Answer:
8cm
Step-by-step explanation:
x is similar to the side 12cm.
We know the second triangle is rotated counter-clockwise from the first because similar triangles have the same angle measurements.
Since the angle in the first triangle between 9cm and 15cm is 53°, it can't be similar to the angle between x and the hypotenuse in the second triangle.
Find the scale factor:
Triangle 1/Triangle 2
Divide two similar sides.
6/9 = 2/3
Multiply the scale factor by the similar side to find x.
x = 12*(2/3)
x = 8
Answer:
Step-by-step explanation:
Distance travelled on graph = AB + BC + CD + DA
AB = CD = (3 +2) = 5
BC = AD = 2 –(-2) = 4
Distance on graph = 2 × 5 + 2 × 4 = 10 + 8 = 18 spaces = 18 blocks
Bridgette jogs 
each day.
Answer:
The values of 
so that 
have vertical asymptotes are 
, 
, 
, 
, 
.
Step-by-step explanation:
The function cosecant is the reciprocal of the function sine and vertical asymptotes are located at values of so that function cosecant becomes undefined, that is, when function sine is zero, whose periodicity is . Then, the vertical asymptotes associated with function cosecant are located in the values of of the form:
, 
In other words, the values of so that have vertical asymptotes are , , , , .
Answer:
105.12 ft²
Step-by-step explanation:
Let's first find the area of the rectangle.
ft², so the rectangle has an area of 80ft².
To find the area of the semi-circle, we find the area of a whole circle and divide by two.
The formula to find the area of a circle is 
. The radius is 4, as the diameter is 8.
Add 80 and 25.12:
Hope this helped!
Answer:
Volume of a cup
The shape of the cup is a cylinder. The volume of a cylinder is:
\text{Volume of a cylinder}=\pi \times (radius)^2\times heightVolume of a cylinder=π×(radius)
2
×height
The diameter fo the cup is half the diameter: 2in/2 = 1in.
Substitute radius = 1 in, and height = 4 in in the formula for the volume of a cylinder:
\text{Volume of the cup}=\pi \times (1in)^2\times 4in\approx 12.57in^3Volume of the cup=π×(1in)
2
×4in≈12.57in
3
2. Volume of the sink:
The volume of the sink is 1072in³ (note the units is in³ and not in).
3. Divide the volume of the sink by the volume of the cup.
This gives the number of cups that contain a volume equal to the volume of the sink:
\dfrac{1072in^3}{12.57in^3}=85.3cups\approx 85cups
12.57in
3
Step-by-step explanation:
