Full question:
Heng was trying to factor 10x²+5x. She found that the greatest common factor of these terms was 5x and made an area model: What is the width of Heng's area model?
Answer:
The width of the area model is 2x + 1
Step-by-step explanation:
Given
Expression: 10x² + 5x
Factor: 5x
Required
Width of the Area Model
To solve this, I'll assume the area model is Length * Width
Provided that we're to solve for the width of the model.
This implies that; Length = 5x
Area = Length * Width
And
Area = 10x² + 5x
Equate these two
Length * Width = 10x² + 5x
Factorize express on the right hand side
Length * Width = 5x(2x + 1)
Substitute 5x for Length
5x * Width = 5x(2x + 1)
Divide both sides by 5x
Width = 2x + 1
Hence, the width of the area model is 2x + 1
3x+4x+5x=54
12x=54
x=4.5
Plug in the value of x into all three segments.
AB= 3*4.5= 13.5
BC= 4*4.5= 18
AC= 5*4.5= 22.5
Answer:
first one is simnple cross multiply and divide
12*7=4x
84=4x
x=21
2nd same process but more steps
7x=5(x+8)
7x=5x+40
7x-5x=40
2x=40
x=20
Step-by-step explanation:
X times 150 =y that is your answer
Answer:
The angle of elevation of the ramp is 64.60°
Step-by-step explanation:
Given;
length of the ramp, L = 35 ft
distance of the platform to the foot of the ramp, d = 15 ft
The length of the ramp forms the hypotenuse side of this right angled triangle;
The angle of elevation of the ramp is in angle between the hypotenuse and adjacent side of the triangle.
Cos x = adjacent / hypotenuse
Cos x = 15 / 35
Cos x = 0.4286
x = Cos⁻¹ (0.4286)
x = 64.62
x = 64.60°
Therefore, the angle of elevation of the ramp is 64.60°