Answer:
b = a + 3.75
Step-by-step explanation:
a = 4b - 15
You are solving for b. Isolate the b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 15 to both sides
a (+15) = 4b - 15 (+15)
a + 15 = 4b
Next, divide 4 from both sides. Remember to divide from all terms.
(4a + 15)/4 = (4b)/4
b = (4a)/4 + (15)/4
b = a + 15/4
b = a + 3.75 is your answer
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A:b = 8:5 b:c = 3:4
since both sides have b. make b the same. multiply the left by the right side b value of 3 and multiply the right by the left side b value of 5.
3(a:b) and 5(b:c)
3 (8:5) and 5(3:4)
24:15 15:20
now that both sides have the same b value
a:b:c = 24:15:20
Answer:
c) 18 cm²
d) 30 cm²
Step-by-step explanation:
c)
You can do this 2 different ways. Either way, you need to use the bottom side of 8 cm and the two congruent segments. Each of the two congruent segments of the bottom side measures 4 cm.
Method 1) Find the area of the large triangle and subtract from it the area of the small triangle.
area of triangle = bh/2
shaded area = 8 cm × 6 cm / 2 - 4 cm × 3 cm / 2
shaded area = 24 cm² - 6 cm²
shaded area = 18 cm²
Method 2) The shaded region is a trapezoid with parallel bases of lengths 3 cm and 6 cm and height 4 cm. Find the area of the trapezoid.
area of trapezoid = (B + b)h/2
shaded area = (6 cm + 3 cm)(4 cm)/2
shaded area = (9 cm)(4 cm)/2
shaded area = 18 cm²
d)
The area of the shaded region is the area of the white triangle subtracted from the area of the rectangle.
area of rectangle = length × width
area of triangle = bh/2
shaded area = (12 cm)(4 cm) - (9 cm)(4 cm)/2
shaded area = 48 cm² - 18 cm²
shaded area = 30 cm²
