Answer:
Angles F and C are congruent
Step-by-step explanation:
In the figure attached, the missing image is shown.
From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .
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Answer:
6 +8√5
Step-by-step explanation:
The leg length can be reduced to simpler form:
3 +√45 = 3 +√(3²·5) = 3 +3√5
The perimeter is the sum of the side lengths, so is ...
(3 +3√5) +(3 +3√5) +(2√5) = 6 +8√5 . . . perimeter
Answer:
Intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction
Step-by-step explanation:
Required vector is consists of the two components
vx= 2+4=6 units and vy= 1 unit and vx ⊥ vy
We will use Pythagorian theorem to find intensity of the vector v
v∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 units
The angle ∡α between vector and east direction we wil find with tanα
tanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°
Good luck!!!
Answer:
h=6 feet
Step-by-step explanation:
Given: 1. The base of a rectangle is three feet longer than its height.
2.Are of the rectangle=54 square meters
Let us say the rectangle has height h and base(breadth) b.
Since, the base of the rectangle is three feet longer than the height, we have b=h+3.
Also, Area of the Rectangle= hb
therefore, 54=h(h+3)
54= h2+ 3h
h2+3h-54=0 (Subtract 54 from both the sides)
To find the value of h we have to solve the quadratic equation.
[We have the equation in the form ax2+bx+c=0, to factorise the equation-
Step1. Find two numbers such that their multiplication is equal to ac and their addition is equal to b.
Step2. Replace b with these numbers.
Step3. Simplify the equation]
So, h2+3h-54=0
h2+9h-6h-54=0
h(h+9)-6(h+9)=0
(h+9)(h-6)=0
Which gives-
h= -9 or h= 6
As h is the height of the rectangle, h can not be -9.
so h=6 feet
and b=h+3=9 feet
So the dimensions of the rectangle are 6 feet for the height and 9 feet for the base.
To convert an equation to slope intercept form, you have to isolate the y variable.
-2x + 3y = 15
Add 2x to both sides.
3y = 2x + 15
Divide all terms by 3.
<h3>y = 1.5x + 5 is the original equation in slope-intercept form.</h3>
I hope this answers your question!
