Given : In Right triangle ABC, AC=6 cm, BC=8 cm.Point M and N belong to AB so that AM:MN:NB=1:2.5:1.5.
To find : Area (ΔMNC)
Solution: In Δ ABC, right angled at C,
AC= 6 cm, BC= 8 cm
Using pythagoras theorem
AB² =AC²+ BC²
=6²+8²
= 36 + 64
→AB² =100
→AB² =10²
→AB =10
Also, AM:MN:NB=1:2.5:1.5
Then AM, MN, NB are k, 2.5 k, 1.5 k.
→2.5 k + k+1.5 k= 10
→ 5 k =10
Dividing both sides by 2, we get
→ k =2
MN=2.5×2=5 cm, NB=1.5×2=3 cm, AM=2 cm
As Δ ACB and ΔMNC are similar by SAS.
So when triangles are similar , their sides are proportional and ratio of their areas is equal to square of their corresponding sides.
![\frac{Ar(ACB)}{Ar(MNC)}=[\frac{10}{5}]^{2}](https://tex.z-dn.net/?f=%5Cfrac%7BAr%28ACB%29%7D%7BAr%28MNC%29%7D%3D%5B%5Cfrac%7B10%7D%7B5%7D%5D%5E%7B2%7D)
But Area (ΔACB)=1/2×6×8= 24 cm²[ACB is a right angled triangle]
→ Area(ΔMNC)=24÷4
→Area(ΔMNC)=6 cm²
The correct answer is C. The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground.
Explanation:
Two key features of living organisms are energy processing and response to stimuli. These two features imply organisms require nutrients, which can be taken from the environment or created through a process such as photosynthesis and they sense their surroundings and respond to it.
Moreover, these two features are exemplified by mushroom (fungi) in the sentence "The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground" because the first section shows the developing mushroom takes nutrients from the soil or its environment and this is essential for growing and survival. Also, the second section of the sentence shows the developing mushroom can sense its environment and respond by developing only in appropriate conditions.
Answer:
D
Step-by-step explanation:
11x + 14 < -8
Cancel the addition by subtracting
11x + 14 - 14 < -8 - 14
11x < -22
11x / 11 < -22/11
x < -2
Therefore, the answer is D
This one is 9.69892 x 10^2 i believe
Answer:
You do -17 + -10 inorder to change the operation used because both negatives does not mathematically look nice.
Step-by-step explanation:
To isolate the unknown, we need to move all the numbers on one side of the equal sign and all the unknow variables on one side.
Here we move 10 on the other side by taking away 10 both sides
10 + 3x = -17
-10 -10
then we are left with only 3x on one side and -27 on the other side because -17 - -10 = -27 , in this case it is acknowledge to change the operation from minus to add because the two minus are together, so we say -17 + -10 .
3x = -27
/3 /3
x = -9
