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notka56 [123]
1 year ago
15

When I triple my number and add ten, I get my number plus `36.` What is my number?

Mathematics
1 answer:
Mice21 [21]1 year ago
7 0

Based on the information given, the number is 13

<h3>How to determine the number</h3>

From the information given;

Let the number be x

We have that;

3(my number) + 10 = my number + 36

Substitute the number as x, we have;

3x + 10 = x + 36

collect like terms

3x - x = 36 - 10

2x = 26

Make 'x' the subject of formula

x = 26/ 2

x = 13

The number is 13

Thus, based on the information given, the number is 13

Learn more about algebraic expressions here:

brainly.com/question/4344214

#SPJ1

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The formula y = mx + b is called the slope-intercept form of a line. Solve this formula for m
Evgesh-ka [11]

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A French restaurant used 848,540 ounces of cream last year. This year, due to a menu update, it used 40% less. How much cream di
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3 years ago
Find the point(s) on the surface z^2 = xy 1 which are closest to the point (7, 11, 0)
leonid [27]
Let P=(x,y,z) be an arbitrary point on the surface. The distance between P and the given point (7,11,0) is given by the function

d(x,y,z)=\sqrt{(x-7)^2+(y-11)^2+z^2}

Note that f(x) and f(x)^2 attain their extrema, if they have any, at the same values of x. This allows us to consider the modified distance function,

d^*(x,y,z)=(x-7)^2+(y-11)^2+z^2

So now you're minimizing d^*(x,y,z) subject to the constraint z^2=xy. This is a perfect candidate for applying the method of Lagrange multipliers.

The Lagrangian in this case would be

\mathcal L(x,y,z,\lambda)=d^*(x,y,z)+\lambda(z^2-xy)

which has partial derivatives

\begin{cases}\dfrac{\mathrm d\mathcal L}{\mathrm dx}=2(x-7)-\lambda y\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dy}=2(y-11)-\lambda x\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dz}=2z+2\lambda z\\\\\dfrac{\mathrm d\mathcal L}{\mathrm d\lambda}=z^2-xy\end{cases}

Setting all four equation equal to 0, you find from the third equation that either z=0 or \lambda=-1. In the first case, you arrive at a possible critical point of (0,0,0). In the second, plugging \lambda=-1 into the first two equations gives

\begin{cases}2(x-7)+y=0\\2(y-11)+x=0\end{cases}\implies\begin{cases}2x+y=14\\x+2y=22\end{cases}\implies x=2,y=10

and plugging these into the last equation gives

z^2=20\implies z=\pm\sqrt{20}=\pm2\sqrt5

So you have three potential points to check: (0,0,0), (2,10,2\sqrt5), and (2,10,-2\sqrt5). Evaluating either distance function (I use d^*), you find that

d^*(0,0,0)=170
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So the two points on the surface z^2=xy closest to the point (7,11,0) are (2,10,\pm2\sqrt5).
5 0
3 years ago
NEED HELP! ASAP! 50 POINTS!
Lerok [7]

Answer:

y=13\text{ miles per gallon}

Step-by-step explanation:

We have the two points: (0, 11) and (3, 50).

And we want to find the rate of change in y relative to x, where x is the gallons and y is the miles.

In simple terms, we want to find the slope between the two points.

So, let's use the slope formula:

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Let (0, 11) be (x₁, y₁) and let (3, 50) be (x₂, y₂). Substitute. Let's also put "miles" in the numerator with the Ys and "gallons" in the denominator with the Xs. This yields:

y=\frac{50-11\text{ miles}}{3-0\text{ gallons}}

Subtract and reduce:

y=39\text{ miles}/3\text{ gallons}=13\text{ miles per gallon}

And we're done!

6 0
3 years ago
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