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3 years ago

Why is 8.8 classified as a rational number?

1 answer:

4 0

A rational number can be expressed as the ratio of two integers.

$\frac{a}{b}$

Where a and b are integers and b is not equal to 0.

The rational number 8.8 can be expressed as two integers. Like $\frac{8.8}{1}$

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Please help i’m so stuck i can’t do calc for the life of me

KATRIN_1 [288]

Answer:

$-3x^2+29x-150+\frac{946x^2-341x-756}{x^3+6x^2-3x-5}$ is the answer. See steps below.

Step-by-step explanation:

$\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}\\\\-3x^5+11x^4+33x^3-26x^2-36x-6\\\\\mathrm{and\:the\:divisor\:}x^3+6x^2-3x-5:\\\\\mathrm{Quotient}=\frac{-3x^5}{x^3}=-3x^2\\\\\mathrm{Multiply\:}x^3+6x^2-3x-5\mathrm{\:by\:}-3x^2\:\:\rightarrow\:\:-3x^5-18x^4+9x^3+15x^2\\\\\mathrm{Subtract\:}-3x^5-18x^4+9x^3+15x^2\mathrm{\:from\:}-3x^5+11x^4+33x^3-26x^2-36x-6\mathrm{\:to\:get\:new\:remainder}.\\\\\mathrm{Remainder}=29x^4+24x^3-41x^2-36x-6$

$=-3x^2+\frac{29x^4+24x^3-41x^2-36x-6}{x^3+6x^2-3x-5}$

Repeat the steps and you will reach a point where no further division is possible.

$=-3x^2+29x-150+\frac{946x^2-341x-756}{x^3+6x^2-3x-5}$

5 0

3 years ago

A force of 60 N is used to stretch two springs that are initially the same length. Spring A has a spring constant of 4 N/m, and

goblinko [34]

Answer:

D:Spring A is 3 m longer than spring B because 15 – 12 = 3.

Step-by-step explanation:

In this question, you should remember the Hooke's Law in physics.

The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.

The mathematical expression for this law is

$F=-kx$

where;

F= force applied on the spring

x = the extension on the spring

k= the spring constant which varies in spring.

The question will need you to calculate the extension on the springs A and B then compare the values obtained.

In spring A

Force, F=60N and spring constant ,k=4 N/m

To find the extension x apply the expression;

$F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x$

Here the spring extension is 15 m

In spring B

Force, F=60N and spring constant , k=5N/m

To find the extension x apply the same expression

$F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x$

Here the extension on the spring is 12 m

Compare

The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m

$=15m-12m=3m$

5 0

3 years ago

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?

HACTEHA [7]

Answer:

Option (1)

Step-by-step explanation:

Fundamental theorem of Algebra states degree of the polynomial defines the number of roots of the polynomial.

8 roots means degree of the polynomial = 8

Option (1)

f(x) = (3x² - 4x - 5)(2x⁶- 5)

When we multiply (3x²) and (2x⁶),

(3x²)(2x⁶) = 6x⁸

Therefore, degree of the polynomial = 8

And number of roots = 8

Option (2)

f(x) = (3x⁴ + 2x)⁴

By solving the expression,

Leading term of the polynomial = (3x⁴)⁴

= 81x¹⁶

Therefore, degree of the polynomial = 16

And number of roots = 16

Option (3)

f(x) = (4x² - 7)³

Leading term of the polynomial = (4x²)³

= 64x⁶

Degree of the polynomial = 6

Number of roots = 6

Option (4)

f(x) = (6x⁸ - 4x⁵ - 1)(3x² - 4)

By simplifying the expression,

Leading term of the polynomial = (6x⁸)(3x²)

= 18x¹⁰

Degree of the polynomial = 10

Therefore, number of roots = 10

3 0

3 years ago

To make fruit punch for a party, Alison used 3 quarts of pineapple juice and 2 gallons if orange juice. There are 4 quarts in a

REY [17]

Since we know there are 3 quarts of pineapple juice and 2 gallons of orange juice the first thing you need to do is convert the units of the orange juice to quarts.
If there are 4 quarts in a gallon and we have 2 gallons then we have 8 quarts (4*2)
So 3 quarts of pineapple juice to 8 quarts of orange juice.
The ratio would be 3:8

3 0

3 years ago

Read 2 more answers

Need help asap pls!!!

lisabon 2012 [21]

Answer:

Step-by-step explanation:

According to the given description, PS is the mid segment of the $\triangle TQR$

Therefore by Mid-segment Theorem:

$PS = \frac{1}{2} QR \\ \\ PS = \frac{1}{2} \times 32 \\ \\ PS =16 \:$

3 0

3 years ago