Using a matrix, you CAN represent adding or subtracting equations by adding or subtracting rows of numbers. Therefore the answer is True
Question 1. Midpoint
Answer: M(-2,4)
Explanation:
1) The coordinates of the midpoint, M (x,y) between two points (x₁,y₁) and (x₂, y₂) are:
x = (x₁ + x₂) / 2 and y = (y₁ + y₂) / 2
2) Replacing the coordinates of the given points P (-4, 1) and Q (0,7) you get:
x = (- 4 + 0) / 2 = - 2, and
y = (1 + 7) / 2 = 4
So, the answer is M (-2,4)
Question 2: The distance between the two midpoints is:
Answer: 7.21
Explanation:
1) Use the formula of distance, which is an application of Pythagora's theorem:
d² = (x₂ - x₁)² + (y₂ - y₁)²
2) Substitute values:
d² = (0 - (-4))² + (7 - 1)² = 4² + 6² = 16 + 36 = 52 ⇒ d = √52 ≈ 7.21
This is division. Let’s set up your problem.
I prefer not using mixed numbers. Instead we’ll use 14/3 for the fraction.
So to start off:
14/3 / 7
the 7 can also be 7/1.
use the saying, “keep, change, flip.”
keep the 14/3, change the sign to multiplication, and flip the last fraction.
14/3 x 1/7
now multiply.
14/21 is your fraction. Now simplify.
You get 2/3.
Your answer is:
She should cut the ribbon 2/3 m.
Answer:
8 dollars
Step-by-step explanation:
if "x" is his weekly allowance:
x-0.5x+8=12
Dan make x dollars, then he spend 0.5x dollars and he earned 8 dollars, and that is 12 dollars.
0.5x=12-8
x=8 dollars
Answer:
The number is 4.
Step-by-step explanation:
We can answer the above question as follow:
The square of a number, x is written as: x²
Eight times the number is written as: 8x
From the question, we were told that the square of the number, x is 16 less than eight times the number. This can be written as:
x² = 8x – 16
Rearrange
x² – 8x + 16 = 0
Solving by factorisation method:
Multiply the 1st term (i.e x²) and the last term (i.e 16) together. The result is 16x² as shown below:
x² × 16 = 16x².
Next, find two factors of 16x² such that when we add them together, it will result to the 2nd term ( i.e – 8x).
The factors are –4x and –4x.
Next, replace – 8x in the equation with –4x and –4x. This is illustrated below:
x² – 8x + 16 = 0
x² – 4x – 4x + 16 = 0
Factorise
x(x – 4) – 4(x – 4) = 0
(x – 4)(x – 4) = 0
x – 4 = 0 or x – 4 = 0
x = 4 or x = 4
Thus, the number is 4.
***** Check *****
x² = 8x – 16
x = 4
4² = 8(4) – 16
16 = 32 – 16
16 = 16
