Ask question

Ask question

All categories

xxTIMURxx [149]

3 years ago

14

Last month Maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. Let x re

present the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. If she hiked a total of 90 miles, which equation can be used to find the number of times Maria hiked each trail?
A. x + y = 90

B. 5x – 10y = 90

C. 90 – 10y = 5x

D. 90 + 10y = 5x

1 answer:

mars1129 [50]3 years ago

7 0

It's the 3rd equation (which is in a disguised form)...we have

90 - 10y = 5x add 10y to both sides

90 = 5x + 10y

This says that the nmber of tmes she hiked the 5 mile trail (x) plus the number of times she hiked the 10 mile trail (y) = 90 miles

You might be interested in

A line passes through the point (8, -7) and has a slope of

katrin2010 [14]

Answer:

y = 3/4x - 13

Step-by-step explanation:

As we already know the slope, we just need to find the y-intercept.

y = 3/4x +b

-7 = 3/4(8) + b

-7 = 6 + b

-13 = b

y = 3/4x - 13

5 0

2 years ago

Which number is the same as this: 2 (5m + 1) is the same as:

alexira [117]

2(5m+1)
= 2*5m+2
= 10m+2.

The correct answer is 10m+2~

4 0

3 years ago

Hi guys can you guys pls help me with this question

Alex787 [66]

Answer:

A.600

B.980

C.350

D.210

Step-by-step explanation:

just see what the arrow

7 0

2 years ago

There are 28 tables in the cafeteria. Each table has 12 students sitting at it. How many total students are there?

mestny [16]

Answer:

336

Step-by-step explanation:

you just have to do 28*12.

The answer is 336. :D

6 0

2 years ago

Read 2 more answers

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

7 0

2 years ago