Suppose that 600 yards of fencing material are available to fence in

two adjacent rectangular corrals sharing a common fence. Find the

dimensions of the corrals that will enclose a maximum area (Please help)

Answer:

  x + y = 3 (infinite solutions)

Step-by-step explanation:

You observe that all of the numbers in the second equation are multiples of 3. When you divide the second equation by 3, it becomes identical to the first equation. The equations are said to be "dependent."

That means both equations graph as the same line, so will intersect at every point on the line. The system of equations has an infinite number of solutions.

_____

Additional comments

There are a number of ways to solve a system of equations. Two methods commonly taught are "substitution" and "elimination". Either one works here.

We can solve the first equation for y by subtracting x from both sides:

  x +y -x = 3 -x

  y = -x +3 . . . . . . simplify

In this form, the slope is the coefficient of x. Here, it is -1.

This expression for y can be substituted into the other equation:

  3x +3(-x +3) = 9

  3x -3x +9 = 9 . . . . . eliminate parentheses

  9 = 9 . . . . . . . . . . . simplify

This is true for all values of x or y. There are an infinite number of solutions.

Answer:

There are infinite numbers of solution.

Step-by-step explanation:

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\small\begin{cases}\sf{x + y= \bf{3}} \\ \\ \sf{3x + 3y= \bf{9}}\end{cases} \end{gathered}\end{gathered}\end{gathered}[/tex]

Solving the question and finding the final answer.

Here,

Now, from equation (i),

[tex]\twoheadrightarrow{\sf{x + y = 3}} [/tex]

[tex]\twoheadrightarrow{\sf{x = 3 - y}} [/tex]

Now, putting the value of x in equation (ii)

[tex]\begin{gathered} \qquad{\longrightarrow{\sf{3x + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{3(3 - y) + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 3y + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 0 = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 0 = 9}}} \\ \\ \qquad{\longrightarrow{\sf{\underline{\underline{\red{9 = 9}}}}}}\end{gathered}[/tex]

This statement is true for all values of x and y.

So, there are infinite numbers of solution.

[tex]\underline{\rule{220pt}{3pt}}[/tex]

Answer:

The answer is 6 cause khan acadamy

Step-by-step explanation:

Answer:

slope = 3/7 or 0.43

Step-by-step explanation:

use the slope(gradient) formula

Answer:

The ladder reaches [tex]15ft[/tex]

Step-by-step explanation:

In the first case we have

[tex]cos\theta =\frac{12}{15}[/tex]

In second case let the height be [tex]x[/tex]

We have

[tex]sin\theta =\frac{x}{25}[/tex]

We know that

[tex]cos\theta =\frac{12}{15}\\\\sin\theta =\sqrt{1-\frac{12^{2}}{15^{2}} } \\\\sin\theta =\sqrt{\frac{81}{225} } \\\\sin\theta =\frac{9}{15} }[/tex]

Substituting

[tex]\frac{9}{15} =\frac{x}{25}\\\\x=\frac{25\times9}{15} =15[/tex]

The ladder reaches [tex]15ft[/tex]

Answer:

10π

Step-by-step explanation:

First, remember the formula for the circumference of a circle is C= 2πr. Then remember that the diameter is twice the radius.

So here, when we have a diameter of 10ft, and we see the formula for circumference is C= 2πr, and because a Diameter is equal to 2 radii, I can also say C= Dπ. So in your case C= 10ft×π = 10ftπ

Answer:

Step-by-step explanation:

We assume the graph is a plot of Sean's distance from home as he drives to work, works 8 hours, then drives home with a 2-hour stop along the way. It also appears that t is measured in hours after midnight.

The graph shows Sean's distance from home between 9 a.m. and 5 p.m. (t=17) is 20 km. Based on our assumptions, ...

  Sean's workplace is located 20 km from his home.

__

Speed is the change in distance divided by the change in time. Between 8 a.m. and 9 a.m. Sean's position changes by 20 km. His speed is then ...

  (20 km)/(1 h) = 20 km/h

  Sean's speed driving to work was 20 km/h.

__

Between 5 p.m. (t=17) and 7 p.m. (t=19), Sean's position changes from 20 km to 10 km from home. That change took 2 hours, so his speed was ...

  (10 km)/(2 h) = 5 km/h

  Sean's speed between 5 p.m. and 7 p.m. was 5 km/h.

_____

Additional comment

The units of speed (kilometers per hour) tell you it is computed by dividing kilometers by hours. ("Per" in this context means "divided by".)

While the slope of the line on the graph between 5 p.m. and 7 p.m. is negative, the speed is positive. The negative sign means Sean's speed is not away from home, but is toward home. When the direction (toward, away) is included, the result is a vector called "velocity." Speed is just the magnitude of the velocity vector. It ignores direction.

Answer:

W= 2

Step-by-step explanation:

Answer:

Linear functions are equations where the greatest power of the variable (typically x) is 1;

They are graphed as straight lines;

So, any function that has the following format:

f(x) = ax + b;

Nonlinear functions would be any equation that has a variable to a power greater than 1;

This could be a quadratic equation or an exponential equation

Answer:

a₄ = - 26

Step-by-step explanation:

Substitute n = 4 into the nth term formula

a₄ = 6 - 2(4)² = 6 - 2(16) = 6 - 32 = - 26

Answer:

.........................

