Step 1.) Multiply both sides of the equation by -6
step 2.) Sum the equations vertically to eliminate at least one variable
step 3.) Divide both sides of the equation by
step 4.) Substitute the given value of into the equation x - 2y = 10
step 5.) Solve the equation for x
step 6.) The possible solution of the system is the ordered pair (x , y)
step 7.) Check if the given ordered pair is the solution of the system of equations
step 8.) Simplify the equalities
step 9.) Since all of the equalities are true, the ordered pair is the solution of the system
So your answer would end up being (40/13 , -45/13) !! Hope that helps you out :D !!
Answer
a. 28˚
b. 76˚
c. 104˚
d. 56˚
Step-by-step explanation
Given,
∠BCE=28° ∠ACD=31° & line AB=AC .
According To the Question,
- a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°
- b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚
thus , ∠ABC=76° .
- c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,
Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°
Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)
∠DAB = 180° - 107° ⇔ 73°
& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°
Now, In Triangle ADC Sum of angles in a triangle is 180°
∠ADC = 180° - (31° + 45°) ⇔ 104˚
- d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre
For Diagram, Please Find in Attachment
Answer:
- sin(θ) = -(4√15)/17
- cos(θ) = 7/17 . . . . . . . given
- tan(θ) = -(4√15)/7
- csc(θ) = -(17√15)/60
- sec(θ) = 17/7
- cot(θ) = -(7√15)/60
Step-by-step explanation:
The relationship between sine and cosine is ...
sin² + cos² = 1
Solving for sine gives ...
sin = ±√(1 -cos²)
In this problem, we want the negative root.
sin(θ) = -√(1 -(7/17)²) = -√(240/289) = -(4√15)/17
tan(θ) = sin(θ)/cos(θ) = ((-4√15)/17)/(7/17) = -(4√15)/7
___
And the inverse functions are ...
sec(θ) = 1/cos(θ) = 17/7
csc(θ) = 1/sin(θ) = -17/(4√15) = -(17√15)/60
cot(θ) = 1/tan(θ) = -(7√15)/60
_____
Of course, you're aware that 1/√15 = (√15)/15.
Answer:
67.73625
Step-by-step explanation:
The dot (scalar) product is also the sum of products of corresponding vector components.
~a • ~b = 9·2.97 +6.75·6.075 +0·0 = 27.73 +41.00625 = 67.73625
