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1 year ago

Drag the explanations used to solve the given equation in the correct sequence.5/6=9)=125

Mathematics

1 answer:

erastova [34]1 year ago

8 0

Given the equation:

$5^{(6x-9)}=125$

Let's solve the equation step by step by step, then drag the explanations used to solve the given equation in the correct sequence.

• Step 1:

Rewrite 125 as a power of 5

$5^{(6x-9)}=5^3$

• Step 2:

Divide each side by 5

$\begin{gathered} \frac{5^{(6x-9)}}{5}=\frac{5^3}{5} \\ \\ 1^{(6x-9)}=1^3 \end{gathered}$

• Step 3:

Since the exponents are equivalent, equate the exponents of the equation:

$6x-9=3$

• Step 4:

Add 9 to each side of the equation.

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The distance in the x-coordinates from A(–2, 2) to the center of dilation F(1, 1) is unit(s).

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Step-by-step explanation:

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3 years ago

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Will mark Brainlest please answer. find the value of a,b. <br>,p,q from the equal order pairs

NARA [144]

Step-by-step explanation:

<h3>Question-1:</h3>

by order pair we obtain:

$\displaystyle \begin{cases} \displaystyle 3p = 2p - 1 \dots \dots i\\2q - p = 1 \dots \dots ii\end{cases}$

cancel 2p from the i equation to get a certain value of p:

$\displaystyle \begin{cases} \displaystyle p = - 1 \\2q - p = 1 \end{cases}$

now substitute the value of p to the second equation:

$\displaystyle \begin{cases} \displaystyle p = - 1 \\2q - ( - 1) = 1 \end{cases}$

simplify parentheses:

$\displaystyle \begin{cases} \displaystyle p = - 1 \\2q + 1= 1 \end{cases}$

cancel 1 from both sides:

$\displaystyle \begin{cases} \displaystyle p = - 1 \\2q = 0\end{cases}$

divide both sides by 2:

$\displaystyle \begin{cases} \displaystyle p = - 1 \\q = 0\end{cases}$

<h3>question-2:</h3>

by order pair we obtain:

$\displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\3y= x + y \dots \dots ii\end{cases}$

cancel out y from the second equation:

$\displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\ x = 2y \dots \dots ii\end{cases}$

substitute the value of x to the first equation:

$\displaystyle \begin{cases} \displaystyle 2.2y-y= 3 \\ x = 2y \end{cases}$

simplify:

$\displaystyle \begin{cases} \displaystyle 3y= 3 \\ x = 2y \end{cases}$

divide both sides by 3:

$\displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2y \end{cases}$

substitute the value of y to the second equation which yields:

$\displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2 \end{cases}$

<h3>Question-3:</h3>

by order pair we obtain;

$\displaystyle \begin{cases} \displaystyle 2p + q = 2 \dots \dots i\\3q + 2p = 3 \dots \dots ii\end{cases}$

rearrange:

$\displaystyle \begin{cases} \displaystyle 2p + q = 2 \\2p + 3q= 3 \end{cases}$

subtract and simplify

$\displaystyle \begin{array}{ccc} \displaystyle 2p + q = 2 \\2p + 3q= 3 \\ \hline - 2q = - 1 \\ q = \dfrac{1}{2} \end{array}$

substitute the value of q to the first equation:

$\displaystyle 2.p+ \frac{1}{2} = 2$

make q the subject of the equation:

$\displaystyle p = \frac{3}{4}$

hence,

$\displaystyle q = \frac{1}{2} \\ p = \frac{3}{4}$

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3 years ago

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In a class full of men and women 5/9of the class are women. What is the ratio of men to women in its

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Answer:

The ratio in its simplest from is 4:5

Step-by-step explanation:

Now, let’s pick an arbitrary value for the total number of students in that class.

Let’s say we have 45 students in the class

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The number of men would be 45-25 = 20

So the ratio of men to women would be;

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