Answer:
Step-by-step explanation:
To find the values of a and b, we can use the given information and apply the properties of rectangles and parallel lines.
First, let's calculate the area of the rectangle PQRS. We are given that the area is 84 cm², and since PQRS is a rectangle, its area is equal to the product of its length and width. Therefore, we can set up the equation:
Length × Width = 84
Next, we know that XY is parallel to PS. This means that the length of XY is equal to the length of PS. Since the length of PS is a + b cm, we can write:
Length of XY = a + b
Now, we are given that the area of PXYS is 21 cm². Using the same logic, the area of PXYS is equal to the product of its length and width, so we can set up another equation:
Length of XY × Width of XY = 21
Since the width of XY is 9 cm (given as RY), we can substitute the values into the equation:
(a + b) × 9 = 21
Simplifying this equation, we get:
9a + 9b = 21
Now, we have two equations:
1) Length × Width = 84
2) 9a + 9b = 21
To solve these equations simultaneously, we need to rearrange equation 1) to solve for either length or width. Let's solve for length:
Length = 84 / Width
Substituting in the value of width from equation 2), we get:
Length = 84 / (9a + 9b)
Now, we can substitute this expression for length into equation 2):
(84 / (9a + 9b)) × (9) + 9b = 21
Simplifying this equation, we get:
84 + 9b = 21(9a + 9b)
Expanding, we get:
84 + 9b = 189a + 189b
Combining like terms, we get:
-180b = 189a - 84
Dividing by -180, we get:
b = (189a - 84) / -180
We have found the expression for b in terms of a.
To find the value of a, we can substitute this expression for b into equation 2):
9a + 9((189a - 84) / -180) = 21
Simplifying this equation will give us the value of a.
Please note that without specific numerical values or additional constraints, it is not possible to determine the exact values of a and b. However, by solving the equations as shown above, we can express the values of a and b in terms of each other.
Answer:
The answer is 1
Step-by-step explanation:
Remember PEMDAS, 1+2 is 3. 2x3 is 6, then 6 divided by 6 is 1.
Answer:
1
Step-by-step explanation:
6 / 2(1 + 2)
6 / 2(3)
6 / 6 = 1
Miguel drove for 8 hours at a constant rate. He drove a total of 424 miles.
Donna also drove at a constant rate. The table shows the number of miles she had driven in different numbers of hours.
How do the unit rates compare?
Miguel has a (blank) unit rate of change than Donna because(blank) is greater than(blank)
Answer:
Miguel has a
greater
unit rate of change than Donna because
53 mph
is greater than
48 mph
Step-by-step explanation:
Answer:
Step-by-step explanation:
Mrs. Chipps buys 30 c + 50 r = $95
Mr. Meehan buys 40 c + 40 r = $116 x (-1.25) to eliminate r
30 c + 50 r = $ 95
-50 c - 50 r = $-145
-20 c = -50
c = 50 / 20
c = $2.5
substitute c = 2.5 into eq. 1
30 c + 50 r = $95
30 (2.5) + 50 r = 95
75 + 50 r = 95
50 r = 95 - 75
r = 20 / 50
r = 0.40
therefore, the individual costs of the compasses and rulers are:
compass = $ 2.50 each
ruler = $ 0.40 each
Answer:
f(x)= 1/4
(4)
x
for x=1→f(1)=
4
1
⋅4
1
=1→(1; 1)
for x=2→f(2)=
4
1
⋅4
2
=
4
1
⋅16=4→(2; 4)
Answer: The graph nr 4.
Other method:
f(x)=\dfrac{1}{4}\cdot4^x=4^{-1}\cdot4^x=4^{x-1}f(x)=
4
1
⋅4
x
=4
−1
⋅4
x
=4
x−1
Used:
\begin{gathered}a^{-1}=\dfrac{1}{a}\\\\a^n\cdot a^m=a^{n\cdot m}\end{gathered}
a
−1
=
a
1
a
n
⋅a
m
=a
n⋅m
Draw the graph of y = 4^x and next shift it 1 unit right.