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lana [24]
2 years ago
8

Find the value of x.

Mathematics
1 answer:
valentina_108 [34]2 years ago
5 0

Answer:

  x = 100

Step-by-step explanation:

The ratios of long side to hypotenuse are the same for all these triangles.

  x/(x+10) = (x+10)/(x+21)

  x^2 +21x = x^2 +20x +100 . . . . . multiply by (x+10)(x+21), expand

  x = 100 . . . . . . . . . . . . . . . . subtract x^2 +20x

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The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T(t)=4t/t^2+1, where trepresents
elena-14-01-66 [18.8K]
The meaning of the horizontal asymptote is that the increase in a person's body temperature is a constant value when long time passes.

You can obtain that value by calculating the limit of the function when t → ∞:

                 4t
T(t) =  ------------- => Lim T(t) when t → +∞ = 0.
             t^2 + 1

That means that at long term the Temperature tends to remain at 98.6°F.
7 0
2 years ago
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
2 years ago
Greatest common factor for 3,27, and 33
Georgia [21]

Answer:

it's 3.

Step-by-step explanation:

Here's why........3 only has 2 factors 1 and it's self and 3 times 9 is 27 and 3 times 11 is 33 they all have 3 as a factor.

7 0
2 years ago
Each problem is worth 10 points each. (For each problem show your work and give a brief explanation of how you solved your probl
maxonik [38]
It’s a big problem it’s deserve 20 points you can’t play people make it fair
5 0
2 years ago
Nancy is asked to use her calculator to find the volume of a cylindrical canister that has a radius of 10.55 cm and a height of
Murljashka [212]

use the formula given:

 V = pi r^2h

 r = 10.55

h = 12.56


 V = 3.14 x 10.55^2 x 12.56 = 4391.81 round off to 4392cm^3

 answer is D 4392

7 0
2 years ago
Read 2 more answers
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