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3 years ago

M<2 = 4x - 26, m<3 = 3x + 4

Mathematics

1 answer:

mestny [16]3 years ago

8 0

Answer:

m<2 = 4x - 26 = 4(30) - 26 = 94 degrees

m<3 = 3x + 4 = 3(30) + 4 = 94 degrees

Step-by-step explanation:

Congruent angles are equal, so m<2 = m<3

4x - 26 = 3x + 4

x = 30

m<2 = 4x - 26 = 4(30) - 26 = 94 degrees

m<3 = 3x + 4 = 3(30) + 4 = 94 degrees

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Given the functionf ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20

vladimir1956 [14]

<em>x = -4 is a vertical asymptote for the function.</em>

<h2>Explanation:</h2>

The graph of $y=f(x)$ is a vertical has an asymptote at $x=a$ if at least one of the following statements is true:

$1) \ \underset{x\rightarrow a^{-}}{lim}f(x)=\infty\\ \\ 2) \ \underset{x\rightarrow a^{-}}{lim}f(x)=-\infty \\ \\ 3) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty \\ \\ 4) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty$

The function is:

$f(x)=\frac{x^2+7x+10}{x^2+9x+20}$

First of all, let't factor out:

$f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20} \\ \\ f(x)=\frac{x(x+5)+2(x+5)}{x(x+5)+4(x+5)} \\ \\ f(x)=\frac{(x+5)(x+2)}{(x+5)(x+4)} \\ \\ f(x)=\frac{(x+2)}{(x+4)}, \ x\neq 5$

From here:

$\bullet \ When \ x \ approaches \ -4 \ on \ the \ right: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(-4^{+}+2)}{(-4^{+}+4)} \\ \\ \\ The \ numerator \ is \ negative \ and \ the \ denominator \\ is \ a \ small \ positive \ number. \ So: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=-\infty$

$\bullet \ When \ x \ approaches \ -4 \ on \ the \ left: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(-4^{-}+2)}{(-4^{-}+4)} \\ \\ \\ The \ numerator \ is \ a \ negative \ and \ the \ denominator \\ is \ a \ small \ negative \ number \ too. \ So: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=+\infty$

Accordingly:

$x=-4 \ is \ a \ vertical \ asymptote \ for \\ \\ f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20}$

<h2>Learn more:</h2>

Vertical and horizontal asymptotes: brainly.com/question/10254973

#LearnWithBrainly

5 0

3 years ago

A rectangular Corn Hole area at the Recreation Center has a width of 5 feet and a length of 10 feet. If

inysia [295]

Answer:

2 feet

Step-by-step explanation:

Let

x ----> the uniform amount added to each side

we know that

The algebraic expression that represent this situation is

$(5+x)(10+x)=84$

solve for x

Apply distributive property

$50+ 5x+10x+x^2=84\\x^2+15x-34=0$

solve the quadratic c equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

$x^2+15x-34=0$

$a=1\\b=15\\c=-34$

substitute in the formula

$x=\frac{-15\pm\sqrt{15^{2}-4(1)(-34)}} {2(1)}$

$x=\frac{-15\pm\sqrt{361}} {2}$

$x=\frac{-15\pm19} {2}$

$x=\frac{-15\pm19} {2}=2$

$x=\frac{-15\pm19} {2}=-17$

therefore

The solution is x=2 ft

8 0

3 years ago

What is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4,-6)

LUCKY_DIMON [66]

Answer:

$y + 6 = -2 (x-4)$

Step-by-step explanation:

Point-slope formula is represented by the equation $y-y_1 = m (x-x_1)$ . When knowing a point a line crosses through and its slope, you can write an equation in this form. Substitute the $m$ , $x_1$ , and $y_1$ for real values.

The $m$ represents the slope of the line. Since we know the slope is -2, substitute -2 for $m$ . The $x_1$ and $y_1$ represent the x and y values of the point the line passes through. Since the line passes through (4, -6), substitute 4 for $x_1$ and -6 for $y_1$ . This gives the following answer and equation:

$y-(-6) = -2 (x - (4))\\y + 6 = -2 (x-4)$