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lbvjy [14]
2 years ago
15

If the polynomial x5 − 105 can be split as the product of the polynomials x − 10 and a, what is a? x4 − 99,990 x4 + 10x3 + 100x2

+ 1,000x − 10,000 x4 + 10x3 + 100x2 + 1,000x + 10,000

Mathematics
2 answers:
katrin2010 [14]2 years ago
3 0
X^4+10x^3+100x^2+1000x+10000
nordsb [41]2 years ago
3 0

Answer:

x^4 + 10x^3 + 100x^2 + 1,000x + 10,000

Step-by-step explanation:

Here, the given polynomial,

x^5-10^5

Since, it can be split as the product of the polynomials x − 10 and a,

So, we can write,

a(x-10) = x^5-10^5

\implies a = \frac{x^5-10^5}{x-10}

By the long division ( shown below ),

We get,

a=x^4 + 10x^3 + 100x^2 + 1,000x + 10,000

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What is the linear function equation that best fits the data set?
slavikrds [6]

Answer:

Option 3

Step-by-step explanation:

Given data set is,

{(1.5, 1), (2.5, 3), (3, 3), (3, 5), (3.5, 5), (4.5, 7), (5, 7), (5, 9), (5.5, 9), (6.5, 11), (7.5, 13)}

By using linear regression calculator,

Equation of the linear function will be,

y = 2x - 2

Therefore, Option 3 will be the correct option.

8 0
3 years ago
What are the solutions to the system of equations? y=2x^2−6x+3 y=2x+3
adoni [48]

Answer:

Step-by-step explanation:

y=2x²-6x+3

y=2x+3

2x²-6x+3=2x+3

2x²-6x+3-2x-3=0

2x²-8x=0

2x(x-4)=0

x=0,4

y=0+3=3

and y=2(4)+3=11

so solutions are (0,3) and (4,11)

5 0
2 years ago
Haley earns $55 for every house that she cleans but it costs her $6 in cleaning products per house.What are Haley’s earnings tot
Marysya12 [62]

55n - 6n

49n

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6 0
2 years ago
Read 2 more answers
Please help ASAP! Thanks! For the figures below, assume they are made of semicircles, quarter circles and squares. For each shap
bazaltina [42]

Answer:

Part 1) A=36(\pi-2)\ cm^2

Part 2) P=6(\pi+2\sqrt{2})\ cm

Step-by-step explanation:

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

so

A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)

we have that the base and the height of triangle is equal to the radius of the circle

r=12\ cm\\b=12\ cm\\h=12\ cm

substitute

A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)

A=(36\pi-72)\ cm^2

simplify

Factor 36

A=36(\pi-2)\ cm^2

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

<em>The circumference of a quarter of circle is equal to</em>

C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r

substitute the given values

C=\frac{1}{2}\pi (12)

C=6\pi\ cm

The hypotenuse of right triangle is equal to (applying the Pythagorean Theorem)

AC=\sqrt{12^2+12^2}

AC=\sqrt{288}\ cm

simplify

AC=12\sqrt{2}\ cm

Find the perimeter

P=(6\pi+12\sqrt{2})\ cm

simplify

Factor 6

P=6(\pi+2\sqrt{2})\ cm

6 0
3 years ago
What is the area of this shape?
zysi [14]
Area = L x H

area = 20 x 15 = 300 square feet
3 0
3 years ago
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