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Nataliya [291]
3 years ago
11

Simplify the radical expression -21√27x^9

Mathematics
1 answer:
padilas [110]3 years ago
6 0
-root 3*63x^2 is the answer you want
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Two canoes travel down a river, starting at 9:00 a.M. One canoe travels twice as fast as the other. After 4.5 hours, the canoes
Vedmedyk [2.9K]

Answer:

v_1=3.33 \ miles/hour\\v_2=6.66 \ miles/hour

Step-by-step explanation:

<u>Constant Speed Motion </u>

When the object travels the same distances in the same period of time, the speed is constant and is can be calculated as

\displaystyle v=\frac{x}{t}

where x is the distance and t is the time

There are two canoes traveling at speeds v1 and v2. One of them has twice the speed as the other. Let's say

v_2=2v_1

When t hours have passed, the canoes have traveled x1 and x2 respectively.

x_1=v_1t

x_2=v_2t

Since

v_2=2v_1

Then

x_2=2v_1t

The distance between them is

X=x_2-x_1=2v_1t-v_1t

X=v_1t

That distance is known and equals 11.25 miles, thus

v_1t=15

Solving for v1 and using t=4.5 hours

\displaystyle v_1=\frac{15}{4.5}

v_1=3.33 \ miles/hour

v_2=2\times 3.33

\boxed{v_2=6.66 \ miles/hour}

6 0
2 years ago
X+3y=14<br> y=3x-14<br> Solving systems using substitution <br> How do i do this?
Free_Kalibri [48]
X + 3y = 14
x + 3(3x - 14) = 14
x + 9x - 42 = 14
10x - 42 = 14
<u>      + 42 + 42</u>
       <u>10x</u> = <u>56</u>
        10     10
           x = 5.6
5.6 + 3y = 14
<u>- 5.6         - 5.6</u>
         <u>3y</u> = <u>8.4</u>
          3       3
           y = 2.7
     (x, y) = (2.7, 5.6)
6 0
3 years ago
Read 2 more answers
In the diagram AB =AD and
Greeley [361]

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.

Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, <em>the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. </em>This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.

8 0
3 years ago
Michael’s weight can be represented by the expression 72x^5. Al’s weight can be represented by the expression 9x^7.
podryga [215]

Answer:

a) \frac{72x^5}{9x^7}

b) =\frac{8}{x^2}

c), Yes;8x^2

Step-by-step explanation:

Michael's Weight: 72x^5

Al's weight: 9x^7

a) Ratio of Michael's weight to Al's weight: \frac{72x^5}{9x^7}

b) This ratio simplifies to:  \frac{8\times 9x^5}{9x^5\timesx^2}

                                         =\frac{8}{x^2}

c) Yes, If the exponent in each expression were negative, then we have:

Ratio of Michael's weight to Al's weight: \frac{72x^{-5}}{9x^{-7}}

This ratio simplifies to:  8x^{-5--7}=8x^2

The two ratios are not the same.

3 0
3 years ago
Determine the equation of the circle graphed below. <br><br> ( please help me )
Brums [2.3K]

Answer:

Equation : \\(x+3)^2 + ( y -2)^2 = 36

Step-by-step explanation:

For standard form the circle's equation we need the centre of the circle and the radius.

Step 1: <em><u>Find the centre</u></em>

If the centre is not given find the end points of the diameter

and then find the mid point.

Let the end points of the diameter be : ( - 3 , 8 ) and ( -3 , -4 )

The mid-point of the diameter is :

                        Mid-point = (\frac{-3 + - 3}{2}, \frac{-4+8}{2}) =  (-3, 2)

Therefore, centre of the circle = ( -3 , 2 )

Step 2 : <u>Find radius</u>

<u></u>Radius = \frac{Diameter }{2}<u></u>

Diameter is the distance between the end points ( -3 , 8) and ( -3 , -4 )

That is ,

 Diameter = \sqrt{(-3-(-3))^2 + ( -4 -8)^2}\\

                 = \sqrt{(-3 + 3)^2 + (-12)^2}\\\\=\sqrt{0 + 144}\\\\=12

Therefore ,

       Radius = \frac{12}{2} = 6

Step 3 : <u>Equation of the circle</u>

Standard equation of the circle with centre ( h ,k )

and radius ,r is :

       (x - h)^2+(y -k)^2 = r^2

Therefore, the equation of the circle with centre ( -3, 2)

and radius = 6 is :

    (x - (-3))^2 +  (y - 2)^2 = 6^2\\\\(x + 3)^2 + (y - 2)^2 = 36

5 0
2 years ago
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