Answer : <em>The</em><em> </em><em>required</em><em> </em><em>ratio</em><em> </em><em>is</em><em> </em><em>(</em><em>1</em><em>4</em><em>m</em><em>-</em><em>6</em><em>)</em><em>:</em><em>(</em><em>8</em><em>m</em><em>+</em><em>2</em><em>3</em><em>)</em><em> </em><em>.</em>
Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .
That is.
As , we know that the sum of n terms of an AP is given by ,
Assume that ,
- First term of 1st AP = a
- First term of 2nd AP = a'
- Common difference of 1st AP = d
- Common difference of 2nd AP = d'
Using this we have ,
Now also we know that the nth term of an AP is given by ,

Therefore,


From equation (i) and (iii) ,



Substitute this value in equation (i) ,

Simplify,

![\longrightarrow\sf\small \dfrac{2[a + (m-1)d]}{2[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\](https://tex.z-dn.net/?f=%5Clongrightarrow%5Csf%5Csmall%20%5Cdfrac%7B2%5Ba%20%2B%20%28m-1%29d%5D%7D%7B2%5Ba%27%20%2B%20%28m-1%29d%27%5D%7D%3D%5Cdfrac%7B%2014m-6%7D%7B8m%2B23%7D%5C%5C)
![\longrightarrow\sf\small \dfrac{[a + (m-1)d]}{[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\](https://tex.z-dn.net/?f=%5Clongrightarrow%5Csf%5Csmall%20%5Cdfrac%7B%5Ba%20%2B%20%28m-1%29d%5D%7D%7B%5Ba%27%20%2B%20%28m-1%29d%27%5D%7D%3D%5Cdfrac%7B%2014m-6%7D%7B8m%2B23%7D%5C%5C)
From equation (ii) ,

Answer:
Equation B
Step-by-step explanation:
Equation B because:
it is 7x + 3
so for the first one, it's 7 + 3
the second one is 14 + 3
the third one is 21 + 3
the fourth one is 28 + 3
Please Mark Brainliest
Answer:
Domain {7,-2,4,-9,0} Range {3,-2,1,0,7}
Step-by-step explanation:
Just remember that domain is the x values and the range is the y values.
Answer:
n= -12
Step-by-step explanation:
- 2n/3 + 7=15 Subtract 7 from both sides and move all terms containing
-7 = -7 n to the right
- 2n/3 = 8 multiply both sides of equation by - 3/2
-3/2 x (-2n/3) = -3/2 x 8
n= -3/2 x 8 cancel the common factor of 3
n= -12
Triangle ABC would remain the same because a dilation generally preserves the measure of an angle.
<h3>What is scale factor?</h3>
A scale factor simply refers to a ratio of two (2) corresponding side lengths or diameter in two (2) similar geometric figures such as triangles.
In this exercise, you're required to construct a dilation of triangle ABC that is centered at B with a scale factor of 2 by using a compass and straightedge.
In conclusion, triangle ABC would remain the same because a dilation generally preserves the measure of an angle.
Read more on scale factor here: brainly.com/question/2826496
#SPJ1