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3 years ago

Referring to the figure, find the value of x

Mathematics

2 answers:

sergiy2304 [10]3 years ago

6 0

Answer:

x = 93

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x - 73 + x + 67 = 180

2x - 6 = 180 ( add 6 to both sides )

2x = 186 ( divide both sides by 2 )

x = 93

elixir [45]3 years ago

5 0

The sum of all the angles of a triangle is 180 degrees. To solve for x you can make a formula of the sum of the angles equal to 180 like so...

(x - 73) + x + 67 = 180

x - 73 + x + 67 = 180

Now you must combine like terms. This means that you must first combing number with the same variables(x and x)...

(x + x) - 73 + 67 = 180

2x - 73 + 67 = 180

Combine like terms -73 and 67...

2x + (-73 + 67) = 180

2x + (-6) = 180

2x - 6 = 180

Now bring -6 to the right side by adding 6 to both sides (what you do on one side you must do to the other). Since -6 is negative on the left side, addition will cancel it out (make it zero) from the left side and bring it over to the right side.

2x - 6 + 6= 180 + 6

2x + 0 = 186

2x = 186

Next divide 2 to both sides to finish isolating x. Since 2 is being multiplied by x, division (the opposite of multiplication) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.

2x / 2 = 186 / 2

x = 93

Hope this helped!

~Just a girl in love with Shawn Mendes

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P(x) = x + 1x² – 34x + 343<br> d(x)= x + 9

Feliz [49]

Answer:

$x=\frac{9}{d-1},\:P=\frac{-297d+378}{\left(d-1\right)^2}+343$

Step-by-step explanation:

Let us start by isolating x for dx = x + 9.

dx - x = x + 9 - x > dx - x = 9.

Factor out the common term of x > x(d - 1) = 9.

Now divide both sides by d - 1 > $\frac{x\left(d-1\right)}{d-1}=\frac{9}{d-1};\quad \:d\ne \:1$ . Go ahead and simplify.

$x=\frac{9}{d-1};\quad \:d\ne \:1$ .

Now, $\mathrm{For\:}P=x+1x^2-34x+343, \mathrm{Subsititute\:}x=\frac{9}{d-1}$ .

$P=\frac{9}{d-1}+1\cdot \left(\frac{9}{d-1}\right)^2-34\cdot \frac{9}{d-1}+343$ .

Group the like terms... $1\cdot \left(\frac{9}{d-1}\right)^2+\frac{9}{d-1}-34\cdot \frac{9}{d-1}+343$ .

$\mathrm{Add\:similar\:elements:}\:\frac{9}{d-1}-34\cdot \frac{9}{d-1}=-33\cdot \frac{9}{d-1}$ > $1\cdot \left(\frac{9}{d-1}\right)^2-33\cdot \frac{9}{d-1}+343$ .

Now for $1\cdot \left(\frac{9}{d-1}\right)^2 > \mathrm{Apply\:exponent\:rule}: \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c} > \frac{9^2}{\left(d-1\right)^2} = 1\cdot \frac{9^2}{\left(d-1\right)^2}$ .

$\mathrm{Multiply:}\:1\cdot \frac{9^2}{\left(d-1\right)^2}=\frac{9^2}{\left(d-1\right)^2}$ .

Now for $33\cdot \frac{9}{d-1} > \mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} > \frac{9\cdot \:33}{d-1} > \frac{297}{d-1}$ .

Thus we then get $\frac{9^2}{\left(d-1\right)^2}-\frac{297}{d-1}+343$ .

Now we want to combine fractions. $\frac{9^2}{\left(d-1\right)^2}-\frac{297}{d-1}$ .

$\mathrm{Compute\:an\:expression\:comprised\:of\:factors\:that\:appear\:either\:in\:}\left(d-1\right)^2\mathrm{\:or\:}d-1 > This\: is \:the\:LCM > \left(d-1\right)^2$

$\mathrm{For}\:\frac{297}{d-1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:d-1 > \frac{297}{d-1}=\frac{297\left(d-1\right)}{\left(d-1\right)\left(d-1\right)}=\frac{297\left(d-1\right)}{\left(d-1\right)^2}$

$\frac{9^2}{\left(d-1\right)^2}-\frac{297\left(d-1\right)}{\left(d-1\right)^2} > \mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}> \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$\frac{9^2-297\left(d-1\right)}{\left(d-1\right)^2} > 9^2=81 > \frac{81-297\left(d-1\right)}{\left(d-1\right)^2}$ .

Expand $81-297\left(d-1\right) > -297\left(d-1\right) > \mathrm{Apply\:the\:distributive\:law}: \:a\left(b-c\right)=ab-ac$ .

$-297d-\left(-297\right)\cdot \:1 > \mathrm{Apply\:minus-plus\:rules} > -\left(-a\right)=a > -297d+297\cdot \:1$ .

$\mathrm{Multiply\:the\:numbers:}\:297\cdot \:1=297 > -297d+297 > 81-297d+297 > \mathrm{Add\:the\:numbers:}\:81+297=378 > -297d+378 > \frac{-297d+378}{\left(d-1\right)^2}$

Therefore $P=\frac{-297d+378}{\left(d-1\right)^2}+343$ .

Hope this helps!

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3 years ago

Do the ratios 5:3 and 13:8 form a proportion?

shepuryov [24]

Answer:

Step-by-step explanation:

Each ratio is irreducible, and they are different. Hence they are not the same value, so cannot be a proportion. A proportion is two equal ratios.

5 : 3 = 40 : 24

13 : 8 = 39 : 24 . . . . not the same as 40 : 24

_____

<em>Examples of proportions</em>

5/3 = 40/24 . . . is a proportion

13/8 = 39/24 . . . is a proportion

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3 years ago

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

HACTEHA [7]

First, let's re-arrange to slope-intercept form.

x + 8y = 27

Subtract 'x' to both sides:

8y = -x + 27

Divide 8 to both sides:

y = -1/8x + 3.375

So the slope of this line is -1/8, to find the slope that is perpendicular to this, we multiply it by -1 and flip it. -1/8 * -1 = 1/8, flipping it will give us 8/1 or 8.

So the slope of the perpendicular line will be 8.

Now we can plug this into point-slope form along with the point given.

y - y1 = m(x - x1)

y - 5 = 8(x + 5)

y - 5 = 8x + 40

y = 8x + 45

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3 years ago

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Harrizon [31]

Answer:

Option (2)

Step-by-step explanation:

Given expression is $\frac{2}{(3x-1)}$ ÷ $\frac{6}{6x-1}$