Answer:
x=50
Step-by-step explanation:
Answer:
9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;
(x - 2)²/2² - (y + 3)²/3² = 1
Step-by-step explanation:
The standard form of a hyperbola is given as follows;
(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1
The given equation is presented as follows;
9·x² - 36·x = 4·y² + 24·y + 36
By completing the square, we get;
(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)
(3·x - 6)² - 36 = (2·y + 6)²
(3·x - 6)² - (2·y + 6)² = 36
(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1
(3·x - 6)²/6² - (2·y + 6)²/6² = 1
3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1
(x - 2)²/2² - (y + 3)²/3² = 1
The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.
Answer:
26 units
Step-by-step explanation:
If point F is on the line segment EG, then EF+FG = EG
Given
FG=8,
EF=2x+4
EG=4x−10
Substitute the given values into the formula;
2x+4+8 = 4x−10
2x+12 = 4x-10
collect like terms
2x-4x = -10-12
-2x = -22
x = 22/2
x =11
Since EF = 2x+4
EF = 2(11)+4
EF = 22+4
EF = 26
Hence the numerical length of EF is 26 units
Answer:
1) 
2) 
3) 
Step-by-step explanation:
1) Length of a ruler = r
Height of Shiela = s
According to the question ,
5 times the length of a ruler increased by 2 .
⇒ 
Also , 5r + 2 is less than height of Shiela.
Hence , the linear inequality is ⇒
2) Let the cost of each t-shirt be 't' & cost of each short be 's'.
⇒ Cost of dozen of t-shirts = 12t and Cost of half a dozen shorts = 6s
According to the question ,
12t & 6s is not greater than Php 960.
Hence the linear inequality is ⇒
3) Let the number of Php 100-peso tickets be 'p' and let the number of Php 50-peso tickets be 'q'.
According to the question ,
Difference of p & q is not less than 30
Hence the linear inequality is ⇒
Answer:
x = 12 degree
Step-by-step explanation:
3x + 19 + 5x = 115 degree (sum of two interior opposite angles are equal to the third side)
8x + 19 = 115
8x = 115 - 19
x = 96 /8
x = 12
