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2 years ago

A projector displays an image on a wall. the area(in square feet) of the rectangular projection can be represented by

Mathematics

1 answer:

andrew-mc [135]2 years ago

3 0

Answer:

The height of the projection will be (x - 5) feet.

Step-by-step explanation:

A projector displays an image on a wall. The area (in square feet) of the rectangular projection can be represented by (x² - 8x + 15).

Now to get the width and the height of the rectangular projection we have to factorize the expression (x² - 8x + 15).

Here, (x² - 8x + 15)

= x² - 3x - 5x + 15

= (x- 3)(x - 5)

Now, if the height of the projection is less than its width then, the height of the projection will be (x - 5) feet. (Answer)

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Find the zeros of the function. f(x) = 2x2 – 2x – 12

Amiraneli [1.4K]

Answer:

Step-by-step explanation:

2x^2-2x-12

This has solutions of x=3 and x= -2

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2 years ago

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A fruit bowl contains apples, oranges, and bananas. The radius of one of the oranges is 1.25 inches. What is the approximate vol

Elden [556K]

Answer:

8.18 cubic inches

Step-by-step explanation:

An orange is a sphere so you will use the formula for the volume of a sphere.

V= 4 /3 * π * r^3 r^3= 1.25* 1.25 * 1.25= 1.953

V= 4/3* 3.14 * 1.953 = 8.176=8.18

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3 years ago

An equivalent expression with a rational denominator is...

Whitepunk [10]

Given the expression,

$(8x-56x^2)/(\sqrt{14x-2})$

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

$[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]$

If we have $(\sqrt{a})(\sqrt{a})$ , we will get $\sqrt{a^2}$ by multiplying them. And $\sqrt{a^2} = a$ .

So here in the problem, we will get,

$[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)$

Now in the numerator we have $(8x-56x^2)$ . We can check 8x is common there. we will take out -8x from it, we will get,

$-8x(-1+7x)$

$-8x(7x-1)$

And in the denominator we have $14x-2$ . We can check 2 is common there. If we take out 2 from it we will get,

$2(7x-1)$

So we can write the expression as

$[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]$

$(7x-1)$ is common to the numerator and denominator both, if we cancel it we will get,

$(-8x)(\sqrt{14x-2})/2$

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

$(-4x)(\sqrt{14x-2})$

$(-4x)(14x-2)^(1/2)$

So we have got the required answer here.

The correct option is the last one.

4 0

2 years ago

What is 8/8 in word form?

dexar [7]

Answer:

EIGHT divided by EIGHT

Step-by-step explanation:

The 8/8 word form is EIGHT divided by EIGHT

6 0

2 years ago

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Use numerals instead of words. If necessary, use / for the fraction bar(s). A parabola is given by the equation y = x2 + 4x + 4.

Anarel [89]

Graph x2 = 4y and state the vertex, focus, axis of symmetry, and directrix.This is the same graphing that I've done in the past: y = (1/4)x2. So I'll do the graph as usual: The vertex is obviously at the origin, but I need to "show" this "algebraically" by rearranging the given equation into the conics form:x2 = 4y Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved
(x – 0)2 = 4(y – 0)This rearrangement "shows" that the vertex is at (h, k) = (0, 0). The axis of symmetry is the vertical line right through the vertex: x = 0. (I can always check my graph, if I'm not sure about this.) The focus is "p" units from the vertex. Since the focus is "inside" the parabola and since this is a "right side up" graph, the focus has to be above the vertex.From the conics form of the equation, shown above, I look at what's multiplied on the unsquaredpart and see that 4p = 4, so p = 1. Then the focus is one unit above the vertex, at (0, 1), and the directrix is the horizontal line y = –1, one unit below the vertex.vertex: (0, 0); focus: (0, 1); axis of symmetry: x = 0; directrix: y = –1Graph y2 + 10y + x + 25 = 0, and state the vertex, focus, axis of symmetry, and directrix.Since the y is squared in this equation, rather than the x, then this is a "sideways" parabola. To graph, I'll do my T-chart backwards, picking y-values first and then finding the corresponding x-values for x = –y2 – 10y – 25:To convert the equation into conics form and find the exact vertex, etc, I'll need to convert the equation to perfect-square form. In this case, the squared side is already a perfect square, so:y2 + 10y + 25 = –x 
(y + 5)2 = –1(x – 0)This tells me that 4p = –1, so p = –1/4. Since the parabola opens to the left, then the focus is 1/4 units to the left of the vertex. I can see from the equation above that the vertex is at (h, k) = (0, –5), so then the focus must be at (–1/4, –5). The parabola is sideways, so the axis of symmetry is, too. The directrix, being perpendicular to the axis of symmetry, is then vertical, and is 1/4 units to the right of the vertex. Putting this all together, I get:vertex: (0, –5); focus: (–1/4, –5); axis of symmetry: y = –5; directrix: x = 1/4Find the vertex and focus of y2 + 6y + 12x – 15 = 0The y part is squared, so this is a sideways parabola. I'll get the y stuff by itself on one side of the equation, and then complete the square to convert this to conics form.y2 + 6y – 15 = –12x 
y2 + 6y + 9 – 15 = –12x + 9 
(y + 3)2 – 15 = –12x + 9 
(y + 3)2 = –12x + 9 + 15 = –12x + 24 
(y + 3)2 = –12(x – 2) 
(y – (–3))2 = 4(–3)(x – 2)Then the vertex is at (h, k) = (2, –3) and the value of p is –3. Since y is squared and p is negative, then this is a sideways parabola that opens to the left. This puts the focus 3 units to the left of the vertex.vertex: (2, –3); focus: (–1, –3)

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2 years ago