3. I believe the answer is C & A, arrange the boards so that the diagonals bisects and are perpendicular. A rhombus is a Quadrilateral with all its sides equal to each other. The diagonals of a rhombus are perpendicular to each other and bisects each other.
4.The corresponding pairs of base angles of a trapezoid add up to 180 degrees, (they are supplementary), While all the angles (the four angles add up to 360 degrees)
Therefore; in this case the two angles are equal
hence, 19x + 8 = 11x+16 solving for x
x = 1
substituting x in either of the expression
The angle = 27 °
5. The diagonals of a rhombus bisects each other at right angles; the are perpendicular,
hence,
m∠1= 10x = 90
x = 9
m∠2 = x + y =90
but x = 9,
thus, y = 81
m∠3 = 5z= 90
z =18
10. A kite is a Quadrilateral with two equal sides and the other two sides equal.
thus, y-4 = 5x+2 and x +22 = 3x +10
solving for x
x+22 = 3x +10
2x = 12
x = 6
y-4 = 5x +2
y-4 = 5(6) +2
y = 36.
11.a. RHOM is a Quadrilateral with four equal sides
b. The four sides RH, OH, OM, and RM are equal, They are all congruent
c HM and HM is the diagonal, which forms the corresponding sides of triangle MRH and triangle MOH
d. Triangle MRH and triangle MOH are congruent, SSS, and similar to each other.
First, let's get rid of the unneeded info.
Oldest brother has $108 (3/5 the total)
Youngest brother has $x (1/10 the total)
Next let's find out the total. We do this by multiplying the oldest brothers money by 5/3 (the reciprocal).
108 × (5/3) = 180.
So the total amount of money is $180.
Finally, do 180 × (1/10) to find the youngest brother's amount.
180 × (1/10) = 18.
The youngest brother has $18.
Answer:
the rate of each train is 139 km/h and 159 km/h.
Step-by-step explanation:
let
v = the rate of the slower train
v + 20 = the rate of the faster train
d = 1490 km the distance that the two train will travel
t = 5 hr the time of the travel
since speed = distance/time => distance = speed*time
v*t + (v+20)t = d
5v + 5(v + 20) = 1490
5v+5(v+20)=1490
Step 1: Simplify both sides of the equation.
5v+5(v+20)=1490
5v+(5)(v)+(5)(20)=1490(Distribute)
5v+5v+100=1490
(5v+5v)+(100)=1490(Combine Like Terms)
10v+100=1490
10v+100=1490
Step 2: Subtract 100 from both sides.
10v+100−100=1490−100
10v=1390
Step 3: Divide both sides by 10.
10v/10 = 1390/10
v = 139km/h
Next
we add 139 to 20
139 + 20 = 159 km/h
the rate of each train is 139 km/h and 159 km/h.
The corresponding height of the triangle is 1.6 units
The formula for calculating the area of a triangle is expressed as:
- b is the base of the triangle
- h is the height of the triangle
Given the coordinates of the base BC of the triangle given as B(3, 2), and C(-1,-1). Using the distance formula:
The area of the triangle passing through the coordinate points A(-1, 1), B(3,2), and C(-1, -1) is expressed as:
![A=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\\](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Bx_1%28y_2-y_3%29%2Bx_2%28y_3-y_1%29%2Bx_3%28y_1-y_2%29%5D%5C%5C)
Substituting the coordinate points:
![A=\frac{1}{2}[(-1)(2-(-1))+3(-1-1)+-1(1-2)]\\A=\frac{1}{2}[(-1)(3)+3(-2)+-1(-1)]\\A=\frac{1}{2}[-3-6+1]\\A=\frac{1}{2} (-8)\\|A| =4 units^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5B%28-1%29%282-%28-1%29%29%2B3%28-1-1%29%2B-1%281-2%29%5D%5C%5CA%3D%5Cfrac%7B1%7D%7B2%7D%5B%28-1%29%283%29%2B3%28-2%29%2B-1%28-1%29%5D%5C%5CA%3D%5Cfrac%7B1%7D%7B2%7D%5B-3-6%2B1%5D%5C%5CA%3D%5Cfrac%7B1%7D%7B2%7D%20%28-8%29%5C%5C%7CA%7C%20%3D4%20units%5E2)
Recall that:
Hence the corresponding height of the triangle is 1.6 units
Learn more on area of triangles here: brainly.com/question/17335144
A = s^2
A' = 2s*s'
When the area is 36 cm^2, the side (s) is 6 cm. The area is increasing at the rate
A' = 2(6 cm)*(6 cm/s) = 72 cm^2/s
