Simplify each expression.
8. (-3)+4

Applying the midpoint formula, the coordinates of B are: (-7, 4).

The midpoint formula is:

M(x, y) = [(x2 + x1)/2, (y2 + y1)/2]

Given:

M(x, y) = (-3, 0)

A(x1, y1) = (1, -4)

B(x2, y2) = (?, ?)

Plug in the values into the midpoint formula:

M(-3, 0) = [(x2 + 1)/2, (y2 + (-4))/2]

Isolate each coordinate

-3 = (x2 + 1)/2

-6 = x2 + 1

-6 - 1 = x2

x2 = -7

0 = (y2 - 4)/2

0 = y2 - 4

y2 = 4

Therefore, applying the midpoint formula, the coordinates of B are: (-7, 4).

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Given equation x + 2y = 15 and 3x -15 = -6y are real numbers so the equation has a solution.

Some equations have no solutions. In these equations, there is no value for the variable that makes the equation true. You can tell that an equation has no solutions if you try to solve the equation and get a false statement.

We have been given that

x + 2y = 15 ..........(1)

3x -15 = -6y ..........(2)

Multiply equation (1) with 3.

3(2y+x)=5

6y+3x=-15

Subtract equation (1) from equation (2)

0=15

Instead of 6y+3x=-15, 3x-15=-6y becomes 6y+3x=15. So, these 2 equations are saying the same thing (this is the first equation times 3), and therefore the solution is all real numbers.

Hence, The equation has a solution since the given values of x + 2y = 15 and 3x -15 = -6y are real numbers.

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The measure of each of the small arcs of the circled glass stained window is 45°.

Congruent in circle:

Circles having the same radii are said to be congruent of one another.

For example,

When two circles are congruent, we can also say that they have the same area and circumference. Thus they can also be said to be equal circles.

Given,

In the stained glass window design, all of the small arcs around the circle are congruent. Suppose the center of the circle is point O.

Here we need to find the measure of each of the small arcs.

We know that.

Congruent circles can be defined as circles which are having the same or equal radii.

So, based on this the circle we need to divided it as equal radius arcs.

We know that, the measurement of the full circle is 360°.

So, here we have to divide it by 8.

Then we have each arc as,

=> 360°/8

=> 45°.

Therefore, each arc has the measurement of 45°.

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A reduction is a dilation from ▢PQRS to ▢WXYZ.

According to the given figure:

Therefore, a reduction is a dilation from ▢PQRS to ▢WXYZ.

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So we are given with three different equations,

[tex]$$\begin{aligned}&x-2 y+3 z=12 \rightarrow(1) \\&2 x-y-2 z=5 \rightarrow(2) \\&2 x+2 y-z=4 \rightarrow(3)\end{aligned}$$[/tex]

We will convert the individual equations into matrices,

[tex]$$\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\2 & -1 & -2 & 5 \\2 & 2 & -1 & 4\end{array}\right]$$[/tex]

   [tex]\begin{aligned}&R_2 \leftarrow R_2-2 \times R_1 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\2 & 2 & -1 & 4\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}&R_3 \leftarrow R_3-2 \times R_1 \\&=\left[\begin{array}{rrr|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\0 & 6 & -7 & -20\end{array}\right] \\&R_2 \leftarrow R_2 \div 3 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}&R_1 \leftarrow R_1+2 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right] \\&R_3 \leftarrow R_3-6 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 9 & 18\end{array}\right]\end{aligned}[/tex][tex]\begin{aligned}&R_3 \leftarrow R_3 \div 9 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right] \\&R_1 \leftarrow R_1+2.3333 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}&R_2 \leftarrow R_2+2.6667 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & 0 & -1 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]

[tex]i. e.$$\begin{aligned}&x=4 \\&y=-1 \\&z=2\end{aligned}$$[/tex]

Solution By Gauss elimination method is,

[tex]$x=4, y=-1$ and $z=2$[/tex]

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Answer:

27.25 feet long

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

The area is 599.5 square feet and it is 22 feet wide. So in order to find the area we have to multiply the width (22 feet wide) and the legth (unknow number which will stand for "x"). Since we area multiplying the width and legth we need to do the inverse operation which is dividing. We didvide the area 599.5 by the width 22 to get 27.25 feet long.

