step explanation:

All this means is that the perimeter, or circumference, is the distance or length around a shape or object. And the area is the amount of space inside the thing.

In today’s geometry lesson, you will review the formulas for finding the area and perimeter of basic geometric shapes.

5 0

1 year ago