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vazorg [7]
3 years ago
6

The quadratic formula gives which roots for the equation 2x^2 + x - 6 = 0?

Mathematics
1 answer:
Jet001 [13]3 years ago
3 0

Answer:

The roots are x = (\frac{3}{2}, -2), which is given by option C.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

In this question, we have that:

2x^2 + x - 6 = 0

Which is a quadratic equation with a = 2, b = 1, c = -6. So

\Delta = 1^{2} - 4*2(-6) = 1 + 48 = 49

x_{1} = \frac{-1 + \sqrt{49}}{2*2} = \frac{6}{4} = \frac{3}{2}

x_{2} = \frac{-1 - \sqrt{49}}{2*2} = \frac{-8}{4} = -2

So the roots are x = (\frac{3}{2}, -2), which is given by option C.

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Contact [7]
1) surface of a rectangular prism=2(length x width)+2(length x height)+2(width x height)

Therefore:
148 cm²=2(5 cm x 4 cm)+2(5 cm x h)+2(4 cm x h)=
148 cm²=40 cm²+10 cm h+8 cm h
18 cm h=148 cm²-40 cm²
18 cm h=108 cm²
h=108 cm² / 18 cm=6 cm.

answer: height=6 cm 

2)
Volume of a rectangular prism= length x width x height 
therefore:
34 cm³=(1.7 cm)(0.5 cm) h
0.85 cm² h=34 cm³
h=34 cm³/0.85 cm²
h=40 cm.

answer: height=40 cm

3)
volume of a cylinder: πr²h
therefore.
118.79 ft³=πr²(5 ft)
r=√(118.79 ft³/5π ft)≈2.75 ft

answer: radius=2.75 ft

4)
 
Surface area of the pyramid with square base=4(A side)+A base
A side=(1/2)(8ft)(12 ft)=48 ft²
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surface area=4(48 ft²)+64 ft²=256 ft²

Answer: the surface area of this pyramid would be 256 ft².

5)
surface of a cone=πrs+πr²
therefore:
radius=diameter/2=6.2 ft/2=3.1 ft
63.3 ft²=π(3.1 ft) s+π(3.1 ft)²
3.1π ft s=33.109 ft²
s=33.109 ft² /3.1π ft
s≈3.4 ft

Answer: the slant height would be 3.4 ft.

6)
volume of a square pyramid=(area of base x heigth)/3
therefore:
area of base=(6 ft)(6 ft)=36 ft²
126.97 ft³=36 ft² h /3
h=126.97 ft³/12 ft²=10.58 ft

answer: the height would be 10.58 ft.

7)
volume of a cone =(base x height)/3
base of a cone=πr²
therefore: 
199.23 cm³=πr²(9 cm)/3
r=√(199.23 cm³ / 3π cm)≈4.6 cm

answer: the radius would be 4.6 cm.

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2 years ago
Please help on number 13
taurus [48]
The simplest form is 15 dies this help
8 0
3 years ago
If the seed company recommends planting approximately 350 grass seeds per square meter, about how many grass seeds will he need?
Svetach [21]

Answer:

83422.5 grass seeds

Step-by-step explanation:

Applying,

A = 1/2bh....................... Equation 1

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But, from the diagram,

tanФ = 20/b

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Substitute equation 2 into equation 1

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Substitute these values into equation 3

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If the seed company recommends planting approximately 350 grass seeds per square meter,

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Number of grass seed need = (350×238.35)

Number of grass seed needed = 83422.5 grass seeds

3 0
3 years ago
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Answer:

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Step-by-step explanation:

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