I need help please help

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

NeX [460]

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

7 0

3 years ago

Please answer this. thank you

Rama09 [41]

Answer: $(-\infty, -4]$

Curved parenthesis at negative infinity

Square bracket at -4

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

Work Shown:

$5(x+4) \le 0 \\\\x+4 \le \frac{0}{5} \\\\x+4 \le 0 \\\\x \le 0-4 \\\\x \le -4 \\\\$

The last inequality shown above is the same as saying $-\infty < x \le -4$

Converting this to interval notation leads to the final answer of $(-\infty , -4]$

Note the use of a square bracket at -4 to include this endpoint. We can never include either infinity, so we always use a parenthesis for either infinity.

5 0

2 years ago

Oliver climbed 222 meters of a steep mountain reach the summit. He then rappelled down the other side of the mountain to return

nikdorinn [45]

B -222

Because he fell/descended 222 meters. And falling or going down produces a negative integer. Also, if you were actually doing the math to try to find where Oliver is currently located, you wouldn't add 222, or 0, or subtract -444. You would subtract 222.

In addition, be aware that the question is asking you an integer to represent a situation, not the answer of where Oliver is.

6 0

3 years ago

A lighthouse operator sights a sailboat at an angle of depression of 12 degrees. If the sailboat is 80m away, how tall is the li

mart [117]

Check out the attached image for the drawing of how this would look. The drawing isn't 100% needed but it helps I think.

Based on the figure shown in the attachment, we have a right triangle with the adjacent leg of 80 (this leg is closest to the bottom 12 degree angle) and an opposite leg of h

In short,
adjacent = 80
opposite = h

We'll use the tangent rule
tan(angle) = opposite/adjacent
tan(12) = h/80
80*tan(12) = h
h = 80*tan(12)
h = 17.0045249336018 <<-- see note below

So the lighthouse is roughly 17.0045249336018 meters tall

Answer: 17.0045249336018

Note: Make sure you are in degree mode. The value is approximate. Round this answer however you need to

4 0

3 years ago

The perimeter of a triangle is 199 inches. If one side of the triangle is six more than the shorter side, and the longer side is

Keith_Richards [23]

Shortest side (a) = 58
middle side (b) = 64
longest side (c) = 77

the 3 sides a + b + c = 199
b = a + 6
c = a + 19

substitute your new values for b & c into your original formula, so:
a + (a+6) + (a+19) = 199
3a + 25 = 199
3a = 174
a = 58

then substitute 58 into your b & c formulas to figure out the rest
b = a + 6 = 58 + 6 = 64
c = a + 19 = 58 + 19 = 77

3 0

3 years ago