......

Answer:

1/10

Step-by-step explanation:

630/6300 = 0.1

0.1*100 = 10

10% a.k.a 1/10

Hope this helped!

Answer: To to find the percentage, you simply need to divide 45 by 60:

Step-by-step explanation:

45/60= .75

Move the decimal from the .75 over 2 times which would get you 75% on his test. So he got a 75%

Answer:

75%

Step-by-step explanation:

To find the percentage of questions Darren got correct, first create a fraction.

question's correct/total question's so 45/60

Then, convert the fraction to a percent.

45/60 = 0.75 =75%

So, Darren got 75% of the questions correct.

hope i helped

Answer:

y= 2, x= -1   (-1, 2)

Step-by-step explanation:

y= x + 3

y= -x+1

substitute y= -x+1

-x + 1 = x + 3

isolate x

-x + 1 = x + 3

x + 1 - x = x + 3 - x

After isolating x you'll get x = -1

for y= - x + 1

y= - (-1) + 1

simplify y = 2

solution:

y= 2, x= -1   (-1, 2)

Answer:

1/2

Step-by-step explanation:

Answer:

Paul has 1/2 of a dollar.

Step-by-step explanation:

A haft of a dollar is 50 cents since 1 dollar is 100 cents so the fraction simplified would be 1/2 or 50/100.

Answer:

The answer is  $22.79. Hope this helped! If the answer is wrong i'm super sorry!

Step-by-step explanation:

$13.50 + $8 = $21.50

0.06 x 21.50 = $1.29

$1.29 + $21.50 = $22.79

Answer:

9√10

Step-by-step explanation:

3√15 x 6  = √90

3√90 = 3 x √9 x √10

3 √90 = 3 x 3 √10 = 9√10

Answer: Her estimate is incorrect because she has to have 25 trucks to be able to ship all her boxes.

Step-by-step explanation: Divide 539 by 22 and if there is a remainder then you need to have one more because you cant take half a truck.

539/22=24.5. Since there is a remainder, you will need 25 trucks total

Answer:

(9 ^ 3) x 0.04 (4/99)

Step-by-step explanation:

This seems overwhelming, but after simplifying, it will look much easier

Numerator (First Row)

First, we will combine like terms and simplify the top row

(9 ^ x + 1) x 8 - (9 ^ x - 1) x 81

(9 ^ x + 1) - (9 ^ x - 1) x (8 x 81)

(9 ^ 2x) x 648

Denominator (Second Row)

Next, we can combine like terms and simplify the second row

(9 ^ x) x 66 - (9 ^ x - 2) x 243

(9 ^ x) - (9 ^ x - 2) x (66 x 243)

(9 ^ 2x + 2) x 16,038

Simplify

Our expression is now

(9 ^ 2x) x 648

(9 ^ 2x + 2) x 16,038

We can simplify it as

(9 ^ 3) x 0.04 (4/99)

Answer:

$150

Step-by-step explanation:

750/5 = 150

Answer:

4.7 kilograms

Step-by-step explanation:

[ 1000 g = 1 kg ]

Change 4700g into kg,

→ 4700 ÷ 1000

→ 4.7 kg

Answer:1. (1,2)    2.(-1,0)

Step-by-step explanation:

1.  5x-4(-3x+5)=3  x=1             2. 3(2y-1)-2y=-3    y=0                                                  

y=-3x1+5    y=2 Plug them in                       X=2x0-1            x=-1       plug them in                

Answer:

C (5,4)

Step-by-step explanation:

(x,y)

fist number in the ordered pair is the X value

Second number in the ordered pair is the Y value

A (-3,0) means you go 3 spaces to the left in the negative direction and zero spaces in the Y axis

B(-2,1) means you go 2 spaces to the left on the x axis (negative) and 1 space up (positive) in the Y axis

C (5,4) means you go 5 spaces to the right on the x axis (positive) and 4 spaces up on the Y axis (positive)

After doing all of these we see that C does not end up on the line

Answer:

graph 4

Step-by-step explanation:

Answer:

your answer is the last option

Step-by-step explanation:

There is no way to prove what the length for line WU is. You can find the side lengths for VW and VU but not WU. Therefore the last option is the correct answer

Answer:

y>5.5

Step-by-step explanation:

4y+3>2y+14

Subtract 2y from both sides.

2y+3>14

Subtract 3 from both sides.

2y>11

Divide 2 by both sides.

y>5.5

-hope it helps

the (y) and mean 1 and you need to multiply al number

Answer:

n

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers.

Answer: times

Step-by-step explanation:

Answer:

$750

Step-by-step explanation:

simple interest equation is:

I (interest) = P (principal) x R (interest rate, as a decimal) x T (time, in years)

I = 7500 x .02 x 5

I = 750

Answer:30 tacos and 70 burritos

Step-by-step explanation:

inequality 1: y≤110−x shade down

inequality 2:y≥80− 1/2x Shade up

Answer (30,70)

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