They will be 15 miles apart after one hour if they left the same point at the same time.
<h3>How do we measure and calculate the distance in Geometry?</h3>
The distance between two points in geometry can be calculated by using the Pythagoras theorem.
Mathematically, the Pythagoras theorem can be expressed as:
where;
- x and y are opposite and adjacent sides respectively.
d = 15 miles
Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.
Learn more about calculating the distance between two points here:
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Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
Answer:
x = - 7, y = 6
Step-by-step explanation:
7x + 7y = - 7 -----> equation 1
- 10x - 7y = 28 -----> equation 2
Add equations 1 & 2,
7x + 7y = - 7
- 10x - 7y = 28
___________
- 3x + 0 = 21
- 3x = 21
x = 21 / - 3
x = - 7
Substitute x = - 7 in equation 1,
7x + 7y = - 7
7y + 7x = - 7
7y + 7 ( - 7 ) = - 7
7y - 49 = - 7
7y = - 7 + 49
7y = 42
y = 42 / 7
y = 6
(4x-3)(x+5)
= 4x^2+20x-3x-15
= 4x^2+ 17x -15.
The final answer is 4x^2+ 17x -15~
Answer:
Given f(x)=32
So we can substitute 32 in place of 'x'
So, f(x)=3x-1
= f(x)=3(32)-1
= f(x)=96-1
= f(x)=95
f(x)=3x-1 = 95
