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antiseptic1488 [7]
3 years ago
15

Find the height of a rectangular prism if the volume is 171 in, the length is 6 in, and the width is 4 3/4.

Mathematics
2 answers:
Delvig [45]3 years ago
8 0
The height <span>of a rectangular prism is 6 in.</span>
kramer3 years ago
4 0
The height would be 7.13 inches.
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ABCD- parallelogram, If the perimeter of Triangle CPQ is 15cm, Find the perimeter of triangle BAQ. Find the perimeter of triangl
melamori03 [73]

Answer:

The answer is below

Step-by-step explanation:

A parallelogram is a quadrilateral (has 4 sides and 4 angle) with two pair of parallel and opposite sides. Opposite sides of a parallelogram are parallel and equal.

Given parallelogram ABCD:

AB = CD = 18 cm; BC = AD = 8 cm

∠P = ∠P, ∠PDA = ∠PCQ (corresponding angles are equal).

Hence ΔPCQ and ΔPDA are similar by angle-angle similarity theorem. For similar triangles, the ratio of their corresponding sides equal. Therefore:

\frac{CD}{PC}= \frac{AD}{CQ}\\\\\frac{18}{6}=\frac{8}{x}  \\\\x=\frac{6*8}{18}=\frac{8}{3}\ cm

Perimeter of CPQ = CP + CQ + PQ

15 = 6 + 8/3 + PQ

PQ = 15 - (6 + 8/3)

PQ = 6.33

∠CQP = ∠AQB (vertical angles), ∠QCP = ∠QBA (alternate angles are equal).

Hence ΔCPQ and ΔABQ are similar by angle-angle similarity theorem

\frac{AQ}{QP}=\frac{AB}{CP}  \\\\\frac{AQ}{6.33} =\frac{18}{6} \\\\AQ=\frac{18}{6}*6.33\\\\AQ = 19

\frac{BQ}{CQ}=\frac{AB}{CP}  \\\\\frac{BQ}{8/3} =\frac{18}{6} \\\\BQ=\frac{18}{6}*\frac{8}{3} \\\\BQ =8

Perimeter of BAQ = AB + BQ + AQ = 18 + 8 + 19 = 45cm

PA = AQ + PQ = 19 + 6.33 = 25.33

PD = CD + DP = 18 + 6 = 24

Perimeter of PDA = PA + PD + AD = 24 + 25.33 + 8 = 57.33 cm

7 0
3 years ago
How would you go about finding the area and perimeter of a composite figure?
fgiga [73]

Explanation:

The area is the sum of the areas of the non-overlapping parts. The figure is called "composite" because it is composed of figures whose area formulas you know. Decompose the figure into those, find the area of each, then sum those areas to find the area of the whole.

<u>For example</u>

If the figure consists of a rectangle and semicircle, find the areas of each of those. Then add the areas together to find the total area.

__

Likewise, the perimeter of a composite figure will be the sum of the "exposed" perimeters of the parts. (Some edges of the figures making up the composition will be internal, so do not count toward the perimeter of the composite figure.)

<u>For example</u>

If the curved edge of the semicircle of the figure described in the example above is part of the perimeter, then its length will be half the circumference of a circle. If the straight edge of the semicircle is "internal" and not a part of the perimeter, its length (the diameter of the semicircle) may need to be partially or wholly subtracted from the perimeter of the rectangle, depending on the actual arrangement of the composite figure. In other words, add up the lengths of the edges that "show."

_____

<em>Additional comments</em>

In the above, we have described how to add the areas of parts of the figure. In some cases, it can be easier to identify a larger figure, or one that is more "complete", then subtract the areas of the parts that aren't there. For example, an L-shaped figure can be decomposed into two rectangles. Or it can be decomposed into a larger rectangle covering the entire outside dimensions, from which a smaller rectangle is subtracted to leave the L-shape. Depending on how dimensions are shown, one computation or the other may be easier.

Likewise, for the purposes of computing the perimeter, lines of the figure may be rearranged in any convenient way, as long as their total length doesn't change. The L-shape just described will have a perimeter exactly equal to the perimeter of the rectangle that encloses its outside dimensions, for example. You can see this if you move the two lines forming the concave edges.

Familiarity with area formulas can help with area. For example, you know that the area of a triangle is the same as that of a rectangle half the height. Likewise, the area of a trapezoid is the area of a rectangle with the same height and a width equal to the midline of the trapezoid.

5 0
3 years ago
The sum of two consecutive integers is 65. Find the two integers.
Oliga [24]
32+33=65 
60/2 is 30, so they have to be in their thirties. Then 2+3=5, therefore they must be 32 and 33
7 0
3 years ago
X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to fo
lapo4ka [179]

Answer:

0.6247

Step-by-step explanation:

The formula for calculating a Z-score is Z = (X - μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question,

μ = 51, σ = 10. We are to find P(36 ≤ X ≤ 56)

Step 1

Find the Probability of X ≤ 36

μ = 51, σ = 10

Z = (X - μ)/σ

Z = 36 - 51/ 10

Z = -15/10

Z = -1.5

We find the Probability of Z = -1.5 from Z-Table

P(X <36) = P(X = 36) = P(Z = -1.5)

= 0.066807

Step 2

Find the Probability of X ≤ 56

μ = 51, σ = 10

Z = (X - μ)/σ

Z = 56 - 51/ 10

Z = 5/10

Z = 0.5

We find the Probability of Z = 0.5 from Z-Table:

P(X < 56) = P(X = 56) = P(Z = 0.5)= 0.69146

Step 3

Find P(36 ≤ X ≤ 56)

P(36 ≤ X ≤ 56) = P(X ≤ 56) - P(X ≤ 36)

= P( Z = 0.5) - P(Z = -1.5)

= 0.69146 - 0.066807

= 0.624653

Approximately to 4 decimal places , P(36 ≤ X ≤ 56) = 0.6247

7 0
3 years ago
Plz anyone help for points
emmainna [20.7K]

Answer:

B. 1,188 cubic units

Step-by-step explanation:

First find the area of the base

A = 1/2b*h (this would only be half the base so our formula would be)

A = b*h (Now enter values)

A = (9)(6)

A = 54 (now plug this into the volume formula)

V = Ab * h

V = (54)(22)

V = 1,188 cubic units

6 0
3 years ago
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