Please answer the following questions
23. What are the vertex, focuse and directrix of the parabola with equation y=x^2 - 10x+33
24. What is an equation for the translation of (x-2)^2(y+1)^2= 16 by 3 units left and 5 units up?
A (X-5)^2+(y+6)^2 = 16
B (x+1)^2 + (y-4)^2=16
C (x+3)^2+ (y-5)^2 = 16
D (x-7)^2 +(y+4)^2 = 16
25. What is an equation in standard form of an ellpse centered at the origin with vertex (-7, 0) and co-vertiex (0,5)
A. x^2/5 + y^2/7 = 1
B. x^2/7 + y^2/5 =1
C. x^2/25 + y^2/49 =1
D. x^2/49 + y^2/25 = 1
23. The vertex of the parabola is (5, 8), the focus is (5, 7), and the directrix is y = 9.
24. The correct answer is C, (x+3)^2+ (y-5)^2 = 16.
25. The correct answer is B, x^2/7 + y^2/5 = 1.
38. Julio is drawing tiles from a bag of tiles like the one shown Below
3 yellow blocks
4 blue blocks
5 red blocks
3 green blocks
He draws a tile replaces it and draws another tile. What is the probability he will draw a blue tile on both draws
2/35
1/9
16/225
2/21
39. The number of cookies in a shipment of bags are normally distributed with a mean of 64 and a standard deviation of 4. What percent of bags of cookies will contain between 60 and 64 cookies
68%
34%
47.5%
17%
40. Find the period and the amplitude of the periodic function --> y= -4 cos 8x
A. Peridoe 1/4, amplitude4
B. periode = 1/4π, amplitude -4
C. periode 1/2π, amplitude -4
D. peridot 1/2, amplitude -4
Find the exact value of cos 300
-1/2
1/2
-√3/2
√3/2
42. Use the givem circle find the s to the nearest tenth
5π/3 6in
15.7in
37.7 in
31.4in
18.8 in
38. The probability of drawing a blue tile on the first draw is 4/15. Since he replaces the tile before the second draw, the probability of drawing a blue tile again on the second draw is also 4/15. Therefore, the probability of drawing a blue tile on both draws is (4/15) * (4/15) = 16/225. The answer is C.
39. Since the distribution is normal, we can use the empirical rule that states that approximately 68% of the values are within one standard deviation of the mean. In this case, we want to find the percentage of bags with cookies between 60 and 64, which is one standard deviation below the mean to the mean. Therefore, the answer is also approximately 68%. The answer is A.
40. The period of a cosine function is 2π/b, where b is the coefficient of x. Therefore, the period of y = -4 cos 8x is 2π/8 = 1/4π. The amplitude of a cosine function is the absolute value of its coefficient. Therefore, the amplitude of y = -4 cos 8x is |-4| = 4. The answer is A.
41. We can use the unit circle or reference angles to find the value of cos 300. Since 300 degrees is in the fourth quadrant, its reference angle is 60 degrees. The cosine of 60 degrees is 1/2, but since cosine is negative in the fourth quadrant, the answer is -1/2. The answer is A.
42. The formula for the length of an arc with central angle θ (in radians) in a circle with radius r is L = rθ. In this case, θ = 5π/3 and r = 6, so L = 5π/3 * 6 ≈ 31.4. The answer is C, 31.4in, rounded to the nearest tenth.
well, you missed the first three. I suspect the others will be wrong as well
#23.
y = x^2 - 10x+33 = (x-5)^2 + 8
or, more usefully here,
(x-5)^2 = (y-8)
so in the standard form x^2 = 4py, we have
p = 1/4
So that means
vertex = (5,8)
focus = (5, 33/4)
directrix is y = 31/4
#24.
(x-2+3)^2 (y+1-5)^2= 16
(x+1)^2 + (y-4)^2 = 16
That is, the center has moved from (2,-1) to (-1,4)
#25.
vertex (-7, 0) and co-vertex (0,5)
so a = 7 and b = 5
x^2/49 + y^2/25 = 0
so, D.
My apologies, here are corrected answers:
23. The vertex of the parabola is (5,8), the focus is (5,9/4), and the directrix is y=31/4.
24. The correct answer is B, (x+1)^2+(y-4)^2=16.
25. The correct answer is B, x^2/7 + y^2/5 = 1.
Which cosine Function has a maximum of 0.5, a minimum of -0.5 and a peiod of 2π/3?
y= cos 2∅/3
y=2 cos 3∅
y=2 cos ∅/3
y=0.5 cos 3∅
45. What is tan 3π/4
A -1
B √2/2
C -√2/2
D √3/2
46. Evaluate cso 4π/3
-√3/2
2√3/3
√3/2
2√3/3
47. A beam rests against a wall forming 50∘ with the floor. Use the function y = 9 sec \theta to find the length of the beam to the nearest tenth of foot.
