Mathematics, 29.07.2019 16:40 spazzinchicago

2) the sum of the measures of angle x and angle y is 90. if the measure of angle x is 30 less than twice the measure of angle y, what is the measure of angle x? a) 20 b) 35 c) 50 d) 65 3) the yearbook club is having a bake sale to raise money for the senior class. large cupcakes are sold for $1.25 each and small cupcakes are sold for $0.75 each. if 105 cupcakes were sold for a total amount of $109.75, how many large cupcakes did the yearbook club sell? a) 43 b) 55 c) 62 d) 16 4) solve the following system of equations using substitution. what is the value of y? 2x+3y=105 x+2y=65 a) 15 b) 20 c) 40 d) 65

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2) The answer is C. 50.

In order to solve this you need to represent the measure of x in terms of y. Since x is 30 less than twice as big as y, we can express it using the following: 2y - 30.

Now we can add that to y and set equal to 90 to solve.
2y - 30 + y = 90
3y - 30 = 90
3y = 120
y = 40.

Now knowing that y = 40, we know that x = 50, since they add up to 90.

3) They sold 62 large cupcakes.

This can be found by setting up a system of equations.

The first equation should represent the number sold totally. x + y = 105, where x is equal to the number of large cupcakes and y is equal to the number of small cupcakes.

The second equation should be equal to the amount of money made. 1.25x + .75y = 109.75.

Now to solve this system, you need to multiply the first equation by -1.25. This will give us a new equation of -1.25x - 1.25y = -131.25.

Now if you add the new equation to the second equation, the x values will cancel, giving you the following: -.5y = -21.5 or y = 43.

We can then determine the number of large cupcakes (x) by subtracting our y value from the 105 total, leaving us with 62.

4) The answer for this question is none of your possible answers. The y value should be 25 (the x-value though should be 15, which is the A answer).

We can find this by solving the second equation for x.
x + 2y = 65
x = -2y + 65.

Now that we have a value for x, we can sub it into the first equation in place of x and solve for y.
2x + 3y = 105
2(-2y + 65) + 3y = 105
-4y + 130 + 3y = 105
-y + 130 = 105
-y = -25
y = 25.

Answer from: Quest

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.

Answer from: Quest

Ais the answer for your question

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2) the sum of the measures of angle x and angle y is 90. if the measure of angle x is 30 less than t...