Determine whether the following expressions are equivalent to 8/7(21+42b)

Strike441 [17]

Answer:

The answer is 4.

Step-by-step explanation:

Since the fractions have the same denominators, all you have to do is subtract 1/5 from 1/5. When you subtract the numerators (1-1) you get 0. That would make the fraction 0/5, but that does not have to be included in the answer since it has no value. Subtract the whole numbers (23-19) to get 4.

Hope I helped you out!

7 0

4 years ago

Read 2 more answers

A box of books has a mass of 4.10 kilogram for ever meter of its height a box of magazines has a mass of 3 pounds for every foot

Tju [1.3M]

No rounding is necessary to answer the question.

We can subtract the (linear) density of the second box from that of the first to see which box is heavier per unit height.

$\dfrac{4.10\,kg}{1\,m}-\dfrac{3\,lb}{1\,ft}=\dfrac{4.10\,kg}{1\,m}\cdot\dfrac{1\,lb}{0.45\,kg}-\dfrac{3\,lb}{1\,ft}\cdot\dfrac{3.28\,ft}{1\,m}\\\\=\dfrac{4.10\,lb}{0.45\,m}-\dfrac{3\cdot 3.28\,lb}{1\,m}=\dfrac{4.10-3\cdot 3.28\cdot 0.45}{0.45}\dfrac{lb}{m}=\dfrac{4.10-4.428}{0.45}\dfrac{lb}{m}$

This value is obviously less than zero, so ...

... the box of magazines has the greater mass per unit height.

_____

The question didn't ask for the mass per height, and we didn't compute it. All we did was make a conversion to comparable units. The units we ended up with are mixed English and metric units, but that doesn't matter for the purpose of comparison.

Since all we're really interested in is <em>the sign of the difference</em> of mass/height, we don't even need to actually compute that difference. We just need to do enough computation to be able to tell whether the sign is positive or negative.

3 0

4 years ago

Find the distance between (-3,2) and (5, -6) using the distant formula.

spin [16.1K]

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[5-(-3)]^2+[-6-2]^2}\implies d=\sqrt{(5+3)^2+(-8)^2} \\\\\\ d=\sqrt{8^2+8^2}\implies d=\sqrt{2(8^2)}\implies d=8\sqrt{2}$

8 0

4 years ago

A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.2 in. The slant height of the pyram

Mice21 [21]

Answer:

<h2>The height is 87.5 in</h2>

Step-by-step explanation:

We can solve the height of a square pyramid using the Pythagoras theorem, this is because the slant height the height and the section of the base form a right triangle

the slant height is equivalent to the hypotenuse

the height is equivalent to the opposite

while the base(half) is the adjacent

Given

the base of the pyramid= $22.2 in$

the adjacent is = $\frac{22.2}{2} = 11.1 in$

the slant height (hypotenuse)= $88.2 in$

we know that Pythagoras theorem states that "The sum of the squares of the lengths of the legs of a right triangle ('a' and 'b' in the triangle) is equal to the square of the length of the hypotenuse ('c').

$c^2=a^2 + b^2$