Answer:
x = 18 y = 10
Step-by-step explanation:
let the first number be x
let the second number be y
x = y + 8..... equation 1
2x + y = 46.... equation 2
x is the larger number
y is the smaller number.
Rearrange the equation and add equation 1 to equation 2.
x - y = 8
+ 2x + y = 46
-------------------
3x + 0 = 54
3x = 54
divide both sides by 3
x = 54/3
x = 18
Substitute x = 18 into equation 1
x = y + 8
18 = y + 8
collect like terms
y = 18-8
y = 10
Answer:
Option a.
Step-by-step explanation:
In the given triangle angle A is a right angle so triangle ABC is a right angled triangle.
Opposite side of right angle is hypotenuse. So, CB is hypotenuse.
From figure it is clear that CA is shorter that segment BA.
All angles are congruent to itself. So angle C is congruent to itself.
We know that, if an altitude is drawn from the right angle vertex in a right angle triangle it divide the triangle in two right angle triangles, then given triangle is similar to both new triangles.
So, triangle ABC is similar to triangle DBA if segment AD is an altitude of triangle ABC.
Therefore, the correct option is a.
Answer:
Triangle PRT is similar to triangle SRQ
Step-by-step explanation:
AA similarity Postulate :If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
one angle is already given : angle RPT congruent to angle RSQ
The other is : angle TRP congruent to angle SRQ (both triangles share the same angle)
Triangle PRT is similar to triangle SRQ (AA postulate)
Answer for 11-13: m<2: 150, m<6: 150, m<7: 150
Step-by-step explanation:
There is 180 degrees in a straight line. If one part of the line (angle) is 30 degrees, then the other part is 150. If you look at the image, you would see that m<2 is congruent to m<6 ,which means same, and m<7 is congruent to m<3.
Answer for 14-16: m<EBG: 150, m<AGH: 150, m<DHF: 30.
Step-by-step explanation:
4x = 150 2x + 50 = 150
x = 37.5 2x = 150 - 50
4(37.5) = 150 2x = 100
x = 50
2(50) + 50 =
100 + 50 = 150
