Answer:
(A) x=40
Step-by-step explanation:
Given: It is given that m is parallel to n.
To find: The value of x.
Proof: It is given that m is parallel to n, from the figure it can be seen that 105° and (3x-15)° forms alternate exterior angles which are equal in measure because m is parallel to n.
Thus, 
⇒
⇒
⇒
⇒
Thus, the value of x is 40, hence option A is correct.
Wa=0.5Wb, Ha=20, Hb is unkown
the area of rectangle a is : Wa*20
the area of rectangle b is : Wb*Hb
Rectangle a has 7 times the area of rectangle b: Wa*20=7*Wb*Hb
Replace Wa with 0.5Wb: 0.5Wb*20=7Wb*Hb => Hb=10/7
Answer:
none
Step-by-step explanation:
We are given a triangle ABC with ∠A = 30°, sides a = 4 and b = 10.
According to the 'Law of Sines- Ambiguous Case', we have,
If a < b×sinA, then no triangle is possible.
If a = b×sinA, only one triangle is possible
If a > b×sinA, two triangles are possible.
So, we have,
b×sinA = 10 × sin30 = 10 × 0.5 = 5.
Now, as
4 = a < bsinA = 5.
We get, according to the rule, no triangle is possible.
Answer:
Sister = 15 years old
Brother = 12 years old
Step-by-step explanation:
Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X
Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have
B = 3X
S = 4X
B-3 = (3/4)(S-3)
Therefore, we have a system of equations
B = (4/5)S
B-3 = (3/4)(S-3)
Substitute (4/5)S for B into the second equation to only have one variable
(4/5)S - 3 = (3/4)(S-3)
(4/5)S - 3 = (3/4)S - 9/4
add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient
(1/20)S = 3/4
multiply both sides by 20 to isolate the S
S = 15
B = (4/5)S = 12
Answer: (x+4)(x^2+16)
Step-by-step explanation:
x^3+4x^2+16x+64
x^3+4x^2+16x+64
=(x+4)(x^2+16)
have a nice day!!
