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3 years ago

Factor 125x^3-1000. Show your work.

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

4 0

The left term is (5x)³.

The right term is 10³.

So, you can use the formula for the factorization of the difference of cubes.

... a³ - b³ = (a-b)(a² +ab +b²)

Here, you have a=5x, b=10, so the factorization is

... 125x³ -1000 = (5x-10)(25x² +50x +100)

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Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.

kozerog [31]

Answer:

6.75g

Step-by-step explanation:

The first step is converting everything to grams, by rules of three. Then we add.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First step: 0.0025kg to g

Each kg has 1000g, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

0.0025kg = 2.5g

Second step: 1750 mg

Each g has 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

$x = \frac{1750}{1000}$

x = 1.75g

1750 mg = 1.75g

2.25g - OK

Third step: 825,000 μg to g

Each g has 1,000,000 ug, so:

1g - 1,000,000 ug

xg - 825,000 ug

1,000,000x = 825,000

$x = \frac{825,000}{1,000,000}$

x = 0.25g

825,000 μg = 0.25g

Final step: adding everyting

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

5 0

3 years ago

2. Draw the image of ∆RST under the dilation with scale factor ⅓ and center of dilation at the origin. Label the image ∆R’S’T’.

Alchen [17]

Since center of dilation is the origin, this is easy. Just divide all of the x and y coordinate values by 3. Place the new point on the graph, and draw the triangle.

R' = R(3,6)/3 = (3/3,6/3)=(1,2). So R'(1,2)
S' = S(-3,6)/3 = (-3/3,6/3)=(-1,2). So S'(-1,2)
T' = T(-6,-6)/3 = (-6/3,-6/3)=(-2,-2). So T'(-2,-2)

So you now know the location of the 3 new points. R' at (1,2), S' at (-1,2) and T' at (-2,-2). Simply draw those 3 points on your graph and connect the lines to make a new triangle.

6 0

3 years ago

A circle has a radius of 7 inches what is the area

Scrat [10]

Answer:

49π and 153.86 when multiplyed by 3.14.

Step-by-step explanation:

Hi!

The formula for finding the area of a circle is πr².

In that case, all we have to do is substitute 7 inches for our r.

7² × π

= 49π

If you want that solved out, we can substitute a rational number for π (3.14)

49 × 3.14 = 153.86

Thus, the area of the circle is $\boxed{49\pi}$ , 153.86 roughly.

Hope this helps!

8 0

3 years ago

What is the slope of the line, y=5−4x?

hoa [83]

Answer:

(m) =

ΔY

ΔX

= 0

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Label the dividend, divisor, and quotient in the problem 27,438 divided by 9 equals 3,048 r6.

Alika [10]

The dividend is the number being divided so the dividend is 27,438
The divisor is the one dividing the number so the divisor is 9
The quotient is your answer so you quotient is 3048

Your answer is C.

Hope this helps!

7 0

3 years ago