Simplify the algebraic expression 5x2/(x2-2x) − (x2-4)/(x2+2x) Find the value of x in the diagram below.

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Here are the solutions to the problems:

: Simplify fraction expression

Convert mixed numbers to improper fractions.
$6\frac{3}{4} = \frac{27}{4}$ $2\frac{4}{15} = \frac{34}{15}$ $1\frac{2}{3} = \frac{5}{3}$
Evaluate the expression inside the parenthesis.
$2\frac{4}{15} - 1\frac{2}{3} = \frac{34}{15} - \frac{5}{3} = \frac{34}{15} - \frac{25}{15} = \frac{9}{15} = \frac{3}{5}$
Perform the "of" operation (multiplication).
$\frac{2}{3} \text{ of } 6\frac{3}{4} = \frac{2}{3} \times \frac{27}{4} = \frac{54}{12} = \frac{9}{2}$
Perform the division.
$\frac{9}{2} \div \frac{3}{5} = \frac{9}{2} \times \frac{5}{3} = \frac{45}{6} = \frac{15}{2}$
The simplified expression is $\boxed{\frac{15}{2}}$ or $\boxed{7\frac{1}{2}}$ .

: Evaluate and leave your answer in standard form
Perform the multiplication in the numerator.
$4.56 \times 3.6 = 16.416$
Perform the division.
$\frac{16.416}{0.12} = \frac{1641.6}{12} = 136.8$
Express the answer in standard form.
$136.8 = 1.368 \times 10^2$
The evaluated value in standard form is $\boxed{1.368 \times 10^2}$ .

: Calories burned per hour
Divide the total calories burned by the total hours.
$\text{Calories per hour} = \frac{\text{Total calories}}{\text{Total hours}}$ $\text{Calories per hour} = \frac{856 \text{ calories}}{4 \text{ hours}}$
Calculate the value.
$\text{Calories per hour} = 214 \text{ calories/hour}$
Bongo burns $\boxed{214 \text{ calories per hour}}$ .

: Simplify the algebraic expression
Factor the denominators and numerators.
$\frac{5x^2}{x^2-2x} - \frac{x^2-4}{x^2+2x} = \frac{5x^2}{x(x-2)} - \frac{(x-2)(x+2)}{x(x+2)}$
Simplify each term by canceling common factors.
$\frac{5x}{x-2} - \frac{x-2}{x}$
Find a common denominator and combine the fractions.
The common denominator is $x(x-2)$ .
$\frac{5x \cdot x}{x(x-2)} - \frac{(x-2)(x-2)}{x(x-2)} = \frac{5x^2 - (x^2 - 4x + 4)}{x(x-2)}$
Expand and simplify the numerator.
$\frac{5x^2 - x^2 + 4x - 4}{x(x-2)} = \frac{4x^2 + 4x - 4}{x(x-2)}$
Factor out common terms in the numerator.
$\frac{4(x^2 + x - 1)}{x(x-2)}$
The simplified expression is $\boxed{\frac{4(x^2 + x - 1)}{x(x-2)}}$ .

: Find the value of x in the diagram
Use the property that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
$(x+17^\circ) + (2x+7^\circ) = 9x^\circ$
Simplify and solve for $x$ .
$3x + 24 = 9x$ $24 = 9x - 3x$ $24 = 6x$ $x = \frac{24}{6}$ $x = 4$
The value of $x$ is $\boxed{4}$ .

: Rectangle dimensions
Define the dimensions.
Let the width of the rectangle be $w$ .
The length $l$ is three times its width, so $l = 3w$ .
Use the formula for the perimeter of a rectangle.
$P = 2(l+w)$
Given $P = 24$ cm.
$24 = 2(3w + w)$
Solve for $w$ .
$24 = 2(4w)$ $24 = 8w$ $w = \frac{24}{8}$ $w = 3 \text{ cm}$
The width of the rectangle is $\boxed{3 \text{ cm}}$ .

: Find the vector r
Add vectors $\mathbf{q}$ and $\mathbf{p}$ .
$\mathbf{q} + \mathbf{p} = \begin{pmatrix} 2 \\ 5 \end{pmatrix} + \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 2+2 \\ 5+3 \end{pmatrix} = \begin{pmatrix} 4 \\ 8 \end{pmatrix}$
Multiply the resulting vector by $\frac{1}{2}$ .
$\mathbf{r} = \frac{1}{2}(\mathbf{q} + \mathbf{p}) = \frac{1}{2} \begin{pmatrix} 4 \\ 8 \end{pmatrix} = \begin{pmatrix} \frac{1}{2} \times 4 \\ \frac{1}{2} \times 8 \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$
The vector $\mathbf{r}$ is $\boxed{\begin{pmatrix} 2 \\ 4 \end{pmatrix}}$ .

Simplify the algebraic expression 5x2/(x2-2x) - (x2-4)/(x2+2x) Find the value of x in the diagram below.

Step-by-step solution

Convert mixed numbers to improper fractions.

Evaluate the expression inside the parenthesis.

Perform the "of" operation (multiplication).

Perform the division.

Perform the multiplication in the numerator.

Perform the division.

Express the answer in standard form.

Divide the total calories burned by the total hours.

Calculate the value.

Factor the denominators and numerators.

Simplify each term by canceling common factors.

Find a common denominator and combine the fractions.

Expand and simplify the numerator.

Factor out common terms in the numerator.

Use the property that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Simplify and solve for $x$ .

Define the dimensions.

Use the formula for the perimeter of a rectangle.

Solve for $w$ .

Add vectors $\mathbf{q}$ and $\mathbf{p}$ .

Multiply the resulting vector by $\frac{1}{2}$ .

Still stuck on this one?

More Mathematics Questions

Simplify the algebraic expression 5x2/(x2-2x) - (x2-4)/(x2+2x) Find the value of x in the diagram below.

Step-by-step solution

Convert mixed numbers to improper fractions.

Evaluate the expression inside the parenthesis.

Perform the "of" operation (multiplication).

Perform the division.

Perform the multiplication in the numerator.

Perform the division.

Express the answer in standard form.

Divide the total calories burned by the total hours.

Calculate the value.

Factor the denominators and numerators.

Simplify each term by canceling common factors.

Find a common denominator and combine the fractions.

Expand and simplify the numerator.

Factor out common terms in the numerator.

Use the property that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Simplify and solve for xxx.

Define the dimensions.

Use the formula for the perimeter of a rectangle.

Solve for www.

Add vectors q\mathbf{q}q and p\mathbf{p}p.

Multiply the resulting vector by 12\frac{1}{2}21​.

Still stuck on this one?

More Mathematics Questions

Simplify and solve for $x$ .

Solve for $w$ .

Add vectors $\mathbf{q}$ and $\mathbf{p}$ .

Multiply the resulting vector by $\frac{1}{2}$ .