2x+4x-4=80
6x-4=80
6x=84
84/6=14
Angle c = 4 x 14= 56 - 4 = 52
Hope this helps.
Alex bought all the string needed for $125.
It costs $18 for the remaining materials to make each puppet.
So if we closely observe then we see that here $125 is the fixed cost because its not going to change with number of puppets.
And the variable cost is $18.
In this case we can model a Total cost function C(x) for for x number of puppets as below

The total cost to make 50 puppets=$1025
If the volume of this pyramid is 234 units, the height of the pyramid is equal to 13 units.
<h3>How to calculate the volume of a pyramid.</h3>
Mathematically, the volume of a pyramid is given by the formula:

<u>For the </u><u>base area</u><u>:</u>
The area of a right triangle is given by:

A = 54 square units.
<u>Given the following data:</u>
Volume of a pyramid = 234 units.
Side lengths of right triangle = 9 and 12 units.
Now, we can calculate the height of the pyramid:

h = 13 units.
Read more on pyramid here: brainly.com/question/16315790
Answer:
x ∈ (- 9/2; 1/2), it can also be written as -9/2 <x< 1/2
Step-by-step explanation:
We have absolute value, so we will have2 inequalities.
2x + 4 < 5 and -(2x +4)< 5
2x < 1 -2x - 4 < 5
x < 1/2 -2x < 9
or x > -9/2
(-∞; 1/2) or (- 9/2; ∞)
(-∞; 1/2) ∩ (- 9/2; ∞) = (- 9/2; 1/2)
The answer is x ∈ (- 9/2; 1/2), it can also be written as -9/2 <x< 1/2.