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4 years ago

Find the perimeter of quadrilateral (-1, 2) (2, 8), (6, 8) (3, 2). Round answer to nearest hundredth. 2 decimal places.

Mathematics

1 answer:

LenaWriter [7]4 years ago

4 0

Answer:

21.42

Step-by-step explanation:

The length of the diagonal sides of this parallelogram are given by the distance formula:

d = √((x2-x1)^2 +(y2 -y1)^2) = √((2-(-1))^2 +(8-2)^2) = √(3^2 +6^2) = 3√5

Of course, the lengths of the horizontal segments are given by the difference in their x-coordinates: 3-(-1) = 4. As with any parallelogram, the perimeter is twice the sum of adjacent side lengths:

P = 2(d +4) = 2(3√5 +4) = 8 +6√5 ≈ 21.4164

P ≈ 21.42 units

The perimeter is about 21.42 units.

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Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts.

jasenka [17]

Answer:

We have the function, $f(x)=(x+3)^{2}-4$

On simplifying, we get,

$f(x)=x^2+6x+9-4$

i.e. $f(x)=x^2+6x+5$

Thus, the standard form of the function is $f(x)=x^2+6x+5$ .

Now, the factors of the given functions are (x+1) and (x+5).

Since, the intercept form of the function is the factored form of the function.

So, we have, intercept form of the function is $f(x)=(x+1)(x+5)$ .

Now, we know that,

Value of x-coordinate of the vertex is $\frac{-b}{2a}$ i.e. $\frac{-6}{2\times 1}$ i.e. $\frac{-6}{2}$ i.e. x= -3

Then, $f(-3)=(-3)^2+6\times (-3)+5$ i.e. $f(-3)=9-18+5$ i.e. f(-3)=-4

So, the vertex of the function is (-3,-4).

Further, we know that, 'the y-intercept of a function is the point where the function crosses y-axis'.

So, when x=0, we have, $f(0)=0^2+6\times 0+5$ i.e. f(0) = 5

Thus, the y-intercept is (0,5)

Also, 'the x-intercept of a function is the point where the function crossese x-axis'.

Then, for f(x)=0, we have $0=x^2+6x+5$ i.e. $0=(x+1)(x+5)$ i.e. x= -1 and x= -5

Thus, the x-intercept are (-1,0) and (-5,0).

8 0

3 years ago

Whats the answer and equation to Two more than four times a number is -10

Artist 52 [7]

2+4a=-10

First, subtract 2 from both sides.

4a=-12

Then divide 4 from both sides.

a=-3

hope it helps!

3 0

3 years ago

A store has 1173 pairs of socks. the socks are sold in packs of 4 pairs. how many packs of socks can the store sell?

Nadusha1986 [10]

Answer:

293 packs is the maximum the store can sell.

Step-by-step explanation:

Determine the number of packs that can be made with 4 pairs of socks.

(1173 pairs)/(4 pairs/pack) = 293.25 packs

We can't sell 0.25 pack (1 pair of socks), so drop that fraction to yield 293 full packs. Donate the spare pair, so to speak, to the local IRS agent.

5 0

2 years ago

1 pt) If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −4≤u≤4,−4≤v≤4, has surface area equal to 1, what is t

natta225 [31]

The area of the surface given by $\vec r_1(u,v)$ is 1. In terms of a surface integral, we have

$1=\displaystyle\int_{-4}^4\int_{-4}^4\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

By multiplying each component in $\vec r_1$ by 5, we have

$\dfrac{\partial\vec r_2(u,v)}{\partial u}=5\dfrac{\partial\vec r_1(u,v)}{\partial u}$

and the same goes for the derivative with respect to $v$ . Then the area of the surface given by $\vec r_2(u,v)$ is

$\displaystyle\int_{-4}^4\int_{-4}^425\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\boxed{25}$

8 0

3 years ago

What is 1×1,000+3×10,000+9×1,000+8×100+5×10+2×1

xenn [34]

Use PEMDAS for this problem.
1 x 1000= + 1000
3 x 10,000= 30,000
---------------------------
+ 31000
9000
---------------------------
+ 40000
800
--------------------------
+ 40800
50
------------------------------
+ 40850
2
------------------------------
Answer: 40,852

Hoped this helped.

~Bob Ross ®

5 0

4 years ago