Answer:
Step-by-step explanation:
Okay, so I think I know what the equations are, but I might have misinterpreted them because of the syntax- I think when you ask a question you can use the symbols tool to input it in a more clear way, otherwise you can use parentheses and such.
Problem 1:
(x²)/4 +y²= 1
y= x+1
*substitute for y*
Now we have a one-variable equation we can solve-
x²/4 + (x+1)² = 1
x²/4 + (x+1)(x+1)= 1
x²/4 + x²+2x+1= 1
*subtract 1 from both sides to set equal to 0*
x²/4 +x^2+2x=0
x²/4 can also be 1/4 * x²
1/4 * x² +1*x² +2x = 0
*combine like terms*
5/4 * x^2+2x+ 0 =0
now, you can use the quadratic equation to solve for x
a= 5/4
b= 2
c=0
the syntax on this will be rough, but I'll do my best...
x= (-b ± √(b²-4ac))/(2a)
x= (-2 ±√(2²-4*(5/4)*(0))/(2*(5/4))
x= (-2 ±√(4-0))/(2.5)
x= (-2±2)/2.5
x will have 2 answers because of ±
x= 0 or x= 1.6
now plug that back into one of the equations and solve.
y= 0+1 = 1
y= 1.6+1= 2.6
Hopefully this explanation was enough to help you solve problem 2.
Problem 2:
x² + y² -16y +39= 0
y²- x² -9= 0
Answer: Angle A = 53.9 degrees
Step-by-step explanation: We have a right angled triangle with two sides clearly given and one angle to be calculated. If the angle to be calculated is angle A, then having angle A as our reference angle, line AC (10 units) is the adjacent, line CB is the opposite while line AB (17 units) is the hypotenuse. Having been given the adjacent and the hypotenuse, we can now use the trigonometric ratio as follows;
CosA = adjacent/hypotenuse
CosA = 10/17
CosA = 0.5882
By use of the calculator or table of values,
A = 53.97
Approximately to the nearest tenth,
A = 53.9 degrees
Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 4)² + (y + 6)² = 16 is in this form
with r² = 16 ⇒ r = 
= 4
---------------------------------------------------------------
given (h, k) = (5, 2) and r = 20, then
(x - 5)² + (y - 2)² = 400 ← represents the delivery area
Answer:
HJ = 17
IK = 30
Step-by-step explanation:
to find HI :
GH : 2
HI : ?
IJ : 12
GI : 7
HI = GI - GH
HI = 7- 2
HI = 5
HI + IJ = HJ
5 + 12 = HJ
17 = HJ
To find IK
IJ = ?
JK = 12
KL = ?
IL = 49
JL = 31
To find IK we need to find KL and IJ
KL = JL - JK
KL = 31 - 12
KL = 19
IJ = IL - (JK + KL)
IJ = 49 - 31
IJ = 18
IK = IJ + JK
IK = 18 + 12
IK = 30
Answer:
Step-by-step explanation:
The orange divisor(s) above are the prime factors of the number 1,620. If we put all of it together we have the factors 2 x 2 x 3 x 3 x 3 x 3 x 5 = 1,620. It can also be written in exponential form as 22 x 34 x 51.
