if the length of certain rectangle is decreased by 4 cm and breadth is increased by 2 cm, it would result in a square of the same area. what is the perimeter of the original rectangle?

Answers

Answer 1

Answer:

Answer:

To find the perimeter of the original rectangle, we first need to find the dimensions of the rectangle.

Let's assume the length of the original rectangle is L cm and the breadth is B cm.

According to the given information, if the length is decreased by 4 cm, the new length becomes (L - 4) cm. Similarly, if the breadth is increased by 2 cm, the new breadth becomes (B + 2) cm.

We are told that this new rectangle with dimensions (L - 4) cm and (B + 2) cm is actually a square with the same area as the original rectangle.

The area of a rectangle is given by length multiplied by breadth. So, the area of the original rectangle is L * B square cm.

The area of the new square is equal to the area of the original rectangle. Therefore, we can set up the equation:

(L - 4) * (B + 2) = L * B

Expanding the equation:

LB - 4B + 2L - 8 = LB

Simplifying the equation:

2L - 4B - 8 = 0

2L = 4B + 8

L = 2B + 4

Now that we have an equation relating the length and breadth of the original rectangle, we can find the perimeter.

The perimeter of a rectangle is given by the formula: 2 * (length + breadth).

Substituting the value of L from the equation above, we get:

Perimeter = 2 * [(2B + 4) + B]

Perimeter = 2 * (3B + 4)

Perimeter = 6B + 8

Therefore, the perimeter of the original rectangle is 6B + 8 cm.

Step-by-step explanation:

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Sara travels twice as far as Eli when going to camp. Ashley travels as far as Sara and Eli together. Hazel travels 3 times as far as Sara. In total, all 4 travel a total of 888 miles to camp. How far do each of them travel?

Answers

Eli travels 74 miles

Sara travels 148 miles

Ashley travels 222 miles

Hazel travels 444 miles

Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

Elimination Method

Substitution Method

Graph Method

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Sara's Distance = s

Eli's Distance = e

Ashely's Distance = a

Hazel's Distance = h

Sara travels twice as far as Eli when going to camp.

$s = 2e$

Ashley travels as far as Sara and Eli together.

$a = s + e = 2e + e = 3e$

Hazel travels 3 times as far as Sara.

$h = 3s = 3(2e) = 6e$

In total, all 4 travel a total of 888 miles to camp.

$s + a + h + e = 888$

$2e + 3e + 6e + e = 888$

$(2 + 3 + 6 + 1)e = 888$

$12e = 888$

$e = 888 / 12$

$e = \boxed {74 ~ \texttt{miles}}$

$s = 2e = 2(74) = \boxed {148 ~ \texttt{miles}}$

$a = 3e = 3(74) = \boxed {222 ~ \texttt{miles}}$

$h = 6e = 6(74) = \boxed {444 ~ \texttt{miles}}$

Learn more

Perimeter of Rectangle : brainly.com/question/12826246

Elimination Method : brainly.com/question/11233927

Sum of The Ages : brainly.com/question/11240586

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

Eli travels the shortest distance, so she'll be the main letter for algebra. She can be 'e'.
Sara travels twice as far, so her distance is 2e.
Ashley travels Sara and Eli, so 2e + e, or 3e
Hazel travels 3 times Sara, so 2e * 3, or 6e. Together they all travel 888 miles.
So e + 2e + 3e + 6e = 888
Simply, 12e = 888
Therefore, e = 888/12, or 74
So Eli travels 1*74 (74) miles
Sara travels 2*74 (148) miles
Ashley travels 3*74 (222) miles
Hazel travels 6*74 (444) miles

Jenny is a 60 percent free-throw shooter. She gets to shoot a second free throw if and only if she makes her first shot. She can score 0 points( if she misses her first shot), 1 point (she makes her first but misses her second), or 2 points ( she makes both shots.) Assuming that the probability for each shot is independent, what number of points is Jenny most likely to make?
How many points on average, can Jenny expect to make when she shoots a one-and-one (when she only gets a second shot if she makes the first)?

A.
0

B.
2

C.
1

D.
.96

E.
.36

Answers

Let the points be X.

x 0 1 2
P(X = x) 0.4 0.24 0.36

The expected points, E(X), are found as follows:
$E(X)=(0*0.4)+(1*0.24)+(2*0.36)=0.96$

Which of the following equations is of a parabola with a vertex at (0, -3)?y = (x - 3)^2
y = (x + 3)^2
y = x^2 - 3
y = x^2 + 3

Answers

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

We need a parabola with a vertex at (0,-3)

If we select the equation:

$y = x^2 - 3$

When we put x = 0, we get

$y=0-3\n\ny=-3$

And similarly, when we put y = -3, we get

$-3=x^2-3\n\n0=x^2\n\nx=0$

Hence, third option is correct.

$The\ vertx\ form:y=a(x-h)^2+k\nwhere\ the\ coordinates\ of\ vertex\ are\ (h;\ k)\n\n-------------------------\n\nvertex:(0;-3)\n\ny=a(x-0)^2+(-3)=ax^2-3\n\nif\ a=1\ then\ y=x^2-3\leftarrow answer$

Choose the best description of the cross-section shown in each image. (True/False)

Answers

Step-by-step explanation:

Please recheck and possibly resend your question as there is no cross section of any image attached.

Which ordered pair will solve the equation 2 × 4 + x = y?A.
(5, 16)

B.
(4, 12)

C.
(3, 12)

D.
(2, 9)

Answers

This answer uses NMF, which you can find out about on my profile:

Preliminary work:
Following the BIDMAS order of operations, we can calculate part of it already, and that's the 2•4, which equals 8.
Therefore, the equation now reads:
8+x = y

x = 5:
8+5 = 13
13 ≠ 16
13 ≠ y

x = 4:
8+4 = 12
12 = 12
12 = y

Therefore, the pair is (4, 12)

Help, please. I really need help one this