Answer:
m∠ABC = 45°
Step-by-step explanation:
See the attached figure.
As shown in the figure
Line C B extends through point D to form the exterior angle that is 135 degrees.
So, m∠ABD = 135°
But m∠ABC + m∠ABD = 180°
∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°
Also, we should know that
m∠ABD = m∠BAC + m∠ACB
So, m∠ACB = 135° - 75° = 60°
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<u>Very important note:</u>
If we replaced the location of B and C
SO, m∠ABC = 60° and m∠ACB = 45°
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9514 1404 393
Answer:
f(x) = 4·3^x
Step-by-step explanation:
We assume the function will be of the form ...
f(x) = a·b^x
Substituting the given values, we can find 'a' and 'b'.
4/9 = a·b^(-2)
108 = a·b^3
Dividing the second equation by the first gives ...
108/(4/9) = b^(3 -(-2))
243 = b^5
b = 3 . . . . . . 5th root
Using the second equation, we can find 'a':
108 = a·3^3 = 27a
a = 108/27 = 4
The formula for the exponential function is ...
f(x) = 4·3^x
Answer:
$553300
Step-by-step explanation:
Let the rate of increase of radius with respect to time be dr / dt. Hence:
dr / dt = 0.4 ft/week
The cost of increasing the radius is $1,100 per cubic foot. We can calculate how fast the cost is growing by determining the rate at which the volume increases with time (dV / dt).
The volume (V) of a spherical object is given by:
Therefore, the cost of increasing volume = 503 feet³/week * $1100 / feet³ = $553300
Answer:
499.2
cm²
Step-by-step explanation:
See attachment for the figure.
The area of a triangle is given by
A = 1/2bh
A = 1/2(12)(10.4)
A = 62.4
cm²
Then, take that area and multiply it by the number of faces. In this problem, there are 8.
62.4 × 8 = 499.2
cm²
Answer:
<u>61.6 units</u>
Step-by-step explanation:
C (-8,-10)
D (8,10)
E (-8,10)
find the distance between the following points
CD = 25.6
DE = 16
EC = 20
Add them all up
<u>61.6 units</u>