What is 431.1 divided by 45

Katrina buys a 42-ft roll of fencing to make a rectangular play area for her dogs.

vekshin1

Answer:

(a) $l = -w + 21$

(b) Domain: $0$ (See attachment for graph)

(c) $f(w) = -w + 21$

Step-by-step explanation:

Given

$2(l + w) = 42$

$l = length$

$w = width$

Solving (a): A function; l in terms of w

All we need to do is make l the subject in $2(l + w) = 42$

Divide through by 2

$l + w = 21$

Subtract w from both sides

$l + w - w = 21 - w$

$l = 21 - w$

Reorder

$l = -w + 21$

Solving (b): The graph

In (a), we have:

$l = -w + 21$

Since l and w are the dimensions of the fence, they can't be less than 1

So, the domain of the function can be $0$

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To check this

When $w = 1$

$l = -1 + 21$

$l = 20$

$(w,l) = (1,20)$

When $w = 20$

$l = -20 + 21$

$l = 1$

$(w,l)= (20,1)$

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See attachment for graph

Solving (c): Write l as a function $f(w)$

In (a), we have:

$l = -w + 21$

Writing l as a function, we have:

$l = f(w)$

Substitute $f(w)$ for l in $l = -w + 21$

$l = -w + 21$ becomes

$f(w) = -w + 21$

5 0

3 years ago

1) A basket of apples are given to a group of students. If 3 apples are given to each student, there will be 8 apples left. If 5

sattari [20]

Answer:

1) either 5 or 6 students in the group

2) 6 rooms are booked

Step-by-step explanation:

1) x students

3x + 8 = apples

5 (x-1) + y (the one get less than 5 apples)

3x + 8 = 5 (x - 1) + y

3x + 8 = 5x - 5 + y

2x + y = 13

X 1 2 3 4 5 6

Y 11 9 7 5 3 1

because y < 5 so x = 5 or x = 6

2) x rooms are booked

4x + 20 total students

8 (x-1) + y (the students in room not full))

4x + 20 = 8 (x-1) + y

4x + 20 = 8x - 8 + y

4x + y = 28

X 1 2 3 4 5 6

Y 24 20 16 12 8 4

y < 8 answer is 6 rooms

4 0

3 years ago

You are biking to the park. After six minutes 40% of the distance still need to be traveled. How long does it take to bike to th

nikklg [1K]

Answer:

$y = (100-10x)\%$

It takes 10 minutes to the park.

Step-by-step explanation:

Given that:

Time taken = 6 minutes

Distance left to be traveled = 40%

To find:

The equation to represent the distance $y$ , that still needs to be traveled after $x$ minutes.

Solution:

As per given statement, distance traveled in 6 minutes = 60%

We can say that:

Distance traveled each minute = $\frac{60\%}{6}$ = 10%

After 1 minute, distance traveled = 10%

Distance left = 100 - 10 = 90%

After 2 minutes, distance traveled = 20%

Distance left = 100 - 20 = 80%

After $x$ minutes, distance traveled = 10 $x$ %

Distance left, $y$ = (100 - 10 $x$ )%

Therefore, the equation is:

$y = (100-10x)\%$

Time taken by the bike to reach to the park can be found by putting $y$ = 0 (i.e. distance left to be traveled = 0)

$0 = 100 -10x\\\Rightarrow 10x = 100\\\Rightarrow x = \bold{10\ minutes}$

8 0

2 years ago

4+3(3x + 1) = 29 - 2x

Mademuasel [1]

Answer:

Step-by-step explanation:

4 + 9x + 3 = 29 - 2x

9x + 7 = 29 - 2x

11x = 22

x = 2

6 0

3 years ago

Read 2 more answers

Aaron has a triathlon. Sunday he bikes 12 5/8 miles and swims 5 2/3 miles. Monday, he runs 6 3/8 miles. How many total miles Aar

Alla [95]

Let’s put these into one fraction each:

Biking:
= (12*5)/8 miles
= 60/8 miles
This can be reduced to,
= 15/2 miles

Swimming:
= (5*2)/3 miles
= 10/3 miles

Running:
= (6*3)/8 miles
= 18/8 miles
This can be reduced to,
= 9/4

Now we add all the distances up:
= (15/2) + (10/3) + (9/4)

Now we just can add the numerators and the denominators. We must find the lowest common factor (LCF) for our 3 denominators (2,3,4). Our LCF turns out to be 12. *Remember what we do to the denominator we must do to the numerator. So:
= (15/2) + (10/3) + (9/4)
= [(15*6)/12] + [(10*4)/12] + [(9*3)/12]
= (90/12) + (40/12) + (27/12)
= (157/12)
Therefore Aaron Ran 157/12 miles or 13.08 miles.

Hope this helps!

4 0

3 years ago