The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.

Angle y forms a linear pair with the one marked 83°, so is supplementary to it:

y = 180°-83° = 97°

The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.

(7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle

10x +27 = 97 . . . . . . . collect terms

10x = 70 . . . . . . . . subtract 27

x = 7 . . . . . . . . divide by 10

The side marked Z is congruent to the opposite parallel side, so ...

z = 19

The missing measures are ...

x = 7
y = 97°
z = 19

_____

<em>Additional comment</em>

You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...

(7x -5) +(3x +32) +83 = 180

Subtracting 83° from both sides gives the equation we used above.

4 0

3 years ago

How much gas is 3/8 gallons when used up 2 1/4 gallon of gas?

fredd [130]

There's is one gallon of gas left in the tank or gas can

7 0

3 years ago

If M=(2,5) is the midpoint of AB, and A=(0,-1), then the coordinates of B are _____.

faust18 [17]

Answer:

The point M(Mx, My) is mid-point of AB with A(Ax, Ay) and B(Bx, By).

=> 2*Mx = Ax + Bx => 2*2 = 0 + Bx => Bx = 4

=> 2*My = Ay + By => 2*(5) = -1 + By => By = 11

=> B(4, 11)

=> Option A is correct

Hope this helps!

7 0

3 years ago

The number of users on a website has grown exponentially since its launch. After 2 months, there were 90 users. After 4 months,

grigory [225]

Answer:

10(3)^x

Step-by-step explanation:

The function contains the points (2,90) and (4,810). Use the general form y=abx to write two equations:

90=ab^2 and 810=ab^4

Solve each equation for a:

a=90/b^2 and a=810/b^4

Since a=a, set the other sides of the equations equal and solve for b.

90/b2=810/b4

Cross multiply, then divide and simplify as follows:

90b^4=810b^2

b^4/b^2=810/90

b^2=90

b^3

Now, use the value of b and the point (2,90) to find the value of a.

90=a(3^2)

a=10

So, substitute answers in original equation for a final answer of f(x)=10(3)^x.

8 0

3 years ago