The missing figure is attached down
Answer:
The measure of EC is 1 foot
Step-by-step explanation:
Let us revise the cases of similarity
- AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangle
- AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.
- SSS similarity : If the corresponding sides of the two triangles are proportional, then the two triangles are similar.
- SAS similarity : In two triangles, if two sets of corresponding sides are proportional and the included angles are equal then the two triangles are similar.
From the attached figure
∵ DE // BC
∴ ∠ADE ≅ ABC ⇒ corresponding angles
∴ ∠AED ≅ ACB ⇒ corresponding angles
In Δs ADE and ABC
∵ ∠ADE ≅ ABC ⇒ proved
∵ ∠AED ≅ ACB ⇒ proved
∵ ∠A is a common angle in the two triangles
∴ Δ ADE is similar to triangle ABC by AAA postulate
From the results of similarity the corresponding sides of the triangles are proportion
∴
∵ AD = 8 feet
∵ DB = 2 feet
∴ AB = AD + DB
∴ AB = 8 + 2 = 10 feet
∵ AE = 4 feet
By using the proportion statement above
∴
By using cross multiplication
∴ 8 × AC = 10 × 4
∴ 8 AC = 40
Divide both sides by 8
∴ AC = 5 feet
∵ AC = AE + EC
∴ 5 = 4 + EC
Subtract 4 from both sides
∴ 1 = EC
∴ The measure of EC is 1 foot
Answer:
a. θ = 6t
b. 1.048 minutes
c. y = 54sin(6t)
Step-by-step explanation:
diameter d = 108 foot
distance above the ground = 58 feet
a.) expression to represent number of radians
radian = 6 rad/min
θ = wt
w = 6
θ = 6t
t is in minutes
b.) we are to find the time period for one full revolution
time period = 2π/6
π = 22/7
= 1.048 minutes
c. Expression showing Justins height above the ground
y = rsinθ -----(1)
θ = wt = 6t
we find the radius r
diameter = 2 * radius
108 = 2r
r = 108/2
= 54 foot
we put these values in the equation 1 above
y = 54sin(6t)
Answer: w=-6/14
Step-by-step explanation:
First you are going to put one equation on top of the other and subtract. Then you will use your new equation to combing like terms then divide your end result by your w value and make an improper fraction.
Answer:
18 Milk Chocolates: 24 dark chocolates
Step-by-step explanation:
The total number of chocolates are 42
So you have Milk: Dark, in the ratio 3:4
You do 3+4 which = 7
You then divide the total ratio outcome by the total number
So you do, 42/7 =6
You then do 6 and put this into the ratio
So you do, 3x6 and 4x6, which = 18 and 24
To check if your answers correct add the ratio outcomes
And If you add 18 and 24 together, you should get your beginning total of 42
Answer:
Commutative Property
Step-by-step explanation:
The property of multiplication that is being demonstrated is known as Commutative Property. This property basically shows that when multiplying two numbers the actual order in which they are multiplied does not matter and does not affect the result at all. For example, the in this scenario to get the total number of oranges we have to multiply the number of bags by the number of oranges in each bag, but whatever way we do this they equal the same
2 bags * 3 oranges per bag = 6 oranges
3 bags * 2 oranges per bag = 6 oranges
Therefore,
2 * 3 = 3 * 2