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vladimir2022 [97]
2 years ago
8

You are using a sturdy building material to design a water fountain basin for a park in the city. The bottom and sides of the ba

sin should be 1 foot thick. Its outer length should be twice its outer width an outer height. Let x represent the outer height and outer width.
1. Use the interior length, interior width, interior height, and the volume to write a polynomial equation that represents the situation.

2. Write the polynomial equation in standard form.

3. Factor the polynomial equation and solve for x.

4. Determine the lengths of the basin.

Mathematics
1 answer:
Luden [163]2 years ago
7 0

Answer:

Social media is a computer-based technology that facilitates the sharing of ideas, thoughts, and information through the building of virtual networks and communities. By design, social media is Internet-based and gives users quick electronic communication of content. Content includes personal information, documents, videos, and photos. Users engage with social media via a computer, tablet, or smartphone via web-based software or applications.

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Y =-15/8 -x
y=-9/8 -7x
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3 years ago
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Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.
Mice21 [21]

Answer:

<em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

Step-by-step explanation:

Making factors of 8y^{6}+ 144y^{5}+ 640y^{4}

Taking 8y^{4} common:

\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)

Using <em>factorization</em> method:

\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times  4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)

Now, Making factors of 2y^{4} + 40y^{3} + 200y^{2}

Taking 2y^{2} common:

\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)

Using <em>factorization</em> method:

\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10)        ............ (2)

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is 2y^{2} (y+ 10).

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

HCF \times LCM = p \times q

Using equations <em>(1)</em> and <em>(2)</em>: \Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)

Hence, <em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

5 0
2 years ago
A kitchen wall tile is shaped like a parallelogram. The base of the tile is two times the height of the tile . The height of the
SIZIF [17.4K]

Answer:

12.5 in²

Step-by-step explanation:

Given:

Height of tile = 2.5 in

Base of tile = 2*height of tile = 2*2.5 = 5 in

Length of other side of tile = 2.5 in

Required:

Area of the tile

SOLUTION:

Area of the tile = area of parallelogram

All we need to calculate the area of the tile, is the base and the height.

Area of parallelogram = base × height

Area of tile = 5 × 2.5 = 12.5 in²

5 0
3 years ago
What are the domain and range of the function f(x)= square rootx-7+9?
FinnZ [79.3K]

Answer:

Domain: [7, ∞)

Range: [9, ∞)

Step-by-step explanation:

1) This question may be easily answered if you are aware of the shape of the graph of sq. root x, and the effect of translations to graphs.

1. x - 7 means that the original graph is translated 7 units in the positive direction of the x-axis (ie. to the right), thus the minimum value for x is also shifted from 0 to 7

2. the + 9 means that the graph is translated 9 units in the positive direction of the y-axis (ie. up), thus the minimum y-value is also shifted from 0 to 9

3. We know that the graph will continue to infinity, both in the x- and y-direction

Thus, the domain would be [7, ∞) and the range [9, ∞)

2) Another way to think about it is to ask yourself when it would make sense for the graph to exist. For this, we must consider that you cannot take the square root of a negative number.

Thus, if we have the square root of (x - 7), for what value of x would (x - 7) be negative? If x = 7:

x - 7 = 7 - 7 = 0

Therefor, any x-value less than 7 will lead to a negative answer, which wouldn't be practical. Any value equal to or greater than 7 will lead to a positive answer, thus the permissible values for x are from 7 to infinity, and so the domain is [7, ∞) (note that square brackets are used for 7 as it is included in the domain, whereas infinity is always closed with round brackets).

If we have already found the domain, then we can simply substitute the values for this into the equation to obtain the range (note that this will work for a square root function, however some functions will have turning points and in this case you must calculate the range based on the turning points as well as the minimum and maximum x-values):

if x = 7: y = sq. root (7-7) + 9

= 9

This is the minimum value for y

if we have x = ∞, then the y value will also be infinitely great, therefor the maximum y-value is also ∞. Thus, the range is [9, ∞).

These questions are much easier to solve however if you are already aware of the basic graph and the effect of dilations, translations and reflections so that you may visualise it better.

4 0
3 years ago
H(m)+42= need help with problem​
kondaur [170]
It depends on H(m) what is it?
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2 years ago
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