6 math books would be 126
5 English books would be 150
126+150=276
Answer:
65.56°
Step-by-step explanation:
We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them
That is let p and q be any two vectors and A be the angle between them
So, p·q=|p|*|q|*cosA
⇒
Given u=-8i-3j and v=-8i+8j
let A be angle before u and v
therefore, 
⇒
Therefore angle between u and v is 65.56°
For this case we have the following function:
n (t) = 2400 * (5) ^ t
For n (t) = 60000 we have:
60000 = 2400 * (5) ^ t
We clear the value of t.
For this we use the logarithm:
(5) ^ t = 60000/2400
log5 ((5) ^ t) = log5 (60000/2400)
t = log5 (60000/2400)
t = 2 days
Answer:
the number of bacteria in the culture will be 60 comma 000 after:
t = 2 days
First you would add the two angles together to get 105. The. you do 180-105 to get 75. That is the missing angle. From there you would correspond the angles with the sides. Therefore the answer is Angle AB, angle BC, angle CA. these are in order from shortest to longest
Given,
3/3x + 1/(x + 4) = 10/7x
1/x + 1/(x+4) = 10/7x
Because the first term on LHS has 'x' in the denominator and the second term in the LHS has '(x + 4)' in the denominator. So to get a common denominator, multiply and divide the first term with '(x + 4)' and the second term with 'x' as shown below
{(1/x)(x + 4)/(x + 4)} + {(1/(x + 4))(x/x)} = 10/7x
{(1(x + 4))/(x(x + 4))} + {(1x)/(x(x + 4))} = 10/7x
Now the common denominator for both terms is (x(x + 4)); so combining the numerators, we get,
{1(x + 4) + 1x} / {x(x + 4)} = 10/7x
(x + 4 + 1x) / (x(x + 4)) = 10/7x
(2x + 4) / (x(x + 4)) = 10/7x
In order to have the same denominator for both LHS and RHS, multiply and divide the LHS by '7' and the RHS by '(x + 4)'
{(2x+4) / (x(x + 4))} (7 / 7) = (10 / 7x) {(x + 4) / (x + 4)}
(14x + 28) / (7x(x + 4)) = (10x + 40) / (7x(x + 4))
Now both LHS and RHS have the same denominator. These can be cancelled.
∴14x + 28 = 10x + 40
14x - 10x = 40 - 28
4x = 12
x = 12/4
∴x = 3
