Answer:
Step-by-step explanation:
Since there exists a scalar
λ
λ
(namely
λ=a⋅b
λ=a⋅b
) such that
b=λa
b=λa
, the directions of the two vertices are the same (they are collinear). This implies that
|a⋅b|=|a||b|
|a⋅b|=|a||b|
.
So,
|a|=|(a⋅b)b|=|a||b||b|
|a|=|(a⋅b)b|=|a||b||b|
which implies that
|b|=1
|b|=1
Answer:
8 maths tests
Step-by-step explanation:
Given data
We are told that in 1/4 hour that is 0.25hour (15 mins) She grades 1 math test
our aim is to find how many maths test she grade in 3 hours (120min)
Hence
in 15 mins she does 1 grading
in 120 mins she does x
cross multiply
15x= 120
divide both sides by 15
x= 120/15
x= 8 maths test
Hence in 2 hours, she can grade 8 maths tests
Answer:
y = –7x – 11
6x – 4y = 10
Step-by-step explanation:
From the question given above, we obtained:
x = –1
y = –4
y = ?x – 11 ....... (1)
6x – ?y = 10b......... (2)
Let the two unknown be a and b. Thus the above equation becomes:
y = ax – 11 ......... (3)
6x – by = 10 .......(4)
Next, we shall determine the value of 'a' and 'b'. This can be obtained as follow:
For a:
y = ax – 11
x = –1
y = –4
–4 = a(–1) – 11
–4 = –a – 11
Collect like terms
–4 + 11 = –a
7 = –a
Multiply through by –1
a = –7
For b:
6x – by = 10
x = –1
y = –4
6(–1) – b(–4) = 10
–6 + 4b = 10
Collect like terms
4b = 10 + 6
4b = 16
Divide both side by 4
b = 16 / 4
b = 4
Finally, we shall substitute the value of a and be into equation 3 and 4 respectively.
y = ax – 11
a = –7
y = –7x – 11
6x – by = 10
b = 4
6x – 4y = 10
Therefore, the complete equation are:
y = –7x – 11
6x – 4y = 10
