P, Q, and R are prime numbers such that 3P + 7Q + 15R = 102. What is Q?

Mathematics

1 answer:

77julia77 [94]3 years ago

8 0

Q is 3

Step-by-step explanation:

The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, ......

They have two factors only 1 and itself
All the them are odd numbers except 2 is an even number
1 is not a prime number because has only one factor

∵ P, Q and R are three prime numbers

∵ 3P + 7Q + 15R = 102

- Factorize 102 into prime numbers

∵ 102 ÷ 2 = 51

∵ 51 ÷ 3 = 17

∴ The prime factorization of 102 is 2 × 3 × 17

∵ 2 , 3 , 17 are prime numbers

- Put them in the equation above to find which one is P and

which is Q and which is R

∵ R has the greatest coefficient, then put R = the smallest prime 2

∵ P has the smallest coefficient, then put P = the greatest prime 17

∴ Q = The last prime 3

- Let us check the value of the left hand side

∵ Left hand side = 3(17) + 7(3) + 15(2) = 51 + 21 + 30 = 102

∵ Right hand side = 102

∴ The prime numbers are P = 17 , Q = 3 , R = 2

Q is 3

Learn more:

You can learn more about the prime numbers in brainly.com/question/4550858

#LearnwithBrainly

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Determine the intercepts of the line that passes through the following points. (-15,5) (-9,10) (-3,15)

notsponge [240]

To find the x and y-intercept, we can write an equation in slope intercept form.
first, we need to find the slope
the formula for slope is
m= (y₂-y₁)/(x₂-x₁)

now just put any two points into the equation
m=(10-5)/(-9-(-15)
m=5/6

so now we can write the slope-intercept equation
y=5/6x + b

in a slope-intercept equation, b is equal to the y-intercept, so we can take one of our 3 pairs of points and put them into the equation to solve for b

15= 5/6(-3) +b
15=-2.5 + b
17.5 = b
so now we know the y-intercept is (0,17.5)

now we can write the equation as
y= 5/6x + 17.5

since the x intercept is when y=0, we can set y to 0 and then solve for x

0= 5/6x +17.5
-17.5 = 5/6x
-21 = x

by setting y to zero, we figured out that the x-intercept is (-21,0)

hope this helped!

6 0

3 years ago

PLEASE HELP<br> (look at pictures)

Vladimir [108]

<h2>Answer:</h2>

This is a theorem called Converse of Alternate Exterior Angles that states that <em>if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel</em>. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that<em> if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. </em>We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,

Reason: Given

Statement: $\angle1\cong\angle2$