An astronomical unit is the mean distance from the center of Earth to the
center of the sun. One astronomical unit is about 9.3 × 10 miles. Pluto
is about 40 astronomical units from the sun. What is the approximate
distance that Pluto is from the sun?
A. 3.72 × 10 miles
B. 4.30 × 10 miles
C. 3.72 × 10 miles
D. 4.30 × 10 miles

By combining the like terms, the simplified form of the expression 0.5x-x is -0.5x

Given,

The algebraic expression = 0.5x-x

Combine the like terms

0.5x-x=(0.5-1)x

= -0.5x

Simplified form is -0.5x

Hence, By combining the like terms, the simplified form of the expression 0.5x-x is -0.5x

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A triangle's exterior angle is always greater than its two remote interior angles. The exterior angle ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

Since, angle 1 is an exterior angle of Δ ABE,

m∠1 > m∠3 and m∠4

Since, angle 1 is an exterior angle of Δ ABD,

m∠1 > m∠5

Since, angle 1 is an exterior angle of Δ ABC,

m∠1 > m∠7 and m∠8

Therefore, ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.

The complete question is:

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.

a. Measures less than m ∠ 1 .

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Answer:

Point H, Point D, Point G, Point F

The correct statements are:

Check all that applies:

A The integer −21 represents the sale of 21 books.

True

B After Monday's sales, 26 copies are available.

False

Saturday = 45 - 21

= 24 books available

Monday = 25 - 14

= 11 books available

Total books available = 24 + 11

= 35 copies available

C The integer 25 represents the new shipment.

True

D After Monday's sales, 35 copies are available.

True

E The integer 14 represents the sale of 14 books.

False

Therefore, option A, C and D are the correct statements.

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Answer: 100 times

Explanation: 6 times 100 would be 600 so 600 would be 100 times bigger than 6.

An equiangular triangle is also an example of an acute triangle is a True statement.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

An equiangular triangle is a triangle whose all angles are the same and since all angles are the same so by geometrical constraint all sides must be the same so it will also be an equilateral triangle.

In an equilateral triangle, all interior angles are 60°, and since an acute angle triangle is a triangle in which all angles must be less than 90°.

So an equiangular triangle will be an acute triangle.

Hence "An equiangular triangle is also an example of an acute triangle is a True statement".

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The total price for a 24 ounce package, with a unit price of 13.5 cents per ounce, is $3.24.

Unit price is defined as the price or the cost per unit of the item. The importance of the unit price is that it allows the buyer to understand how the total price has been calculated. By multiplying the unit price by the total weight of the item will give the total price of that item.

total price = unit price x total weight

If the total weight of the package is 24 ounces and its unit price is 13.5 cents per ounce, multiplying will give the total price.

total price = unit price x total weight

total price = 13.5 cents per ounce(24 ounces)

total price = 324 cents

total price = $3.24

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(x + 100, y - 75) is the function notation used to characterise the translation to a bottom of the hill.

The Pythagorean theorem states that the sum of a squares on a legs of a right triangle equals the square on hypotenuse (this same side opposite this same right angle)—or, in recognizable algebraic notation, a² + b² = c².

Now, as per the given question;

From the shown diagram,

AC  = b

Ab  = c

We must find the coordinates of a point B. If C(x,y), then the coordinates of points A and B are:

A(x, y−b) and B(x+c, y−b)

We need to figure out b and c. To find c, we should use sine function.

sinC = perpendicular/hypotenuses

sinC = c/BC

​Thus, c = BC sinC

c = 125sin53°

  =125⋅0.79863551

c ≈100

To find b, we are using the Pythagorean Theorem.

BC² = AC² + AB²

125² = b² + 100²

b² = 125² - 100²

b = √5625

b = 75

The coordinates of a point B are as follows:

B(x+c, y−b)

B(x+100, y−75).

Therefore, the translation to the bottom of the hill defined by the function notation is B(x+100, y−75).

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The number of meters away that dolphins cab hear sounds underwater will be 0.0024 m

From the information, Dolphins can hear sounds underwater that are 24 kilometers away.

The number of meters away that dolphins can hear sounds underwater will be:

= 24 / 1000

= 0.0024 m

Therefore, the correct option is D.

