Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm
Let ∠ACD be x. Therefore using sine rule:
Let C = the Chinese books.
Let E = the English language books.
C = 4/5 E
E - 300 = C - 180 Notice how you get this equation. You take 300 away from the English books and 180 from the Chinese and according to the question, you get an equal number of both. Put c = 4/5E into the second equation.
E - 300 = 4/5 E - 180 Add 300 to both sides.
E = 4/5 E - 180 + 300
E = 4/5 E + 120 Now subtract 4/5 E from both sidies.
E - 4/5 E = 120
1/5 E = 120 Now multiply by 5
E = 120 * 5
E = 600
So the number of books are
600 written in English
4/5 of 600 = 2400 /5 = 480 Chinese books.
English 600
Chinese 480
Answer:
64
Step-by-step explanation:
If you measure the cubes inside for the length, width and height, you get:
Length - 5 cubes
Width -5 cubes
Height - 3 cubes
The volume of the prism is 5 * 5 * 3 = 75. This means the prism can hold a total of 75 cubes
The amount of cubes already in there is 11
so 75 - 11= 64
Answer:
Therefore (x,y)=(3,7)
Step-by-step explanation:
put the second equation into the first
x+4=3x-2
x-3x=-2-4
-2x=-6
x=3
plug x=3 into the second equation
y=3+4=7
I believe the answer is B. -3.