Your test in math class has problems worth 2 points and problems worth 4 points. Altogether the test has 100 points. Write an equation that represents the total points on the test formed by the
number of 2-point problems and the number of 4-point problems
Labels: x= Click here
y= Click here
A
Write an equation in standard form
Click here
How many 4 point problems are on the test if there are 32 2 points questions? Click here

Equation: 100 = 2x + 4y

There are 9 4 points problems

Step-by-step explanation:

In this case, we know that we have a test that in total, we must sum 100 points. This could be with question of 2 points or questions of 4 points.

We do not know exactly how many questions of 2 or 4 point are, but we can write an equation that could give us an idea.

Let's call "x" the number of questions worth 2 points.

Let's call "y" the number of questions worth 4 points.

All together must give 100 points, therefore, the logic equation to do this is:

Now, for the second part of this problem, we want to know how many 4 points problems would be in the test if we have 32 questions of 2 points. For that, we use the above equation, and solve for y:

100 = 2(32) + 4y

100 = 64 + 4y

100 - 64 = 4y

36 = 4y

Hope this helps

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

i believe the answer is the polygon, heptagon.