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3 years ago

⦁ To the nearest tenth, find the perimeter of ∆ABC with vertices A(2,4), B(-2,1) and C(2,1). Show your work.

Mathematics

1 answer:

Colt1911 [192]3 years ago

5 0

We need the length of the sides.
AB=√(2-(-2))²+(4-1)²=√16+9=√25=5; BC=√4²+0=4; CA=√0+9=3. AB+BC+CA=5+4+3=12.

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Use the properties of equality to simplify the equation. Tell whether the equation has zero, one, or infinitely many solutions.

Ganezh [65]

Answer
One solution

8 0

3 years ago

A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid

Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = $2 \times width$

Base area = lb

= $2x^2$

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

$h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}$

Now, cost is

$= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}$

now we have to minimize C(x)

So, we need to compute the C'(x)

$= 52x - \frac{648}{x^2}$

C"(x) $= 52x - \frac{1,296}{x^3}$

now for the critical points, we will solve the equation C'(x) = 0

$= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}$

$C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0$

So, x is a point of minima that is

= $(\frac{648}{52} )^\frac{1}{3}$

Now, Base material cost is

$= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}$

= 139.75

Side material cost is

$= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }$

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

4 0

3 years ago

Help please, also explain

olga55 [171]

Firstly, It says that the two triangles are similar .

The scale factor is 2 as 12 / 6 = 2

25 + 85 = 110

180 - 110 = 70.

70 degrees

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2 years ago

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worty [1.4K]

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3 years ago

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mars1129 [50]

The inverse, converse and contrapositive of a statement are used to determine the true values of the statement

<h3>How to determine the inverse, converse and contrapositive</h3>

As a general rule, we have:

If a conditional statement is: If p , then q .

Then:

Inverse -> If not p , then not q .
Converse -> If q , then p .
Contrapositive -> If not q , then not p .

Using the above rule, we have:

<u>Statement 1</u>

Inverse: If a parallelogram does not have a right angle, then it is not a rectangle.
Converse: If a parallelogram is a rectangle, then it has a right angle.
Contrapositive: If a parallelogram is a not rectangle, then it does not have a right angle.

All three statements above are true

<u>Statement 2</u>

Inverse: If two angles of one triangle are not congruent to two angles of another, then the third angles are not congruent.
Converse: If the third angles of two triangle are congruent, then the two angles are congruent to two angles of another
Contrapositive: If the third angles of two triangle are not congruent, then the two angles are not congruent to two angles of another

All three statements above are also true

Read more about conditional statements at:

brainly.com/question/11073037

8 0

2 years ago