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Olin [163]
2 years ago
7

In order for Tim to simplify the expression below, what step will he need to use for each variable's exponent? 6 x y^2 z^4 2 x^2

y^5 z A Divide the exponents B Multiply the exponents C Add the exponents D Subtract the exponents
Mathematics
1 answer:
denpristay [2]2 years ago
3 0

Answer:

C. Add the exponents

Step-by-step explanation:

The given expression is presented as follows;

6·x·y²·z⁴·2·x²·y⁵·z

The expression can be rearranged by according to like terms as follows;

6·2·x·x²·y²·y⁵·z⁴·z = 3·2·2·x·x²·y²·y⁵·z⁴·z

By the law of indices, we add the exponents of the like terms to simplify the expression as follows;

3·2·2·x·x²·y²·y⁵·z⁴·z = 3·2⁽¹⁺¹⁾·x⁽²⁺¹⁾·y⁽⁵⁺²⁾·z⁽⁴⁺¹⁾ = 3·2²·x³·y⁷·z⁵

In order to simplify the expression the step Tim needs to use for each variable's exponent is to add the exponents.

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Please help me with this !:(
ahrayia [7]

Answer:

75.062cm^{2}

Step-by-step explanation:

To find the missing side use pythagorean theorem

So 6^{2} +b^2=8.5^2

Solve for b, b= 6.021

To find the area use \frac{1}{2}bh

So \frac{1}{2}(6.021+19)(6)= area

And you get 75.062

7 0
3 years ago
a cylindrical vase has a diameter of 6 inches at the bottom of the vase there are 9 marbles each of diameter 3 inches the vase i
KiRa [710]

Answer:

<h2>The volume of water in the vase is 339.33 in^3</h2>

Step-by-step explanation:

To calculate the volume of water in the vase we need the following parameters

1. the diameter/radius of the vase

2. the height /level of water in the vase

Given data

diameter d= 6 in

radius = d/2= 6/2 = 3 in

height of water h= 12 in

we know that the expression for the volume of a cylinder is given as

volume=  \pi r^2h

Inserting our data we have

volume= 3.142*3^2*12\\\volume= 3.142*9*12\\\volume= 339.33 in^3

3 0
3 years ago
Write 72xy^2? as a prime factorization. Show all of your work!​
kolezko [41]

9514 1404 393

Answer:

  2³·3²·x·y²

Step-by-step explanation:

Unique prime factors are 2, 3, x, y. Each of those is raised to a power to obtain the given expression.

  72xy² = 8·9·x·y² = 2³·3²·x·y²

6 0
3 years ago
Find an asymptote of this conic section. 9x^2-36x-4y^2+24y-36=0
ki77a [65]
We will begin by grouping the x terms together and the y terms together so we can complete the square and see what we're looking at. (9x^2-36x)-(4y^2+24y)-36=0.  Now we need to move that 36 over by adding to isolate the x and y terms.  (9x^2-36x)-(4y^2+24y)=36.  Now we need to complete the square on the x terms and the y terms.  Can't do that, though, til the leading coefficients on the squared terms are 1's.  Right now they are 9 and 4.  Factor them out: 9(x^2-4x)-4(y^2-6y)=36.  Now let's complete the square on the x's. Our linear term is 4.  Half of 4 is 2, and 2 squared is 4, so add it into the parenthesis.  BUT don't forget about the 9 hanging around out front there that refuses to be forgotten.  It is a multiplier.  So we are really adding in is 9*4 which is 36.  Half the linear term on the y's is 3.  3 squared is 9, but again, what we are really adding in is -4*9 which is -36.  Putting that altogether looks like this thus far: 9(x^2-4x+4)-4(y^2-6y+9)=36+36-36.  The right side simplifies of course to just 36.  Since we have a minus sign between those x and y terms, this is a hyperbola.  The hyperbola has to be set to equal 1.  So we divide by 36.  At the same time we will form the perfect square binomials we created for this very purpose on the left: \frac{(x-2)^2}{4}- \frac{(y-3)^2}{9}=1.  Since the 9 is the bigger of the 2 values there, and it is under the y terms, our hyperbola has a horizontal transverse axis.  a^2=4 so a=2; b^2=9 so b=3.  Our asymptotes have the formula for the slope of m=+/- \frac{b}{a} which for us is a slope of negative and positive 3/2.  Using the slope and the fact that we now know the center of the hyperbola to be (2, 3), we can solve for b and rewrite the equations of the asymptotes.  3= \frac{3}{2}(2)+b give us a b of 0 so that equation is y = 3/2x.  For the negative slope, we have 3=- \frac{3}{2}(2)+b which gives us a b value of 6.  That equation then is y = -3/2x + 6.  And there you go!
8 0
2 years ago
What is the solution to the following equation?<br><br> 5 + 3 (y - 4) = 4y +10
Umnica [9.8K]

Answer:

5 +3(y-4) = 4y +10

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-7 +3y = 4y + 10

3y - 4y = 10 + 7

-y = 17

y= -17

8 0
2 years ago
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