22x = 599.5

----- -------- <------ Fraction bar/divide

22 22

x = 27.25

Check:

When a number is next to parenthesis it means to multiply the 2 numbers.

22 (27.25) = 599.5

599.5 = 599.5

True statement.

Answer:

Step-by-step explanation:

OK, so you see how its like 4/10 right? (not four tenths but ya know four on top and ten underneath)

Look how for your Y axis it goes: 2, 4. 6, 8, 10

what comes after ten by counting by twos? 12!

Also the correct equation is; Y = K X ( Y =_ x) ( blank is whatever your constant of proportionality is.

Thank you Pre-Algebra\

Signed~ Earl

Answer:

Step-by-step explanation:

the correct answer would be  -5/-1=|6x|

The absolute value equation for each of the graphs are |x + 3| = 2 and |x - 4| = 1 respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

An inequality shows the non equal comparison of numbers and variables.

A) For the inequality shown, the midpoint is [(-1) + (-5)]/2 = -3. The distance from each of the endpoint to the midpoint is 2 units (i.e. from -1 to -3 or from -5 to -3). Hence:

Absolute inequality is:

|x - midpoint| = distance from endpoint to midpoint

This gives:

|x - (-3)| = 2

|x + 3| = 2

B) For the inequality shown, the midpoint is [3 + 5]/2 = 4. The distance from each of the endpoint to the midpoint is 1 units (i.e. from 3 to 4 or from 5 to 4). Hence:

Absolute inequality is:

|x - midpoint| = distance from endpoint to midpoint

This gives:

|x - 4| = 1

The absolute value equation for each of the graphs are |x + 3| = 2 and |x - 4| = 1 respectively.

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Answer:

all real x other than 2

Step-by-step explanation:

[tex]\frac{3x-6}{x-2}=3 \\ \\ 3x-6=3x-6[/tex]

Thus, the equation is true for all x in its domain, which is all real x other than 2.

Answer:

Step-by-step explanation:

so you get a better perspective of it

Answer:

x=7, y=11

Step-by-step explanation:

Using simultaneous equations we can sub y in equation 1 into equation 2.

Equation 1. y=2x-3

Equation 2. x+y=18

Since y=2x-3 we can replace it so that

2'. x+2x-3=18

Now simplify

= 3x-3=18

Add 3 onto both sides to undo the subtraction of 3 so that,

3x=21

Now divide both sides by three to undo the multiplication of 3 so that,

x=7

Now sub in x (which is 7) into one of the equations to find y

7+y=18

To undo the five, subtract 7 from both sides so that

y=11

The required answers are-

Part a: The equation that represents the total cost C is C = 250 + 7x.

Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.

Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.

Part d: The average cost keeps on decreasing exponentially and then becomes straight.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now it is given that,

Rental of banquet hall = $250

One time charge for meal = $7 per plate

x = the number of people who attend.

Part a: The equation that represents the total cost C

Since there are x people in the banquet

So, number of plates = x

Thus, Total One time charge for meal = 7x

So Total Cost = Rental of banquet hall + Total One time charge for meal

⇒ C = 250 + 7x

this is the equation that represents the total cost C

Part b: The equation that represents the average cost A per person

Putting x = 1 in the above equation of total cost we get,

A = 250 + 7 = 257

this is the equation that represents the average cost A per person

Part c: The estimate number of people who must attend before the average cost drops to $15 per meal

From the graph it is seen that there are 25 people who must attend before the average cost drops to $15 per meal.

Part d: what happens to the average cost as the number of people who attend increases.

The average cost keeps on decreasing exponentially and then becomes straight.

The required answers are-

Part a: The equation that represents the total cost C is C = 250 + 7x.

Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.

Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.

Part d: The average cost keeps on decreasing exponentially and then becomes straight.

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Simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]  is equal to 3/(x-6).

