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3 years ago

the volume of a box is 45x^3 + 198x^2 + 189x. find expressions for the possible dimensions of the prism

Mathematics

1 answer:

Oxana [17]3 years ago

7 0

Answer:

length, width, and height are (b+2), (b-2), (b+3)

Step-by-step explanation:

Doing what the problem statement tells you to do, you get ...

(b^3 +3b^2) -(4b +12)

= b^2(b +3) -4(b +3) . . . factor each pair of terms

= (b^2 -4)(b +3) . . . write as a product

= (b -2)(b +2)(b +3) . . . use the factoring of the difference of squares

The three factors are (b-2) , (b+2) , and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.

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Give the diagram shown at the right, find the value of 3x.<br><br><br> Pls help!!

EastWind [94]

Answer:

Step-by-step explanation:

Use the Pythagorean Theorem here:

30² = (3x)² + (4x)², or:

30² = 9x² + 16x² = 25x²

Taking the square root of both sides, we get √(30)² = √(25x²), or:

30 = ± 5x

Neglect -5x, since we are measuring distances, and distances are positive.

Then 5x = 30, and so x = 6

Thus, 3x = 3(6) = 18

4 0

3 years ago

The mystery number is a four-digit number. Its digits are 5, 4, 7, and 3. The 5 and the 7 are the two middle digits.The 5 comes

Flura [38]

4753 seems to me like the right one

7 0

3 years ago

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The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of len

ch4aika [34]

Length: 1/5 = 2/10
Width: 1/2 = 5/10

Perimeter = 2 (Length + Width)
= 2 (2/10 + 5/10)
= 2 ( 7/10)
= 14/10
= 1 and 4/10 = A. 1 and 2/5

6 0

3 years ago

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A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 12, length of BC is 11.5. A similar right trian

expeople1 [14]

Answer:

Option D is correct.

Length of PQ is 36 unit.

Explanation:

If the measures of two sides in one triangle are proportional to the corresponding sides in the another triangle and their including angles are congruent, then the triangles are similar.

Given: Right angle triangle ABC at B , Length of AB = 12 unit and length of BC = 11.5 unit and in right angle triangle PQR at Q , length of QR = 34.5 unit.

Also it is given that Angle A is congruent to angle P and angle C is congruent to angle R.

To find the length of QR:

It is given that ΔABC and ΔPQR are Similar triangle

then, by the definition of similar triangle:

$\frac{PQ}{AB} = \frac{QR}{BC}$

Substitute the value of AB, QR and BC to solve for PQ;

$\frac{PQ}{12}=\frac{34.5}{11.5}$ or

$PQ = \frac{34.5 \times 12}{11.5}$

On simplify:

$PQ = 3 \times 12 = 36$

Therefore, the length of side PQ is 36 units.

8 0

3 years ago

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Need help with this question too, just took a guess, but cannot explain or not sure if it's correct, please see pic for math pro

Oksi-84 [34.3K]

Answer:

0 ≤ x ≤ 70

Step-by-step explanation:

The range is defined by all values in the y-axe that are represented in the graph. In this case, we see the graph goes from 0 to 70, that will be the range.

PD. The representation is a non function.

5 0

3 years ago