Answer:
x = -7 ±√5 /2
That is;
x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Step-by-step explanation:
To find the solutions to the equation, we will follow the steps below
(2x + 3)² + 8(2x + 3) + 11 = 0 --------------------------------------------------------------(1)
let u = 2x + 3
we will replace 2x+ 3 by u in equation (1)
u² + 8u + 11 = 0 -----------------------------------------------------------------------------(2)
we will solve equation (2) using the formula method
a=1 b=8 and c=11
u = -b ± √b² - 4ac /2a
u = -8 ±√(-8)² - 4(1)(11) /2(1)
u = -8 ±√64 - 44 /2
u = -8 ±√20 /2
u = -8/2 ± √20/2
u= -4 ± √20/2
u= -4 ± √5×4 /2
u= -4 ± 2√5 /2
u= -4 ± √5 ---------------------------------------------------------------------------(30
but u = 2x + 3
Substitute u =2x+3 in equation (3)
2x + 3 = -4 ± √5
subtract 3 from both-side of the equation
2x + 3-3 = -4 -3 ± √5
2x = -7±√5
Divide both-side of the equation by 2
2x/2 = -7 ±√5 /2
x = -7 ±√5 /2
21 containers for the ice cream
Answer:
is this algebra 1
Step-by-step explanation:
One can is $0.40
six cans bought seperatly is (6 * $0.40) $2.40
$2.40 - $1.98 = $0.42 this is how much we could save between buying the six cans seperatly or together
to find out how much we save per can, divide $0.42 by six
$0.42 / 6 = $0.07
by buying six cans together you save $0.07 per can compared to buying six cans seperatly.
Answer:
30√3 ≈ 51.96 miles
Step-by-step explanation:
The distance between the two ships can be found using the Law of Cosines, or using your knowledge of the side relationships in special triangles.
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Each ship is traveling at 10 mph, so after 3 hours will have traveled 30 miles.
The triangle OS1S2 formed by the harbor and the two ship locations is an isosceles triangle with base angles of 30°. Each half of OS1S2 is a 30-60-90 triangle whose longer leg is √3 times half the hypotenuse. The sum of those two "longer legs" is the distance between the ships.
The distance between ships is 2×15√3 = 30√3 ≈ 51.96 miles.
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<em>Additional comment</em>
If you prefer to use the Law of Cosines, you are looking for the length of the side opposite the 120° angle in a triangle with sides of 30 miles.
c² = 30² +30² -2·30·30·cos(120°) = 30²(2-2·(-0.5)) = 3·30²
c = 30√3 . . . . . take the square root (miles)
