$f(x)=3x-23,\ g(x)=-4.5x+7\\\\f(x)=g(x)\iff3x-23=-4.5x+7\qquad\text{add 23 to both sides}\\\\3x=-4.5x+30\qquad\text{add 4.5x to both sides}\\\\7.5x=30\qquad\text{divide both sides by 7.5}\\\\\boxed{x=4}$

6 0

3 years ago

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A bus covers a distance of 90km at a uniform speed. Had the speed been 15km/hour it would have taken 30 minutes less for the jou

Brrunno [24]

Answer:

Step-by-step explanation

Let's say d = distance, r = speed and t = time

We know the distance formula is :

distance = speed x time

d = r multiplied by t

d = rt

If the speed is 15km/hr, the time would be 30 minutes shorter.

Since d = rt,

90 = 15t

t = 6,

This means the time taken for the bus to complete the journey at 15km/hr would be 6hrs.

Originally though, the journey takes 30 minutes longer.

So we can say t = 6.5 hrs , and we know d = 90

Now we use the distance formula:

d = rt, since we want to find the original speed, we want to find r.

Speed = distance/time

r = d/t

r = 90/6.5

r = 180/13

Therefore the original speed is 180/13 km/hr

4 0

3 years ago

lbvjy [14]

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\$

$\bf \cfrac{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{\sqrt{48\pi }}{\sqrt{75\pi }}\implies \cfrac{s}{s}=\cfrac{\sqrt{(2^2)^2\cdot 3}}{\sqrt{5^2\cdot 3}}\implies \cfrac{s}{s}=\cfrac{4\sqrt{3}}{5\sqrt{3}}
\\\\\\
\cfrac{s}{s}=\cfrac{4}{5}$

8 0

2 years ago

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If Mike does his mathematics homework today, the probability that he will do it tomorrow is 0.8. The probability that he will do

harina [27]

Answer:

d. 14:11

Step-by-step explanation:

There is a 7 in 10 chance that Mike does his homework today and a 8 in 10 chance he will do it tomorrow, the probability that he will do it both today and tomorrow is:

$P = \frac{7}{10}* \frac{8}{10}\\P=\frac{56}{100}=0.56$

The odds are the probability that an event occurs over the probability that it does not occur:

$Odds = \frac{0.56}{1-0.56}=\frac{56}{44}=\frac{14}{11}$

The odds that he will do it both today and tomorrow are 14:11.

3 0

3 years ago