Answer:
x= 40°
Step-by-step explanation:
since the angles of the quadrilateral add up to 360°
then to find the agle x:
step:1
add alll the angles given in the quadrilateral
100+120+100
= 320
step:2
now subtract the sum of the quadrilateral from the sum of alll angles
360°-320° = 40°
therefore the answer equates to 40°
Let h=height where top of ladder touches wall and x be distance from wall to bottom of ladder...
tana=h/x
a=arctan(h/x) and a≤75
arctan(h/x)≤75 now taking tan of both sides :P
h/x≤tan75 now we have an ugly x value that we need to get rid of:
Using the pythagorean theorem we know:
144=x^2+h^2, x^2=144-h^2, x=√(144-h^2) now we can use this in our inequality for x
h/√(144-h^2)≤tan75
h^2/(144-h^2)≤(tan75)^2
h^2≤144(tan75)^2-h^2(tan75)^2
h^2+h^2(tan75)^2≤144(tan75)^2
h^2(1+(tan75)^2)≤144(tan75)^2
h^2≤[144(tan75)^2]/(1+(tan75)^2)
h^2≤134.353829
h≤11.5911
So he cannot have the top of the ladder 11.8 ft above the ground and not exceed a 75° angle with the ground.
I worked it the hard way just to go through the process. However we could have used a simple trig function to see that maximum height of the top of the ladder....
sin75=h/12
h=12sin75
h≈11.59 ft. That would be the maximum height given that we did not want to exceed 75° with the ground.
The whole graph is shifted 4 units to the left then 5 units down
The expressions that represent number of tiles that Devon used on her mosaic:
A. 20 + 2t + 2c
D. 20 + t + t + c + c
<h3>What is an expression?</h3>
An expression refers to a mathematical equation which shows the relationship between two or more numerical quantities or variables.
For the expressions that represent number of tiles that Devon used on her mosaic:
- Let the triangle tiles be t.
- Let the circle tiles be c.
- Two rows of t triangle tiles = t + t = 2t.
- Two rows of c circle tiles = c + c = 2t.
Mathematically, the expression is given by:
Total tiles = 20 + t + t + c + c
Total tiles = 20 + 2t + 2c.
Read more on expressions here: brainly.com/question/12189823
#SPJ1
Complete Question:
Devon made a mosaic in art class with different-shaped tiles. She started by putting 2 rows of t triangle tiles at the top of the mosaic and 2 rows of c circle tiles at the bottom. She finished by putting 20 square tiles in between the triangle and circle tiles.
Pick all the expressions that represent how many tiles Devon used on her mosaic.
A. 20 + 2t + 2c
B. 20 + 4 ( t + c )
C. 2 ( 20 + t + c )
D. 20 + t + t + c + c
Answer:
x ≈ 3.29
Step-by-step explanation:
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x = 
Decimal Form:
x = 3.29202967
… ≈ 3.29 (Round to what the question asks, in this case, I rounded to 2 decimal places)
