Answer:
A: False
B: False
C: True
D: True
E: False
F: True
G: True
H: True
Step-by-step explanation:
A: 9(x - 2) = 9x + 2
9x - 18 = 9x + 2 FALSE
B: 65 - y = y - 65
(equation rearranged) -y + 65 = y - 65 FALSE
C: g (times) h = h (times) g (TRUE due to the commutative property of multiplication)
D: a (times) 0 = 0 (TRUE because anything times 0 equals 0)
E: (4 (times) 2) - r = 4 (2 (times) r)
8 - r = 8 - 4r FALSE
F: k + 0 = k TRUE
G: (a + x) + y = a + (x + y)
a + x + y = a + x + y TRUE
H: 5(2x - 9) = 10x - 45
10x - 45 = 10x - 45 TRUE
The value of x is 1.
The value of y is 4.
Solution:
Given TQRS is a rhombus.
<u>Property of rhombus:
</u>
Diagonals bisect each other.
In diagonal TR
⇒ 3x + 2 = y + 1
⇒ 3x – y = –1 – – – – (1)
In diagonal QS
⇒ x + 3 = y
⇒ x – y = –3 – – – – (2)
Solve (1) and (2) by subtracting
⇒ 3x – y – (x – y) = –1 – (–3)
⇒ 3x – y – x + y = –1 + 3
⇒ 2x = 2
⇒ x = 1
Substitute x = 1 in equation (2), we get
⇒ 1 – y = –3
⇒ –y = –3 – 1
⇒ –y = –4
⇒ y = 4
The value of x is 1.
The value of y is 4.
Answer:
The second number in an ordered pie of numbers that corresponds to a point on a coordinate system is the y<u>-value.</u>
Step-by-step explanation:
We will use pythagoras' Theorem for this question
where c is the longest side (in this case, the diagonal)
a and b are the 2nd and 3rd longest side (interchangeable)
given a = 10.6, b = 16.8,
Answer:
t = 4 h
Step-by-step explanation:
Painter A initial fee 40 $ and each hour charge 45 $
Painter B initial fee 100 $ and each hour charge 30 $
The equations for painters are straight lines.
The initial fee is the intercept of the line with the y-axis ( painters receive 40 and 100 $ respectively and they have done nothing.
The equation for a straight line is:
y = m*x + b where m is the slope and b the intercept with the y-axis
Then
Painter A when x = 0 y = b = 40
And each hour of work cost 45 $ then f x = t in hours
The equation for Painter A is y = 45*t + 40
Similarly, the equation for Painter B is
y = 30*t + 100
We have a two equations system, the solution will indicate when the two painters will charge the same amount of money
y = 45*t + 40 (1)
y = 30*t + 100 (2)
Equation 1 - equation 2
0 = 15*t - 60
15*t = 60
t = 60/15
t = 4 h
