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lawyer [7]
3 years ago
9

. The prime numbers p, q, r satisfy the simultaneous equations

Mathematics
2 answers:
Nesterboy [21]3 years ago
4 0
first\ equation :\\pq+pr=80\\pq=80-pr..........[1]\\\\secon\ equation :\\pq+qr=425..........[2]

Now\ substituting\ equation\ 1\ into\ 2:\\\\pq+qr=425\\(80-pr)+qr=425\\-pr+qr=425-80\\-pr+qr=345\\r(q-p)=345\\\\we\ have :\\ p(q+r)=80=2^{4} \times 5,\\q(p+r)=425=5^{2} \times 17\\r(q-p)=345=3 \times 5 \times 23\\\\so\ : p = 2\ or\ 5, ~q=5\ or\ 17,~ r = 3,5,or\ 23.

From\ : p(q+r)=80, if~p=5~then\ q+r=16, which\ has\ no\ solution\\So~~p=2, then\ ~q+r=40, hence~~q=17~~and~~r=23.\\\\\therefore~~ p+q+r~~~is~~~\boxed{2+17+23=42}
Allisa [31]3 years ago
3 0
Pq + pr = 80  => p (q+r) = 80
pq + qr = 425 => q (p+r ) = 425

Factorize 80 with having one factor as prime number
80 =  2 * 40 = 5 *16 

Factrorize 425 with having one factor as prime number
425 = 5 * 85 = 17 * 25...

Therfore, p has to be 2.
q = 17 and r= 23...
p + q +r = 2 + 17+ 23 = 42
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A researcher records the odometer reading and age of used Hondas. What kind of correlation is likely to be obtained for these tw
tresset_1 [31]

Using the concept of correlation, it is found that a strong positive correlation is expected between these two variables.

  • When two variables are direct proportional, that is, both increase together, there is a <em>strong positive correlation.</em>

In this problem, <u>the older the car</u>, the more it should have traveled, that is, the <u>higher the read on the odometer</u>, hence, there is a <em>direct proportional</em> relationship, which means that the variables have a strong positive correlation.

A similar problem is given at brainly.com/question/15468813

5 0
2 years ago
Which equation represents a linear function that has a slope of 5 and a y-interceptof-6?
Alexus [3.1K]

Answer:

y=5x-6

Step-by-step explanation:

Comparing y=5x-6 with y=mx+c,the slope is 5 and y intercept is-6

6 0
3 years ago
Which equation represents the function graphed on the coordinate plane?????
Y_Kistochka [10]

Since you haven't provided the graph, I'll explain each one and you choose the one suiting your given.

<u>The parent modulus function is:</u>

g(x) = |x|

It is centered at the origin and opens upwards.

A coefficient inside the modulus |x+k| means that the function is shifted along the x-axis

If "k" is <u>positive</u>, the shift will be to the <u>left</u>. If "k" is <u>negative</u>, the shift will be to the <u>right</u>.

A coefficient outside the modulus |x| + h means that the function is shifted along the y-axis

If "h" is <u>positive</u>, the shift will be <u>upwards</u>. If "h" is <u>negative,</u> the shift will be <u>downwards</u>.

<u>Now, let's check each of the options:</u>

<u>g(x) = |x+4| - 2 :</u>

This function is shifted 4 units to the left and 2 units down. It will be centered at (-4,-2). Check the blue graph in the attachment.

<u>g(x) = |x-4| - 2 :</u>

This function is shifted 4 units to the right and 2 units down. It will be centered at (4,-2). Check the black graph in the attachment.

<u>g(x) = |x-2| - 4 :</u>

This function is shifted 2 units to the right and 4 units down. It will be centered at (2,-4). Check the red graph in the attachment.

<u>g(x) = |x-2| + 4 :</u>

This function is shifted 2 units to the right and 4 units up. It will be centered at (2,4). Check the green graph in the attachment.

All 4 graphs are shown in the attached picture.

Hope this helps :)


3 0
3 years ago
Read 2 more answers
Can Some one please help me on these math questions<br><br>I'll give 20 points please
MArishka [77]

Answer:

☐ -2 < 2x + 4

☐ -3x - 2 > 5

Step-by-step explanation:

-3x - 2 > 5

+ 2 + 2

___________

-3x > 7

___ ___

-3 -3

x < -2⅓ [Anytime you <em>divide</em> or <em>multiply</em> by a negative, reverse the inequality symbol.]

-2 < 2x + 4

-4 - 4

___________

-6 < 2x

__ ___

2 2

-3 < x

If you plug in -3 for <em>x < -2</em><em>⅓</em><em>,</em><em> </em>you will see that it is a genuine statement because the more higher a negative gets, the lesser the integer will be, so in this case, -3 IS <em>less</em><em> </em><em>than</em><em> </em>-2⅓.

I am joyous to assist you anytime.

** If it is not multi-select, then choose <em>-2 < 2x + </em><em>4</em><em>.</em>

4 0
3 years ago
BRAINLIST ASAP
kifflom [539]

Answer:

25.50

Step-by-step explanation:

-5 notebooks $2 each

-4 pencils $1.50 each

-2 packs of markers $3.75 each

5(2)+4(1.50)+2(3.75)

$23.5

23.5 times 8.5/100

1.9975

plus 23.5

25.4975

rounded to 25.50

6 0
2 years ago
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