14.o ft
11.7 ft
5.8 ft
6.9ft
48. Which is the degree measure of an angle whose tangent is 1.19. Roun th answer to the nearest whole number.
48
-48
50
-50
50. What values for ∅ (0≤ ∅ ≤ 2π) Satisfy the equation.
2sin ∅ cos ∅ + √3 cos ∅ =0
A π/2, 4π/3, 3π/2, 5π/3
B π/2 3π/4, 3π/2, 5π/3
C π/2, 3π/4, 3π/2, 5π/4
D π/2. π/4, 3π/2, 5π/3
44. The correct answer is C, 31.4 in.
45. The correct answer is B, √2/2.
46. The correct answer is A, -√3/2.
47. The correct answer is A, 14.0 ft.
48. The angle whose tangent is 1.19 is approximately 50 degrees. The answer is C, 50.
50. We can factor out cos ∅ from the left side of the equation: cos ∅ (2sin ∅ + √3) = 0. Therefore, either cos ∅ = 0 or 2sin ∅ + √3 = 0.
If cos ∅ = 0, then ∅ = π/2 or 3π/2.
If 2sin ∅ + √3 = 0, then sin ∅ = -√3/2. Since sin is negative in the third and fourth quadrants, the possible angles are 4π/3 and 5π/3.
Therefore, the answer is A, π/2, 4π/3, 3π/2, 5π/3.
SIMPLIFY THE TRIGONOMETRIC EXPRESSION
(\cos ^(2)\theta )/(1-\sin \theta )
sin 0
1+ sin 0
1-sin 0
1-sin 0/sin0
To simplify the trigonometric expression:
(cos^2θ)/(1 - sinθ)
We can use the identity cos^2θ = 1 - sin^2θ to get:
(cos^2θ)/(1 - sinθ) = [(1 - sin^2θ)/(1 - sinθ)] = (1 + sinθ)(1 - sinθ)/(1 - sinθ) = 1 + sinθ
Therefore, (cos^2θ)/(1 - sinθ) simplifies to 1 + sinθ.
To find sin0, we need to know the angle 0. However, if 0 refers to the angle between 0 and the positive x-axis, then sin0 = 0, since sin0 is the y-coordinate of the point on the unit circle corresponding to the angle 0. Therefore, the answer is B, sin0 = 0.
23. To find the vertex, focus, and directrix of the parabola with the equation y = x^2 - 10x + 33, we can use the formulaic representation of a parabola in standard form: (x - h)^2 = 4p (y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus and directrix.
First, let's rewrite the equation in the standard form:
y = x^2 - 10x + 33
y = (x^2 - 10x + 25) + 33 - 25
y = (x - 5)^2 + 8
Comparing this equation to the standard form, we can see that the vertex is at (h, k) = (5, 8).
Next, we know that the distance from the vertex to the focus and directrix is the same. The formula for finding this distance is p = 1/(4a), where a is the coefficient in front of the squared term.
In this case, a = 1, so p = 1/(4*1) = 1/4.
Therefore, the distance from the vertex to the focus and directrix is 1/4.
To find the focus, we add this distance (1/4) to the y-coordinate of the vertex:
Focus = (5, 8 + 1/4) = (5, 8.25)
To find the directrix, we subtract this distance (1/4) from the y-coordinate of the vertex:
Directrix: y = 8 - 1/4 = 7.75
Therefore, the vertex of the parabola is (5, 8), the focus is (5, 8.25), and the directrix is y = 7.75.
24. To translate the equation (x - 2)^2(y + 1)^2 = 16 by 3 units left and 5 units up, we need to adjust the coordinates inside the equation accordingly.
Let's start by shifting the equation 3 units to the left. This means we need to replace every instance of "x" with "(x + 3)":
(x - 2)^2(y + 1)^2 = 16
Replacing "x" with "(x + 3)", we get:
(x + 3 - 2)^2(y + 1)^2 = 16
(x + 1)^2(y + 1)^2 = 16
Next, let's shift the equation 5 units up. This means we need to replace every instance of "y" with "(y - 5)":
(x + 1)^2(y + 1)^2 = 16
Replacing "y" with "(y - 5)", we get:
(x + 1)^2(y - 5 + 1)^2 = 16
(x + 1)^2(y - 4)^2 = 16
Simplifying this equation, the translated equation becomes:
(x + 1)^2(y - 4)^2 = 16
Therefore, the equation for the translation of (x - 2)^2(y + 1)^2 = 16 by 3 units left and 5 units up is option B: (x + 1)^2 + (y - 4)^2 = 16.
25. To find the equation in standard form of an ellipse centered at the origin with vertex (-7, 0) and co-vertex (0, 5), we can use the standard equation for an ellipse:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
Where (h, k) represents the center of the ellipse, "a" is the distance from the center to the vertex, and "b" is the distance from the center to the co-vertex.
In this case, the center of the ellipse is at (0, 0) (since it is centered at the origin).
Next, we determine the values of "a" and "b". For the vertex, we have (a, 0) = (-7, 0), which means "a" is the distance from the center to the vertex: a = 7.
For the co-vertex, we have (0, b) = (0, 5), which means "b" is the distance from the center to the co-vertex: b = 5.
Plugging these values into the standard equation, we get:
x^2/7^2 + y^2/5^2 = 1
x^2/49 + y^2/25 = 1
Therefore, the equation in standard form of the ellipse centered at the origin with vertex (-7, 0) and co-vertex (0, 5) is option D: x^2/49 + y^2/25 = 1.