MATHEMATICS HIGH SCHOOL

Help me find the degree of this polynomial

Answers

Answer 1

Answer:

Answer:

polynomial of degree 8

Step-by-step explanation:

the degree of a polynomial is the value of the exponent of the term with the largest exponent

given

6 $s^(8)$ + 2 $s^(6)$ - 5s

the term with the largest exponent is 6 $s^(8)$ , with exponent of 8

then the polynomial is of degree 8

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Dena's softball team can win (W) or lose (L) each game. Which of the following are elements in the sample space for 2 softball games?

Answers

In a softball game, the odds are only win or lose the game. When 2 games are already being considered, the elements in the sample space are already 2 in each set. The sets are {W,W}, {W,L}, {L,W} and {L,L}. Hence, there are 4 sets all in all to describe the odds of the two games.

How would i solve 4x-3y=8
5x-2y=-11

using the elimination method?
i'm in algebra 1 and we had a sub the day we were doing this and he was terrible explaining the situations on the worksheet. please explain

Answers

To use the elimination method, the coefficient of one variable in one equation must be the opposite number of the coefficient of the same variable in the second equation.

$4x-3y=8 \n5x-2y=-11$

Here you can multiply the first equation by 2, and the second equation by -3.

$4x-3y=8 \ \ |\cdot 2 \n5x-2y=-11 \ \ |\cdot (-3) \n \n8x-6y=16 \n-15x+6y=33$

Now you just add the equations by sides and solve for one variable.

$8x-6y=16 \n \underline{-15x+6y=33 } \n8x-6y-15x+6y=16+33 \n8x-15x=16+33 \n-7x=49 \nx=-7$

Now you solve for the other variable by substituting -7 for x in one of the equations.

$4x-3y=8 \n4 \cdot (-7)-3y=8 \n-28-3y=8 \n-3y=8+28 \n-3y=36 \ny=-12$

You could choose x at the beginning as well. Then you'd have:
$4x-3y=8 \ \ |\cdot (-5)\n5x-2y=-11 \ \ |\cdot 4 \n \n-20x+15y=-40 \n\underline{20x-8y=-44 \ \ \ \ \ \ } \n-20x+15y+20x-8y=-40-44 \n15y-8y=-40-44 \n7y=-84 \ny=-12 \n \n4x-3y=8 \n4x-3 \cdot (-12)=8 \n4x+36=8 \n4x=8-36 \n4x=-28 \nx=-7$

So the answer is:
$x=-7 \n y=-12$

Answer:

x=-7 and y=-12

Step-by-step explanation:

Which of the following is the rational exponent expression of fifth root of 7 n?

Answers

The rational exponent expression of $\sqrt[5]{7n}$ will be $(7n)^(1)/(5)$ .

What is rational exponent ?

Rational exponent are exponents of numbers that are expressed as rational numbers, that is, in $a^{(p)/(q) }$ form.

i.e. $a^{(p)/(q) }=\sqrt[q]{a^n}$

We have,

$\sqrt[5]{7n}$

so, Using the mentioned formula,

$a^{(p)/(q) }=\sqrt[q]{a^n}$

$\sqrt[5]{7n}=(7n)^(1)/(5)$

So, this is the rational expression $(7n)^(1)/(5)$ using above mentioned formula.

Hence, we can say that the rational exponent expression of $\sqrt[5]{7n}$ will be $(7n)^(1)/(5)$ .

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5n7 (7n)5 7 times n to the one fifth power quantity of 7n to the one fifth power

Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.Which product should Tomas choose?

(2x + 1)(2x2 + 2x – 1)
(2x + 1)(4x3 + 2x – 1)
(2x + 1)(4x2 – 2x + 1)
(2x + 1)(2x2 – 2x + 1)

Answers

This is a simple substitution problem. Clearly the answer here is (2x + 1)(4x2 – 2x + 1). We just have to replace a with 2x and b with 1. The tricky part here is the first term in the second group of terms. 2x is to be squared. Common mistake here is raising the x with 2 and not including the coefficient.

The product that Tomas should choose given that the pattern resulted in a sum of cube is (2x + 1)(4x² – 2x + 1)

Data obtained from the question

Polynomial => (a + b)(a² – ab + b²)
a = 2x
b = 1
Product =?

How to determine the product

(a + b)(a² – ab + b²)

But

a = 2x

b = 1

Substituting the value of a and b, we have

(a + b)(a² – ab + b²)

(2x + 1)[(2x)² – (2x × 1) + 1²]

(2x + 1)(4x² – 2x + 1)

Thus, the product that Tomas should choose is (2x + 1)(4x² – 2x + 1)

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A bank pays 5% interest compounded annually. What principal will grow to $12,000 in 10 years.

Answers

Answer: 7366.96 dollars

========================================================

Use the compound interest formula:

A = P(1+r/n)^(n*t)

where in this case,

A = 12000 = amount after t years

P = unknown = deposited amount we want to solve for

r = 0.05 = the decimal form of 5% interest

n = 1 = refers to the compounding frequency (annual)

t = 10 = number of years

-------

Plug all these values into the equation, then solve for P

A = P(1+r/n)^(n*t)

12000 = P(1+0.05/1)^(1*10)

12000 = P(1.05)^(10)

12000 = P(1.62889462677744)

12000 = 1.62889462677744P

1.62889462677744P = 12000

P = 12000/1.62889462677744

P = 7366.95904248911

P = 7366.96

Can you explain 3x+4/5=7/10. Solve

Answers

$3x+ (4)/(5)= (7)/(10)\ \ | -(4)/(5)\n \n3x+ (4)/(5) -(4)/(5)= (7)/(10)-(4)/(5)\n \n3x = (7)/(10)-(8)/(10) \n \n3x = -(1)/(10) \ \ /*(1)/(3)\n \nx=-(1)/(30)$

$or \n \n (3x+ 4)/(5)= (7)/(10) \ \ /*10 \n \n 2(3x+4)=7\n \n6x+8 = 7\ \ |-8$

$6x+8-8=7-8\n \n6x=-1\ \ /:6 \n \n x=-(1)/(6)$

$3x+ (4)/(5)= (7)/(10) \n \n3x= (7)/(10)-(4)/(5)\n \n3x=(7)/(10)-(8)/(10)\n \n3x=- (1)/(10) \ /:3\n \nx=-(1)/(10)\cdot (1)/(3)\n \nx=-(1)/(30)$

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$(3x+4)/(5) = (7)/(10) \n \n10(3x+4)=5\cdot 7\n \n30x+40=35\n \n30x=35-40\n \n30x=-5\ /:30\n \nx=- (5)/(30) \n \nx=-(1)/(6)$

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