(5x3 + 48x2 + 25x − 18) ÷ (x + 9)

If a solid has faces that consist of 2 equilateral triangles and 3 congruent rectangles, what type of solid is it?

svlad2 [7]

A right triangular prism is a solid that has faces that consist of 2 equilateral triangles and 3 congruent rectangles. It is also described to have two parallel faces and 3 other faces that belong to the same place (and are not parallel to the parallel pair of faces).

5 0

3 years ago

A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions

faust18 [17]

Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet

<h3>Solution:</h3>

Given that

Area of rectangular parking lot = 15000 square feet

Length is 20 feet more than the width.

Need to find the dimensions of rectangular parking lot.

Let assume width of the rectangular parking lot in feet be represented by variable "x"

As Length is 20 feet more than the width,

so length of rectangular parking plot = 20 + width of the rectangular parking plot

=> length of rectangular parking plot = 20 + x = x + 20

The area of rectangle is given as:

$\text {Area of rectangle }=length \times width$

Area of rectangular parking lot = length of rectangular parking plot $\times$ width of the rectangular parking

$\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}$

But it is given that Area of rectangular parking lot = 15000 square feet

$\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}$

Solving the above quadratic equation using quadratic formula

General form of quadratic equation is

${ax^{2}+\mathrm{b} x+\mathrm{c}=0$

And quadratic formula for getting roots of quadratic equation is

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case b = 20, a = 1 and c = -15000

Calculating roots of the equation we get

$\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}$

$\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}$

As variable x represents width of the rectangular parking lot, it cannot be negative.

=> Width of the rectangular parking lot "x" = 112.882 feet

=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882

Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.

3 0

3 years ago

A S A P ! ! ! ! I nEEd help again!!

atroni [7]

Answer:

3.00 feet

Step-by-step explanation:

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6 0

3 years ago

3. Taylor has a $30.00 gift card that she can

Andrew [12]

7 journals is the answer

4 0

3 years ago

Read 2 more answers

If a diagonal is drawn in a parallelogram, then two congruent triangles are... formed

Vsevolod [243]

Correct. Two congruent triangles are formed.
The two triangles are congruent because
1. diagonal = common side between two triangles
2. Considering the diagonal as a transversal that cuts the two pairs of parallel lines, we have two sets of internal alternate angles.
BY the rule of ASA, the two triangles are congruent.

3 0

3 years ago

Read 2 more answers