Answer:
2 sqrt(3)
Step-by-step explanation:
Simplify the following:
sqrt(363) - 3 sqrt(27)
sqrt(27) = sqrt(3^3) = 3 sqrt(3):
sqrt(363) - 33 sqrt(3)
sqrt(363) = sqrt(3×11^2) = 11 sqrt(3):
11 sqrt(3) - 3×3 sqrt(3)
-3×3 = -9:
11 sqrt(3) + -9 sqrt(3)
11 sqrt(3) - 9 sqrt(3) = 2 sqrt(3):
Answer: 2 sqrt(3)
Answer:
B = 12800 grams or 12kg 800 grams.
Step-by-step explanation:
Let the two puppies be A and B respectively.
Translating the word problem into an algebraic expression, we have;
A + B = 22kg 300g
A = 9kg 500g
Conversion;
1 Kilograms = 1000 grams.
9kg 500g = 9*1000 + 500 = 9500 grams
22kg 300g = 22*1000 + 300 = 22300 g
Substituting into the above formula, we have;
9500 + B = 22300
B = 22300 - 9500
B = 12800 grams or 12kg 800 grams
Answer: The volume is 120
.
Step-by-step explanation:
-The volume formula for a triangular prism is:
(Height × Base × Length) /2
-So, you put the height, base, and length:
(4 × 6 × 10)
-Then, you solve:
(4 × 6 × 10)
(24 × 10)
240
-Divide 240 by 2:
240 ÷ 2
120
Therefore, the volume of a Triangular Prism is
.
Answer: 5425
Step-by-step explanation:
Answer:
1,2,3 and 6 are similar triangles by AA similarity
Step-by-step explanation:
1) ∠DEC ≅ ∠FEG {Vertically opposite angles}
DC // GF
∠ECD ≅ ∠EGF {Alternate interior angles}
∠EDC ≅ ∠EFG {Alternate interior angles}
ΔDEC & ΔFEG are similar triangles by AA similarity
2)MN // QP
∠LQP ≅ ∠QMN {Corresponding angles }
∠LPQ ≅ ∠PNM {Corresponding angles}
ΔLQP & ΔLMN are similar triangles by AA similarity
3) In ΔSYE ,
∠S = 180 - 90 - 39
∠S = 51°
In ΔCHW,
∠H = 180 - 51 - 90
∠H = 39
ΔSYE and ΔCHW
∠S ≅ ∠W = 51°
∠Y ≅ ∠C = 90°
∠E ≅∠H = 39°
ΔSYE & ΔWCH are similar triangles by AA similarity
6) ∠P ≅ ∠Z {Given}
∠PXQ ≅∠ZXY {Vertically opposite angles}
ΔPXQ & ΔZXY are similar triangles by AA similarity