<u>Answer</u><u> </u><u>:</u><u>-</u>
9(3+√3) feet
<u>Step </u><u>by</u><u> step</u><u> explanation</u><u> </u><u>:</u><u>-</u>
A triangle is given to us. In which one angle is 30° and length of one side is 18ft ( hypontenuse) .So here we can use trignometric Ratios to find values of rest sides. Let's lable the figure as ∆ABC .
Now here the other angle will be = (90°-30°)=60° .
<u>In ∆ABC , </u>
=> sin 30 ° = AB / AC
=> 1/2 = AB / 18ft
=> AB = 18ft/2
=> AB = 9ft .
<u>Again</u><u> </u><u>In</u><u> </u><u>∆</u><u> </u><u>ABC</u><u> </u><u>,</u><u> </u>
=> cos 30° = BC / AC
=> √3/2 = BC / 18ft
=> BC = 18 * √3/2 ft
=> BC = 9√3 ft .
Hence the perimeter will be equal to the sum of all sides = ( 18 + 9 + 9√3 ) ft = 27 + 9√3 ft = 9(3+√3) ft .
<h3>
<u>Hence </u><u>the</u><u> </u><u>perim</u><u>eter</u><u> of</u><u> the</u><u> </u><u>triangular</u><u> </u><u>pathway</u><u> </u><u>shown</u><u> </u><u>is</u><u> </u><u>9</u><u> </u><u>(</u><u> </u><u>3</u><u> </u><u>+</u><u> </u><u>√</u><u>3</u><u> </u><u>)</u><u> </u><u>ft</u><u> </u><u>.</u></h3>
Answer:
x = - 2, x = - 
Step-by-step explanation:
Given
5x² + 1 = - 13x - 5 ( add 13x - 5 to both sides )
5x² + 13x + 6 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 5 × 6 = 30 and sum = 13
The factors are 10 and 3
Use these factors to split the x- term
5x² + 10x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )
5x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(5x + 3) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - 
Answer:
Height above the bottom gorge is 113 feet
Step-by-step explanation:
The width of the gorge = 40 feet
The height of the higher cliff = 158 feet
The height of the lower cliff = 98 feet
The length of the bridge = √((158-98)² + 40²) = 72.11 feet
The slope of the bridge = (158-98)/40 = 1.5
The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet
The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°
The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet
Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;
Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.
If 1.5cm = 4ft
1.5÷4 =0.375
0.375cm= 1ft
16×0.375=6
12×0.375=4.5
hopefully this is correct and helped! ♡
Answer: Nine less than two thirds of a quantity is smaller than one more than that same quantity.