MATHEMATICS HIGH SCHOOL

The length of a rectangle is twice the with. If the perimeter of the rectangle is 60 units, find the area of the garden

Answers

Answer 1

Answer:

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60 divide both sides by 6

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200

Answer: The area of the garden is equal 200 square units.

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A coin is tossed 8 times. Which of the following represents the probability of the coin landing on heads all 8 times?

Answers

Answer:

$\large\boxed{\large\boxed{Probability=1/256\approx 0.0039}}$

Explanation:

Since, there are two possible outcomes for every toss (head or tail), the sample space for a coin tossed 8 times is 2×2×2×2×2×2×2×2 = 2⁸ = 256.

Landing on heads all 8 times is just one of the possible outcomes: HHHHHHHH ⇒ 1.

Hence, the probability is calculated from its own definition:

Probability = number of favorable outcomes / number of possible outcomes

$Probability=1/256\approx 0.0039\text{ }\leftarrow answer$

Answer:

1/256

Step-by-step explanation:

Which represents the solution(s) of the system of equations, y = x2 – 4x – 21 and y = –5x – 22? Determine the solution set algebraically.(–1, –17)
(1, –27)
(–1, –17) and (1, –27)
no solutions

Answers

Answer:

D. No solutions.

Step-by-step explanation:

We have been given a system of equations and we are asked to find the solution set for our given system.

$y=x^2-4x-21$

$y=-5x-22$

To find the solution for our given system we will equate our both equations as:

$x^2-4x-21=-5x-22$

$x^2-4x+5x-21=-5x+5x-22$

$x^2+x-21=-22$

$x^2+x-21+22=-22+22$

$x^2+x+1=0$

We will use discriminant formula to check for the solution of our given system.

$√(b^2-4ac) \geq 0$ for real solutions.

Upon substituting our given values in above formula we will get,

$√(1^2-4*1*1) \geq 0$

$√(1-4) \geq 0$

$√(-3) \ngeq 0$

Therefore, our given system has no solutions and option D is the correct choices.

Answer:

Step-by-step explanation:

on edge 2021

Solve the system of equations below by graphing both equation . what is the solution?

Answers

y=2x-3
y=-2x+5
2x-3 = -2x+5
4x=8
x=2
y=2(2)-3
y=1
the answer is A.(2,1)

What is the discriminant and number of solutions to the problem- y=2x2+6x+12

Answers

Δ = b² - 4ac
Δ = (6)² - 4(2)(12)
Δ = 36 - 4(24)
Δ = 36 - 96
Δ = -60

y = 2x² + 6x + 12
0 = 2x² + 6x + 12
0 = 2(x²) + 2(3x) + 2(6)
0 = 2(x² + 3x + 6)
2 2
0 = x² + 3x + 6
x = -(3) ± √((3)² - 4(1)(6))
2(1)
x = -3 ± √(9 - 4(6))
2
x = -3 ± √(9 - 24)
2
x = -3 ± √(-15)
2
x = -3 ± i√(15)
2
x = -1.5 ± 0.5i√(15)
x = -1.5 + 0.5i√(15) or x = -1.5 - 0.5i√(15)

The discriminant is -60 and the number of solutions is 2.

Solve: 3x + 1 = 3

With working out

Answers

$3x + 1 = 3 \n \n3x + 1-1 = 3 -1\n \n 3x = 2 \n \n (3x)/(3) = (2)/(3) \n \n x = (2)/(3)$

$3x+1 =3 \n \n 3x =3 -1 \n \n 3x =2 \n \n \n (3x)/(3) = (2)/(3) \n \n x = (2)/(3) \n \n \framebox[1.1\width]{Good Luck!} \par$

The height of an object after it is released can be modeled by the function f (x) = negative 16 t squared v t s, where t is the number of seconds after the object is released, v is the upward speed in feet per second at release, and s is the starting height in feet. if a quarterback throws a ball from his hand 6 feet in the air at an upward speed of 25 feet per second, how much time does his teammate have to catch the ball?

Answers

The amount of time his teammate have to catch the ball is equal to 1.774 seconds.

Given the following function:

f(x) = -16t² + vt + s.

Displacement, s = 6ft.

Velocity, v = 25 ft/s.

How to calculate the amount of time?

In order to determine the amount of time his teammate have to catch the ball, we would evaluate the given position-time function as follows:

f(t) = -16t² + 25t + 6.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c =0

Where:

a = -16.

b = 25.

c = 6.

Solving the function by using the quadratic formula, we have:

t = [-b ± √(b² - 4ac)]/2a

t = [-25 ± √[(25² - 4(-16)(6))]/2(-16)

t = [25/32 ± (-1/32)√1009]

t = 25/32 ± (-0.993)

t = 0.781 ± 0.993

t = 0.781 + 0.993

Time, t = 1.774 seconds.

Note: We ignored the negative value because time cannot be negative.

Read more on quadratic equation here: brainly.com/question/1214333

Answer:

Step-by-step explanation:

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On the basis of data from 1990 to 2006, the median income y in year x for men and women is approximated by the equations given below, where xequals0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, in what year will the median income of men and women be the same?Men: -255x+2y=56,937Women: - 842x+3y=42,751