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3 years ago

5

A car is traveling at a rate of 72 kilometers per hour. What is the car's rate in meters per second? How many meters will the ca

r travel in 15 seconds? Do not round your answers.

1 answer:

Korolek [52]3 years ago

8 0

72 Kilometers = 72000 meters

1 hour = 3600 seconds

So if 72000m = 3600 secs
To find 1 sec, divide through by 3600
20m = 1 sec
To find the distance travelled in 15 secs we multiply by 15
300m = 20 secs

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Help:<br> <img src="https://tex.z-dn.net/?f=1.%5C%20%26x%5E4-61x%5E2%2B900%3D0%20%5C%5C%202.%20%5C%20%26%20x%5E4-25x%5E2%2B144%3

yawa3891 [41]

$\bf{1) \ x^4-61x^2+900=0 }$

Applying the factorization method, for example:

$\bf{ 0=(x^2)^2-61(x^2)+900=(x^2-36)(x^2-25)}$

$\bf{\\ &=(x+6)(x-6)(x+5)(x-5); }$

$\bf{ x_1=6 \quad x_2=-6 \quad \ \ \ x_3=5 \quad x_4=5 }$

$\bf{2) \ x^4-25x^2+144=0 }$

Applying the factorization method:

$\bf{0&=(x^2)^2-25(x^2)+144=(x^2-16)(x^2-9) }$

$\bf{ =(x-4)(x+4)(x-3)(x+3); }$

$\bf{ x_1=4 \quad x_2=-4 \quad x_3=3 \quad x_4=-3 }$

7 0

2 years ago

Is this equation true or false? 4(-5) = (-25)

aleksandr82 [10.1K]

4*-5 is -20 is does not equal -25 so it’s false

3 0

3 years ago

Which equation represents the line that passes through (-6, 7) and (-3, 6)

Tju [1.3M]

Plug the given x and y values (x, y) into the equations and solve
It look like the second equation is the answer.
$6 = - \frac{1}{3} ( - 3) + 5 \\ 6 = 1 + 5 \\ true$

4 0

3 years ago

Read 2 more answers

what is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube

Dmitrij [34]

Let the least possible value of the smallest of 99 cosecutive integers be x and let the number whose cube is the sum be p, then

$\frac{99}{2} (2x+98)=p^3 \\ \\ 99x+4,851=p^3\\ \\ \Rightarrow x=\frac{p^3-4,851}{99}$

By substitution, we have that $p=33$ and $x=314$ .

Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>

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

3 years ago