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2 years ago

Given that y varies directly as x, and y= 27 when x = 54. Find the value of x when y = 54?

Mathematics

1 answer:

Aleonysh [2.5K]2 years ago

8 0

X equals 54 and y equals 27

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Eli uses 1/4 pound of apples to make 4 servings of fruit salad. He uses the same amount of apples for each serving. What amount

DochEvi [55]

Answer:

1/16 pound

Step-by-step explanation:

1/4 ÷ 4 = 1/4 x 1/4 = 1/16

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4 years ago

An object falls from a position of rest and

kumpel [21]

Answer:

About 4.1323 meters.

Step-by-step explanation:

We can use the following kinematic equations:

$\displaystyle v_f = v_0 + at \text{ and } \Delta d = v_0 t + \frac{1}{2} at^2$

We want to determine the distance the object has dropped after falling from rest and reaching an instantenous speed of 9 m/s.

We are given that the acceleration due to gravity is 9.8 m/s².

Using this fact and the first equation, find the time for which it took the object to reach 9 m/s. Note that the initial velocity is 0 m/s since the object started from rest.

$\displaystyle \begin{aligned} v_f = v_0 + at \\ \\ (9\text{ m/s}) & = (0\text{ m/s}) + (9.8\text{ m/s$^2$})t \\ \\ 9\text{ m/s} & = (9.8 \text{ m/s$^2$})t \\ \\ t &\approx0.9184 \text{ s} \end{aligned}$

To find how far the object dropped, we can use the second equation:

$\displaystyle\begin{aligned} \Delta d & = v_0 t + \frac{1}{2} at^2 \\ \\ & = (0\text{ m/s})(0.9184 \text{ s}) + \frac{1}{2}(9.8 \text{ m/s$^2$})(0.9184 \text{ s})^2 \\ \\ & = 4.1323 \text{ m} \end{aligned}$

In conclusion, the object would have dropped about 4.1323 meters.

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3 years ago

Find a common solution for each system of equations:<br> y=3x+5<br> y=-5x-3

Nina [5.8K]

$\left\{\begin{array}{ccc}y=3x+5\\y=-5x-3\end{array}\right\\\\substitution\ method\\\\3x+5=-5x-3\\3x+5x=-3-5\\8x=-8\ \ \ \ \ /:8\\x=-1\\\\y=3(-1)+5=-3+5=2\\\\Solution:x=-1\ and\ y=2.$

$graphing\ method\\\\ \left\{\begin{array}{ccc}y=3x+5\\y=-5x-3\end{array}\right\\------------------\\y=3x+5\\y-intercept\ (x=0)\\y=3(0)+5=5\\(0;\ 5)\\x-intercept\ (y=0)\\3x+5=0\\3x=-5\\x=-\frac{5}{3}\\(-\frac{5}{3};\ 0)\\---------------------$
$y=-5x-3\\y-intercept\ (x=0)\\y=-5(0)-3=-3\\(0;-3)\\x-intercept\ (y=0)\\-5x-3=0\\-5x=3\\x=-\frac{3}{5}\\(-\frac{3}{5};\ 0)\\\\Solution:((-1;\ 2)\to x=-1\ and\ y=2.$

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