Answer:
Katie is 6 years old and Thomas is 3 years old
Step-by-step explanation:
Given that we should let K and T be the current ages of two siblings, Katie and Thomas.
If Katie is currently twice the age of Thomas then,
K = 2T
and in 6 years, Katie will be 4 times Thomas's current age then
K + 6 = 4T
Solving both equations simultaneously by substituting the value of K given in the first equation into the second
2T + 6 = 4T
Collect like terms
6 = 4T - 2T
6 = 2T
Divide both sides by 2
T = 3
Recall that K = 2T
K = 2 * 3
= 6
Hence Katie is 6 years old while Thomas is 3 years old
Answer:
1) (n+5)(n-1)
2) (n-4)(n+3)
3) (v-4)(v-1)
4) (p-4)(p+2)
5)(7x-10)(x+1)
6)(7n-1)(n-9)
Step-by-step explanation:
1) Factors of -5 that add up to 4
2) Factors of --12 that add up to -1
3) Factors of 4 that add up to -5
4) Factors of -5 that add up to 4
5) 7
-3x-10
7
+7x-10x-10
7x(x+1)-10(x+1)
(7x-10)(x+1)
6)7
-64n+9
7
-63n-n+9
7n(n-9)-(n-9)
(7n-1)(n-9)
It appears that the Pythagorean theorem can be applied to this problem
(distance to shadow)² = (height of building)² + (length of shadow)²
(38 m)² = (height of building)² + (28 m)²
660 m² = (height of building)²
Then the height of the building is
height of building = √660 m ≈ 25.7 m
P = 2(L + W)
P = 28
L = 2W - 1
28 = 2(2W - 1 + W)
28 = 2(3W - 1)
28 = 6W - 2
28 + 2 = 6W
30 = 6W
30/6 = W
5 = W ....width is 5 ft
L = 2W - 1
L = 2(5) - 1
L = 10 - 1
L = 9 <=== length is 9 ft