Answer:
From the graph: we have the coordinates of RST i.e,
R = (2,1) , S = (2,-2) , T = (-1,-2)
Also, it is given the scale factor and center of dilation C (1,-1)
The mapping rule for the center of dilation applied for the triangle as shown below:
or
or
Now,
for R = (2,1)
the image R' = or
⇒ R' =
For S = (2, -2) ,
the image S'= or
⇒ S' =
and For T = (-1, -2)
The image T' = or
⇒ T' =
Now, label the image of RST on the graph as shown below in the attachment:
18 gallons of milk had passed the expiration date.
Explanation step by step
Multiply 120x 15%
Turn 15% into a decimal which is 0.15 so now it’s 120x0.15 which equals to 18.
Answer:
16. Angle C is approximately 13.0 degrees.
17. The length of segment BC is approximately 45.0.
18. Angle B is approximately 26.0 degrees.
15. The length of segment DF "e" is approximately 12.9.
Step-by-step explanation:
<h3>16</h3>
By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.
For triangle ABC:
- ,
- The opposite side of angle A ,
- The angle C is to be found, and
- The length of the side opposite to angle C .
.
.
.
Note that the inverse sine function here is also known as arcsin.
<h3>17</h3>
By the law of cosine,
,
where
- , , and are the lengths of sides of triangle ABC, and
- is the cosine of angle C.
For triangle ABC:
- ,
- ,
- The length of (segment BC) is to be found, and
- The cosine of angle A is .
Therefore, replace C in the equation with A, and the law of cosine will become:
.
.
<h3>18</h3>
For triangle ABC:
- ,
- ,
- , and
- Angle B is to be found.
Start by finding the cosine of angle B. Apply the law of cosine.
.
.
.
<h3>15</h3>
For triangle DEF:
- The length of segment DF is to be found,
- The length of segment EF is 9,
- The sine of angle E is , and
- The sine of angle D is .
Apply the law of sine:
.
Answer:
18.0
Step-by-step explanation:
==>Given:
Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°
==>Required:
Value of x to the nearest tenth
==>Solution:
Using the Cosine rule: c² = a² + b² - 2abcos(C)
Let c = x,
a = 16
b = 30
C = 30°
Thus,
c² = 16² + 30² - 2*16*30*cos 30°
c² = 256 + 900 - 960 * 0.8660
c² = 1,156 - 831.36
c² = 324.64
c = √324.64
c = 18.017769
x ≈ 18.0 (rounded to nearest tenth)
I think they’re perpendicular lines