Question:
In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, m angle G=80 degrees, and m angle H=55 degrees. If triangle ABC GHF, which statement is true?
(A) AB = 12.3 cm
(B) AB = 10.6 cm
(C) m∠C = 55°
(D) m∠C = 80°
Answer:
Option B:
AB = 10.6 cm
Solution:
The image of the triangle is attached below.
In ΔFGH,
FG = 12.3 cm, GH = 10.6 cm, m∠G = 80° and m∠H = 55°
Option A: AB = 12.3 cm
Given ΔGHF 
ΔABC.
Corresponding parts of congruence triangles are congruent.
GH = AB = 10.6 cm
So, option A is not true.
Option B: AB = 10.6 cm
Already proved in option A that AB = 10.6 cm
So, option B is true.
Option C: m∠C = 55°
ΔGHF ΔABC
Corresponding parts of congruence triangles are congruent.
m∠G = m∠A = 80°
m∠H = m∠B = 55°
Sum of the angles of a triangle = 180°
⇒ m∠A + m∠B + m∠C = 180°
⇒ 80° + 55° + m∠C = 180°
⇒ m∠C = 180° – 80° – 55°
⇒ m∠C = 45°
So, option C is not true.
Option D: m∠C = 80°
Already proved in option C that m∠C = 45°.
So, option D is not true.
Hence option B is the true statement that AB = 10.6 cm.
Answer:
(100 – 12) – 3x
Step-by-step explanation:
(100 – 12) – 3x would be the correct answer because:
100 is the total amount he paid
12 is the cost of pants
because we don't know the price of shirts yet so it would be called x
He buy in total of 3 shirts so the equation for the price would be 3 * x = 3x
So it would be:
total money paid - pants costs - shirts cost
= 100 - 12 - 3x or (100 - 12) -3x
Hope this helped :3
Answer: 
Step-by-step explanation:
The formula for calculate the area of a rectangle is:
Where "l" is the lenght and "w" is the width.
Based on the information given in the exercise, you can draw the fish tank attached, where the dimensions are: 18 inches high (
), 14 inches deep (
), and 30 inches long (
).
The area that was convered will be the sum of the areas of all the faces, but the top of the tank.
Therefore, the area that was convered is the following:
1.) y=3
2.) y=13
2y + y = 3y , 22+17= 39
3y = 39 , divide 3 on each side (which cancels out the 3 with the y which leaves you with y)
3.) y=10
3y - y = 2y , 35-15= 20
2y=20 , do the same as # 2.
4.) y=4
9y - 5y = 4y , 48-32= 16
4y=16, do the same as #2 & #3
5.) (4,5)
x + 3y = 19
2x - 3y = -7
solve for x first ; x + 2x= 3x , 19-7 = 12; 3x = 12 ; divide 3 ; x= 4. You know have to make the x's cancel out. so I will multiply -2 on the first equation. -2(x+3y=19)
-2x - 6y = -38
2x - 3y = -7
Now solve for y ; -6y + -3y = -9y , -38 + -7 = -45; -9y=-45 ; divide by -9 (since they are both negative your answer will be positive) ; y= 5
6.) (6,8)
x + 4y = 38
-x - 3y = -30
solve for y first ; 4y - 3y = y , 38-30 = 8; y=8 (that simple!) Now you need to find a common multiple for 4 & 3 which is 12. So you will have to multiply each equation by either 4 or 3.
(x + 4y = 38)*3 = 3x + 12y = 114
(-x - 3y = -30)*4 = -4x - 12y = -120
solve for x ; 3x - 4x = -x , 114-120= -6 ; -x=-6. Since the x has a negative that means there's still a 1 there so -1x=-6 ; you will need to divide this which makes the 6 a positive; x=6
Answer:
0.84 square in
Step-by-step explanation:
Since the capacity of the cable is proportional to its cross-sectional area. If a cable that is 0.3 sq in can hold 2500 lb then per square inch it can hold
2500 / 0.3 = 8333.33 lb/in
To old 7000 lb it the cross-sectional area would need to be
7000 / 8333.33 = 0.84 square in
