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3 years ago

Help me with this problem please

Mathematics

1 answer:

elixir [45]3 years ago

8 0

Answer:

Step-by-step explanation:

Given

$\frac{1}{3}$ x² - 14 ← substitute x = 9 into the expression

= $\frac{1}{3}$ × 9² - 14

= $\frac{1}{3}$ × 81 - 14

= 27 - 14

= 13

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ankoles [38]

Answer:

Step-by-step explanation:

3 0

3 years ago

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

4 years ago

The lemonade cooler at the class picnic holds 12.5L. One liter is approximately equal to 0.26 gallons. How many gallons does the

lora16 [44]

Answer: There are 3.25 or 3 1/4 gallons in one cooler

Step-by-step explanation:

If one liter is appx .26 gallons we need to multiply the number of liters there are. So 12.5 times .26 to get the answer 3.25

4 0

4 years ago

All members of a class of 27 students participated in at least one event on sports day. 20 students participated in individual e

creativ13 [48]

5 students took part in both individual and team events.

Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Given:

Total students participated = 27

20 students participated in individual events

12 students took part in team events.

We have N(All students) = 27

N(individual) = 20

N(Team)= 12

So,

$N_{\text{individual \; and \; team}} & = N_{\text{individual}} + N_{\text{team}} - N_{\text{All students}}$

=20+12-27

=32-27

Hence, 5 students took part in both individual and team events.

Learn more about data here:

brainly.com/question/10980404

#SPJ4

6 0

2 years ago

The sales tax in your city is %8.8, point, percent, and an item costs \$63$ before tax.

Flura [38]

Answer:

$68.54

Step-by-step explanation:

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3 years ago