All categories

3 years ago

For which values of P and Q does the following equation have infinitely many solutions ?

Mathematics

1 answer:

solmaris [256]3 years ago

4 0

Answer:

(P, Q) = (-75, 57)

Step-by-step explanation:

The equation will have infinitely many solutions when it is a tautology.

Subtract the right side from the equation:

Px +57 -(-75x +Q) = 0

x(P+75) +(57 -Q) = 0

This will be a tautology (0=0) when ...

P+75 = 0

P = -75

and

57-Q = 0

57 = Q

_____

These values in the original equation make it ...

-75x +57 = -75x +57 . . . . . a tautology, always true

You might be interested in

What is the answer to 9x8 2/3

Ira Lisetskai [31]

The answer is 78. This is because you change 8 2/3 into a improper fraction which is 26/3. Then do 26/3×9/1. You should cross cancel so cancel out 3 and change it into 1 and change 9 into 3. So now your problem is 26×3=78.
~JZ
Hope it helps.

7 0

4 years ago

Read 2 more answers

Karen’s batting average was 0.444 she was at bat 45 times. How many hits did she get ?

Luden [163]

The answer is that she would have been up to bat 19 times

8 0

3 years ago

What is the measure of x?

victus00 [196]

Answer: x = 156°

Step-by-step explanation:

So it is proven all triangles equal 180° and all straight angles are 180° so

85+71= 156

180-156=24°

but since you are trying to find x (to create the straight angle) and now know the other missing angle is 24°

180-24= 156

x=156°

8 0

2 years ago

Write an equation of the line that is:

Marysya12 [62]

$a)\\y=4x+1\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\substituting\point\ (2,3)\\3=4*2+c\\c=-5\\y=4x-5\\b)\\2y-6x=9\\2y=6x+9\\y=3x+4,5\\a=3\\new\ y=bx+c\\if\ parallel a=b\\y=3x+c\\substituting\ point\ (-2,1)\\1=4*(-2)+c\\c=9\\y=3x+9\\ c)\\y=4x+3\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\c=-3\\y=4x-3\\e)\\2y-4x=8\\2y=4x+8\\y=2x+4\\a= 2 \\new\y=bx+c\\if\ perpendicular b=-1/a\\y=- \frac{1}{2} x+c\\point(6,-6)\\-6=-1/2*6+c\\c=-3\\y=-1/2x-3\\f)\\2y-5x=15\\2y=5x+15\\y=\frac{5}{2}x+\frac{15}{2}$

4 0

4 years ago

A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the lif

yawa3891 [41]

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

$z = \dfrac{x - \mu}{\sigma}$

For x = 34000

$z = \dfrac{34000 - 35000}{2250}$

$z = \dfrac{-1000}{2250}$

z = −0.4444

For x = 37000

$z = \dfrac{37000 - 35000}{2250}$

$z = \dfrac{2000}{2250}$

z = 0.8889

For x = 3000

$z = \dfrac{30000 - 35000}{2250}$

$z = \dfrac{-5000}{2250}$

z = -2.222

From the above z- score that corresponds to their life span; it is glaring that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

$z = \dfrac{30500 - 35000}{2250}$