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3 years ago

Complete the table using equivalent ratios. 21:6 7: :4

Mathematics

2 answers:

cluponka [151]3 years ago

7 0

21:6 (given)
7:2 (21/3 and 6/3)
14:4 (7*2 and 2*2)

Brrunno [24]3 years ago

7 0

Answer:

7:2

14:4

Step-by-step explanation:

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Place the indicated product in the proper location on the grid. (4x^3+7y^3 z^ 4) ^2

ella [17]

Answer:

$16x^{6} +56x^{3}y^{3} z^{4} +49y^{6} z^{8} \\$

Step-by-step explanation:

To solve this type of problems first need to review some laws of exponents:

When you are multiplying the same base, you need to add the exponents.

$x^{2} +x^{8} = x^{2+8} = x^{10}$

When you are raising a base with power to another power, you should keep the base and multiply the exponents:

$(x^{2} y^{5})^3 = x^{2*3} y^{5*3} = x^{6} y^{15}$

Now for the expression $(4x^{3} + 7y^{3} z^{4} )^2$

Write the multiplying factors:

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} )$

Multiply the term $4x^{3}$

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{3+3} + 28x^3y^{3} z^{4}$

Then multiply the term $7y^{3}z^{4}$

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{3+3} + 28x^3y^{3} z^{4}\\\\+ 28x^3y^{3} z^{4} + 49y^{3+3} z^{4+4}$

Simplify the exponents:

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{6} + 28x^3y^{3} z^{4}\\\\+ 28x^3y^{3} z^{4} + 49y^{6} z^{8}$

Add like terms:

$= 16x^{6} + 56x^3y^{3} z^{4} + 49y^{6} z^{8}$

5 0

3 years ago

A city’s population, P, is modeled by the function P(x) = 78,500( 1.02 )x where x represents the number of years after the year

serg [7]

I presume this is meant to be exponential.

When f(x) = a(b)^x, a represents the starting value, b represents change, and x represents time.

The population began in 2000 (x = 0). This makes the equation equal to 78,500, which is your starting value and population in 2000.

1.02 means that the initial value is multiplied by 1.02 or 102% each year. Therefore, there is a 2% increase.

6 0

4 years ago

Write the reciprocal of a) 7/10 b)3.5

Thepotemich [5.8K]

Answer:

$\frac{10}{7}$