Answer:
Volume = 1596.2 cubic cm
Step-by-step explanation:
Volume = volume of box - volume of cylinder
Volume = (LxWxH) - 1/3 (pi * r^2 *h)
Volume = (10 x 12 x 20) -1/3 (3.14 x 8^2 x 12)
Volume = 2400 - 803.8
Volume = 1596.2 cm^3
An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression
can be simplified as shown below.

Hence, The simplified version of the given expression is (3√2-2)√x³.
Learn more about Expression:
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If two similar triangles have side lengths 3cm and 7cm then we can determine that the scale factor for the lengths is: 7/3
Now, we have to work out the area scale factor !
This is simple, since area is given in cm² then all we have to do is square our original scale factor!
So,
7/3² = 49/9
So, we can say that the ratio of the area would be:
x : 49/9x
Hope this helps! <3
Step-by-step explanation: The <em>intersection</em> of two figures can
be defined as the set of points that is contained in both figures.
In this figure, lines <em>h</em> and <em>i</em> intersect at C or we can
say that C is the intersection of lines <em>h </em>and <em>i</em>.
In this figure, C is the intersection of lines <em>h</em> and <em>i</em>
because C is the point contained by both <em>h</em> and <em>i</em>.
Answer:
Answer for 2nd is option c, for 3rd is option d, for 4th is option e
Step-by-step explanation:
As we know 1 ft.=12 in.
- In ΔABC
∴ The congruent sides are AB and AC respectively
- CB =12 ft. 4 in.=148 in.
- AB=
CB =111 in. =9 ft. 3 in. - AC=
CB =111 in. =9 ft. 3 in.
∵ <em>Perimeter of ΔABC</em> =AB+AC+CB
=9 ft. 3 in. + 9 ft. 3 in. +12 ft. 4 in.
=30 ft. 10 in.
2. In ΔDEF
∴ The congruent sides are DE and DF respectively
- DE = 6 ft. 3 in. =75 in.
- DF = 6 ft. 3 in. =75 in.
- Let the length of FE is equal to x
- 0.75FE =DE =DF
- 0.75x = 6 ft. 3 in. =75 in.
- x =100 in. =8 ft. 4 in.
∵ <em>Perimeter of ΔDEF</em> =DE+DF+FE
= 6 ft. 3 in. +6 ft. 3 in. +8 ft. 4 in.
= 20 ft. 10 in.
3. In ΔJKL
∴ The congruent sides are JL and KL respectively
- JK = x+3
- KL =4x-17
- JL =6x-45
- JL≅KL
- 4x-17 =6x-45 . . . . . . . . . . . . . . . . . . . . . . . (1)
- Subracting 4x from both sides from eq 1
- -17 =2x-45
- Adding 45 on both the sides
- 28 =2x
- Dividing by 2 on both sides
- 14 =x
- JK = 14+3 =17
- KL = 4×14-17 =39
- JL = 6×14-45 =39
∵ <em>The dimensions of the ΔJKL are 39,39 and 17.</em>