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PolarNik [594]
3 years ago
7

What is the difference

Mathematics
1 answer:
azamat3 years ago
6 0

Answer:

4

Step-by-step explanation:

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The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the
yuradex [85]

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

y=x\,(10-x)=10x-x^2

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

y=ax^2+bx+c

is given by the formula:

x_{vertex}=-\frac{b}{2\,a}

which in our case gives:

x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25

8 0
3 years ago
Ava is making punch for the entire class. She mixed 3 gallons of lemonade with every 7 gallons of Hawaiian Fruit Punch to make t
irina [24]

Answer:

3:7

Step-by-step explanation:

3 parts of lemonade to 7 parts punch

5 0
2 years ago
Read 2 more answers
The formula for the cost of buying a car=
svet-max [94.6K]
8000-2600=5400
5400/12=450
monthly pavement =450
12x450+2600=8000
5 0
3 years ago
Where do you find a vertical shift in the exponential parent function?
Montano1993 [528]

For the given expressions we will have:

y = exp(x - 4)   →we have a shift of 4 units to the right.

y = exp (x +9)  → we have a shift of 9 units to the left.

y = exp(x) + 7 → we have a shift of 7 units up.

y = exp(x) - 6  → we have a shift of 6 units down.

<h3>How to work with vertical and horizontal shifts?</h3>

Remember that the shifts work as follows.

For a function f(x), we define a vertical shift of N units as:

g(x) = f(x) + N

  • If N > 0, the shift is upwards.
  • If N < 0, the shift is downwards.

For a function f(x), we define a horizontal shift of N units as:

g(x) = f(x + N)

  • If N > 0, the shift is to the left.
  • If N < 0, the shift is to the right.

Then, if we have:

exp(x - 4) we have a shift of 4 units to the right.

exp (x +9) we have a shift of 9 units to the left.

exp(x) + 7 we have a shift of 7 units up.

exp(x) - 6  we have a shift of 6 units down.

Learn more about translations

brainly.com/question/24850937

#SPJ1

4 0
1 year ago
Solve for x.<br> 4<br> 15<br> 6<br> X<br> x = [?]<br> Enter the number in decimal form
posledela

Answer:

66

Step-by-step explanation:

x / 6 + 4 = 15

To find x ;

Subtrac4 from both sides

x / 6 + 4 - 4 = 15 - 4

x / 6 = 11

Multiply both sides by 6

x / 6 * 6 = 11 * 6

x = 66

Value of x = 66

6 0
3 years ago
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