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1 year ago

Find the value of x in the given figure

Mathematics

1 answer:

RSB [31]1 year ago

3 0

To solve this problem, you will first use the Angle Sum Property to determine the value of <em>x </em>after creating an algebraic equation, combining like terms, and subtracting from both sides of an equation.

<h3>Use the Angle Sum Property</h3>

The Angle Sum Property states that all interior angles of a triangle will summate to 180º.

An equation can be created to find this when you are given two angles and missing a third. That third angle can be referred to as <em>x</em> in this scenario.

Adding the two known angles and the unknown angle will result in a sum of 180º. This means that our unknown is <em>x</em> and can therefore be placed in an equation:

$65+42+x=180$

<h3>Combine Like Terms</h3>

Combine the like terms by combining the constants on the left side of the equation using addition:

$65+42+x=180$

$107+x=180$

<h3>Subtract</h3>

After combining like terms, subtract 107 from both sides of the equation:

$107 - 107 +x = 180-107$

$\boxed{x=73}$

The final answer is <em>x</em> = 73 degrees.

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The data given below contain the state cigarette taxâ€‹ (in $) for all 20 regions of a country.

g100num [7]

Answer:

(a) $\bar x= 1.583$ -- Population Mean

(b) $s = 1.032$ --- Population standard deviation

Step-by-step explanation:

Given:

Cigarette tax for 20 regions

Solving (a): The population mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

$\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84$

$\sum x = 31.66$

$n = 20$

So, we have:

$\bar x= \frac{31.66}{20}$

$\bar x= 1.583$

Solving (b): The population standard deviation

This is calculated as:

$s = \sqrt{\frac{\sum( x - \bar x)^2}{n}$

$\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2$

$\sum (x -\bar x)^2 = 21.29222$

So:

$s = \sqrt{\frac{21.2922}{20}$

$s = \sqrt{1.06461}$

$s = 1.032$

Solving (c):

Population mean tells the average amount while the standard deviation represents the spread from the calculated mean

Option (4) is correct

6 0

3 years ago

What is the value of (j+3k)(5)?<br><br> j(x) = (x + 4)^2; k(x) = 8 - x<br><br> (j + 3k)(5) =

jeyben [28]

Step-by-step explanation:

J=(x+4)²

K=(8-x)

X=5

=J+3k

=(x+4)(x+4)+3(8-x)

=(x²+8x+16+24-3x)

=25+25+40

=90

Alternatively:

J=(5+4)²

J=81

K=8-5

K=3

J+3k

81+3(3)

81+9

3 0

3 years ago

What is the product?

ra1l [238]

-9x(5 - 2x) Distribute/multiply 9x into (5 - 2x)

(-9x)5 - (-9x)2x

-45x - (-18x²) 2 negative signs cancel each other out and become +

-45x + 18x² Your answer is A ( the first option)

3 0

3 years ago

If you are traveling 543 miles and you know that your car gets 18 miles per gallon of gasoline, approximately how many gallons o

Inga [223]

we know that

the car gets 18 miles per -----------> 1 gallon of gasoline

for 543 miles ---------------------> x gallons of gasoline

by proportion

543/18=x/1---------->x=543/18------->x=30.17 gallons

therefore

the answer is

30.17 gallons

6 0

3 years ago

The equation 9 x 2 − 12 x + 4 = 0 9 x 2 − 12 x + 4 = 0 has how many different solutions?

Hatshy [7]

We have the equation:

$9x^2-12x+4=0$

so:

$a=9\qquad b=-12\qquad c=4$

and:

$\Delta=b^2-4ac=(-12)^2-4\cdot9\cdot4=144-144=\boxed{0}$

This equation has one solution.

5 0

2 years ago

Find the value of x in the given figure​

Find the value of x in the given figure