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3 years ago

What statements about prisms are always true if the top base is directly above the bottom base?

2 answers:

meriva3 years ago

6 0

The following are true:

1. The bases are congruent. This is what makes it a prism.

3. When the bases are polygons- which they should be for it to be a prism, the lateral faces are rectangles. This is always true because the edges of the polygon wil create a rectangle when it connects to the other edge on the opposite side of the prism.

Ilya [14]3 years ago

3 0

Answer:

The bases are congruent.

Step-by-step explanation:

Two figures are said to be Congruent if both figures are identical in their shape and size that means both figures have the same shape and also they have some dimension.

Since, if the top base is directly above the bottom base then the bases must be congruent. So, the first option is only true here.

The lateral faces may be a rectangle or may not be. So, it is not the correct option.

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Solve for kkk. 8(10-k)=2k8(10−k)=2k

Ivan

Answer:

k = 8

Step-by-step explanation:

We know that 8(10-k) = 2k so:

8(10−k)=2k

Simplify both sides of the equation:

8(10−k)=2k

(8)(10)+(8)(−k)=2k

80+−8k=2k

−8k+80=2k

Subtract 2k from both sides:

−8k+80−2k=2k−2k

−10k+80=0

Subtract 80 from both sides:

−10k+80−80=0−80

−10k=−80

Divide both sides by -10:

$\frac{-10k}{-10} =\frac{-80}{-10}$

k = 8

5 0

3 years ago

I have no idea how to solve this. Help would me much appreciated.

Otrada [13]

Answer:

Adam is 9 years old.

Step-by-step explanation:

Let d and c represent Adam's and Alicia's ages.

d = c - 15, and

c + 6 = 2(d + 6)

Rearrange d = c - 15 as c = d + 15, and then substitute d + 15 for c in the second equation. We obtain:

d + 15 + 6 = 2(d + 6), or

d + 21 = 2d + 12

Combining like terms, we get 21 = d + 12, or 9 = d.

If d = 9 then c = d + 15, or c = 9 + 15, or c = 24.

Adam is 9 years old.

7 0

4 years ago

A box (with no top) is to be constructed from a piece of cardboard of sides a and b by cutting out squares of length h from the

Drupady [299]

h = (19 - sqrt(97))/6, which is approximately 1.525190366 The volume of the box will be V = lwh And l will be a - 2h And w will be b - 2h So using the above, the volume of the box will be V = lwh V = (a - 2h)(b - 2h)h V = (11 - 2h)(8 - 2h)h V = (88 - 22h -16h + 4h^2)h V = (88 - 38h + 4h^2)h V = 88h - 38h^2 + 4h^3 Since you're looking for a maximum, that screams "First derivative" So let's calculate the first derivative of the function and solve for 0. V = 88h^1 - 38h^2 + 4h^3 V' = 1*88h^(1-1) - 2*38h^(2-1) + 3*4h^(3-1) V' = 1*88h^0 - 2*38h^1 + 3*4h^2 V' = 88 - 76h + 12h^2 We now have a quadratic equation. So using the quadratic formula with A=12, B=-76, and C=88, calculate the roots as: (19 +/- sqrt(97))/6 which is approximately 1.525190366 and 4.808142967 We can ignore the 4.808142967 value since although it does indicate a slope of 0, it produces a negative width and is actually a local minimum of the volume function. So the optimal value of h is (19 - sqrt(97))/6, which is approximately 1.525190366

5 0

4 years ago

A plane in R 3 is a subspace generated by two nonlinear vectors. Let P be the plane in R 3 that goes through the points (0, 0, 0

balandron [24]

Answer:

Yes, it lies on the plane

Step-by-step explanation:

Note that the generator (1,2,0) will always make vectors whose third coordinate is always 0. In order to obtain a 4 in the third coordinate, we need to use the generator (0,0,1). Specifically, we need (0,0,1) to be multiplied by 4, if we do that we obtain 4*(0,0,1) = (0,0,4).

We still need to obtain (3,6,4)-(0,0,4) = (3,6,0) from the generator (1,2,0), which is possible because (3,6,0) = 3*(1,2,0). Therefore

3*(1,2,0) + 4 *(0,0,1) = (3,6,4)

Thus, the point (3,6,4) is generated by the two vectors and, as a result, this points lies in the plane.

6 0

4 years ago

Without solving an equation, determine whether 1/4% of 80 is less than, equal to, or greater than 25% of 80?

Anettt [7]

1/4= 0.25%

25%>0.25

So, 25% of 80 is more than 1/4% of 80 and 1/4% of 80 is less than 25% of 80.

3 0

4 years ago

Read 2 more answers