For what values of a is the distance between P(a,3) and Q(5,2a) greater than √26

1 answer:

6 0

$P(a,3)\ \ \ Q(5,2a)\\\\ PQ=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}\\\\ PQ>\sqrt{26}\\\\\sqrt{(5-a)^2+(2a-3)^2}>\sqrt{26}\\\\\sqrt{25-10a+a^2+4a^2-12a+9}>\sqrt{26}\\\\\sqrt{5a^2-22a+34}>\sqrt{26}\ \ |^{2}\\\\
5a^2-22a+34=26\ \ \ |Subtract\ 26\\\\
5a^2-22a+8=0\ \ \ |Factoring\\\\(a-4)(5a-2)=0\\\\
a=4\ \ or\ \ 5a=2\\
a=4\ \ or\ \ a=\frac{2}{5}$

You might be interested in

What is 27 is what % of 60?

natta225 [31]

Let 27 be x% of 60

so,
x/100 *60 = 27
x = 27*100/60 = 270/6 = 45

So,
27 is <em>45%</em> of 60.

6 0

4 years ago

After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies

ira [324]

Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes be 'x'.

Let the number of nickels be ' $\dfrac{3}{2}x$ '.

Let the number of pennies be $\dfrac{3}{2}\times 2x=3x$

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

$0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14$