MATHEMATICS HIGH SCHOOL

How many solutions exist for the given equation?

1/2
(x + 12) = 4x – 1

Answers

Answer 1
Answer: There are two ways to look at this, one is by solving this and the other is by looking at the variable

First, if we want to solve it, we would take our equation, (i like decimals) .5(x+12)=4x-1 and distribute the .5 to both things in the parentheses. when we do that we get .5x+6=4x-1. now we get our variables to the same side by subtracting .5x from both sides. When we do this, we are left with 6=3.5x-1. next we add 1 to each side and get 7=3.5x. Now we divide each side by 3.5, and get x=2. Now we have to plug it into the original equation and get .5(2+12)=4(2)-1.   when we simplify this we get .5(14)=7, which goes to 7=7. this is a true statement, so we know that x=2.  since we only have one value for x, we know the answer is that only one solution exists. 

Another way that is simpler, but not always accurate, is to look at the variable. There can only be as many solutions for x as the highest exponent x is to, in this case, x has no exponent so there can't be more than one solution, so we say that it has one solution. This way is a lot faster, but can be wrong if the equation has a false solution. This false solution happens when you solve the equation and get a value, but it doesn't work for the original equation. 

The second way is a lot faster, but the first way will always give you the right answer 
Answer 2
Answer:

Answer:

One solution, option B for edge2020

Step-by-step explanation:

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Find the coordinates of the midpoint of the segment whose endpoints are given. W (-3, -7) and X (-8, -4)

Answers

Midpoint coordinates: x-coordinate: (-3+(-8))/2=-11/2 
y-coordinate: (-7+(-4)/2=-11/2
So coordinates of the midpoint are: (-11/2, -11/2).

Find the perimeter and area of a rectangle whose length is (x + 1) and whose width is (x - 3). Express your answer in terms of x. With explanation if you can plz and thx​

Answers

Answer:

Perimeter=2L+2w

P=2(x+1)+2(x-3)

P=2x+2+2x-6

P=4x-4

Area=Lxw

A=(x+1)x(x-3)

A=x^2-3x+x-3

A=x^2-2x-3

Step-by-step explanation:

I don't have one :v

Final answer:

The perimeter of the rectangle is 4x - 4 and the area is x^2 - 2x - 3.

Explanation:

The perimeter of a rectangle is calculated by the formula 2*(Length + Width). Hence, the perimeter for the rectangle in question will be 2*((x + 1) + (x - 3)) = 2*(2x - 2) = 4x - 4.

The area of a rectangle is calculated by the formula Length * Width. Therefore, the area for the rectangle equals (x + 1) * (x - 3) = x^2 - 3x + x - 3 = x^2 - 2x - 3.

Learn more about Rectangle Area and Perimeter here:

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What is the original price if the percent of the discount is 15% and the sale price is $146.54​

Answers

Answer:

$976.93

Step-by-step explanation:

so if the sale price is 146.54 and the discount is 15% then divide 146.54 by 15% or .15.

Doors for the small cabinets or 19.5 inches long. Doors for the large cabinets are 3.9 times as long as the doors for the small candidates. How many large doors can be cut from a board that is 11 feet long.

Answers

Answer: 1 large door.

Step-by-step explanation:

You know that the lenght of each door for the small cabinets is:

lenght_((small))=19.5\ in

Since the lenght of the doors for the large cabinets are 3.9 times as long as the doors for the small candidates, the lenght of any of these doors is:

lenght_((large))=3.9(19.5\ in)=76.05\ in

The lenght of the board is 11 feet, so you need to convert it to inches:

(11\ ft)((12\ in)/(1\ ft))=132\ in

Then, the number of large doors that can be cut from that board is:

(132\ in)/(76.05\ in)=1.73

So, 1 large door can be cut from that board.

Which of the following figures are quadrilaterals?

Answers

square , rectangle , rombus , parallelogram

Answer:

a four-sided figure.

Step-by-step explanation:

Solve the system of equations​

Answers

Answer:

Step-by-step explanation:

You can solve it by substitution, by setting the first equation to y=1-x.

Replace the y in the equation by y=1-x.

4x + 3(1-x) = 8.

Distribute the 3.

4x + 3-3x = 8

Combine like terms.

x + 3 = 8

x =5

Plug 5 into y=1-x.

y=1-5

y= -4
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