MATHEMATICS HIGH SCHOOL

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if parallelogram ABCD is proven to be a rectangle?

Answers

Answer 1

Answer:

Option 3.

Step-by-step explanation:

A parallelogram is said to be a rectangle if

1. Opposite pair of lines are equal and parallel

2. Adjacent lines meet each other at 90 degrees.

Hence we have third option which satisfies both the conditions.

Answer 2

Answer:

Answer:

Step-by-step explanation:

I just took the mastery test and got 100 for plato

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Which inequality represents all the values of x for which the product below is defined?xA: x≥-1B: x≥4C:x≤4D:x≥0
Answer this please !!!!!!
Number 6 mainly and any other if you want to help:) looka t the pic
Find y for x= 1,2,3,and 4y=2x y=3x+1 y=x-5 y=-5x+6

-4x-8 and -4(x-2) *
A: Yes, they are equivalent
B: No, they're not equivalent

Answers

Answer:

Step-by-step explanation:

The problem on the right works out to -4x+8 and the right is -4x-8

so one is + and one is -

1.) A ladder is leaning against the side so that the distance on the ground betweenthe base and the house is 7 feet.
If the ladder is 15 feet long, then what is the angle at which the ladder is leaning?

Answers

The angle at which the ladder is leaning is 62.18°.

What is trigonometry?

Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.

For the given situation,

The length of the ladder = 15 feet

The distance between the house and the ladder base = 7 feet

The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.

we know that, $cos$ θ = $(Base)/(Hypotenuse)$

The figure below shows the relationship between the sides.

⇒ $cos$ θ = $(7)/(15)$

⇒ θ = $cos^(-1)((7)/(15) )$

⇒ θ = $62.18$

Hence we can conclude that the angle at which the ladder is leaning is 62.18°.

Learn more about trigonometry here

brainly.com/question/24174128

#SPJ2

Answer:

62.182°

Step-by-step explanation:

Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.

a new motor home costs $89000. It is expected to depreciate 9% each year.Find the value of the motor home in 4 years.

Answers

The function which represents the situation is:

$\boxed{y=89000*(0.91)^t}$

where t is the time in years and y is the depreciated value of the motor.

In 4 yars value will depreciated to:

$y=89000(0.91)^4\n \n y=89000(0.6857)\n \n \boxed{y=US\$ \ 61031.71}$

Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below.x – y = 4

x + y = 18

Which two numbers did Mira pick?

(10, 8)

(18, 4)
(20, 16)
(40, 32)

Answers

Based on the description, the system can be explained in equation form as x - y =4, an (x + y)/2 = 18. Based on these equations, we can plus in numbers from the given answers and come up with a solution where both equations are satisfied. The two numbers that satisfy both equations are (20, 16).

Let

x------> the first number

y-----> the second number

Assume $x> y$

we know that

$x-y=4$ ----> equation A

$(x)/(2)+ (y)/(2)=18$

Multiply by $2$ both sides

$x+y=36$ -----> equation B

Adds equation A and equation B

$x-y=4 \nx+y=36\n------- \n x+x=4+36\n 2x=40\n x=20$

Find the value of y

$20-y=4$

$y=20-4=16$

therefore

the answer is the option

$(20,16)$

Factor the following expression completely
X4-y4

Answers

$x^4-y^4=\left(x^2\right)^2-\left(y^2\right)^2=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)\n\n\na^2-b^2=(a-b)(a+b)$

1)(x-y)(x+y)(x^2+y^2)
=(x^2-y^2)(x^2+y^2)
=x^4-y^4

2)(x-y)^2(x+y)^2
=(x^2-2xy+y^2)(x^2+2xy+y^2)
=x^4+y^4

3)(x-y)^4
=x^4-4x^3y+6x^2y^2-4xy^3+y^2

4)(x^2-y^2)(x^2+y^2)
=x^4-y^4

I need an answer to this "How many tickles does it take to make an octopus laugh

Answers

Answer:

it takes ten tickles for an octopus to laugh

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