1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna71 [15]
3 years ago
5

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

Mathematics
1 answer:
netineya [11]3 years ago
6 0
The area of the shaded region is going to be the area of the rectangle minus the area of the square.

Area of a rectangle is L * W.
A = L * W
A = (x + 10)(2x + 5)
A = x(2x + 5) + 10(2x + 5)
A = 2x^2 + 5x + 20x + 50
A = 2x^2 + 25x + 50 .....this is the area of the rectangle

area of a square is : A = a^2...where a is one side
A = (x + 1)^2
A = (x + 1)(x + 1)
A = x(x + 1) + 1(x + 1)
A = x^2 + x + x + 1
A = x^2 + 2x + 1

now we subtract the area of the square from the area of the rectangle to get the area of the shaded region.

2x^2 + 25x + 50 - (x^2 + 2x + 1) =
2x^2 + 25x + 50 - x^2 - 2x - 1 =
x^2 + 23x + 49 <== the area of the shaded region
You might be interested in
Please tell me what x is 3(x+6)=48
Alekssandra [29.7K]

Answer

X=10

Step by step explanation

48÷3 = 16

16-6 = 10

7 0
3 years ago
The lengths of the legs of a right triangle are consecutive even integers. The hypotenuse is 58 inches. What is the sum of the l
miskamm [114]

Answer:

82 inches

Step-by-step explanation:

The difference between consecutive even integers is 2, thus

let the legs be n and n + 2

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

n² + (n + 2)² = 58² ← expand and simplify left side

n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )

2n² + 4n - 3360 = 0 ( divide all terms by 2 )

n² + 2n - 1680 = 0 ← in standard form

(n + 42)(n - 40) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 42 = 0 ⇒ n = - 42

n - 40 = 0 ⇒ n = 40

But n > 0 ⇒ n = 40

and n + 2 = 40 + 2 = 42

Thus sum of legs = 40 + 42 = 82 inches

3 0
3 years ago
What is the initial value of the equation shown? (1 point) y = −7x − 6 −13 −7 −6 −1
Liula [17]

Answer:

-6

Step-by-step explanation:

The equation is y = -7x - 6.

The initial value is found when x = 0.

y = -7(0) - 6

y = 0 - 6

y = -6

6 0
2 years ago
The topic is volume &amp; surface area, can someone help?
marishachu [46]
This pic should help

3 0
3 years ago
What is 154 plus 74 equal
Sergio [31]
154 + 74 = 228 is the answer.
3 0
3 years ago
Read 2 more answers
Other questions:
  • This graph shows how the total length Kimi has knit depends on the number of nights she has spent knitting.
    6·1 answer
  • Please help fast and show all work thanks
    5·1 answer
  • a bag is filled with blue and green marbles. there are three rimes as many blues as green ones. if the bag contains 280 marbles
    8·2 answers
  • The volume of a 1968 ford mustang gt engine is 390 cubic inches"
    6·1 answer
  • Elena and Jada are 12 miles apart on a path when they start moving towards each other Elena runs at a constant speed of 5 miles
    14·2 answers
  • Please help me please will give brainliest to ​
    9·1 answer
  • PLS HELP!
    13·1 answer
  • Two trapeziums are similar, thee area of one of the trapezium is 4times that of the other. Determine the ratio of the perimeter
    9·1 answer
  • HELP ME PLEASEEEE!!!!
    15·1 answer
  • HELP! Problem- Tim has a rectangular garden with an area of 36.63 square meters. The length of the garden is 4.5 meters. What is
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!