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OlgaM077 [116]
3 years ago
12

Which equation has the solutions x = (5 +- 2 \sqrt(7))/(3)?

Mathematics
2 answers:
asambeis [7]3 years ago
8 0
Recall the formula to find the solutions for an equation ax² + bx + c:
x₁₂ = (- b +/- √(b²-4ac) )/ 2a

Since at the denominator of our solution we have 3, which is an odd number, therefore it cannot be 2a, but only a, we should use the formula:

x₁₂ = <span>(-β +/- √(β²-ac) )/ a

Where </span>β = b/2

Hence, the only options that have an even number as b coefficient are C and D.

Now, we need to find what values give √(β² - ac) = 2√7 = √(4·7) = √28:

C) √(β² - ac) = √(25 - 3·6) = √7
D) √(β² - ac) = <span>√(25 - 3·(-1))</span> = √28

Hence, the correct answer is D) 3x² - 10x - 1 = 0
S_A_V [24]3 years ago
6 0

Answer:D

Step-by-step explanation:

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MatroZZZ [7]
The picture contains two geometric objects: semicircle and right triangle

First, find the area of semicircle
This is the formula for area of semicircle
a = 1/2 × area of circle
a = 1/2 × π × r²

Before we find the area, we should determine the value of r. Given from the question that the diameter is equals to 8 m. Radius (r) is half of diameter (d)
r = 1/2 d
r = 1/2 × 8
r = 4 m

Caculate the area
a = 1/2 × π × r²
a = 1/2 × 3.14 × 4²
a = 1/2 × 3.14 × 16
a = 1/2 × 50.24
a = 25.12 m²

Second, find the area of the right triangle
The formula is
a = 1/2 × b × h

Given from the question that the base (b) is 12 m, and the height (h) is 8 m.

Calculate the area, input the value of b and h to the formula
a = 1/2 × b × h
a = 1/2 × 12 × 8
a = 1/2 × 96
a = 48 m²

Third, sum both area
a = area of semicircle + area of right triangle
a = 25.12 + 48
a = 73.12 m²

Solution:
The area is 73.12 m²
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Step-by-step explanation:

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