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3 years ago

Anona hires a decorator to redecorate her bedroom. The decorator offers her 2 different plans: the basic plan has

Mathematics

1 answer:

ElenaW [278]3 years ago

7 0

Answer:

The correct option is;

x³ + 4·x² + 3·x < x³ + 13·x² + 54·x + 72.

Step-by-step explanation:

The given parameters are;

The basic plan of the decorator = x wall-color options, x + 1 ceiling-colr options, and x + 3 floor options

The gold plan of the decorator = All of the basic plan options plus 3 additional options in each category

Therefore, the gold plan of the decorator = (x + 3) wall-color options, (x + 1 + 3) ceiling-color options, and (x + 3 + 3) floor options

The total number unique layouts offered by the basic plan = x × (x + 1) × (x + 3) = x³ + 4·x² + 3·x

Also, the total number unique layouts offered by the gold plan = (x + 3) × (x + 1 + 3) × (x + 3 + 3) = (x + 3) × (x + 4) × (x + 6) = x³ + 13·x² + 54·x + 72

Which gives;

The comparison between the total number of unique layouts offered by the basic and gold plans as x³ + 4·x² + 3·x < x³ + 13·x² + 54·x + 72.

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Three times one number added to five times another number is 54. The second number is two less than the first. Use a system of e

worty [1.4K]

Answer:

8 and 6

Step-by-step explanation:

If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.

You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.

The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.

Next, we add 10 to both sides. This gives 8x=64.

From there, we isolate the x by dividing both sides by 8, giving x=8.

To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).

This comes to y=8-2, therefore y=6.

**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!

3 0

3 years ago

What are all prime numbers x which:<br> x<10

ivanzaharov [21]

Answer:

5,7,3,2

Step-by-step explanation:

It's pretty simple: a prime number is a number that can *only* be divided by the number 1 and it's own.

I just checked all the numbers from 1 to 10 in order to solve this problem.

If you have any questions about the way I solved it, don't hesitate to ask!

8 0

3 years ago

Given: ∠JOH = 27° and arc NML = 98°. Find the measure of arc JH.

stepladder [879]

We need an image because of this

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3 years ago

Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY.

alisha [4.7K]

A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is D.

<h3>What is a parallelogram?</h3>

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, the opposite sides are equal and parallel to each other. We can write,

AD ≅ BC

Since BX ≅ DY, therefore, we can write,

AB = CD

AX + XB = DY + YC

XB = DY, cancelling both the sides,

AX = YC.

Also, XY is the common side.

Since all the sides are equal also the angle are equal, therefore, it can be written,

AXDY ≅ CYXB

Given the area of CYXB is 71.5 square units. Therefore,

ABCD = CYXB + AXDY

ABCD = 2(CYXB)

ABCD = 143 square units.

Hence, the correct option is D.

Learn more about Parallelogram:

brainly.com/question/1563728

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2 years ago

Four friends are planning to play 18 holes of golf. two of them need to rent clubs at $5 per set. total cart rental is $10. the

natka813 [3]

B how much did the friends pay in green fees

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3 years ago