First one
remember that all triangles internal angles (the 3 at the vertices) add to 180
we want BCD
we know BAD already
and ABC is a right angle
the measure of BDA is just there to throw us off
so
all adds to 180
BAD+ABC+BCD=180
59+90+BCD=180
149+BCD=180
minus 149 both sides
BCD=31
BCD=31 degrees
2nd problem
all angles add to 180 degrees
so
CAB+ABC+BCA=180
6x+147+2x+78+126+x=180
6x+2x+x+147+78+126=180
9x+351=180
minus 251 both sides
9x=-171
divide both sides by 9
x=-19
x=-19 degrees
Answer:
17) x = 58.1 units
18) x = 17 units
Step-by-step explanation:
The concept of similar triangles will be applied.
It is evident that the AAA congruence property is responsible for the similarity of the two triangles in the 2 cases. The theorem is
- Triangles are similar if the measure of all three interior angles in one triangle are the same as the corresponding angles in the other.
So, the corresponding sides from the two triangles can be written as a ratio of one another
17)
The most obvious tell here is the largest angle in the two triangles, the sides directly opposite this angle in the two triangles can be written in a ratio such that
(95.2/13.6) = 7
indicating that the bigger triangle is exactly 7 times the smaller one.
So,
(95.2/13.6) = (53.2/7.6) = (x/8.3) = 7
x = 7 × 8.3 = 58.1
18)
The obvious tell here is the smallest common angle for the two triangles, the two other corresponding sides can then be written in a ratio, matching the bigger side in the two triangles to each other.
(39.5/7.9) = (37.5/7.5) = (x/3.4)
(x/3.4) = 5 (Indicating thay the bigger triangle is 5 times bigger than the smaller one.
x = 3.4 × 5 = 17 units.
Hope this Helps!!!
If the length of a rectangle is 3m longer than its width, then:
L=W+3
Is the area really 154^2? Or is it 154m^2? If yes, then:
A=LW
154=(W+3)(W)
154=(W^2+3W)
0=W^2+3W-154
0=(W-11)(W+14)
This means either (W-11) or (W+14) is equal to zero so:
W=11 and W=-14
To find out let's substitute the numbers:
154=(11+3)(11)
154=154
Therefore, the width of the rectangle is 11m
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
9x+7y=4
7y = - 9x + 4
y = -9x/7 + 4/7
Comparing with the slope intercept form, slope = - 9/7
If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (7,-4) is 7/9
To determine the intercept, we would substitute m = 7/9, x = 7 and y = -4 into y = mx + c. It becomes
- 4 = 7/9×7 + c = 49/9 + c
c = - 4 - 49/9 = -85/9
The equation becomes
y = 7x/9 - 85/9
2<span>, 3, 5, 7, 11, </span>13<span>, 17, 19, 23, 29, 31, </span>37<span>, </span>41<span>, </span>43<span>, </span>47<span>. are the only numbers prime that are less than 50</span>
