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valentinak56 [21]
3 years ago
15

The senate in a certain state is comprised of 51 republicans, 48 democrats, and 1 independent. How many committees can be formed

if each committee must have 3 republicans and 2 democrats
Mathematics
1 answer:
Sedaia [141]3 years ago
5 0
17 since 51 goes into 3 17 times and 2 goes into 48 24 times and 17 is the largest number that can have 3 republicans and 2 democrats. The andwer would be 17 comittees,
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F(x)=-2x+4 when f(-3)
VladimirAG [237]
F(x)=10 would be the easiest way to put that
3 0
3 years ago
Please help
Firdavs [7]

Answer:

(–10, –2), (6, 6)

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

<u><em>Verify each case</em></u>

case 1) (5, –4), (–2, 1)

substitute in the formula

m=\frac{1-(-4)}{-2-5}

m=\frac{1+4}{-2-5}

m=\frac{5}{-7}

m=-\frac{5}{7}  ----> the slope is negative

case 2) (6, –10), (2, 10)

substitute in the formula

m=\frac{10-(-10)}{2-6}

m=\frac{10+10}{2-6}

m=\frac{20}{-4}

m=-5  ----> the slope is negative

case 3) (–10, –2), (6, 6)

substitute in the formula

m=\frac{6-(-2)}{6-(-10)}

m=\frac{6+2}{6+10}

m=\frac{8}{16}

m=0.5  ----> the slope is positive

case 4) (5, –1), (–6, 6)

substitute in the formula

m=\frac{6-(-1)}{-6-5}

m=\frac{6+1}{-6-5}

m=\frac{7}{-11}

m=-\frac{7}{11}   ----> the slope is negative

3 0
3 years ago
In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E. The measure of one of the angles of a ∆P
allsm [11]
The rhombus has a couple of very interesting properties. The first is that the diagonals meet at 90o angles.

The second is that all the sides are congruent. That's actually the key to the problem (or one of them.

The third is that the diagonals are line segments that bisect the angles where the vertex of the angle is. 

So just to make sure you understand what that last statement means <PKM  =  <NKM
K is the vertex of angle PKN 

Now the really heavy duty stuff about your question.
Given
K is obtuse. Therefore <PKM can't be 16o because MKN would also have to be 16 degrees and together they don't add up to anything over 90o.
So the 16o angle is at <EPK

Remember that the diagonals meet at right angles. <PEK = 90o

Finally all triangles have 180o
< PKE = 180 - 16 - 90 = 74. So to review
<PKE = 74o
<EPK = 16o
<PEK = 90o That's one half the problem.

Moving on to triangle PMN
By the properties of parallel lines and a rhombus  and isosceles triangles, that since PKN is bisected (rhombus property) Then PKN = 2* PKM =2*74 = 148o
The angle opposite <PKN is equal to <PKN so <PMN = <PKN
Since PKN = 148 then PMN = 148
Since KPN = 16o then PMN = 16o
Since triangle <PMN is isosceles <PNM = 16o

Summing up 
PMN = 148o
MPN = 16o
MNP = 16o

That's both triangles solved. This is a really nice little problem. If you google properties of a rhombus, you will find all the properties I have used proven. 
 
5 0
3 years ago
Read 2 more answers
How can we find the measure of an exterior angle if we know the measurement of an interior angle
Alik [6]

Step-by-step explanation:

Put the interior angle equal to 180.


It would look something like this:

x+45=180

-45     -45

180-45= 135 so the exterior angle would be 135!

3 0
3 years ago
I need help with number 2
horrorfan [7]

Answer:

Slope= 0.20

Y-intercept=12.50

Equation= Y=0.20+12.50

Step-by-step explanation:

6 0
3 years ago
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