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3 years ago

If the two angles below are supplementary, solve for x.

Mathematics

2 answers:

vagabundo [1.1K]3 years ago

6 0

$\bf \stackrel{\textit{supplementary angles add up to }180^o}{(7x)+(5x+24)=180}\implies 12x+24=180\\\\\\12x=156\implies x=\cfrac{156}{12}\implies x=13$

IrinaVladis [17]3 years ago

3 0

Supplementary angles always equal 180. Then you just solve from there.

7x+5x+24=180
12x+24=180
-24 -24
12x=156
/12 /12
X=12

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

4 years ago

The sum of John and Sally’s ages is 24. John is 6 years older than Sally. Which system of equations below represents this relati

tankabanditka [31]

J+S=24 and J=S+6 represents the relationship between ages.

John is 15 years old and Sally is 9 years old.

Step-by-step explanation:

Let,

John's age = J

Sally's age = S

According to given statement, the sum of their ages is 24;

$J+S=24$ Eqn 1

John is 6 years older than Sally means we will add 6 in Sally's age;

$J=S+6$ Eqn 2

Putting value of J from Eqn 2 in Eqn 1;

$(S+6)+S=24\\S+6+S=24\\2S=24-6\\2S=18$

Dividing both sides by 2

$\frac{2S}{2}=\frac{18}{2}\\S=9$

Putting S=9 in Eqn 2

$J=9+6\\J=15$

J+S=24 and J=S+6 represents the relationship between ages.

John is 15 years old and Sally is 9 years old.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

4 0

4 years ago

What is the y-value of point A?

Marianna [84]

Answer:

Step-by-step explanation

1,6

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3 years ago

One of the tallest living men has a height of 236 cm. One of the tallest living women is 224 cm tall. Heights of men have a mean

Roman55 [17]

Answer:

A. The woman is relatively taller because the z score for her height is greater than the z score for the man's height.

Step-by-step explanation:

Whoever has the highest z-score, is taller relative to the population of the same gender.

The z-score of a value X in a set with mean $\mu$ and standard deviation $/sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

Solution:

Heights of men have a mean of 170 cm and a standard deviation of 6 cm. One of the tallest living men has a height of 236 cm. So the z-score of his height is:

$Z = \frac{X - \mu}{\sigma} = \frac{236-170}{6} = 11$

Heights of women have a mean of 161 cm and a standard deviation of 5 cm.

One of the tallest living women is 224 cm tall. The z-score of the women's height is

$Z = \frac{X - \mu}{\sigma} = \frac{224-161}{5} = 12.6$

The women has a higher z-score, so she is relatively taller.

The correct answer is A

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4 years ago

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Citrus2011 [14]

Answer:

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Step-by-step explanation:

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