As given in the question,

Given complex fraction is [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]

Simplify the denominator by taking least common multiple,

[tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }\\\\\\= \frac{3}{\frac{x-4}{\frac{x-4-2}{x-4} } }\\\\\\= \frac{3(x-4)}{(x-6)(x-4)} \\\\\\=\frac{3}{x-6}[/tex]

Therefore, simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]  is equal to 3/(x-6).

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The total change is 82.5 (or 82 and 2/5) bushels remaining and has sold 82.25 (or 81 and 2/5) bushels

He has sold (16+3/5) bushels/day x 6 days

=(16 x 6 ) + (3 / 5 * 6)

= 96 + 6/5

= 97 + 1/2

= 97.5

The change in the number of bushels is 180 – 97.5 = 82.5 or 82 and 2/5 bushels. A measure of capacity equal to 8 gallons (equivalent to 36.4 litres), used for corn, fruit, liquids, etc. A measure of capacity equal to 64 US pints (equivalent to 35.2 litres), used for dry goods.

Hence , the total change in  82.5 (or 82 and 2/5) bushels remaining and has sold 82.25 (or 81 and 2/5) bushels.

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Answer:

Just multiply each by 5

Step-by-step explanation:

5x125= 625

explanation:

multiply the previous term by 5

Answer:

384

Step-by-step explanation:

8x4=32 32x 12 cans=384 sq centimeters

The solutions for each of the equations provided in the reference picture is as follows:

(1) [x = (-3)]

(2) [y = (-10)]

(3) (m=3/4)

(4) (b = 0)

(5) (r = 7)

(6) (v = -60)

As per question statement and reference picture, we are provided with 6 different equations which are

(1) [(4 x+1)=(2 x-5)]

(2)[(y-3)=(-3 y-43)]

(3) [(7-14 m)=(2 m-5)]

(4)[(-10 b+5)=(7 b+5)]

(5)[(r+15)=(4 r-6)]

(6)[(10-2 v)=(-5 v-50)]

We are required to find the solution of all the equations mentioned above.

Considering equation (1), we get,

{[(4 x+1)=(2 x-5)] }

or,(4 x-2 x)=[(-1)-5]

or, 2 x=-(1+5)

or, 2 x=-6

or, x={-6}/{2}=(-3)

Considering equation (2), we get,

{[(y-3)=(-3 y-43)] }

or, (y+3 y)=(3-43)

or, 4 y=(-40)

or, y=(-10)

Simplifying equation (3), we get,

{[(7-14 m)=(2 m-5)] }

or, (7+5)=(2 m+14 m)

or, 12=16 m

or, m={12}/{16}={3}/{4}

Simplifying equation (4), we get,

{[(-10 b+5)=(7 b+5)] }

or, (5-5)=(7 b+10 b)

or, 17 b=0

or, b=0

Simplifying equation (5), we get,

{[(r+15)=(4 r-6)] }

or, (15+6)=(4 r-r)

or, 3 r=21

or, r=7

Finally, Simplifying equation (6), we get,

{[(10-2 v)=(-5 v-50)] }

or, (5 v-2 v)=[(-10)-50]

or, 3 v=-(10+50)

or, 3 v=-60

or, v=(-20)

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The Salesman's salary is modeled by the linear equation:

y = $1000 + $500*x

We know that the businessman earns a basic salary of $1000 (it does not depend on how many items he sells) and $500 for each item he sells as a commission.

Then, if we define x as the number of items he sells, the amount he gets in commissions is: x*$500

Then the equation for his total salary, y, in terms of x which is defined above is:

y = $1000 + $500*x

That is the linear equation we wanted to write.

