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3 years ago

15

Ian land 2/5 of a mile and walked 16/20 of a mile while returning home from school which pair of equivalent fractions can be use

d to find the total distance that he covered

1 answer:

Anarel [89]3 years ago

4 0

Answer:

2/5: 4/5

Step-by-step explanation:

2/5 of a mile : 16/20 of a mile

It can be made equivalent in 2 ways. Either make the first fraction equivalent by multiplying it with 4 or make the second fraction equivalent to the first by dividing it by 4

2*4/5*4: 16/20

= 8/20: 16/20

2. 2/5: 16/4/20/4

= 2/5: 4/5

It is better to choose a smaller fraction as they are easy to solve .

So the total distance he covered = 2/5+ 4/5= 6/5= 1 1/5 miles or 1.20 miles from school to home.

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What is the x-coordinate of the solution of the system?<br> x+y+3<br> 4x-y=-38

steposvetlana [31]

<em>Note: I am assuming the first equation is:</em>

<em>x+y = 3</em>

Answer:

The solution to the system of equations is:

(x, y) = (-2, 36)

Therefore, the x-coordinate of the solution of the system

x = -2

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}x+y=34\\ x-y=-38\end{bmatrix}$

subtracting the equations

$x-y=-38$

$-$

$\underline{x+y=34}$

$-2y=-72$

solve -2y for y

$-2y=-72$

Divide both sides by -2

$\frac{-2y}{-2}=\frac{-72}{-2}$

$y=36$

For x+y=34 plug in y = 36

$x+36=34$

Subtract 36 from both sides

$x+36-36=34-36$

Simplify

$x=-2$

Thus, the solution to the system of equations is:

(x, y) = (-2, 36)

Therefore, the x-coordinate of the solution of the system

x = -2

6 0

3 years ago

How do you solve this ?

mel-nik [20]

I think the anwser is sixteen

4 0

3 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of <em>f</em> :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of <em>g</em> :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So <em>f</em> has a minimum of -7 and a maximum of 299.

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Juan learned that gear ratio refers to the number of times one gear rotates in relation to another gear. The ratio of the gears

Yuri [45]

Let's define variables:
x1: gear 1
x2: gear 2
The relationship between gears is:
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Rewriting:
x1 / x2 = (3/2) / (1/2)
x1 / x2 = (3 * (1/2)) / (1/2)
x1 / x2 = 3
Another unit rate is:
x2 / x1 = (1/2) / (1 1/2)
x2 / x1 = (1/2) / (3/2)
x2 / x1 = (1/2) / (3 * (1/2))
x2 / x1 = 1/3
Answer:
two unit rates to represent the gear ratio are:
x1 / x2 = 3
x2 / x1 = 1/3

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atroni [7]

Answer:

Step-by-step explanation:

Simplifying

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