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According to the given statement The preceding population was =  62,500.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is a one-hundred part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Percent originated from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century. Later, it was abbreviated to % with a period. The period was eventually eliminated, and the two components amalgamated to form the contemporary one-word form %.

The current population of a city = 80000

A city's population has grown by 28% since the last census.

measured.

We have to calculate the previous population before increasing 28%.

Let the previous population be p

p +(28% × p) = 80000

p + 0.28p = 80000

1.28p = 80000

p = 80000/1.28

p = 62,500

The preceding population was =  62,500.

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Answer:

4.24-(8*2)/4)=

4.24- 4= 0.24

A variable is any property, number, or quantity that can be measured or counted. Variables can also be referenced as data items.

Inference: Inference uses selected samples from a population to estimate the properties of unknown people.

A record (or record) is a collection of data. For tabular data, a record corresponds to one or more database tables, each table column represents a specific variable, and each row corresponds to a particular record in that data set.

Therefore:

All the data collected in particular is referred to as Data Set.

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The location point of S if RS is 7 will be 4

When two vectors are added using the vector addition postulate, it is known as the vector sum.

Suppose that R and S are points on the number line. If RS=7 and R lies at -3, then;

RS = S - R

Given the following

RS = 7

R = -3

Substitute

7 = S  - (-3)

7 = S + 3

S = 7 - 3

S = 4

Hence the location point of S if RS is 7 will be 4

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Answer:

Step-by-step explanation:

1. We know it travels 346 meters in a second, we now need to multiply 346 by 20. This equals 6920

2. Sound travels 5971 meters per second. We need to multiply this by 12 to find the distance it travels in 12 seconds. 71652 meters

3. We know sound travels 5971 meters per second in stone and 5000 meters per second from the chart. We need to find the difference between these and multiply that by 17 to find the distance covered in 17 seconds.

5971-5000=971

971*17=16507

Sound travels 16507 more meters in 17 seconds through stone than it would travel in aluminum

The sentence describes the error is that A) Both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

It should be noted that the expression given is illustrated as 32x and 16.

In this case, it should be noted that the common factor between the expression is 8.

Therefore, the sentence describes the error is that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

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Answer: Therefore, the sentence describes the error in that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

Step-by-step explanation:

Answer:

Greater than

Step-by-step explanation:

2x2+7x+2

----------

Answer:

[tex]y - 2 = -\frac34(x - 4)[/tex]

Step-by-step explanation:

Hello!

The equation in #17 is written in Slope-Intercept Form: [tex]y=mx+b[/tex]

Point Slope form is the equation given slope and a point: [tex]y - y_1 = m(x - x_1)[/tex]

The point given to us is (4,-2), which we can use as x1 and y1.

The slope is given in the slope-intercept form equation: -3/4

Plug in the values to find the equation:

The equation is [tex]y - 2 = -\frac34(x - 4)[/tex].

hi

let take two points :  

( 0; -1)  and  (4 ;  2)

here is  a = 0 ; f(a) = -1

            b = 4   ; f(b) = 2

Slope is  :   f(a) -f(b)   / a-b

let's apply :   -1 - 2  / 0-4   =    -3/-4   =  3/4

Slope is   3/4

if you want to check result, you can calculate the coordonate of an other point and see if it match.

here I read that      there is a point on the line for  -4 ; -4  

here  I can read that  Y axis  value for   X = 0  is  -1  

as a line is defined  by :   mx+p  

with m =  slope  and p  value for  x = 0

so  : p = - 1

with   m =  3/4  ;   x = -4  and   p = -1  

I can test my line equation   and see if it match the result  :

3/4 ( -4)  - 1 =   -12/4 - 1 =   -3 -1 = -4  

Result match what I see on the graph, so previous result is correct.  

:  Slope is  3/4

ps :  if line grows, the slope can only be  positive. if line decrease, slope is negative, if line is constant, then slope is  still and equal 0

Answer:

DF=12√2

FG=12√2

DG=24

Step-by-step explanation:

Ratio of special Right Triangle (45:45:90): x:x:x√2

Triangle DEF: x:x:x√2

x=12

12: 12: 12√2

So, DF= 12√2

Opposite (if q, then p) Base angle theorem. So, FD≅FG.

