Answer: d) (3, 3)
<u>Step-by-step explanation:</u>
Inverse is when you swap the x's and y's.
Let's look at the points and find their inverse:
f(x) f⁻¹(x)
(0, -2) --> (-2, 0)
(1, -1) --> (-1, 1)
(2, 0) --> (0, 2)
(3, 3) --> (3, 3) f(x) = f⁻¹(x) so this is where they intersect!
Answer:
ΔABC and ΔXYZ are SIMILAR by SSS property of similarity.
Step-by-step explanation:
SSS Similarity Theorem:
Two triangles are said to be similar if their CORRESPONDING SIDES are proportional.
In ΔABC and ΔXYZ, if
, then △ABC∼△YZX
Here, in ΔABC and ΔXYZ
AB = 9, BC = x , AC = 12
Similarly, XY = 3, YZ = 2, ZX = 4
Here,

⇒ Corresponding sides are in the ratio of 3, if BC =6 units
Hence, if BC = 6 units, then the ΔABC and ΔXYZ are SIMILAR by SSS property of similarity.
Answer: n=4
Step-by-step explanation: 4/4=1 and 16/4=4 (1,4) n=4
Answer:
137 ft²
Step-by-step explanation:
The shop is rectangular in shape. The area of a rectangle is given by:
Area = length * width
Since the length of the shop = 20 ft and the width = 10 ft, therefore:
Area of the shop = length * width = 20 ft * 10 ft = 200 ft²
The part that would not be tiled is of triangular shape. The area of a triangle is given as:
Area = (1/2) * base * height
The base of the triangle = 18 ft, the height = 7 ft. Hence:
Area of non tiled part = (1/2) * base * height = (1/2) * 18 ft * 7 ft = 63 ft²
The total square feet of tile needed to complete the job = Area of shop - Area of non tiled part
The total square feet of tile needed to complete the job = 200 ft² - 63 ft² = 137 ft²
Answer:
32 and 58
Step-by-step explanation:
Let's set up equations.
The sum of two numbers (x and y) is 90: x + y = 90
The larger number (y) is 6 less than twice the smaller number (x): y = 2x - 6
We have our system of equations:
x + y = 90
y = 2x - 6
Let's use substitution.
Substitute y = 2x - 6 into the first equation.
x + y = 90
x + (2x - 6) = 90
Combine like terms.
x + 2x - 6 = 90
3x - 6 = 90
Add 6 to both sides to isolate x.
3x = 96
Divide both sides by 3 to further isolate x.
x = 32
Now that we know x, let's find y.
Plug in x = 32 into one of our original equations.
y = 2x - 6
y = 2(32) - 6
Multiply.
y = 64 - 6
y = 58
Now we have x = 32, y = 58.
Check your answer by plugging these values into one of our original equations.
x + y = 90
32 + 58 = 90
Add.
90 = 90
Your solution is correct.
Hope this helps!