MATHEMATICS HIGH SCHOOL

Solve for x and y simultaneously x-2y=3. 3x²-5xy-16y=24

Answers

Answer 1

Answer:

Value of x = 0 or 1 and value of y = $(-3)/(2)$ or -1 for the given quadratic equation.

What is quadratic equation?

" Quadratic equation is defined as the polynomial whose highest degree of the given variable is equals to 2."

According to the question,

Given equations,

$x-2y=3$

⇒ $x=3 + 2y$ ____(1)

Quadratic equation,

$3x^(2) -5xy-16y=24$ ____(2)

Substitute the value of 'x' from (1) in (2) quadratic equation we get,

$3(3+2y)^(2) -5(3+2y)y-16y=24$

⇒ $3(9+12y+4y^(2) )-5y(3+2y) -16y-24=0$

⇒ $27+36y+12y^(2) -15y-10y^(2) -16y-24=0$

⇒ $2y^(2) +5y+3=0$

⇒ $2y^(2) +2y+3y+3=0$

⇒ $2y(y+1)+3(y+1)=0$

⇒ $(2y+3)(y+1)=0$

⇒ $(2y+3)=0 or (y+1)=0$

⇒ $y=(-3)/(2) or y = -1$

Substitute in (1) to get the value of 'x' ,

$x= 3+ 2((-3)/(2)) or x = 3 + 2 (-1)$

⇒ $x = 0 or x = 1$

Hence, value of x = 0 or 1 and value of y = $(-3)/(2)$ or -1 for the given quadratic equation.

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Answer 2

Answer: x-2y=3 ⇒y=(x-3)/2
3x²-5xy-16y=24

We can suggest this system of equations by substitution method.
y=(x-3)/2

3x²-5x(x-3)/2-16(x-3)/2=24
least common multiple=2
6x²-5x(x-3)-16(x-3)=48
6x²-5x²+15x-16x+48=48
x²-x=0
x(x-1)=0
Now, we solve two equations:
1)x=0 ⇒y=(0-3)/2=-3/2
2)x-1=0
x=1 ⇒y=(1-3)/2=-1

Answer: we can two solutions:
solution1: x=0; y=-3/2
solution2: x=1, y=-1

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HELP! a square field has an area of 479 ft squared. what is the approximate length of a side of the field? give your answer to the nearest foot. explain your answer.

Answers

An area of a square is side multiplied by side, so since 479 is the area you would square root it. that would give you 21.88606862823929, just round that up to 22 feet and you got the approximate side length! so there ya go! good luck!

Final answer:

The problem involves finding the side length of a square field given its area. The side length is found by taking the square root of the area. Rounded to the nearest foot, the side length is approximately 22 feet.

Explanation:

The subject here is Mathematics, specifically focusing on geometry. More specifically, the problem is addressing the characteristics of square fields. A square is a shape which has all sides equal in length. The area of a square is calculated by squaring the length of one side (i.e., side * side) or more visually demonstrated as side2.

Given that the area of the square is 479 square feet, you need to find the length of one side. To do this, you would take the square root of the area, because the area of a square field is side2.

Mathematically expressed, this would be:

Side length = √Area
Side length = √479

Using a calculator, you will find the square root of 479 is approximately 21.89. We are asked to give the answer to the nearest foot, so you would round 21.89 to the nearest whole number to get 22 feet. Therefore, the approximate length of a side of the field is 22 feet.

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Name 2 linear expressions whose difference is 5x-4

Answers

For this case we can write the following linear expressions:

We now subtract both linear expressions:

From here, we must subtract similar terms.

We have then:

Rewriting we have:

That is, we obtain the desired result.

Answer:

2 linear expressions whose difference is 5x-4 is:

What is the volume of the pyramid? A rectangular pyramid with a base of 8 centimeters by 6 centimeters and a height of 5 centimeters. 10 centimeters cubed 80 meters cubed 120 centimeters cubed 240 centimeters cubed

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

ABCDEFGH is a regular octagon. The minimum degree of rotation by which this octagon can map onto itself is

Answers

The regular octagon has rotational symmetry. Since it is comprised of 8 "equal parts", divide 360º/8 to determine the smallest angle of rotation. 360º/8 = 45º.

Answer:

The regular octagon has rotational symmetry. Since it is comprised of 8 "equal parts", divide 360º/8 to determine the smallest angle of rotation. 360º/8 = 45º.

Step-by-step explanation:

For a standard normal distribution, which of the following expressions must always be equal to 1?A) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
B) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
C) P(z≤-a)+P(-a≤z≤a)-P(z≥a)
D) P(z≤-a)+P(-a≤z≤a)+P(Z≥a)

Answers

P(z ≤ -a) + P(-a ≤ z ≤ a) + P(z ≥ a) = 1 - P(z ≤ a) + [P(z ≤ a) - P(z ≤ -a)] + 1 - P(z ≤ a) = 2 - 2P(z ≤ a) + P(z ≤ a) - [1 - P(z ≤ a)] = 2 - P(z ≤ a) - 1 + P(z ≤ a) = 1

Therefore, option D is the correct answer.

Answer:

D. $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)$

Step-by-step explanation:

Properties of normal distribution-

The normal curve is symmetrical about the mean (μ).
The mean is at the middle of the graph and it divides the area into two equal halves.
The total area under the curve is equal to 1.

The total area under the curve can be divided into parts like,