Answer:
the answer is (A)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Angle 1 is 55 degrees.
The whole angle of the upward left corner is 90 degrees.
Corresponding angles are equal. The 35 degrees angle and angle 2 are corresponding angles.
Angle 2 is 35 degrees.
It is 70 because common sense people
Answer: The book costs $10 and the pen costs $4✔️
Step-by-step explanation:
Let B the cost of the book and let P the cost of the pen.
Then we know:
The book and the pen cost $14:
B + P = $14 } Equation 1
We also know:
The cost of the book is two dollars more than twice the cost of the pen.
B = 2P + $2 } Equation 2
Now we can substitute the value of B from the equation 2 in the equation 1:
2P + $2 + P = $14
3P = $14 - $2 = $12
P = $12/3 = $4 , cost of the pen
Since we know the value of B from the equation 2, we can calculate B:
B = 2P + $2 = 2x$4 + $2 = $8 + $2 = $10 , cost of the book
Answer: The book costs $10 and the pen costs $4✔️
<h3>Verify </h3>
We can substitute these values in equations 1 and 2 and check the results:
B + P = $14 } Equation 1
$10 + $4 = $14 ✔️check!
B = 2P + $2 } Equation 2
$10 = 2x$4 + $2 = $8 + $2 = $10 ✔️check!
<h2><em>Spymore</em></h2>
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
