Tile 1:In any triangle (regardless its type), the sum of measures of the internal angles is 180°.
This means that:
∠ABC + ∠BAC + ∠ACB = 180°
Tile 2:The sum of measures of internal angles of a triangle is 180°.
We are given that:
ΔABC is isosceles where AB = AC
This means that:
∠ABC = ∠ACB
We are also given that measure angle BAC is 70 degrees
180 = ∠ABC + ∠ACB + 70
∠ABC + ∠ACB = 110°
We know that both angles are equal, therefore:
∠ABC = ∠ACB = 110/2 = 55°
Tile 3:We are given that ΔQPR is an isosceles triangle where PQ = QR
This means that:
∠QPR = ∠QRP
We are given that ∠QRP = 30°
This means that:
∠QPR = 30°
Tile 4:A diagram representing the given scenario is attached.
Now we have:
point D is midpoint to AB and point E is midpoint to BC
There is a theorem stating that: "In a triangle, a line joining the midpoints of two sides is parallel to the third side and equals half its length"
Applying this to the givens, we would conclude that:
ED is parallel to AC
Now, since these two lines are parallel, then angles BAC and BDE are corresponding angles which means that they are equal.
This means that:
∠BAC = ∠BDE = 45°
Hope this helps :)
Answer: ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Step-by-step explanation:
y=mx+b is the equation for a non-proportional relationship. Essentially, you can use this for a proportional relationship as well, since the y-intercept of a proportional relationship will always be zero.
and
are the variables of the equation, and represent the coordinates of the line.
is the slope of the equation. To find the slope, use rise over run, or the change in y between two points over the change in x between two points. The last part is the y-intercept, or
. This shows when the line intercepts the y-axis.
P+ p(.08)= 51.84
p is the original price of the item
if you take 51.84 which is the total amount after taxes are added and divide it
by 1+tax you will get the original price
so if p + p(.08)=51.84 then 51.84/1.08= p
p =48
48+ 48(.08)=51.84
Answer:
f(8)=-31
Step-by-step explanation:
since 8 replaces x in f(x), x should be substituted as 8 in the expression. From there, after you substitute, it becomes 6(1-8)+11. Simplifying that expression is now 6(-7)+11. Multiply 6 and -7, you get -42. -42+11=-31. I hope this helps :)
Answer:
t = 3
Step-by-step explanation:
- 16t^2 +144 you can rewriting in this form 144 -16t^2 = (12 -4t)(12+4t)
12-4t=0
12 =4t divide both sides by 4
t=3
hope helped add me as friend