No solution / no x
D=b^2-4*a*c -> D=-4^2-4*1*21 -> D=-28 -> D<0, no solution
Adding both equations cancels y:
<span>4x + 8y = 16
</span><span>4x - 8y = 0
-----------------+
8x = 16 => x=2
filling in x=2 in the first equation gives:
4*2 + 8y = 16 => 8y = 8 => y=1
So (2,1) is the (x,y) pair that solves the two equations. Answer C.</span>
Answer:
136+ m ≥ 189 is the required inequality : m: The earning in 4th week
Arthur needs to earn AT LEAST $53 in the fourth week to buy the coat which costs at least $189.
Step-by-step explanation:
The amount earned by Arthur in first 3 weeks = $136
The amount needed to buy a coat = AT LEAST $189
Let us assume the amount Arthur needs to earn more to buy coat = $m
⇒ $ 136 + Amount Earned in 4th week ≥ $189
⇒ 136+ m ≥ 189
The above equation is the NEEDED inequality of the given situation.
Now, solving for the value of m, we get:
136+ m ≥ 189
⇒ m ≥ 189 - 136 = 53
or, m ≥ $53
Hence, Arthur needs to earn AT LEAST $53 in the fourth week to buy the coat which costs at least 189.
Answer:
(x - 10)² + (y + 9)² = 20
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre to a point on the circle
To calculate r use the distance formula
r = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, - 9) and (x₂, y₂ ) = (12, - 13)
r = 
= 
= 
, hence
(x - 10)² + (y - (- 9))² = ()², that is
(x - 10)² + (y + 9)² = 20
Answer:
19.5 ounces of spices
Step-by-step explanation:
Raheem made 14 ounces of curry sauce which contained (among other things), 3.25 ounces of spices. He wants to make a larger batch for a family dinner and decides he will need a total of 84 ounces of sauce altogether. How many ounces of spices will he need to complete his recipe?
The question above is calculated as:
14 ounces of sauce = 3.25 ounces of spices
84 ounces of sauce = x ounces of spices
Cross Multiply
14x = 84 × 3.25
x = 84 × 3.25/14
x = 19.5 ounces of spices
Hence, for 84 ounces of curry sauce he would need 19.5 ounces of spices
