Answer:
pls i don't know the answer but i need the point
Answer:
See explanation
Step-by-step explanation:
In ΔABC, m∠B = m∠C.
BH is angle B bisector, then by definition of angle bisector
∠CBH ≅ ∠HBK
m∠CBH = m∠HBK = 1/2m∠B
CK is angle C bisector, then by definition of angle bisector
∠BCK ≅ ∠KCH
m∠BCK = m∠KCH = 1/2m∠C
Since m∠B = m∠C, then
m∠CBH = m∠HBK = 1/2m∠B = 1/2m∠C = m∠BCK = m∠KCH (*)
Consider triangles CBH and BCK. In these triangles,
- ∠CBH ≅ ∠BCK (from equality (*));
- ∠HCB ≅ ∠KBC, because m∠B = m∠C;
- BC ≅CB by reflexive property.
So, triangles CBH and BCK are congruent by ASA postulate.
Congruent triangles have congruent corresponding sides, hence
BH ≅ CK.
Step-by-step explanation:
Line is passing through the points:
Equation of line in two point form is given as:
![\frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \frac{y -3}{ 3 -5} = \frac{x -(-2) }{-2 -2} \\ \\ \therefore \frac{y -3}{ - 2} = \frac{x -(-2) }{-4} \\ \\ \therefore \frac{y - 3}{1} = \frac{x +2}{2} \\ \\ \therefore \: y-3= \frac{x}{2} + \frac{2}{2} \\ \\\therefore \: y= \frac{x}{2} + 1 +3\\ \\ \huge \red{ \boxed{\therefore \: y= \frac{1}{2} \:x+ 4}}\\ is \: the \: required \: equation \: of \: line.](https://tex.z-dn.net/?f=%5Cfrac%7By%20-y_1%20%7D%7By_1%20-y_2%20%7D%20%3D%20%5Cfrac%7Bx%20-x_1%20%7D%7Bx_1%20-x_2%20%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20%5Cfrac%7By%20-3%7D%7B%203%20-5%7D%20%3D%20%5Cfrac%7Bx%20-%28-2%29%20%7D%7B-2%20-2%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20%5Cfrac%7By%20-3%7D%7B%20-%202%7D%20%3D%20%5Cfrac%7Bx%20-%28-2%29%20%7D%7B-4%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20%5Cfrac%7By%20-%203%7D%7B1%7D%20%3D%20%5Cfrac%7Bx%20%2B2%7D%7B2%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20%5C%3A%20y-3%3D%20%5Cfrac%7Bx%7D%7B2%7D%20%2B%20%5Cfrac%7B2%7D%7B2%7D%20%5C%5C%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5C%3A%20y%3D%20%5Cfrac%7Bx%7D%7B2%7D%20%2B%201%20%2B3%5C%5C%20%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%20%5Chuge%20%5Cred%7B%20%5Cboxed%7B%5Ctherefore%20%5C%3A%20y%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5C%3Ax%2B%204%7D%7D%5C%5C%20is%20%5C%3A%20the%20%5C%3A%20required%20%5C%3A%20equation%20%5C%3A%20of%20%5C%3A%20line.)
Answer:
![\dfrac{5}{8}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B8%7D)
Step-by-step explanation:
Alvin takes pictures with his smartphone.
Of the pictures
are animals.
of the animals are dogs.
To find which fraction of all pictures are pictures with dogs, you can simply multiply two fractions:
![\dfrac{5}{6} \times \dfrac{3}{4} =\dfrac{15}{24} =\dfrac{5}{8}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B6%7D%20%5Ctimes%20%5Cdfrac%7B3%7D%7B4%7D%20%3D%5Cdfrac%7B15%7D%7B24%7D%20%3D%5Cdfrac%7B5%7D%7B8%7D)
<u>Another way</u> to solve this question:
Let the number of all pictures be 24 (divisible by both 4 and 6).
Then the number of pictures with animals is
![\dfrac{5}{6} \times 24=5\times 4=20](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B6%7D%20%5Ctimes%2024%3D5%5Ctimes%204%3D20)
and the number of pictures with dogs is
![\dfrac{3}{4} \times 20=3\times 15](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B4%7D%20%5Ctimes%2020%3D3%5Ctimes%2015)
Hence, the fraction of pictures with dogs of all pictures is
![\dfrac{15}{24}=\dfrac{5}{8}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B24%7D%3D%5Cdfrac%7B5%7D%7B8%7D)