3. Yes the cost of each item is proportional because in each pack each t-shirt cost $2.33. You can check that by dividing the amount of money each pack cost by the amount of shirts in each pack. For example the pack of 3 is $7, so 7/3 = $2.33. The pack of 5 cost $11.65, so 11.65/5 = $2.33. And the pack of 7 cost $16.31, so 16.31/7 = $2.33
4) Yes, it is proportional because each x is being squared or multiplied by it’s self.
If your directrix is a "y=" line, that means that the parabola opens either upwards or downwards (as opposed to the left or the right). Because it is in the character of a parabola to "hug" the focus, our parabola opens upwards. The vertex of a parabola sits exactly halfway between the directrix and the focus. Since our directrix is at y = -2 and the focus is at (1, 6) AND the parabola opens upward, the vertex is going to sit on the main transversal, which is also the "line" the focus sits on. The focus is on the line x = 1, so the vertex will also have that x coordinate. Halfway between the y points of the directrix and the focus, -2 and 6, respectively, is the y value of 2. So the vertex sits at (1, 2). The formula for this type of parabola is
where h and k are the coordinates of the vertex and p is the DISTANCE that the focus is from the vertex. Our focus is 4 units from the vertex, so p = 4. Filling in our h, k, and p:
. Simplifying a bit gives us
. We can begin to isolate the y by dividing both sides by 16 to get
. Then we can add 2 to both sides to get the final equation
, choice 4 from above.
<h3>Given</h3>
trapezoid PSTK with ∠P=90°, KS = 13, KP = 12, ST = 8
<h3>Find</h3>
the area of PSTK
<h3>Solution</h3>
It helps to draw a diagram.
∆ KPS is a right triangle with hypotenuse 13 and leg 12. Then the other leg (PS) is given by the Pythagorean theorem as
... KS² = PS² + KP²
... 13² = PS² + 12²
... PS = √(169 -144) = 5
This is the height of the trapezoid, which has bases 12 and 8. Then the area of the trapezoid is
... A = (1/2)(b1 +b2)h
... A = (1/2)(12 +8)·5
... A = 50
The area of trapezoid PSTK is 50 square units.
Answer:
28 cm^2
Step-by-step explanation:
a^+21^2=36^2
a^2+441=1225
a=28
Answer:
The area is 522.935 square inches.
Step-by-step explanation:
A trapezoid's area is calculated as follows: h(b1+b2)/2
Plugging numbers in gives 34.3+12.6=46.9
so now all that's left is to multiply 22.3 and 46.9, and divide by 2.
This gives 522.935
Hope this helps!