Please help if you can, thank you

Write an expression for the area and perimeter for the figure shown

nikklg [1K]

Answer:

Area = 3x² + 7x + 3

Perimeter = 8x + 8

Step-by-step explanation:

The figure can be decomposed into two: a large rectangle and a smaller rectangle.

✍️Dimensions of the large rectangle:

Length = (x + 1) + x = x + 1 + x = (2x + 1)

Width = (x + 3)

Area = length × width

Area = (2x + 1)(x + 3)

Expand

2x(x + 3) +1(x + 3)

2x² + 6x + x + 3

Area = 2x² + 7x + 3

✍️Dimensions of the large rectangle:

Length = x

Width = x

Area = length × width

Area = x × x = x²

✍️Area of the figure = area of the large rectangle + area of the smaller rectangle

Area of the figure = (2x² + 7x + 3) + x²

Area of the figure = 2x² + x² + 7x + 3

✅Area = 3x² + 7x + 3

✍️ Perimeter of the figure = sum of the length of all sides of the figure = (x + 3) + x + x + x + (x + 1) + (x + 3) + (x + 1) + x

✅Perimeter = 8x + 8

4 0

3 years ago

En un triángulo obtusángulo, uno de los ángulos mide 20° mas que el otro. El tercer ángulo, mide el doble que el mayor de los do

Troyanec [42]

Answer:

La medida del primer ángulo es 30°, la medida del segundo ángulo es 50° y el tercer ángulo mide 100°.

Step-by-step explanation:

Siendo "x" el valor de un ángulo del triángulo obtusángulo, sabes que uno de los ángulos, llamado segundo ángulo, mide 20° más que el primero. Este segundo ángulo se representa como x + 20°.

Además, un tercer ángulo mide el doble que el mayor de los dos, que en este caso es el ángulo cuya expresión es x + 20°. Por lo que el doble de este será 2*(x + 20)°, que será la medida del tercer ángulo.

Teniendo en cuenta que la suma de los ángulos interiores de un triángulo es 180°. Entonces, es posible sumar los valores de cada uno de los ángulos e igualarlos a 180°:

x + x + 20° + 2*(x + 20°) = 180°

Resolviendo:

x + x + 20° + 2*x + 2*20° = 180°

x + x + 20° + 2*x + 40° = 180°

4*x + 20° + 40° = 180°

4*x + 60° = 180°

4*x = 180° - 60°

4*x = 120°

x = 120° ÷ 4

x = 30°

Entonces, la medida del primer ángulo es 30°. El segundo ángulo es calculado como x + 20° = 30° + 20° = 50° mientras que el tercer ángulo es 2*(x + 20°) = 2*(30° + 20°) = 2*(50°) = 100°

<u><em>La medida del primer ángulo es 30°, la medida del segundo ángulo es 50° y el tercer ángulo mide 100°.</em></u>

3 0

3 years ago

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

$_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\$

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

$_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\$

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

$_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\$

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>

5 0

3 years ago

7. If A = 2x + 3 and B = x^2 - 5x + 1, what is the value of A-5B?

taurus [48]

Answer:

$\huge \boxed{ \boxed{ \tt - 5 {x}^{2} + 27 x- 2}}$

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

algebra
PEMDAS

<h3>given:</h3>

A=2x+3
B=x²-5x+1

A-5B

<h3>let's solve:</h3>

$step - 1 : define$

A-5B=2x+3-5(x²-5x+1)

$step - 2 : solve$

distribute -5 to the parentheses:2x+3-5x²+25x-5
rewrite:-5x²+2x+25x-5+3
combine like terms:-5x²+27x-2

and

we are done

7 0

3 years ago

Write down the fifth term and the general term of<br> following sequence : 8,4,2,...

morpeh [17]

Answer:

The terms listed are 8, 4, and 2 in that order. From what we can see, it is a geometric sequence whose next term is gotten by dividing the previous term by 2. The formula for finding the nth term of a geometric sequence is given as $ar^{n-1}$ , where

a = first term which is 8

r = common ratio, 1/2 or 0.5

n = is the term we're looking for, 5

Putting all these together into one solid equation, we have

8 * $0.5^{5-1}$ =

8 * $0.5^{4}$ =

8 * 0.0625 = 0.5

Therefore, the 5th term of the sequence is 0.5. Similar example can be seen here brainly.com/question/9300199

8 0

3 years ago