MATHEMATICS HIGH SCHOOL

-x + y = 2
3х – 5у = -4
solve the system of linear equation by substitution

Answers

Answer 1
Answer: X=-2 + y
X=5y-4/3
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Numbers 20 - 22 please
Write in function form X+y=6..?
Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube?

Square root of 64 over 25

Answers

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Knowing that 64 = 8^2\quad\text{and}\quad25 = 5^2, we have

\sqrt{(64)/(25)} = (√(64))/(√(25)) = \boxed{(8)/(5)}
so \sqrt{(64)/(25) }

that is equal to  ( √(64))/( √(25)) = (8)/(5)

Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining balance of $0. Which equation represents the relationship between y, the remaining balance on Renata’s gift card, and x, the number of songs purchased?

Answers

$20 bought 16 songs
Therefore each song costs $20/16 = $5/4 = $1.25
So:
2 songs would cost 2 * $1.25
3 songs would cost 3 * $1.25
...
x songs would cost x * $1.25

Since Renata started with $20, then her balance (y) after buying x songs would be:

y = 20 - 1.25*x

The equation that represents the relationship between the remaining balance and the number of songs purchased is y = $20 - $1.25x.

What is the equation?

The first step is to determine the cost of one song.

Cost of one song = $20 / 16 = $1.25

Remaining balance = value of the gift card - (number of songs purchased x cost of one song)

y = $20 - $1.25x

To learn more about mathematical equations, please check: brainly.com/question/26427570

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Please Help me Check the image below!!!!!

Answers

Answer:

First question:

The graph of  y=(3-2x)/(2-3x) has a vertical asymptote at x =  (2)/(3)and a horizontal asymptote at y =  (2)/(3)

Second question:

The graph of equation y=(1-3x)/(2+x) has a horizontal asymptote at y = -3 ⇒ C

Step-by-step explanation:

The vertical asymptotes will occur at the values of x for which make the  denominator is equal to zero

The horizontal asymptotes will occur if:

  • Both polynomials are the same degree, divide the coefficients of the highest degree terms
  • The polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote

First question:

∵ y=(3-2x)/(2-3x)

- To find the vertical asymptote equate the denominator by 0

   to find the value of x

∵ The denominator is 2 - 3x

∴ 2 - 3x = 0

- Add 3x to both sides

∴ 2 = 3x

- Divide both sides by 3

∴ (2)/(3) = x

∴ The graph has a vertical asymptote at x =  (2)/(3)

To find the horizontal asymptote look at the highest degree of x in both numerator and denominator

∵ The denominator and the numerator has the same degree of x

- Divide the coefficient of x of the numerator and denominator

∵ The coefficient of x in the numerator is -2

∵ The coefficient of x in the denominator is -3

∵ -2 ÷ -3 = (2)/(3)

∴ The graph has a horizontal asymptote at y =  (2)/(3)

The graph of  y=(3-2x)/(2-3x) has a vertical asymptote at x =  (2)/(3) and a horizontal asymptote at y =  (2)/(3)

Second question:

The graph has a horizontal asymptote at y = -3

means the numerator and the denominator has same highest degree and the coefficient of the highest degree in the numerator divided by the coefficient of the highest degree in the denominator equal to -3

  • In all answers the numerator and the denominator have the same highest degree
  • Lets look for the coefficients of x up and down to find which one gives quotient of -3

∵ In answer A the quotient is 1 because x up and down have

  coefficient 1

∵ In answer B the quotient is -(1)/(3) because the coefficient of x

   up is 1 and down is -3

∵ In answer D the quotient is -1 because the coefficient of x

   up is 3 and down is -3

∵ In answer C the quotient is -3 because the coefficient of x up

   is -3 and down is 1

∴ The graph of equation y=(1-3x)/(2+x) has a horizontal asymptote at y = -3

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?f(X) 3x4 +2xfox)- (6x -4x5-10 3x2-4

Answers

Answer:
A. (3x²-4x-5)(2x⁶-5)

Explanation:
The fundamental theorem of Algebra states that:
"A polynomial of degree 'n' will have exactly 'n' number of roots"

We know that the degree of the polynomial is given by the highest power of the polynomial.
Applying the above theorem on the given question, we can deduce that the polynomial that has exactly 8 roots is the polynomial of the 8th degree

Now, let's check the choices:
A. (3x²-4x-5)(2x⁶-5)
The term with the highest power will be (3x²)(2x⁶) = 6x⁸
Therefore, the polynomial is of 8th degree which means it has exactly 8 roots. This option is correct.

B. (3x⁴+2x)⁴
The term with the highest power will be (3x⁴)⁴ = 81x¹⁶
Therefore, the polynomial is of 16th degree which means it has exactly 16 roots. This option is incorrect.

C. (4x²-7)³
The term with the highest power will be (4x²)³ = 64x⁶
Therefore, the polynomial is of 6th degree which means that it has exactly 6 roots. This option is incorrect

D. (6x⁸-4x⁵-1)(3x²-4)
The term with the highest power will be (6x⁸)(3x²) = 18x¹⁰
Therefore, the polynomial is of 10th degree which means that it has exactly 10 roots. This option is incorrect

Hope this helps :)
The number of roots of a polynomial is determined by the highest power of the variable after all simplifications has been done. For the first option, after the brackets has been expanded, the highest power of x will be 8. The second option will have the highest power of x as 16. The third option will have the highest power of x as 6 while the last option will have the highest power of x as 10. Therefore, the polynomial function with exactly 8 roots is f(x) = (3x^2 - 4x - 5)(2x^6 - 5).

Find the area of the rectangle with a length of (x^2-2) and a width of (2x^2-x+2)

Answers

area=legnth times width

so multiply them together use distributive property
a(b+c)=ab+ac so
in this problem
(a+b)(c+d+e)=(a+b)(c)+(a+b)(d)+(a+b)(e)

so
x^2-2 times (2x^2-x+2)=(x^2)(2x^2-x+2)-(2)(2x^2-x+2)=(2x^4-x^3+2x^2)-(4x^2-2x+4)
add like terms
2x^4-x^3+(2x^2-4x^2)-2x+4
2x^4-x^3-2x^2-2x+4

A 32 year old mother realized that her age is twice the sum of her two children ages. Her son Jose is two years older than her daughter sophia how old are sophia (x) and Jose (y) ? help me and explain me pls

Answers

Again, guess and test should work perfectly fine.  Since 2(x+y)=32, x+y = 16. Because y-2 =x, y could be = 9 and x = 7. Hope that help!

 jose is 9 and Sophia is 7 because 32 divided by 2= 16 and 9+7=16 and jose is 2 years older so he has to be nine and she is seven!!! hahaha I figured it out finally
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