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Answer:

Step-by-step explanation:

to find the y intercept of AB, first find the slope of AB: m=(1-(-1))/(2-14)=-1/6

the equation of line AB is y=-(1/6)x+b

use either of the given two points to find out b: 1=(-1/6)*2+b => b=4/3

BC is perpendicular to AB, so the slope of BC is the negative reciprocal of the slope of AB, therefore, the slope of BC is 6

Equation of BC is y=6x+b

find out b by using the coordinates of point B: 1=6*2+b => b=-11

the equation of BC is: y=6x-11

the x coordinate of point C: 13=6*x -11 =>x=4

The equation of the circle with radius 8 and center at (5 , -2) is (x - 5)^2 + (y + 2)^2 = 64.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius 8 and center at (5 , -2), substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (5 , -2)

r = 8

(x - 5)^2 + (y - -2)^2 = 8^2

(x - 5)^2 + (y + 2)^2 = 64

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The equation of a line is ax + by = c.

full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)

equation of a line is ax + by = c

x=d

put x=d in the equation of line

ad + by = c

by = c-ad

y=(c-ad)/b

full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)

The phrase equation and its cognates in other languages can also have subtly extraordinary meanings; as an example, in French an équation is described as containing one or more variables, even as in English, any well-shaped components together with two expressions related with an equals sign is an equation.

fixing an equation containing variables includes figuring out which values of the variables make the equality real.

The variables for which the equation must be solved are also referred to as unknowns, and the values of the unknowns that satisfy the equality are referred to as answers of the equation.

There are two kinds of equations: identities and conditional equations. An identity is authentic for all values of the variables. A conditional equation is simplest genuine for particular values of the variables

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Step-by-step explanation:

Let radius of circle is r=18 units

Perimeter of full circle is given by 2πr

Thus, perimeter of three quarters circle is given by,

( ¾ × 2πr) + (2 × r)

The perimeter of this "circle" would be:

( ¾ × 2 × π × 18) + (2 × 18) = 27π + 36 ≈ 120.78 m

Answer: 36 feet of wood

Step-by-step explanation:

P=perimeter. P=total length of wood

s= side length. A=area

A=s^2

81=s^2

s^2=9^2

s=9

P=4s

P=4(9)

P=36 feet of wood

Answer:

P = 36 ft

Step-by-step explanation:

The given length is,

→ a = ?

Formula we use,

→ A = a²

Now the length of one side is,

→ A = a²

→ a² = 81

→ a = √81

→ [ a = 9 ]

The total length of wood needed is,

→ P = 4a

→ P = 4 × 9

→ [ P = 36 ]

Hence, the total length is 36 ft.

Answer:yes b

Step-by-step explanation:

because you subtract it

Answer: 3

Step-by-step explanation:

A function exists described as a relation between a set of inputs containing one output each. The value of h(g(3)) is 5.

A relationship between a group of inputs and one output is referred to as a function.

In plain English, a function is an association between inputs in which each input is connected to precisely one output.

A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Where, g(3) = 0

To get h, replace g(3) with 0 in the requested equation (0).

Since h(0) = 5 according to the question, your final response is 5.

Therefore, the value of h(g(3)) is 5.

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Answer:

a30= -15

Step-by-step explanation:

Answer: Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4

Step-by-step explanation:

Take sin of 60 to calculate side opposite to angle 60

sin 60=[tex]\frac{\sqrt{3} }{2}[/tex]

cos 60=1/2  

7.2 / 1/2=

7.2 * 2=14.4

[tex]\frac{\sqrt{3} }{2}[/tex]*14.4=

[tex]\frac{14.4\sqrt{3} }{2}[/tex]=7.2[tex]\sqrt{3}[/tex]

The hypotenuse:

[tex](\frac{\sqrt{3} }{2})^2[/tex]+(1/2)^2=

3/4 + 1/4 = 1

1 * 14.4 =14.4

Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4

Step-by-step explanation:

The 30-60-90 triangle is one of the most important trigonometry concept you will learn throughout your secondary schooling.

Attached below is a triangle that you should memorize for easy practice. The way this triangle is formed can be proven trigonometrically and/or with the unit circle, but that's not what this question is asking for.

When comparing the numbers on the attachment and your question, we can generate that the side 7.2=x, because the side with the 60 degree angle and right angle contains the variable x.

Since we have x now, all we would have to do is to plug in the x values and solve the question.

The hypotenuse (longest side of the triangle) = 2x = 2(7.2) = 14.4

The side opposite to the 60 degree angle (left most side)= [tex]x\sqrt{3}[/tex] = [tex]7.2\sqrt{3}[/tex] = 12.6

I hope this helped!

Write an example from daily life that uses rational numbers .

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