Change 12x-6y=24 into slope-intercept form

colleen purchased a large bag of apple. She used 1/2 of them to make applesauce. of those she had left,she used 3/4 to make an a

Brut [27]

I think the answer is 4 1/4

5 0

3 years ago

The perimeter of a rectangular baking sheet is 58 inches and its area is 201.25 in.2. What are the length and width of the bakin

anzhelika [568]

Answer:

$Length=17.5\ in\\\\Width=11.5\ in$

Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

And the formula for calculate the peimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

We know that the perimeter of the rectangular baking sheet is 58 inches and its area is 201.25 in². Then:

$A=201.25\ in^2\\\\P=58\ in$

The steps are:

1. Solve for the "l" from the formula $A=lw$ :

$A=lw\\\\l=\frac{A}{w}\\\\\l=\frac{201.25}{w}$

2. Substitute $l=\frac{201.25}{w}$ into the formula $P=2l+2w$ and solve for "w":

$58=2(\frac{201.25}{w})+2w\\\\58=\frac{402.5}{w}+2w\\\\58=\frac{402.5+2w^2}{w}\\\\58w=402.5+2w^2\\\\2w^2-58w+402.5=0$

Applying the Quadratic formula $x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$ , we get:

$x=w=\frac{-(-58)\±\sqrt{(-58)^2-4(2)(402.5)}}{2(2)}\\\\w_1=17.5\\\\w_2=11.5$

3. Substitute $w_1=17.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{17.5}=11.5$

4. Substitute $w_2=11.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{11.5}=17.5$

Therefore, since the value of the lenght of a rectangle must be greater that the value of the width, we can conclude that the lenght and the width of the rectangular baking sheet are:

$l=17.5\ in\\\\w=11.5\ in$

8 0

3 years ago

Brent purchased a used vehicle that depreciates under a straight-line method. The initial value of the car is $7500, and the sal

Ilia_Sergeevich [38]

Let the value of the vehicle be described by the equation
V = a + bx
where x = number of years since purchase
a,b are constants.

When x = 0, V = $7500. Therefore
a + b*0 = 7500
a = 7500

When x = 7, V = $500. Therefore
7500 + 7b = 500
7b = 500 -7500 = -7000
b = -7000/7 = -1000

The equation is
V = 7500 - 1000x

The slope of this equation is the depreciation rate, and it is -$1000 per year.

Answer: $1000 depreciation per year.

5 0

3 years ago

Rashi borrowed rs 12000 from a bank . if the bank charges interest at the rate of 11 percent p.a. what amount will he pay to ban

Vlada [557]

Answer:

INTEREST=Rs 3960

Step-by-step explanation:

INTEREST=PTR/100

INTEREST=12000*3*11/100

INTEREST=3960

3 0

2 years ago

Read 2 more answers

Please help! if abcd is dilated by a factor of 3, the coordinate of b would be

Nikolay [14]

Answer:

(-6, 6)

Step-by-step explanation:

The coordinates of B to start with is

(-2, 2)

To dilate this by a factor of 3....

-2 * 3 = -6

2 * 3 = 6

The new coordinates of B' would be

(-6, 6)

A few things to know:

- The number 3 is called a "scale factor"

- Dilation means we are multiplying all the (X, Y)'s by the scale factor

- If the scale factor is greater than 1, the size of the shape overall increases

- If the scale factor is less than 1, the size of the shape overall decreases

- If the scale factor is negative, the shape size stays the same. The shape just rotates 180 degrees and moves to the opposite quadrant.

7 0

2 years ago

Read 2 more answers