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2 years ago

Apply the distributive property to factor out the greatest common factor.

Mathematics

1 answer:

ruslelena [56]2 years ago

4 0

80+32=112 so all you do is just add or use a brain .

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(08.01 MC)

Juli2301 [7.4K]

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

4 0

2 years ago

Read 2 more answers

Elapsed time was 9 hours and 45 min that ended at 6:00 what was the starting time

LiRa [457]

8:15 is the answer assuming the clock is at PM.

6 0

2 years ago

Read 2 more answers

$1500 is invested at a rate of 3% compounded monthly. Write a compound interest function to model this situation. Then find the

Marianna [84]

Answer:

Equation: $F=1500(1.0025)^{12t}$

The balance after 5 years is: $1742.43

Step-by-step explanation:

This is a compound growth problem . THe formula is:

$F=P(1+\frac{r}{n})^{nt}$

Where

F is future amount

P is present amount

r is rate of interest, annually

n is the number of compounding per year

t is the time in years

Given:

P = 1500

r = 0.03

n = 12 (compounded monthly means 12 times a year)

The compound interest formula modelled by the variables is:

$F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}$

Now, we want balance after 5 years, so t = 5, substituting, we get:

$F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43$

The balance after 5 years is: $1742.43

3 0

2 years ago

Identify the like terms in the expression. -3x^2+3x-x^2-2+6x

ololo11 [35]

like terms: -3x^2, -x^2

and 3x, 6x

6 0

2 years ago

Rationalise the denominator of: 1/(√3 + √5 - √2)

Paul [167]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} }$

can be re-arranged as

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} - \sqrt{2} + \sqrt{5} }$

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} }$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \dfrac{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

So, using this, we get

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5}) }^{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{5 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{ - ( - \sqrt{3} + \sqrt{2} + \sqrt{5}) }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}}$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\rm \: = \: \dfrac{- \sqrt{18} + \sqrt{12} + \sqrt{30}}{2 \times 6}$

$\rm \: = \: \dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}$

$\rm \: = \: \dfrac{- 3\sqrt{2} + 2 \sqrt{3} + \sqrt{30}}{12}$

Hence,

$\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} } =\dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}}}$

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<h3>More Identities to know:</h3>

$\purple{\boxed{\tt{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}}$

$\purple{\boxed{\tt{ {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}}$

6 0

2 years ago