MATHEMATICS HIGH SCHOOL

Which of the following figures in a plane separates itinto half-planes?
F. A line
G. A ray
H. An angle
J. A point
K. A line segment

Answers

Answer 1
Answer: F. A line

Which of the following figures in a plane separates it into half-planes is a line. In addition, a line is the only given entity or object that can elicit an unlimited and infinite figure to separate the given assumed limitless plane thus, it will unceasingly divide the plane endlessly if given that the plane is unknown in measure and length. For example, a given figure of rectangle with an unknown length or measure, the only figure that can divide itself is the line perpendicularly speaking in its shape or position of the line.



Answer 2
Answer:

Answer:

F. A line

Step-by-step explanation:

A line separates a plane into three parts the line and two half-planes.

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Initially, Greg has a total of 60 DVDs and CDs in his collection. He then sold 1/8 of his CDs and 1/2 of his DVDs. If the number of DVDs he sold is twice the number of CDs he sold, how many DVDs did he sell?

Answers

Greg has 40 CD's and 20 DVD's. He sold 10 DVDs and 1/8 of his CD(40/8 = 5).

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Initially, Greg has a total of 60 DVDs and CDs in his collection.

He then sold 1/8 of his CDs and 1/2 of his DVDs.

Let the number of CD is c and DVD is d

c + d = 60

2(c/8) = d/2

d = 60 - c

4(2c/8) = 4(60-c)/2    

c = 120 - 2c

c = 40

d = 60-40 = 20

Thus, Greg has 40 CD's and 20 DVD's. He sold 10 DVDs and 1/8 of his CD(40/8 = 5).

Learn more about the linear equation here:

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Answer:

10 DVD's were sold.

Step-by-step explanation:

c = number of CD's

d = number of DVD's

so we know:

c + d = 60

2*c/8 = d/2

this can be solved:

d = 60 - c

2c / 8 = (60-c)/2

4*(2c/8) = 4*(60-c)/2    [multiply by 4]

c = 120 - 2c

3c = 120

c = 40

d = 60-40 = 20

So Greg had 40 CD's and 20 DVD's. He sold half of his DVD's, i.e., 20/2=10 and 1/8 of his CD, i.e., 40/8 = 5

Find all solutions to the equation.

sin x = sqrt(3)/2

Answers

Answer:

x=(\pi)/(3) and x=(2\pi)/(3)

Step-by-step explanation:

We are given that sin x=(\sqrt3)/(2)

We have to find all solutions of the given equation

We know that sin (\pi)/(3) =sin60^(\circ)=(\sqrt3)/(2)

sin x is positive then  the value of sin x will lie in I quadrant and II quadrant.The value of sin x is negative in III and IV quadrant .

We are given that sin x is positive then the solution will lie in I and II quadrant only.Therefore, the solution of sin x will not lie in III and  IV quadrant .

sin x =sin (\pi)/(3) ...(I equation )and sin x =sin(\pi-(\pi)/(3))...(II equation)

In II quadrant \theta change into(\pi-\theta )

Cancel  sin on both side of equation I

Then, we get

x=(\pi)/(3)

sin x =sin ((3\pi-\pi)/(3))

sin x =sin (2\pi)/(3)...(II equation )

Cancel sin on both side of equation II

Then we get

x=(2\pi)/(3)

Hence, the solutions of equation are

x=(\pi)/(3) and x=(2\pi)/(3)

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

We have,

The solutions to the equation sin(x) = √3/2 are any angles where the sine of the angle is equal to √3/2.

So,

sin 60 = √3/2

sin 120 = sin (π - 60) = sin 60 = √3/2

In trigonometry 180 is written as π.

Since (π - 60) is in the secondquadrant sin 60 is positive.

sin 420 = sin (360 + 60) = sin 60 = √3/2

In trigonometry 360 is written as 2π.

Since (2π + 60) is in the Firstquadrant sin 60 is positive.

Similarly,

sin 480 = sin (2π + 120) = sin 120 = sin (π - 60) = sin 60 = √3/2

Thus,

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

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Find the final sale price rounded to the nearest cent of a $239 television with a 10% discount.

Answers

Answer:

215

Step-by-step explanation:

239 x .10 = 23.9

239 - 23.9 = 215.1

then to round it would be 215!

Find the positive value of x if: 5^(x^2 - 2x) = 1

Answers

5^(x² - 2x) = 1
5^(x²) - 5^(2x) = 1
5^x² - 5²x = 1

What is the quotient (x3 + 3x2 + 5x + 3) ÷ (x + 1)?x2 + 4x + 9
x2 + 2x
x2 + 2x + 3
x2 + 3x + 8

Answers

Answer:  The correct option is (C) x^2+2x+3.

Step-by-step explanation:  We are given to find the quotient by dividing the following :

Q=(x^3+3x^2+5x+3)/(x+1).

We will try to factorize the numerator ad then divide by the denominator to find the quotient.

We have

Q\n\n\n=(x^3+3x^2+5x+3)/(x+1)\n\n\n=(x^2(x+1)+2x(x+1)+3(x+1))/(x+1)\n\n\n=((x+1)(x^2+2x+3))/((x+1))\n\n=x^2+2x+3.

Thus, the required quotient is x^2+2x+3.

Option (C) is correct.
Hello,

Answer C

x^3+3x²+5x+3=x^3+2x²+3x + x²+2x+3=x(x²+2x+3)+1(x²+2x+3)=(x²+2x+3)(x+1)

Write a following relationship as a ratio using a colon. 2 students out of 10

Answers

We use ratios to make comparisons between two things. When we express ratios in words, we use the word "to"--we say "the ratio of something to something else." Ratios can be written in several different ways: as a fraction, using the word "to", or with a colon.

Let's use this illustration of shapes to learn more about ratios. How can we write the ratio of squares to circles, or 3 to 6? The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6." Finally, we could write this ratio using a colon between the two numbers, 3:6. Be sure you understand that these are all ways to write the same number.

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