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1 year ago

6x2 + 108x + 707 = 5

Mathematics

1 answer:

Phantasy [73]1 year ago

4 0

Answer:

$x=-9\pm6i$

Step-by-step explanation:

$6x^2+108x+707=5$

$6x^2+108x+702=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-108\pm\sqrt{(108)^2-4(6)(702)}}{2(6)}$

$x=\frac{-108\pm\sqrt{-5184}}{12}$

$x=\frac{-108\pm72i}{12}$

$x=-9\pm6i$

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Prove that for a triple element x, y, z the distributive law is always satisfied if one of the elements equals 0 or 1, or if two

solmaris [256]

The distributive law is satisfied if the numbers 1,2, and 3 are used as multyplying factors.

<h3>What is the distributive law?</h3>

This is basic mathematical law that states:

A multiplied by (b+c) equals (a x b) + (a x c)

<h3>Is this law satisfied if there are three numbers involved?</h3>

The law is always satisfied if one of the numbers is 1. Here is an example

2 x (1+2+3) = 2 x 6 = 12

(2x1) + (2x2) + (2x3)
2+4+6 = 12

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3 0

1 year ago

Need help with this question ! Due soon*

Doss [256]

Answer:

x = 10, AB = 57

Step-by-step explanation:

In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. From this, we have:

$\frac{1}{2} (5x + 7 + 8x - 11) = 63$

$13x - 4 = 126$

$13x = 130$

$x = 10$

$5(10) + 7 = 50 + 7 = 57$

5 0

2 years ago

Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$

3 0

2 years ago

Big ideas math 1.2 Practice A number 19

slega [8]

By applying Segment Addition Postulate, segment FH is equal to 24 units.

<h3>What is a point?</h3>

A point can be defined as a zero dimensional geometric object and it is generally represented by a dot.

<h3>What is a line segment?</h3>

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

<u>Given the following data:</u>

Line segment FG = 37.

Segment HG = 13.

Since point H lies on line segment FG, we would apply Segment Addition Postulate to determine segment FH as follows:

FG = HG + FH

37 = 13 + FH

FH = 37 - 13

FH = 24 units.

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Complete Question:

Given that line segment FG = 37 and segment HG = 13, find segment FH.

4 0

1 year ago

I don’t understand what to do on these question, some help would be nice (trigonometry)

Bumek [7]

Step-by-step explanation:

> find the angle of center circle:

cos~¹ 5/(5+12) = cos~¹ 5/17 = 72°

so the sector area of the shaded

region =

(360-72)/360 × 3.14 × 5²

= 288/360 × 78.5

= 62.8

> the height of triangle (red Line) =

4×tan 72° = 4× 3.078 = 12.31

the height of pyramid (green

Line) = √12.31²-8.5² =√74.16

= 8.61

so the volume of pyramid =

⅓×(17×8)×8.61 = 390.32

8 0

2 years ago