Length from R(-2, 4) to S(3, 4) is sqrt((3 - (-2))^2 + (4 - 4)^2) = sqrt(5)^2 = 5 units
Length from S(3, 4) to T(3, -1) is sqrt((3 - 3)^2 + (-1 - 4)^2) = sqrt(-5)^2 = 5 units
Therefore, total length = 5 + 5 = 10 units.
Answer:
vertex = (- 10, - 10 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
h(x) = x² + 20x + 90
add/subtract ( half the coefficient of the x- term )²
h(x) = x² + 2(10)x + 100 - 100 + 90
= (x + 10)² - 10 ← in vertex form
with (h, k ) = (- 10, - 10 )
16/20 = 8(2)/10(2) = 8/10. 8/10 can also be further reduced to 4/5.
<span><span>1.
If we get an odd number first (probability 5/10 = 1/2), then the only way to get a number greater than 9 is the 10 (probability 1/9, since only 9 papers remain). This gives 1/2 * 1/9 = 1/18.</span></span><span><span>
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</span></span><span><span>2.
We would expect that P(2 white cards) = P(1 white card)*P(2nd white card given 1 white card).</span></span><span><span /></span><span><span>This gives the equation 14/95 = 2/5 * x<span>
</span></span></span><span><span><span>Solving for x gives x = 7/19.</span></span></span><span><span>
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</span></span><span><span>3. There are a total of 4 favorable results: 1, 4, 5, 6. Out of the 6 possibilities, this is a probability of 4/6 = 2/3.</span></span>