2/3 * 2/3 divid (2/5 divide 3/5) answer plz

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

Which of the following is a polynomial with roots 3, 5i, and −5i?

jek_recluse [69]

$x_{1}=3 \\ \\ x_{2}=5i \\ \\ x_{2}=-5i \\ \\ f(x)=(x-x_{1})(x-x_{2})(x-x_{3})=(x-3)(x-5i)(x+5i)= \\ \\ =(x-3)(x^{2}+25)=x^{3}+25x-3x^{2}-75=x^{3}-3x^{2}+25x-75$

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6 0

3 years ago

How many times 6 goes into 31

Tju [1.3M]

It goes in 5 times but with 1 remainder

4 0

3 years ago

Read 2 more answers

1 Which sequence of transformations takes AA to its image, AB ?

lianna [129]

A rigid transformation preserves the dimensions of the image

The option that gives the sequence of transformation that takes ΔB to ΔB is the option B.

(B) Reflection across y-axis and a translation 2 units down

Reason:

Question: The sequence of transformation that takes ΔA to image ΔB

From a similar question, we have, ;

The vertices of triangle ΔA are; (-8, 9), (-9, 4), (-3, 4)

The vertices of triangle ΔB are; (8, 7), (3, 2), (9, 2)

The options are;

(A) Reflection over the x-axis and 2 units translation down

(B) Reflection over the y-axis and 2 units translation down

(C) 90° rotation after a translation of 2 units down

(D) 90° rotation after a translation of 12units right

Solution;

The length of the base of ΔA = -3 - (-9) = 6

The length of the base of ΔB = 9 - 3 = 6

Therefore, the length s of triangle A and triangle B are equal

The orientation of the base of ΔA and ΔB are both horizontal

The location of the the side that traverses four cells are both furthest from the y-axis, or the vertical

Therefore, ΔB is a reflection of ΔA across the y-axis

We also have;

The base of ΔB is 2 units lower than the base ΔA

Therefore, the correct option is option B, reflection across y-axis and a translation 2 units down

Learn more here;

brainly.com/question/23461633

7 0

3 years ago

What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? point:(11, 3)

Galina-37 [17]

Y=4/11x-1

:c) :c) :c)
-Oliver

8 0

3 years ago