Question 7(Multiple Choice Worth 3 points)

the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?

RideAnS [48]

Well, first off, let's find what is the slope of BC

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 2}}\quad ,&{{ -3}})\quad 
% (c,d)
C&({{ 10}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2}
\\\\\\
\cfrac{4}{8}\implies \cfrac{1}{2}$

now, a line perpendicular to that one, will have a negative reciprocal slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\
slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}$

now, we know the slope "m" of AB is -2 then, thus

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ a}}\quad ,&{{ 3}})\quad 
% (c,d)
B&({{ 2}}\quad ,&{{ -3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2}
\\\\\\
\cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a
\\\\\\
-1=a$

6 0

3 years ago

The first term of a geometric sequence is 6, and the common ratio is 3. What is the 7th term of the sequence?

-BARSIC- [3]

An = a1 r^(n-1)

here a1 = 6 and r = 3 so

a7 = 6 * 3^(7-1)

= 4374 answe

8 0

3 years ago

Please help and thank you

mamaluj [8]

Answer:

C

Step-by-step explanation:

a is defined first as 5. So a = 5.

b is defined after the circle b = -2

a^2 = 5^2 = 25

B^4 =(- 2)^4 = 16

Therefore sqrt(a^2 * b^4) = sqrt(25 * 16) = sqrt(400) = 20

The answer is C

5 0

3 years ago

Read 2 more answers

Which linear equation has no solution?

attashe74 [19]

9514 1404 393

Answer:

5x + 12 = 5x - 7

Step-by-step explanation:

There will be no solution when the coefficients of x are the same on both sides of the equal sign and the constants are different. That is the case for ...

5x + 12 = 5x - 7

This reduces to ...

19 = 0 . . . . . no value of x will make this be true: NO SOLUTION

3 0

3 years ago

An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviatio

Lena [83]

Answer:

The width is $w = \$ 729.7$