Answer:
L=93
Step-by-step explanation:
Perimeter of a rectangle is 2(L+W)
So 2(L+83)=352
L+83=176
L=93
Answer:
(1,3)
Step-by-step explanation:
Given : 2x+3y=11 ---(a)
-4x+2y=2---(b)
Solution:
Multiply equation a by -2 both sides.
So, equation becomes : -4x-6y= - 22
Now , Subtract the equation b from resultant equation :
⇒(-4x-6y+22)-(-4x+2y-2)
⇒-4x-6y+22+4x-2y+2=0
⇒-8y+24=0
⇒-8y=-24
⇒![y=\frac{-24}{-8}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-24%7D%7B-8%7D)
⇒y = 3
Now to find x put value of y in equation a
⇒2x+3*3=11
⇒2x+9=11
⇒2x=2
⇒x=1
Thus the solution is (x,y)=(1,3)
Answer: x = ![52^{0}](https://tex.z-dn.net/?f=52%5E%7B0%7D)
Step-by-step explanation:
The exterior angle of a triangle = sum of the opposite interior angle.
The interior angles given are :
and ![90^{0}](https://tex.z-dn.net/?f=90%5E%7B0%7D)
Which are opposite to x + 72
Therefore :
x + 72 =
+ ![90^{0}](https://tex.z-dn.net/?f=90%5E%7B0%7D)
x + 72 = ![124^{0}](https://tex.z-dn.net/?f=124%5E%7B0%7D)
x =
- ![72^{0}](https://tex.z-dn.net/?f=72%5E%7B0%7D)
x = ![52^{0}](https://tex.z-dn.net/?f=52%5E%7B0%7D)
The numerical sum of the degree measures of m ∠DEA and m ∠AEF and m ∠DEF is 360°; The numerical measures of the angles is,
m ∠DEA = 56°
m ∠AEF = 158°
m ∠DEF = 146°
Based on the given data,
m ∠DEA= x + 30,
m ∠AEF= x + 132, and
m ∠DEF= 146 degrees
If the sum of two linear angles is 360° then, they are known as supplementary angles.
∠A + ∠B + ∠C = 360°, (∠A and ∠B and ∠C are linear angles.)
So,
We can write,
m ∠AEF + m ∠DEA + m ∠DEF = 360°
( x + 132) + (x + 30) + 146 = 360°
x + 30 + x + 132 + 146 = 360°
2x + 308 = 360°
2x = 360° - 308
x = 52/2
x =26
Now, we will substitute the value of x = 26° in the ∠DEA and ∠AEF, hence we get:
m ∠DEA = x + 30
m ∠DEA = 26 + 30
m ∠DEA = 56 degrees
Also,
m ∠AEF = x + 132
m ∠AEF = 26 + 132
m ∠AEF = 158
Hence,
m ∠DEA + m ∠AEF + m ∠DEF = 360°
56 + 158 + 146 = 360°
360° = 360°
Therefore,
Therefore, the numerical sum of the degree measures of m ∠DEA and m ∠AEF and m ∠DEF is 360°; The numerical measures of the angles is,
m ∠DEA = 56°
m ∠AEF = 158°
m ∠DEF = 146°
To learn more about information visit Supplementary angles :
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"You" ran faster. 3 1/2 mi. turn into 3 5/10 mile. 1 2/5 mi. turn into 1 4/10 mile. 3/4 of an hour is 45 min. 1/3 of an hour is 20 min. Therefore you multiply 1 4/10 times 2 to get 2 8/10 mi. in 40 min. Since your friend needs 5 more min. to be at the same time as you, you divide 20 (1/3 of an hour) by 4. Which gives you 5 minutes. Now, take the 1 2/5 of the mile. and divide that by 4. Which according to Symbolab.com gives you 1/10. Now go back to the beginning, you ran 3 5/10 mi. in 45 minutes. Your friend ran 2 8/10 in 40 min. Now that we know 5 min. equals 1/10 miles, you can add that to your friend. which means she/he ran 2 9/10 mi. in 45 min. In conclusion, you ran farther that your friend in 45 min. "You" ran faster. (: