Answer:
3y = -2x -7
Step-by-step explanation:
The equation of the line;
y = 
x + 8
Unknown:
Equation of the line passing through (4, -5);
Solution:
To solve this problem;
the equation of a line is given as;
y = mx + c
where x and y are the coordinate
m is the slope
c is the intercept
To solve this problem,
The slope if the same as that of the new line since they are parallel;
Equation of the new line;
x = 4 and y = -5
-5 = x 4 + c
-5 = 
+ c
c = -5 + 
c = 
So, the equation of the line is;
y = x - 
or ;
3y = -2x -7
For this case we have the following expression:
For simplicity we follow the steps:
We apply distributive property to the terms within the parenthesis, bearing in mind that:
We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.
ANswer:
Observe attached picture.
On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
C = height of sign = 6 ft
D = length of sign's shadow = 3 ft
When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.
We can apply trigonometry rules to find height of flagpole.
From small triangle containing sign we can find tangens function:
Similarly we can do for large triangle containing flagpole:
We see that these two equations have same left sides. This means that their right sides must also be same:
We can solve for A:
Height of flagpole is 48 feet.
Answer:
a. D and E are similar but not congruent.
Step-by-step explanation:
Let's analyse each statement and determine which is true about the 3 given quadrilaterals:
a. "D and E are similar but not congruent." TRUE.
D is similar to E because, every segment of D is proportional to the corresponding segments of E. The ratio of their corresponding segments are equal.
D and E are not congruent because their segments are not of equal length. Thus, they have the same shape but different sizes.
b. "E and F are similar and congruent." NOT TRUE.
E and F has the same size, hence they are congruent. However, they are not similar, because they don't have the same shape. Their corresponding lengths are not proportional.
c. "D and E are similar and congruent." NOT TRUE.
Since statement (a) is TRUE, statement (c) cannot be true.
D and E are similar because they have the same shape and the ratio of their corresponding sides are the same. D and E are not congruent, because they are not of the same size.
d. "F and D are similar but not congruent." NOT TRUE.
F and D has the same size but the ratio of their corresponding sides are not the same.
