Answer:
x = 2 and x = 4
Step-by-step explanation:
The solution of the given equation is shown on the graph
<u>There are two intercepts with coordinates of</u>
<u>The x-coordinates are </u>
Correct option is 3 or C.
Answer:
equilateral
Step-by-step explanation:
In an equilateral triangle, all sides and angles are equal.
Answer:
<em>Karim will never have triple age as his brother, it has happened already 1 year ago, thus he won't give him a gift</em>
Step-by-step explanation:
<u>Equations</u>
Let's make:
x = the number of years from now
Karim now is 22 and Ziad is 8. x years from now Karim will be
22 + x years old and Ziad will be
8 + x years old.
Karim will give Ziad a wonderful gift when:
22 + x = 3(8 + x)
22 + x = 24 + 3x
Solving:
x = -1
This means that Karim will never have triple age as his brother, it has happened already 1 year ago, thus he won't give him a gift
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
To find out if they are parallel we need to see if the gradient is the same, to do this we need to get y in terms of x:
assuming the first equation is x+y+7=0
y=-x-7
and
y=x-3
The gradient is the coefficient of x (the number infront of x)
For equation 1 the gradient is -1, and for number 2 it is 1, therefore they are not parallel.
However to check if they are perpendicular we need to see if their gradients multiply to equal -1.
-1*1=-1 therefore they are perpendicular