Answer:
1. 2w + 3p = 7.05
2. p = 1.35
w = 1.50
p = 1.35
- The solution means that a bottle of water costs $1.50 and a bag of pretzels costs $1.35
Explanation
1) Translate the verbal language to algegraic language to create the equations which you can solve.
w = cost of one bottle of water
p = cost of one bag of pretzels
the cost of 2 bottles of water: 2w
the cost of 3 bags of pretzels: 3p
the cost of 2 bottles of water and 3 bags of pretzels is $7.05:
2w + 3p = 7.05 Equation 1
the cost of a bag of pretzels is $ 1.35: p = 1.35 Equation 2
1. 2w + 3p = 7.05
2. p = 1.35
2) Solve the system using substitution method: substitute p with 1.35 in the first equation:
3) Steps to solve the equation:
- Simplify: 2w + 4.05 = 7.05
- Subtract 4.05 from both sides: 2w = 3
- Divide both sides by 2: w = 3/2 = 1.50
Answer: you have found the costs of both a bottle of water and a bag of pretzels, which, repectively, are $ 1.50 and $ 1.35
A square has four corners.
The slope of a function at a point is the value of its derivative there.
... f'(x) = 5·(2x) + 0 = 10x . . . . . . using the power rule: (d/dx)(xⁿ) = n·xⁿ⁻¹
Then
... f'(4) = 10·4 = 40 . . . . . the slope at x=4
Answer:
12a cm2
2b cm2
(6a + b) cm2
Step-by-step explanation:
The complete question is
The figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2.
Which expressions represent the area of the entire shaded region, including the light and dark shading? Check all that apply.
12a cm2
2b cm2
(6a - b) cm2
(12a + 2b) cm2
(6a + b) cm2
The picture of the question in the attached figure
we know that
The area of the entire shaded region is equal to the area of the the light and dark shading
so
step 1
Find the area of the light shading
The area is equal to the area of six congruent equilateral triangles
step 2
Find the area of the dark shading
The area is equal to the area of the regular hexagon
step 3
1) Find the total area
2) Remember that the figure consists of 12 congruent equilateral triangles
so
3) The area of the light shading is the same that the area of the dark shading
so
6a=b
therefore