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Pachacha [2.7K]
3 years ago
11

The rectangle below has an area of x^2+8x+15x

Mathematics
1 answer:
Darina [25.2K]3 years ago
7 0

Answer:

The length of the rectangle is x+5.

Step-by-step explanation:

Given : The rectangle below has an area of x^2+8x+15 square meter and a width of  x+3 meter.

To find : What expression represents the length of the rectangle?

Solution :

The area of the rectangle is given by,

\text{Area}=\text{Length}\times \text{Breadth}

\text{Area}=x^2+8x+15

\text{Breadth}=x+3

x^2+8x+15=\text{Length}\times(x+3)

\text{Length}=\frac{x^2+8x+15}{x+3}

\text{Length}=\frac{(x+5)(x+3)}{x+3}

\text{Length}=x+5

Therefore, the length of the rectangle is x+5.

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1. M is the midpoint of LN and O is the midpoint of NP.
Reptile [31]
1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation
MO= (1/2) LP

If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be:
2x+6= (1/2)( 8x-20)
2x+6= 4x-10
2x-4x= -10 - 6
-2x= -16
x=8

2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2

Then, the answer would be:
A.F= 1/(1+2) * AC
A.F= 1/3 * 12= 4

FC= 2/(1+2) * AC
FC= 2/3 * 12= 8

3. Since
∠BAD=∠DAC
∠ABD=∠ACD
AD=AD
The triangle ABD and ACD are similar. You can get this equation
BD=DC
x+8= 3x+12
x-3x= 12-8
-2x=4
x=-2

DC=3x+12= 3(-2) +12= 6

4. Orthocenter made by intersection of triangle altitude
A
BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be:
y=-x +a
0= 1+a
a=-1
y=-x-1
B
AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be:
y=1/3x+a
-1=1/3(4)+a
a=-7/3
y=1/3x - 7/3

C
BC lines slope would be (-1)-(-1)/4 = 0/4. 
The line would be 
0=x+a
a=-1
0=x-1
x=1

y=-x-1 = 1/3x-7/3
-x-(1/3x)=-7/3 +1
-4/3x= -4/3
x=1

y=-x-1
y=-1-1= -2
The orthocenter would be (1,-2)

5. 
a. Circumcenter: the intersection of perpendicular bisector lines<span>
b. Incenter: the intersection of bisector lines
c. Centroid: </span>the intersection of median lines<span>
d. Orthocenter: </span>the intersection of altitude lines
5 0
3 years ago
24. To what fraction is the arrow pointing to
sp2606 [1]
Image? where is it? id love to help
3 0
3 years ago
Someone pls show me
vlada-n [284]

Answer:

  x = 4

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the remote interior angles.

  18x +5 = (46) +(-1 +8x)

  10x = 40 . . . . . . . . . . . . . subtract (5+8x) from both sides, simplify

  x = 4 . . . . . . divide by 10

__

<em>Additional comment</em>

The exterior angle is (18)(4) +5 = 77°. The marked unknown interior angle is -1+(8)(4) = 31°. The sum of the two remote interior angles is 46°+31° = 77°. The unmarked interior angle is 180°-77° = 103°.

7 0
3 years ago
What is the following sum? 5(3sqrtx)+9(3sqrtx)
drek231 [11]

Answer:

5(3√x) +9(3√x)  = 15√x+27√x= 42√x

5∛x + 9∛x = 14∛x

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Please help :(<br><br>thank you!
harina [27]

Answer:

pls stop deleting my answers brainly thx. also its b! ^-^

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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