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2 years ago

What expression represents the area of the triangle?

Mathematics

2 answers:

Natasha_Volkova [10]2 years ago

4 0

<h2>Answer:</h2>

Option first is the answer.

Step-by-step explanation:

For finding the are of a right angle triangle, we use the base and the height of the triangle. The height is the right angle leg of the triangle. Hypotenuse is not considered here.

In the given diagram, the base or 'b' is = 10 units

And the height or 'h' is = 24 units

Area of a right triangle is given as :

$A=\frac{bh}{2}$

So, in the given options the correct option is : Option first.

$A= \frac{10*24}{2 }$ or $\frac{1}{2}(10*24)$

inysia [295]2 years ago

3 0

A=bh/2, that is area is equal to half of the product of the base and height, so in this case:

A=(1/2)*10*24

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A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav

Georgia [21]

The intervals included in solution are:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

Solution:

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

Given inequality is:

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}$

We have to solve the inequality

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x} - 10\geq \frac{2}{24}$

$\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0$

$\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0$

$\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}$

When we multiply or divide both sides by negative number, then we must flip the inequality sign

$\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0$