Answer: m∠CAD = 81°
Step-by-step explanation: <u>Diagonal</u> is a line that unites opposite sides.
ABCD is a prallelogram. One property of diagonal in a parallelogram is it separates the parallelogram in 2 congruent triangles.
The figure below shows ABCD with its diagonals.
Since diagonal divides a parallelogram in 2 congruent triangles, it means the internal angles are also congruent. So
m∠BAC = m∠CAD
4x + 5 = 5x - 14
x = 19
Then, m∠CAD is
m∠CAD = 5(19) - 14
m∠CAD = 81
The angle m∠CAD is 81°.
If Zia is 8 years younger than twice her sisters Sasha's age. This must be the expression.
2S = Z-8
<em>Where:</em>
Z is Zia's age
S is Sasha's age
Now we rearrange for Z:
Z = 2S + 8
Hope this helps!
⅝ of the votes were for blue. That leaves ⅜ of the votes remaining. 5/9 of the remaining ⅜ votes were for green, so you multiply 5/9 x ⅜ = 15/72 votes for green. ⅝ of the votes were for blue, so you can multiply the fraction by 9/9 to get 45/72. So 45/72 votes were for blue, and 15/72 votes were for green. That leaves 12/72 votes remaining, which were for red. Since the question says 48 votes out of the total number of votes were for red, this means 48/v = 12/72 (v = the total number of votes). Cross multiply and solve for v to get v = 288. The fraction for blue is ⅝, so you can say x/288 = ⅝ (x = the number of votes for blue). Cross multiply and solve for x to get x = 180 votes for blue.
Answer:
270
Step-by-step explanation:
Given that :
Ratio = 14:8:5
Houses : flats : bungalow
Number of bungalow = 50
Sum of ratio = (14 + 8 + 5) = 27
Let total number of households = x
Bungalow = 5/27 * x
5/27 * x = 50
5x / 27 = 50
5x = 50 * 27
5x = 1350
x = 1350 / 5
x = 270
Number of places to live = 270
Answer:
The teacher will take 720 minutes or 12 hours to grade 32 reports.
Step-by-step explanation:
32 reports= x
4 reports= 90 minutes
Cross multiply method
90*32= 4x
2880= 4x
x= 720
The teacher will take 720 minutes or 12 hours to grade 32 reports.
Hope this helps!
