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Andrei [34K]
3 years ago
13

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9).

Mathematics
1 answer:
Svetllana [295]3 years ago
5 0
First we write standard form that includes both vertex and focus. The formula goes like this:

(x-h)^2 = 4*p*(y-k)

h and k are coordinates of vertex. since vertex is at beginning that means that h=k=0

p is focal lenght and in our case it is 9

expressing al of this we get:
x^2 = 4*9*y
x^2 = 36y
y = 1/36 * x^2
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Triangle STV has vertices S (-3, -2) , T (-4, 3) and V (-2, 3). If (x, y) arrow (x+2, y-3), what are the vertices of its image?
jeka94

Answer:

  see below

Step-by-step explanation:

The mapping tells you how to find the vertices of the image:

  (x, y) ⇒ (x +2, y -3)

  S(-3,-2) ⇒ S'(-3 +2, -2 -3) = S'(-1, -5) . . . . . matches choice D

  T(-4, 3) ⇒ T'(-4 +2, 3 -3) = T'(-2, 0)

  V(-2, 3) ⇒ V'(-2 +2, 3 -3) = V'(0, 0)

8 0
3 years ago
2.
laiz [17]

Answer:

B) 0.02

Step-by-step explanation:

<u>Use the Binomial Theorem</u>

\displaystyle P(X=x)=\binom{n}{x}p^xq^{n-x}\\\\P(X=4)=\binom{30}{4}(0.30)^4(1-0.30)^{30-4}\\\\P(X=4)=\frac{30!}{4!(30-4)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30!}{4!(26)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30*29*28*27}{4*3*2*1}(0.30)^4(0.70)^{26}\\ \\P(X=4)=27405(0.30)^4(0.70)^{26}\\\\P(X=4)\approx0.0208

We have the probability of success, p=0.30, and the probability of failure, q=1-0.30=0.70. The binomial coefficient, \binom{n}{k}, represents the amount of possible combinations that k items can be chosen out of n items, with its respective formula \frac{n!}{k!(n-k)!}.

Hence, the best choice for the probability that 4 students chosen at random from the class of 30 that want the next test to be on Monday will be option B, 0.02

7 0
2 years ago
Hey everybody I have a quick math question but idk what the answer is! It would mean a lot if someone helped me. PS the pic is t
mote1985 [20]

Answer:

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8 0
3 years ago
What is the area of the kite below.<br> 15 m<br> D<br> 3 m<br> 3 m<br> 12 m<br> С
ohaa [14]

Answer:

51 meters

Step-by-step explanation:

The area can be found by adding the areas of all the triangles. The top right triangle has an area of 7.5. The bottom right triangle has an area of 18. The bottom left, also has an area of 18. And finally, the top left which has an area of 7.5. 18 + 18 + 7.5 + 7.5 = 51.

5 0
3 years ago
Read 2 more answers
Does the residual plot show that the line of best fit is
Iteru [2.4K]

Answer:

e_1 = 3.5-4.06= -0.56

e_2 = 2.3-2.09= 0.21

e_3 = 1.1-0.12= 0.98

e_4 = -2.2-(-1.85)= -0.35

e_5 = -4.1-(-3.82)= -0.28

The plot is on the figure attached. And we can see that the residuals shows a curved pattern so then the best conclusion for this case would be:

Yes, the points are in a curved pattern.

Step-by-step explanation:

The correct formula for the residuals is given by:

e_i =y_i -\hat y_i

Who represent the observed value minus the predicted. We can find the individual residuals and we got:

e_1 = 3.5-4.06= -0.56

e_2 = 2.3-2.09= 0.21

e_3 = 1.1-0.12= 0.98

e_4 = -2.2-(-1.85)= -0.35

e_5 = -4.1-(-3.82)= -0.28

The plot is on the figure attached. And we can see that the residuals shows a curved pattern so then the best conclusion for this case would be:

Yes, the points are in a curved pattern.

4 0
3 years ago
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