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Mashutka [201]
3 years ago
6

The width of a rectangle is 2 inches smaller than its length. The perimeter is 24 inches. Find the length and width of the recta

ngle.
Mathematics
1 answer:
Travka [436]3 years ago
4 0

Answer:

7 inches and 5 inches

Step-by-step explanation:

The length the length and width of the rectangle be l and b.

Accodrding to question,

Width, b = l-2

Perimeter, P = 24 inches

We know that,

The perimeter of a rectangle is given by :

P = 2(l+b)

24 = 2(l+l-2)

12 = 2l-2

14=2l

l = 7 inches

Width, b = 7-2 = 5 inches

Hence, the length and width of the rectangle are 7 inches and 5 inches respectively.

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The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?
daser333 [38]

Answer:

d=\frac{3}{2}=1.5

Step-by-step explanation:

We have the function:

y=a(x-2)(x-1)

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

d=\frac{1+2}{2}=3/2=1.5

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

x=-\frac{b}{2a}

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

x=-\frac{-3a}{2a}=\frac{3}{2}=1.5

Confirming our answer.

4 0
3 years ago
Solve the equation 4x - 6 = x + 3. Check your solution.
eimsori [14]
,
4x - 6 = x + 3

4x - x = 3 + 6

3x = 9

Divide by 3

x = 3
5 0
2 years ago
Read 2 more answers
There are x number of students at helms. If the number of students increases by 7.8% each year, how many students will be there
vodomira [7]

There will be 1.078x students next year and equation is number of students in next year = x + 7.8% of x

<h3><u>Solution:</u></h3>

Given, There are "x" number of students at helms.  

The number of students increases by 7.8% each year which means if there "x" number of students in present year, then the number of students in next year will be x + 7.8% of x

Number of students in next year = number of students in present year + increased number of students.

\begin{array}{l}{\text { Number of students in next year }=x+7.8 \% \text { of } x} \\\\ {\text { Number of students in next year }=x\left(1+\frac{7.8}{100}\right)} \\\\ {\text { Number of students in next year }=x(1+0.078)=1.078 x}\end{array}

Thus there will be 1.078x students in next year

3 0
3 years ago
The total cost of 5 boxes of pasta is $13.00. Each box of pasta costs the same amount.
schepotkina [342]

Answer:

$2.60

Step-by-step explanation:

13.00÷5=2.6

6 is in tens placement

8 0
2 years ago
I can't seem to figure this out
antiseptic1488 [7]

Answer:

c. 4

Step-by-step explanation:

tan (30)/1 = x/7 *cross multiply*

x = 7 (tan(30))

x = 4.04

x = 4

6 0
3 years ago
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