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3 years ago

Solve for x. Geometry

Mathematics

1 answer:

Galina-37 [17]3 years ago

6 0

Answer:

x =17

Step-by-step explanation:

Given shape is of a irregular hexagon.

Sum of all angles of an irregular hexagon

$=(6 - 2) \times 180 \degree = 4 \times 180 \degree = 720 \degree \\ \\ \therefore \: (6x - 2)\degree + (7x + 19)\degree + 116 \degree \\ \: \: \: + (5x + 36)\degree + (8x - 1)\degree + 110 \degree \\ \: \: \: = 720 \degree \\ \\ \therefore \:(26x + 52)\degree + 226\degree = 720 \degree \\ \\ \therefore \:26x\degree + 278\degree = 720 \degree \\ \\ \therefore \:26x\degree = 720 \degree - 278\degree \\ \\ \therefore \:26x\degree = 442 \degree \\ \\ \therefore \:x = \frac{442\degree}{26\degree} \\ \\ \huge \red{ \boxed{\therefore \:x = 17}}$

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Find an equation of the line that satisfies the given conditions.

8090 [49]

Answer:

$x=8$

Step-by-step explanation:

Given:

The equation of the given line is $y=9$

A point on the unknown line is (8, 5).

The unknown line is perpendicular to the line $y=9$ .

A line of the form $y=a$ where 'a' is a constant is a line parallel to the x axis. The line has a constant value for 'y' irrespective of the value of 'x'. The slope of such lines are equal to 0. So, slope of the known line is 0.

Now, when two lines are perpendicular, the product of their slopes is -1.

Let the slope of the unknown line be 'm', then:

$m\times 0 =-1\\m=-\frac{-1}{0}=$ undefined.

Therefore, the slope of the unknown line is undefined. A line parallel to y axis has undefined slope. So, the equation of the unknown line is of the form:

$x=b$ where, 'b' is a constant and is equal to the abscissa (x value) of the line.

As per question, (8, 5) lies on this line. Therefore, the value of 'x' is 8.

So, the equation of the unknown line is $x=8$

8 0

4 years ago

Read 2 more answers

Find X: tangent, cosine or sine?

Gnom [1K]

Answer:

x ≈ 2.76

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan78° = $\frac{opposite}{adjacent}$ = $\frac{AB}{BC}$ = $\frac{13}{x}$ ( multiply both sides by x )

x × tan78° = 13 ( divide both sides by tan78° )

x = $\frac{13}{tan78}$ ≈ 2.76 ( to 2 dec. places )

4 0

2 years ago

Which summation formula represents the series below? 13 + 9 + 5 + 1

Ket [755]

Answer:

The summation formula for the series is ⇒ 15n - 2n²

Step-by-step explanation:

* Lets check the series 13 , 9 , 5 , 1

∵ 9 - 13 = -4

∵ 5 - 9 = -4

∵ 1 - 5 = -4

∴ The series has a common difference

∴ It is an arithmetic series with first term a and constant difference d

* That means

- a1 = a , a2 = a + d , a3 = a + 2d , a4 = a + 3d

∴ an = a + (n - 1)d, where n is the position of the number in the series

* The sum of the arithmetic series can find by the rule

- Sn = n/2[2a + (n - 1)d], where n is the number of terms you want to add

* Lets use this rule in our problem

∵ Sn = n/2[2(13) + (n - 1)(-4)]

∴ Sn = n/2(26 + (-4n + 4)] ⇒ open the small bracket

∴ Sn = n/2[26 - 4n + 4] ⇒collect the like terms

∴ Sn = n/2[30 - 4n] ⇒ open the bracket

∴ Sn = (n/2)(30) - (n/2)(4n)

∴ Sn = 15n - 2n²

* The summation formula for the series is 15n - 2n²

7 0

3 years ago

Read 2 more answers

Need help with this question

Lemur [1.5K]

Answer:

$\overline{AB} \cong \overline{DB} \:\: and \:\: \overline{AC} \cong \overline{DC}$

Step-by-step explanation:

$\red{ \boxed{ \bold{\overline{AB} \cong \overline{DB} \:\: and \:\: \overline{AC} \cong \overline{DC}}} }\\ \overline{BC} \cong \overline{BC}... (common\: side) \\$

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3 years ago

can someone please write a 5 sentence paragraph on what they do when they put up Christmas decorations at your house

Tpy6a [65]

Answer:

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Step-by-step explanation:

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3 years ago