Answer:
5. A) two solutions
6. one solution
Step-by-step explanation:
5. A graph shows the curve has two x-intercepts, so two solutions. You can also figure this by looking at the discriminant:
b^2 -4ac = (7)^2 -4(-4)(8) . . . . a positive number
When the discriminant is positive, there are two real solutions.
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6. The equation factors as ...
0 = 3(x +3)^2
This will have one real solution at x=-3.
Answer:
AC ≈ 7.6 cm
Step-by-step explanation:
I've attached a drawing of this problem below as a visual aid.
We know that this is a right triangle (one of the angles is 90°), one of the other angles (mA) is 33°, and the hypotenuse (AB) is 14 cm. We need to calculate the length of one of the other sides. We can use sine, cosine, or tangent.
Remember SOHCAHTOA?
→ soh (Sine = Opposite / Hypotenuse)
→ cah (Cosine = Adjacent / Hypotenuse)
→ toa (Tangent = Opposite / Adjacent)
The side we want to calculate happens to be <u>adjacent</u> to the angle mA (33°). So, we use cosine. We put in the values we know and solve for <em>x</em>, the missing side:
→ sin(33°) =
→ x = sin(33°) × 14
→ x ≈ 7.6
The length of AC is 7.6 centimeters.
