Answer:
The left side 7 is greater than the right side −9
, which means that the given statement is always true.
True
Step-by-step explanation:
Answer:
8 milkshakes
Step-by-step explanation:
16 cups in a gallon. 2 cups per milkshake. 8 milkshakes is the answer
The dimensions of the prism can be 2x, 2x+3 and x+6.
We first factor out the GCF of the trinomial. The GCF of the coefficients is 2. Each term has an x in common as well, so the GCF is 2x.
Factoring out the 2x, we have
2x(2x²+15x+18).
To factor the remaining trinomial, we find factors of 2*18=36 that sum to 15. 12*3 = 36 and 12+3 = 15. We split up 15x into 12x and 3x:
2x(2x²+12x+3x+18)
Now we group together the first two terms in parentheses and the last two:
2x((2x²+12x)+(3x+18))
Factor out the GCF of the first group:
2x(2x(x+6)+(3x+18))
Factor out the GCF of the second group:
2x(2x(x+6)+3(x+6))
Factoring out what these have in common,
2x(x+6)(2x+3)
1. Length of CD
Considering Triangle CDB
Angle DCB = 30
Using trigonometric ratio
Cos θ = adjacent/hypotenuse
Cos 30 = CD/CB
Cos 30 = CD/6
CD = 6(Cos 30)
= 5.196 cm
2. The area of triangle ABC
area of Δ ABC = ares of Δ ACD + Area of DCB
Area of Δ DCB
= 1/2 × 3× 5.195
= 7.79 cm²
length of AD
Tan 60 = AD/5.196
AD= 8.999
≈ 9 cm
Area of of ADC
= 1/2 × 9 × 5.196
= 23.382 cm²
Therefore area of Δ ABC
= 23.382 cm² + 7.79 cm²
= 31.172 cm²