FD=12√2

FG=12√2

Ratio of 45:45:90 Triangle: x:x::x√2

x in triangle FDG= 12√2

12√2:12√2:12√2(√2)

12√2*√2=24

=12√2: 12√2: 24

DG=24

When 2 men pushes car with mass 1800 kg and their combined horizontal forces are 1000 N, then frictional force acting on the car is 550 N.

The situation can be depicted in the attached picture. F1 and F2 are the horizontal forces of both men, while Fr is the frictional force. Remember that a frictional force is always the opposite of the direction of velocity.

Apply the 2nd Newton law of motion:

∑F = m.a

Where:

∑F = resultant of forces

m = mass of object

a = acceleration

In this situation, ∑F = F1 + F2 - Fr

The given parameters:

m = 1800 kg

a =  0.25 m/s²

F1 + F2 = 1000 N

Substitute these parameters into the  2nd Newton law:

F1 + F2 - Fr = m.a

1000 - Fr = 1800 . (0.25)

1000 - Fr  = 450

Fr = 1000 - 450 = 550 N

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Answer:

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so alinear pair of angles must add up to 180 degrees

So, x + y = 180

x = 1/3(y)

1/3(y) + y = 180

4/3(y) = 180

y = 135

Vertically Stretching and Compressing

It multiplies a function by a positive constant that yields a position whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done and you will get vertical compression.

Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values ​​are affected.

Solution

Y=x

Multiplying the right side by ½

Y= (1/2) *X

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The statement "The distance between a line and a plane can be found" is sometimes true.

Given,

The statement "The distance between a line and a plane can be found".

The distance between the point and the plane can be found by the taking a point on the line and finding the perpendicular distance from line to the plane.

But we can't apply this method in every case. We can only apply when either the line is parallel to the plane or the line intersects the plane.

Hence, the statement "The distance between a line and a plane can be found" is sometimes true.

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Answer:|x| means “distance between a number and zero

Step-by-step explanation:

Also known as absolute value

ex l5l=5 & l5l=-5

The equation which represents the situation is 13 = 2x − 5 while Bernadette ran 9 miles so option (A) will be correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Given that,

Andrew ran 5 miles less than two times the number of miles Bernadette ran.

If Bernadette ran x miles then,

13 = 2x - 5 is the correct representation.

Now,

2x -  5 = 13

2x = 18

x = 9 miles.

Hence " The number of miles that Bernadette ran is 9 miles while the equation of constraint is 13 = 2x − 5".

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The co-ordinates of point B is (4, -5).

Let the endpoints of a line segment be [tex]x_{1}[/tex], [tex]y_{1}[/tex], and [tex]x_{2}[/tex], [tex]y_{2}[/tex]. The midpoint is equal to half of the sum of the two points' x-coordinates and half of the sum of the two points' y-coordinates.

Point at A ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) = (8,1)

Point at B ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) = (x,y)

The mid point AB is M (2,-2)

Using the mid point formula:
( [tex]\frac{x_{1} +x_{2} }{2}[/tex], [tex]\frac{y_{1} +y_{2} }{2}[/tex] ) = ( x,y )

[tex]\frac{8 +x_{2} }{2}[/tex] = 2

8 + [tex]x_{2}[/tex] = 4

[tex]x_{2}[/tex] = - 4

And

[tex]\frac{1 + y_{2} }{2}[/tex] = -2

1 + [tex]y_{2}[/tex] = -4
[tex]y_{2}[/tex] = - 5

So, the co-ordinate of point B is (4, -5).

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Answer: (8w) - 6 = 7

Step-by-step explanation:

         To write an equation, we will look at the phrase given.

Six less than ➜ - 6

the product of ➜ multiplication

is equal to 7 ➜ = 7

Six less than the product of 8 and a number is equal to 7.

(8w) - 6 = 7

The simplest version is one that utilizes fundamental algebraic and mathematical ideas, such as exponents.  The simplified equation of (7/2c) - (2/c²) is (7c - 4)/(2c²).

Let the expression be (7/2c) - (2/c²)

Taking LCM of the denominator

⇒ (7/2c²) - (4/2c²)

simplifying the above equation, we get

⇒ (7c - 4)/(2c²)

Simplifying a mathematical expression means putting it in the most basic form. Typically, the simplest version is one that utilizes fundamental algebraic and mathematical ideas, such as exponents. The phrase is intended to be made simpler by eliminating any repetition or duplication.

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