Answer:
B. ![\frac{b}{2a^{2}c^3}\sqrt[3]{15b}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B2a%5E%7B2%7Dc%5E3%7D%5Csqrt%5B3%5D%7B15b%7D)
Step-by-step explanation:
Given:
The expression to simplify is given as:
![\sqrt[3]{\frac{75a^7b^4}{40a^{13}c^9}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B75a%5E7b%5E4%7D%7B40a%5E%7B13%7Dc%5E9%7D%7D)
Use the exponent property 

Use the exponent property 


Reducing
to simplest form, we get:

Therefore, expression becomes:
![\sqrt[3]{\frac{15(a^{-2})^3\times b\times b^3}{2^3(c^3)^3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B15%28a%5E%7B-2%7D%29%5E3%5Ctimes%20b%5Ctimes%20b%5E3%7D%7B2%5E3%28c%5E3%29%5E3%7D%7D)
Use the cubic root property:
. Thus, the expression becomes:
![\frac{a^{-2}b}{2c^3}\sqrt[3]{15b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B-2%7Db%7D%7B2c%5E3%7D%5Csqrt%5B3%5D%7B15b%7D)
Using the exponent property 

So, the final expression is:
![\frac{b}{2a^{2}c^3}\sqrt[3]{15b}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B2a%5E%7B2%7Dc%5E3%7D%5Csqrt%5B3%5D%7B15b%7D)
Therefore, the correct option is option B.
Answer:
It is showing a slope of 1/4.
Step-by-step explanation:
It is also what a linear equation would look like on a graph.
Answers:
mode = 1
range = 5
-----------------------------------------
Explanation:
The mode is 1 because it is the most frequent value. It shows up four times compared to the other values (5,6) which only show up once and the value 4 only shows up twice.
The range is 5 because we subtract the max and min values to get 5.
In other words,
Range = Max - Min
Range = 6 - 1
Range = 5
FIG A : ANGLE OF BAC = 67.38 °
FIG B : LENGTH OF RT = 10.549 cm
FIG C: LENGTH OF AB = 5.282 cm
FIG D: ANGLE OF ACB = 37.303°
Step-by-step explanation:
Fig A:
ABC angle = ( Opposite side) / (Hypotenuse)
Sin Ф = (12) / (13)
Ф = Sin⁻¹ ( 12/13)
Ф = 67.38 °
Fig B:
By the basic property of trigonometry
Tan Ф = (Opposite side) / (Adjacent side)
Tan Ф = (14)/ X
X= 14 / (Tan 53° )
Length of RT = 10.549 cm
Fig C:
By the basic property of trigonometry
Sin Ф = (Opposite side) / (Hypotenuse)
Sin Ф = (X) / 12.5
X = 12.5
Sin 25°
X= 5.282 cm
Fig D:
From the basic property of Trigonometry
Tan Ф = (Opposite side) / (Adjacent side)
Tan Ф = (8/10.5)
Ф = Tan⁻¹ ( 8/10.5)
Ф = 37.303°
Answer:
(2,3)
Step-by-step explanation:
Rotation through 90 clockwise gives the expression
<em>(</em><em> </em><em>x</em><em> </em><em>,</em><em> </em><em>y</em><em> </em><em>)</em><em>_</em><em>_</em><em>_</em><em> </em><em>(</em><em> </em><em>y</em><em> </em><em>,</em><em>-</em><em> </em><em>x</em><em> </em><em>)</em>
<em>so</em><em> </em><em>whe</em><em>n</em><em> </em><em>you</em><em> </em><em>pu</em><em>t</em><em> </em><em>the</em><em> </em><em>poin</em><em>ts</em><em> </em><em>-</em><em>3</em><em> </em><em>,</em><em>2</em><em> </em><em>in</em><em> </em><em>the</em><em> </em><em>relat</em><em>ion </em><em>,</em><em> </em><em>it</em><em> </em><em>becom</em><em>es</em>
( -3 , 2 ) ___ ( 2, - -3 )
= ( x, y ) __ ( 2, 3 ). meaning when you rotate -3,2 through 90 clockwise you will get the image ( 2 ,3 )