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MariettaO [177]
2 years ago
15

Find a quadratic equation with integer coefficient ,if one of the roots is 7-root3

Mathematics
1 answer:
solmaris [256]2 years ago
6 0
One of the roots of a quadratic equation is 7 - √3.

Because rational roots occur in conjugate pairs, the other root is 7 + √3.
The quadratic equation is
(x -(7-√3))(x - (7+√3))
= x² - (7+√3)x  - (7-√3)x + (49-3)
= x² - 7x - (√3)x - 7x + (√3)x + 46
= x² - 14x + 46

Answer: x² - 14x + 46


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Which describes the amount of product a seller is able to make?
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Supply is the amount of product a seller is able to make
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3 years ago
What's 3.318 divided by 0.07? <br><br>THIS IS HOMEWORK AND IT'S DUE IN 2 DAYS
Bond [772]
The answer is ...............47.4
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Field book of an land is given in the figure. It is divided into 4 plots . Plot I is a right triangle , plot II is an equilatera
Kazeer [188]

Answer:

Total area = 237.09 cm²

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Field book of an agricultural land is given in the figure. It is divided into 4 plots. Plot I is a right triangle, plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium, Find the area of each plot and the total area of the field. ( use √3 =1.73)

From the figure attached,

Area of the right triangle I = \frac{1}{2}(\text{Base})\times (\text{Height})

Area of ΔADC = \frac{1}{2}(\text{CD})(\text{AD})

                        = \frac{1}{2}(\sqrt{(AC)^2-(AD)^2})(\text{AD})

                        = \frac{1}{2}(\sqrt{(13)^2-(19-7)^2} )(19-7)

                        = \frac{1}{2}(\sqrt{169-144})(12)

                        = \frac{1}{2}(5)(12)

                        = 30 cm²

Area of equilateral triangle II = \frac{\sqrt{3} }{4}(\text{Side})^2

Area of equilateral triangle II = \frac{\sqrt{3}}{4}(13)^2

                                                = \frac{(1.73)(169)}{4}

                                                = 73.0925

                                                ≈ 73.09 cm²

Area of rectangle III = Length × width

                                 = CF × CD

                                 = 7 × 5

                                 = 35 cm²

Area of trapezium EFGH = \frac{1}{2}(\text{EF}+\text{GH})(\text{FJ})

Since, GH = GJ + JK + KH

17 = \sqrt{9^{2}-x^{2}}+5+\sqrt{(15)^2-x^{2}}

12 = \sqrt{81-x^2}+\sqrt{225-x^2}

144 = (81 - x²) + (225 - x²) + 2\sqrt{(81-x^2)(225-x^2)}

144 - 306 = -2x² + 2\sqrt{(81-x^2)(225-x^2)}

-81 = -x² + \sqrt{(81-x^2)(225-x^2)}

(x² - 81)² = (81 - x²)(225 - x²)

x⁴ + 6561 - 162x² = 18225 - 306x² + x⁴

144x² - 11664 = 0

x² = 81

x = 9 cm

Now area of plot IV = \frac{1}{2}(5+17)(9)

                                = 99 cm²

Total Area of the land = 30 + 73.09 + 35 + 99

                                    = 237.09 cm²

7 0
3 years ago
How many edges does a rectangle prism have?
creativ13 [48]

the answer to your question there would be 12

4 0
3 years ago
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The table shows a proportional relationship between the number of stars Roberto collects in a game and his total points. A row o
maks197457 [2]

Answer:

1) 20 stars; 30 points.

2) 28 stars, 42 points.

3) 38 stars, 57 points.

Step-by-step explanation:

<h3> The missing table is attached.</h3>

Let  be "x" the numbers of stars Roberto collects and "y" his total points.

The proportional relationship has this form:

y=kx

Where "k" is the constant of proportionality.

We can choose the point (8,12) from the table, where:

x=8\\y=12

Substituting these values into  y=kx and solving for "k", we get:

 12=k(8)\\\\\frac{12}{8}=k\\\\k=1.5

Knowing the value of "k", we determine that the  following Numbers of stars and the Total points could be used as the missing values in the table:

1) For x=20 :

y=(1.5)(20)=30

2) For x=28 :

y=(1.5)(28)=42

3) For x=38 :

y=(1.5)(38)=57

4 0
3 years ago
Read 2 more answers
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