All categories

2 years ago

PLEASE HELP ME WITH THIS MATH PROBLEM!!

Mathematics

1 answer:

Leviafan [203]2 years ago

6 0

Given : The Area of the Rectangle = x⁴ - 100

We know that : (a + b)(a - b) = a² - b²

⇒ x⁴ - 100 can be written as : (x²)² - (10)²

⇒ (x²)² - (10)² can be written as : (x² + 10)(x² - 10)

We know that, Area of a Rectangle is given by : Length × Width

Comparing (x² + 10)(x² - 10) with Area of the Rectangle formula, We can notice that :

⊕ Length = x² + 10

⊕ Width = x² - 10

Given : Length of the Rectangle is 20 units more than Width

⇒ Width + 20 = Length

⇒ x² - 10 + 20 = x² + 10

⇒ x² + 10 = x² + 10

<u>Answer </u>: x² - 10 represents the width of the rectangle. Because the area expression can be rewritten as (x² - 10)(x² + 10) which equals

(x² - 10)((x² - 10) + 20)

⇒ Option A

You might be interested in

Is the graphed function linear?

djyliett [7]

Nooooooooooooooooooooooo

5 0

2 years ago

Read 2 more answers

The two triangles below are similar.

umka2103 [35]

I have a picture of the work for it but I don’t know how to upload it I can put a file maybe!

3 0

1 year ago

Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the

Bond [772]

Answer:

1) Vertex point (-1.5,-20.25)

2) axis of symmetry: x=-1.5

3) x-intercepts: (-6,0) and (3,0)

4) y-intercept: (0,18)

5) Graph in attachment.

Step-by-step explanation:

1) The given parabola has equation:

$y = {x}^{2} + 3x - 18$

We need to complete the square.

$y = {x}^{2} + 3x + {1.5}^{2} - {1.5}^{2} - 18$

$y = ( {x + 1.5)}^{2} - 20. 25$

This function is in the vertex form:

$y = a( {x - h)}^{2} + k$

where (h,k) is the vertex, x=h is the axis of symmetry.

By comparing our equation to the general vertex form:

The vertex point is (-1.5,-20.25)

2) The axis of symmetry divides the parabola into two congruent halves.

Since this is a vertical parabola, the axis of symmetry occuring at x=h is a vertical line.

The axis of symmetry is x=-1.5

3) Y-INTERCEPT.

The y-intercept is the point where the graph cross the y-axis.

At this point, the value of x is zero.

To find the y-intercept, we substitute x=0 in the equation of the parabola and simplify.

when x=0,

$y = {(0)}^{2} + 3(0) - 18 = - 18$

The y-intercept is (0,-18).

4) X-INTERCEPT

The x-intercepts are the points where the graph touches or intersect the x-axis.

To find the x-intercept, we substitute y=0.

$( {x + 1.5)}^{2} - 20.25 = 0$

Add 20.25 to both sides;

$( {x + 1.5)}^{2} = 20.25$

Take square root.

$(x + 1.5)= \pm \sqrt{20.25}$

$x = - 1.5\pm 4.5$

$x = - 1.5 - 4.5 \: \: or \: \: x = - 1.5 + 4.5$

$x = - 6 \: or \: x = 3$

The x-intercepts are(-6,0) and (3,0).

4) GRAPH

To graph this function, we can use transformation.

To graph the function,

$y = {(x + 1.5)}^{2} - 20.25$

We shift the parent quadratic function 1.5 units left and 20.25 units down.

See attachment for graph.

5 0

2 years ago

What is the additive inverse of -4a

ANEK [815]

The additive inverse of something is the number that, if you add it to the original number, you get 0.

The additive inverse of 5, for example, is -5. 5 plus -5 = 0.

You should be able to see how additive inverses are always going to be just the original number with the signs changed. (i.e., times -1)

The additive inverse of -4a would be 4a. -4a + 4a = 0.

3 0

2 years ago

Select all that apply.

irinina [24]

Answer: Circle.

Depending on the angle and the place of intersection, when a plane intersects a cube, the sections created may be a square, a pentagon, a trapezoid, a triangle or a rectangle (even you can obtain an octagon), but you will never get a circle.

5 0

2 years ago