MATHEMATICS HIGH SCHOOL

The points -5,2 and -5,8 lie on a circle with a radius of 3. Find the center of the circle.

Answers

Answer 1
Answer:

The formula of a distance between two points:

d=√((x_2-x_1)^2+(y_2-y_1)^2)

We have two points A(-5, 2) and B(-5, 8). Substitute:

d=√((8-2)^2+(-5-(-5))^2)=√(6^2+0^2)=√(6^2)=6

d is a diameter of a circle because d = 2r = 2(3).

The center of a circle is in midpoint of AB.

The formula of a midpoint:

M\left((x_1+x_2)/(2),\ (y_1+y_2)/(2)\right)

Substitute:

(-5+(-5))/(2)=(-10)/(2)=-5\n\n(2+8)/(2)=(10)/(2)=5

Answer: (-5, 5).

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Jordan uses a linear equation to model the data in a table. Which reasoning might Jordan have used in the decision to model the data with a linear equation?The products of corresponding x- and y-values are equal.
The ratios of consecutive y-values are equal for evenly spaced x-values.
The change in y-values is not constant, but the change is constant for evenly spaced x-values.
The change in y-values is constant for evenly spaced x-values.

Answers

The change in x values and y values are proportional to each other for the given case. The correct option is (D).

What is the slope of straight line?

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

In order to form a linear equation from a table,

The slope has to be found first.

For this, the ratio of the difference in the values of x and y are taken.

Which implies that the change in x values are directly proportional to the change in the values of y.

And the proportionality constant is known as the slope.

=> (y₂ - y₁) ∝ (x₂ - x₁)

=>  (y₂ - y₁)/(x₂ - x₁) = m

Hence, the change in y values are constant for change in x values.

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ANSWER:

the answer is D.

How to change 4.1 into a decimal?

Answers

Well you can't change 4.1 into a decimal because it's already a decimal with a decimal point included in it, so there's really no point of asking that question when you've already done it yourself! Just wanted to notify you on that point.
You can't change it to a decimal because it is already a decimal.

For the graph shown, select the statement that best represents the given system of equations.Number graph ranging from negative five to five on the x axis and negative six to four on the y axis. A line with a negative slope is drawn on the graph.
6x + 4y = 2
3x + 2y = 1

A.
not enough information

B.
coincident

C.
consistent and independent

D.
inconsistent

Answers

Answer:

B. coincident

Step-by-step explanation:

An coincident system of equations means that it has infinite solutions, because one line is on the other one. This happens when their equation are the same, or their "parent" line is the same.

So, given equations are:

6x + 4y = 2 and 3x + 2y = 1

Observe that if we divide the first by 2, we have

(6x + 4y)/(2)=(2)/(2)\n(6x)/(2)+(4y)/(2)=1\n  3x+2y=1

As you can see, using the first equation, we found that it has the same "parent" equation than the second equation. In other words, they are basically the same. This means that they represent the same line, so, the system is coincident and they have infinite solutions.

After analyzing the data provided in this question one can conclude that they are coincident. For the first system equation we have: 6x + 4y = 2. If we divide everything by 2 we will get: 3x + 2y = 1. Coincident means the same line.


The answer is choice B). Coincident.

I hope it helps, Regards.

Which fraction is bigger 5/8, 9/16, 1/2, 15/32

Answers

work them out as decimals first to make it easier:
5/8 = 62.5 (5÷8 ×100) <---- Use this equation
9/16 = 56.25
1/2 = 50
15/32 = 46.875
so this means 5/8 is biggest because it makes the biggest decimal.
(5)/(8) , (9)/(16) , (1)/(2) , (15)/(32) \n(5)/(8)= (5)/(8) * (4)/(4)= (20)/(32) \n (9)/(16)= (9)/(16)* (2)/(2)= (18)/(32) \n (1)/(2)= (1)/(2)* (16)/(16)= (16)/(32) \n (15)/(32) \n \n (15)/(32)\ \textless \ (16)/(32) \ \textless \ (18)/(32)\ \textless \ (20)/(32) \n \n (15)/(32)\ \textless \ (1)/(2) \ \textless \ (9)/(16)\ \textless \ (5)/(8)

Mercury is about 57,000,000 from the sun,whereas neptune is about 4.5 x 10 to the 9th power km from the sun. What is the difference between mercury and neptune's distance from the sun

Answers

Answer:

4,443,000,000 or 4.443 * 10^9 km.

Step-by-step explanation:

Neptune's distance from the sun = 4.5 * 10^9

=  4,500,000,000 km.

The required difference is

4,500,000,000 - 57,000,000

= 4,443,000,000  or 4.443 * 10^9.

Final answer:

The difference in distance from the sun between Mercury and Neptune is approximately 4,443,000,000 kilometers.

Explanation:

To find the difference in distance between Mercury and Neptune from the sun, we first need to understand that these distances are given in kilometers (km). Mercury is roughly 57,000,000 km from the sun, and Neptune is approximately 4.5 x 10 to the 9th power km from the sun. The 9th power, or exponent, denotes how many times a number (in this case, 10) is used in a multiplication. Hence, Neptune's distance from the sun is 4.5 x 10^9 km, or 4,500,000,000 km. To get the difference, we subtract Mercury's distance from Neptune's i.e., 4,500,000,000 km - 57,000,000 km = 4,443,000,000 km. So, the difference in distance from the sun between Mercury and Neptune is approximately 4,443,000,000 km.

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Enter the plan width for the rectangular room. Round your answer to the nearest tenth.plan length:
4 in.
actual width:
18 ft
actual length: 16 ft


The plan width is
in.

Answers

Answer:

4.5 inches

Step-by-step explanation:

Given: plan length = 4 inches, actual width = 18 feet, actual length = 16 feet

To find: plan width

Solution:

1 feet = 12 inches

Plan length = 4 inches

Actual width = 18 feet= 18× 12 = 216 inches

Actual length = 16 feet = 16× 12 = 192 inches  

Plan length/plan width  =  actual length/actual width

(4)/(plan\,\,width)=(192)/(216)\n plan\,\,width=(216)/(192)(4)=4.5\,\,inches
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