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
nekit [7.7K]
3 years ago
6

The length of a rectangle is (x + 1) cm and its width is 5cm less than its length.

Mathematics
1 answer:
NeX [460]3 years ago
7 0

Answer:

a) the area of a square is in terms of x is

(x+1)^2 centimeter square

b)The length of the rectangle is l = (x+1)

                                       l = 7+1 =8 cm

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 =3 cm

Step-by-step explanation:

a) the area of a square is in terms of x is

 area of square is l^{2} = (x+1)(x+1)

                                 = (x+1)^2

b)  Given length is  l = (x+1) cm and

the width is 5 cm less than its length.

so we have take width is w = (x+1)-5 cm

Given area of triangle is  24 cm

Area of rectangle = length X width

24  =  (x+1)(x+1 -5 )

now simplification 24 = (x+1)^2 - 5 (x+1)

apply (a+b)^2 = a^2+2 a b+b^2

x^2+2 x+1-5 x-5 =24

x^2 -3 x -4-24=0

x^{2} -3 x -28 =0

now find factors of 28  = 7 X 4 is  

x^{2} -7 x+4 x-28=0

x(x-7)+4(x-7)=0

(x+4)(x-7)=0

x = -4 and x=7

there fore you have to choose x = 7

The length of the rectangle is l = (x+1)

                                       l = 7+1 =8

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 = 3

<u>Verification:-</u>

Given area of rectangle  = 24 = 8 X 3

                                           24 =24

so we can not choose x=-4

we have to choose x =7 only

You might be interested in
Tom could grow potatoes, cabbages, and cauliflower on his farm. However, he has decided to grow only potatoes. What is Tom doing
dimaraw [331]
He is growing potatoes, probably to sell them
3 0
3 years ago
Read 2 more answers
A pair of equations is shown below:
horrorfan [7]

Answer:

A. x=2, y = 7.

B. (2, 7).

Step-by-step explanation:

A. You can eliminate y by subtracting the equations:

y =  8x - 9

y =  4x - 1       Subtract:

0 =  4x - 8

4x = 8

x = 8/4 = 2.

Now substitute for x in the first equation:

y = 8(2) - 9 = 7.

Check in the second equation:

y = 4x - 1

7 = 4(2) - 1 = 7.  Check is OK.

B. On the graph they will intersect at the point (2, 7).

They will intersect here because the values x=2 and y=7 satisfy both the 2 equations.

4 0
3 years ago
Quadrilateral ABCD is a a square and the length of BE is 6 cm.<br><br>What is the length of AC?
Aloiza [94]

The answer is: 12 centimeters.

The explanation is shown below:

1. By definition, all four sides of the square are equal and the diagonals are equal too.

2. Keeping the information above on mind, you know that AC and BD are equal:

AC=BD

3. Then, the length of BD is twice BE. So, you can calculate it as following:

BD=2BE

BD=2(6cm)\\BD=12cm

4. Therefore, the lenght of AC is:

AC=12cm

5 0
3 years ago
What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 54° A) 126 B) 72 C) 63 D) 10
Amiraneli [1.4K]
An isosceles triangle has congruent base angles, so if one of the base angles measure 54 degrees, then the other base angle does, too.
And a triangle measures up to 180 degrees.
180 = x + 2(54)
180 = x + 108
x = 72
So the answer is B) 72
5 0
3 years ago
Read 2 more answers
Please answer all or what you can do &lt;3
aleksandrvk [35]

Answer:

+150

-15

-75

+35

-24.75

Hope this helps!!

4 0
3 years ago
Read 2 more answers
Other questions:
  • Mark reads 42 pages of a book every 3/4 hour. Write an equation that models the relationships between x, the number of hours Mar
    10·1 answer
  • What’s the answer to 0.462 / 0.2
    5·2 answers
  • Given ΔDEF : ΔRST, find the scale factor.
    9·2 answers
  • This table shows a proportional relationship between the number of cups of sugar and flour used for a recipe.
    13·1 answer
  • Half of Robert's piece of wire is equal to 2 thirds of Maria's wire. The total length of their wires is 10 feet. How much longer
    12·2 answers
  • Solve this systems of linear equations.separate the x- and y-values with a comma 2x+3y=-6 6x-4y=-44
    9·1 answer
  • If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {2, 4, 6, 8, 10, 12}, the
    13·2 answers
  • Omar the tent maker wishes to support a 13.4-ft tent wall by attaching 25-ft cable to the top of it, and then anchoring the cabl
    9·1 answer
  • What percent of 20 is 15?
    13·2 answers
  • What is the inverse of the function f(x) = 2x + 1?<br><br> h(x) = one-halfx – one-half
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!