Answer:
cos2∅= -0.557
tan2∅= --1.49
Step-by-step explanation:
Given:
cos∅=-8/17
By trigonometric ratios:
as cos∅=adjacent/hypotenuse
hypotenuse= 17
adjacent=-8
Now finding perpendicular using Pythagoras theorem:
c2=a2+b2
17^2=(-8)^2+b^2
289-64=b^2
b^2=225
b=±15
b=-15 as ∅ is in third quadrant so both the opposite and adjacent sides be in 3rd quadrant
tan∅=opposite/adjacent
tan∅=-15/-8
sin∅=-15/17
Now finding cos2∅
cos2∅= 1-2sin^2∅
=1 - 2(-15/17)^2
=1 -450/289
= -161/289
=-0.557
finding tan2∅
tan2∅= 2tan∅/1-tan^2∅
= 2(-15/-8) / 1-(-15/-8)^2
= (15/4) / 1-225/64
=(15/4) / (-161/64)
= -240/161
=-1.49 !
Answer:
See below in bold.
Step-by-step explanation:
A. (x + 7)^2 + (y - 7)^2 = 10.
This is the equation of a circle.
It is NOT a function
One to many correspondence.
B. y = x^2 + 2x - 3
This is a parabola which opens upwards.
It is a function.
For 2 values of x ( except at the vertex) there is one value of y so it is
many to one correspondence.
<h3>Answer:
122 degrees</h3>
==========================================================
Explanation:
Angle BAC can be shortened to "angle A" since the letter A is in the middle.
Angle BCA can be shortened to "angle C" for similar reasoning.
We're told that angles A and C are base angles. For any isosceles triangle, the base angles are congruent
-----------
Let's use this fact to solve for x.
angle A = angle C
7x+1 = 5x+9
7x-5x = 9-1
2x = 8
x = 8/2
x = 4
Once we know what x is, we can find each base angle
- angle A = 7x+1 = 7*4+1 = 28+1 = 29
- angle C = 5x+9 = 5*4+9 = 20+9 = 29
Both angles A and C are 29 degrees each, so this confirms we have the correct x value.
-----------
The last step is to use the fact that all three angles of a triangle add to 180 degrees. This will help us find angle B, which is the vertex angle.
A+B+C = 180
29+B+29 = 180
B+58 = 180
B = 180-58
B = 122
The vertex angle is 122 degrees.
So we can say either angle B = 122, or we could say angle ABC = 122
"angle ABC" is the same as "angle CBA".
Answer: B
Step-by-step explanation:
To solve the system of equations, use substitution.
x+y =24
Subtract x on both sides
y=-x+24
We can now substitute -x+24 in for y in the second equation.
3x+5y=100
3x+5(-x+24)=100
Distribute the 5
3x-5x+120=100
Subtract the 120 on both sides
-2x=-20
Divide by 2 on both sides
x=10
Substitute 10 in for x in the first equation.
x+y=24
10+y=24
Subtract 10 inches on both sides
y=14
So there are 10 3point questions and 14 5 point questions, so choice B
Hope this helped!
