The partial factorization of x2 – 3x – 10 is modeled with algebra tiles. Which unit tiles are needed to complete the factorizati

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

Leona [12618]

Answer:

The upper limit for the height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> represent the height of the prism

It is known that

the area of the base of the prism must not exceed

$A=L*W$

$A\leq 27\ m^{2}$

thus

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Insert equation B into equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substituting equations B and D into inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The resultant solution for x lies in the interval----------> $[0,12]$

consult the attached figure

but bear in mind that

The width of the base must be $9$ meters shorter than the height of the prism

thus

the solution for x is confined to the interval ------> $(9,12]$

The maximum height of the prism equals $12\ m$

8 1

3 months ago

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Evaluate 0.1m+8-12n0.1m+8−12n0, point, 1, m, plus, 8, minus, 12, n when m=30m=30m, equals, 30 and n=\dfrac14n= 4 1 n, equals,

PIT_PIT [12445]

Answer:

8

Step-by-step explanation:

The task is to evaluate:

0.1m + 8 - 12n

When $m=30, n=\frac{1}{4}$

By substituting these values into the expression, we have:

$0.1m+8-12n=0.1(30)+8-12(\frac{1}{4})\\=3+8-\frac{12}{4}\\=3+8-3\\=8$

8 0

1 month ago

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Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length

tester [12383]

Answer:

y=4x+7.75; continuous

Step-by-step explanation:

Let’s first establish the equation. Julie requires one segment of yarn measuring 7.75 inches: that's already known.

y = 7.75

Now, for the four pieces of yarn, each will be of equal length x. If she wants them to measure 1 inch, she'd need 4 inches of yarn. Therefore, the calculation would be:

y = 7.75 + 4x

Now, is this graph discrete or continuous? Continuous indicates there's a smooth line without gaps, while discrete has interruptions or spaces. In this scenario, x is continuous, as Julie can cut the yarn to any size for the four pieces. She is not limited to whole numbers; each piece could be, for instance, 2.5 inches or 3.1415 inches.

5 0

3 months ago

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QUESTION THREE (30 MARKS) 3.1 The mass of a standard loaf of white bread is, by law meant to be 700g with a population standard

lawyer [12517]

Utilizing the normal distribution and the central limit theorem, there's a 0.0284 or 2.84% chance of observing a sample mean mass of 695g or less.

7 0

2 months ago

A job calls for installing 270 lighting fixtures. If 81 fixtures have been installed so far, what

tester [12383]

70%Step-by-step explanation:First, determine how many fixtures are left to install.270-81=189. The fraction representing the work still to be done is the count of fixtures to install divided by the total amount. So, % of work remaining equals 189 divided by 270, which equals 0.7. Converting this to percentage form gives us 0.7 * 100% = 70%.

5 0

1 month ago