MATHEMATICS HIGH SCHOOL

Patti is using mental math to evaluate the expression (70 + 12.8 + 30) + 6.1. She recognizes that the expression will be easier to simplify if she can combine 70 and 30 before she works with the other numbers. How do the properties of operations allow Patti to take that approach?

Answers

Answer 1

Answer:

Answer:

D. She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1

Step-by-step explanation:

Answer 2

Answer:

Answer:54

Step-by-step explanation:

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Polynomials
(14x3y2z)4

Answers

With the problem in figures, solving the given polynomials would be based on how it is being situated. If 3,2 and 4 are exponents, you are going to distribute the 3rd exponent which is 4 to the rest of the numbers so the figure goes 14 to the power of 4 then x to the power of 3 multiplied by 4 and y to the power of 2 multiplied by 4. With its polynomial term, the simplified term is 38416 x to the power of 12 y to the power of 8 and z to the power of 4

Final answer:

The result of raising the polynomial (14x3y2z) to the 4th power is 38416x12y8z4. This is calculated by individually multiplying each part of the polynomial by itself 4 times.

Explanation:

The problem is asking you to calculate the result of raising a polynomial (14x3y2z) to the 4th power.

The operation refers to using the rule of powers which states that any base with an exponent is multiplied by itself the amount of times indicated by the exponent. The result should therefore be calculated as follows:

(14x3y2z)4 = 38416x12y8z4

To find the answer, we raised each part of the polynomial to the 4th power. 144 equals 38416, (x3)4 results in x12 because you multiply the exponents, (y2)4 results in y8 for the same reason and z4 because anything to the power of 4 is itself raised 4 times.

Learn more about Polynomial calculation here:

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Please, solve this exercice:1+2+2²+2³+2⁴+....+ 2²⁰¹¹

It can be solved by using geometric progression?

Answers

$1+2+2^2+2^3+2^4+...+2^(2011)\n\na_1=1;\ a_2=1\cdot2=2;\ a_3=2\cdot2=2^2;\ a_4=2^2\cdot2=2^3\n\vdots\na_(2012)=2^(2010)\cdot2=2^(2011)$

$The\ sum\ of\ a\ terms\ of\ geometric\ progression:S_n=(a_1(1-r^n))/(1-r)\n\na_1=1;\ r=2\n\nsubtitute:\n\nS_(2012)=(1(1-2^(2012)))/(1-2)=(1-2^(2012))/(-1)=2^(2012)-1\n\nOnly\ that...(606\ digits,\ if\ you\ want\ how\ length\ this\ number)$

Find the midpoint of the line segment joining points A and B A(2,-5); B(6,1)

Answers

Answer:

The answer is ( 4 , - 2)

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

$M = ( (x1 + x2)/(2) , \: (y1 + y2)/(2) ) \n$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(2,-5); B(6,1)

So we have

$M = ( (2 + 6)/(2) \: , \: ( - 5 + 1)/(2) ) \n = ( (8)/(2) \: , \: - (4)/(2) )$

We have the final answer as

( 4 , - 2)

Hope this helps you

The image of -4,6 reflected along the y axis is?

Answers

The image of the point is still a point. The reflection point across the y-axis is (4,6)

A driveway is 10 feet long, 15 feet wide, and 7 inches deep. how many cubic feet of concrete will be required for the driveway? round your answer to the nearest cubic foot, if necessary.

Answers

The amount of concrete that will be required for the driveway is 151200 cubic inches.

What is volume?

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write volume as -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that a driveway is 10 feet long, 15 feet wide, and 7 inches deep.

The amount of concrete that will be required for the driveway will be equal to the volume of the driveway.

V = 10 x 12 x 15 x 12 x 7

V = 120 x 180 x 7

V = 21600 x 7

V = 151200 cubic inches

Therefore, the amount of concrete that will be required for the driveway is 151200 cubic inches.

To solve more questions on Volumes, visit the link-

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Answer:

Step-by-step explanation:

V=l x w x h

(10) (15) (.58) = 87.5. Rounding=88

remember it's 7 inches not feet. 7/12=.58

A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. What is the acceleration of the particle at time t = 0 seconds?