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3 years ago

Solve this equation. Please show work. log(4m-10)=1

Mathematics

1 answer:

Ede4ka [16]3 years ago

5 0

Answer:

m=5

Step-by-step explanation:

1. Convert the logarithm into exponential form using the fact that $log_{a}$ (x)=b is equal to x= $a^{b}$ so ... 4m-10= $10^{1}$

2. Any expression raised to the power of 1 equals itself so ... 4m-10=10

3. Move the constant to the right-hand side and change its sign so ... 4m=10+10

4. Add the numbers so ... 4m=20

5. Divide both sides of the equation by 4 so ... m=5, m> $\frac{5}{2}$

6. Check if the solution is in the defined range so ... m=5

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The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

(x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

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maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

Learn more:

You can learn more about reflection in brainly.com/question/11203617

#LearnwithBrainly

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