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2 years ago

Find the perimeter of △ABC with vertices A(−5, 3), B(4, −5), and C(−5, −5). Round your answer to the nearest hundredth.

Mathematics

1 answer:

sertanlavr [38]2 years ago

8 0

The perimeter of △ABC with vertices A(−5, 3), B(4, −5), and C(−5, −5) is 29.04 units

<h3>Perimeter of a triangle</h3>

The perimeter of a triangle is the sum of the sides of the triangle.

Given the coordinate points A(−5, 3), B(4, −5), and C(−5, −5)

Determine the distance AB, AC and BC using the distance formula

AB = √(-5-3)²+(4+5)²

AB = √64+81
AB = √145

AB = 12.04 units

AC = √(-5-3)²+(-5+5)²

AC = √64

AC = 8 units

BC = √(-5-4)²+(-5+5)²

BC = √81
BC = 9 units

Take the sum

Perimeter of triangle ABC = 9 + 8 + 12.04

Perimeter of triangle ABC = 29.04 units

Hence the perimeter of △ABC with vertices A(−5, 3), B(4, −5), and C(−5, −5) is 29.04 units

Learn more on perimeter of triangle here: brainly.com/question/24382052

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What is the difference between an algebraic expression and a linear expression?

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Step-by-step explanation:

A mathematical phrase that groups together numbers, variables, and operators, to show the value of something is called expression.

An expression is a sentence fragment that stands for a single numerical value. On the contrary, an equation is a sentence showing equality between two expressions.

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

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3 years ago

I am trying to figure this question: <br><br> 1 + tan^2A = Sec^2A

chubhunter [2.5K]

Answer:

see explanation

Step-by-step explanation:

Using the Pythagorean identity

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1 + tan²A = sec²A ← as required

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3 years ago

A car rental agency has 150 cars. The owner finds that at a price of $48 per day, he can rent all the cars. For each $2 increase

hram777 [196]

Given that for each <span>$2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
$(48 + 2x) \times (150 - 4x)=7,200+108x-8x^2$ .

Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
$5(150-4x)=750-20x$

Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span> $(7,200+108x-8x^2)-(750-20x)=6,450+128x-8x^2$

For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span> $\frac{d}{dx} (6,450+128x-8x^2)=0 \\ \\ 128-16x=0 \\ \\ x= \frac{128}{16} =8$

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Therefore, the </span><span>rental charge will maximize profit is $64.</span>

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3 years ago

Someone help and please make sure the answer is right

lord [1]

Answer:

it's 12

Step-by-step explanation:

5(12) =60

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3 years ago

A snail can move 1/30 miles in 1/3 hour. How fast does a snail move in miles /hours

bekas [8.4K]

Answer: 1/10 miles/hour

To find how fast a snail moves in miles per hour, we can find the unit rate using a proportion.

The unit rate is the amount per one unit. In this problem, the unit is for one hour. One way to find the unit rate is by using a proportion.

<h2>Proportions</h2>

Proportions look like two fractions set equal to each other with a missing variable to solve.

<h3>State our variables</h3>

let <em>x</em> be the number of miles per hour

<h3>Write a proportion</h3>

The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

<h2>Solve</h2>

We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.

<h3>Find the scale factor</h3>

Start with the proportion.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

To find the scale factor,

Take the denominator from the fraction with a variable: $1\ hr$
Take the denominator from the fraction that has no variable: $\frac{1}{3}\ hr$
Divide step 1 by step 2 and solve: $1\ hr\ \div\ \frac{1}{3}\ hr = 3$

Our scale factor is <u>3</u>.

<h3>Solve for x</h3>

We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}$

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{3}{30}\ mi}{1\ hr}}$

Simplify 3/30 by dividing the fraction by 3.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{1}{10}\ mi}{1\ hr}}$

x = 1/10

∴ a snail moves 1/10 miles per hour.

Learn another way to solve proportions here: brainly.com/question/18437927

7 0

2 years ago