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3 years ago

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A rectangular painting has a length of 8 inches and an unknown width, w. The area of the painting is less than 64 square inches.

Which inequality represents the possible values of w?

1 answer:

Kipish [7]3 years ago

3 0

Answer:

The inequality which represents the possible values of w is w < 8.

Step-by-step explanation:

A rectangle has two dimensions, the length(l) and the width(w).

The area of a rectangle is:

$A = lw$

In this question, we have that:

$l = 8, A < 64$

So

$lw < 64$

$8w < 64$

$w < \frac{64}{8}$

$w < 8$

The inequality which represents the possible values of w is w < 8.

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Which polynomial can be simplified to a difference of squares

Mrrafil [7]

<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)$

<h2>Why?</h2>

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

$First=10a^{2}$

$Second=16a^{2}$

$Third=25a^{2}$

$Fourth=24a^{2}$

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

$16a^{2} =(4a)^{2} \\\\25a^{2} =(5a)^{2}$

The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

$16a^{2} -4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2} =(4-1)(4+1)$

So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

$25a^{2} +6a-6a+36=16a^{2}+36=(5a)^{2}+(6)^{2}$

So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}$

7 0

3 years ago

Read 2 more answers

Please help WOrth 10 points

rjkz [21]

Answer:

52 cubic units

Step-by-step explanation:

1. Divide the shape into 2 parts:

The first one: a 2 by 4 by 6 rectangular prism.

The second one: a 1 by 4 by 1 rectangular prism.

2. Find the volumes of the prisms.

2*4*6=48

1*4*1=4

3. Add the two volumes

48+4=52 cubic units (or units^3)

6 0

3 years ago

A sleep time of 15.9 hours per day for a newborn baby is at the 10h percentile of the distribution of sleep times for all newbor

Nuetrik [128]

Answer:

option (D) 16.5

Step-by-step explanation:

Data provided:

Sleep time of , X = 15.9 is at the 10th percentile

Standard deviation, σ = 0.5 hour

also,

10th percentile of normal distribution is

Z = F⁻¹(0.10)

or

Z = - 1.28 (Using Standard Normal distribution)

Now,

$\\Z=\frac{X-\mu}{\sigma}$

or

X = μ + ( σ × Z )

or

μ = X - ( σ × Z )

on substituting the respective values, we get

μ = 15.9 - 0.5 × (-1.28)

or

μ = 16.5

Hence, the correct answer is option (D) 16.5

8 0

2 years ago

A can of tuna fish is a cylinder with a height of 1.75 inches and a diameter of 3 inches. If the can is half full, how many cubi

zlopas [31]

Answer: $6.185in^3$

Step-by-step explanation:

The formula for calculate the volume of a cylinder is:

$V_{cylinder}=\pi r^2h$

r is the radius of the cylinder and h is the height of the cylinder.

Given the diameter of 3 inches, calculate the radius of the cylinder with:

$r=\frac{d}{2}$ (Where d is the diameter)

$r=\frac{3in}{2}=1.5in$

Knowing the height and the radius, you can calculate the volume of the entire can of tuna:

$V_{can}=\pi (1.5)^2(1.75in)=12.37in^3$

As you want to know the cubic inches of tuna that are in the can (volume of tuna), and you know that the can is half full, then:

$V_{tuna}=\frac{V_{can}}{2}\\\\V_{tuna}=\frac{12.37in^3}{2}\\\\V_{tuna}=6.185in^3$

5 0

3 years ago

Read 2 more answers

William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. They have budge

erica [24]

The greatest number of people that William and Debra may invite and still stay within their budget is 63.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Since William and Debra have budgeted $2,500 for their reception. Therefore, their total expenses should be equal to the total expenses in the reception.

Budget = Total expenses

Budget = Reception hall Cleanup charge + $38 per person fee

Let the number of people invited to the party be represented by x,

$2,500 = $100 + $38(x)

2500 = 100 + 38x

2500 - 100 = 38x

2400 = 38x

x = 2400 / 38

x = 63.157 ≈ 63

Hence, the greatest number of people that William and Debra may invite and still stay within their budget is 63.

Learn more about Equation here:

brainly.com/question/14686792

#SPJ1

5 0

1 year ago