Answer:
B
Step-by-step explanation:
Answer:
x = -2+√3i and -2-√3i
Step-by-step explanation:
The formula for the general formula is expressed as;
x = -b±√b²-4ac/2a
Given the expression
x²+4x+7 = 0
a = 1, b = 4 and c = 7
Substitute
x = -4±√4²-4(1)(7)/2(1)
x = -4±√16-28/2
x = -4±√-12/2
x = -4±√4*-3/2
x = -4±2√-3/2
x = -4±2√3i/2
x = -4+2√3i/2 and -4-2√3/2
x = -2+√3i and -2-√3i
Answer:
Parking lot is 60m wide
Step-by-step explanation:
In this question. We are asked to calculate the width of the parking lot. We proceed as follows:
We know that the total length of the field and the parking lot is 300m while the total width is 200m. We should remember that the field is rectangular in nature.
Since the parking lot is x meters, the length of the field would simply be (300-2x)m while the width of the field would be (200-x). The width would also have been 200-2x but we must remember that the field is only covered on 3 sides.
Area of the field is 30,000. This means if we multiply both, we get 30,000.
Mathematically;
(300-2x)(200-x) = 30,000
60,000-300x-400x+ 2x^2 = 30,000
2x^2-700x-30,000= 0
We can see we now have a quadratic equation we need to solve.
2x^2+500x-1200x-30,000= 0
2x(x+250) -120(x+250) = 0
(2x-120)(x+250) = 0
2x-120= 0 or x+250=0
2x = 120or x = -250
x = 120/2 or x= -250
x = 60 or x=-250
We discard x = -100 as x is length and cannot be negative
Hence, x = 60m
Answer:
is it 5y/8_5y/16 or 5y/8-5y/16 ?
Step-by-step explanation:
X = 17.5
Note: This is done in the interior triangle as the angle will be equivalent to the other two angles.
Here's how you solve it:
You have to use the law of cosine for the interior triangle; the law of cosine is: c^2 = a^2 +b^2 - 2ab times cos (C)
Substitute each factor so that the equation now appears as so:
h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80)
This will give you: h = 11.67
Now, you have to apply this to the law of sin which is a over sin(A) = b over sin (B) = c over sin (C). (Lowercase letters are the opposite side of uppercase angles.)
This will then give you:
11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)
sin -1 ((8 times sin (80)) over 11.67) is equal to S
sin -1 ((10 times sin (80)0 over 11.67)) is equal to T
Because you now know the angles of S and T, you need to use the law of sin again.
t over sin (T) = s over sin (S)
t = 10 + x
s = 8 + 18 = 22
Thus, you need to substitute the variables to get this equation:
10 + x over sin (57.54) = 22 over sin (42.45)
x = 22 times sin (57.54) over sin (42.45) and next to this is -10
Thus, getting the answer of x = 17.50
