1
type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar.
given the directrix = 6 and the focus (3,-5), what is the vertex form of the equation of the parabola?
the vertex form of the equation is r =
(y +
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Answer:

2  ,  4  ,  8  ,  16  ,  32

Step-by-step explanation:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  

2  gives the next term. In other words,  a n = a1 ⋅r n − 1 . Geometric Sequence:  r = 2

Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr

As the radius r is shrinking at the rate of two inches per hour, it can be represented as;

dr/dt = -2 in / hr

Here, the negative sign represents the shrinking of the snowball with time t.

The surface area of a sphere can be represented by the formula;

S = 4πr²

Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;

dS/dt = d/dt (4πr²)

dS/dt = 4π (d/dt) (r²)

dS/dt = 4π × 2r (dr/dt)

Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;

dS/dt = 4π × 2(4)(-2)

dS/dt = -64π

Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.

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Answer:

Anything after x determines if it goes up since it's a positive 5 it's 5 units up

Answer:

d=8$

Step-by-step explanation:

Answer:

He or she got around -32 points per turn.

Step-by-step explanation:

-288 points (the total) divided by the player's 9 turns equals -32. This means that they got negative 32 points on average every round.

Answer:

Part (A) → x = 5

Part (B) → m(arc RS) = 55°

Step-by-step explanation:

In the picture attached,

RU and SV are the diameters of the given circle.

Part (A),

Since RU is the diameter,

m(arc RVU) = 180°

m(arc RV) + m(arc VU) = 180°

(24x + 5) + (10x + 5) = 180

34x + 10 = 180

34x = 170

x = \(\frac{170}{34}\)

x = 5

Part (B),

Since m(arc RS) = m(arc VU) [Angles intercepted by these arcs at the center are equal because they are the vertical angles]

m(arc RS) = (10x + 5)

                = (10×5 + 5)

                = 55°

Answer:

#CarryOnLearning

LHS

\(\\ \sf\longmapsto \dfrac{1}{sec\Theta+\tan\Theta}\)

\(\\ \sf\longmapsto \dfrac{sec^2\Theta-tan^2\Theta}{sec\Theta+tan\:Theta}\)

\(\\ \sf\longmapsto \dfrac{(sec\Theta+tan\Theta)(sec\Theta-tan\Theta)}{(sec\Theta+tan\:Theta)}\)

\(\\ \sf\longmapsto sec\Theta-tan\Theta\)

\(\\ \sf\longmapsto \dfrac{1}{cos\Theta}-\dfrac{sin\Theta}{cos\Theta}\)

\(\\ \sf\longmapsto \dfrac{1-sin\Theta}{cos\:Theta}\)

Answer:

x = 12

Step-by-step explanation:

You apply distributive property on the parenthesis:

3.3x - 26.4 - x = 1.2

You then add like terms.

3.3x - x = 2.3x

2.3x - 26.4 = 1.2

You add 26.4 to both sides to isolate x.

(Additive property of equality.)

2.3x = 27.6

Divide both sides by 2.3

(Division Property of equality.)

x = 12

The percent of the original contaminants will be removed from the water sample is 99.19 %.

Let the contaminant in water be x

70% contaminant remove by one pass

Then the remaining contaminants be 30%

In 1st as,

30x/100

= 3x/10

In 2nd pass,

3x/10 x 30/100

= 9x/100

In 3rd pass,

9x/100 x 30/100

= 27x/1000

In 4th pass,

27x/1000 x 30/100

= 81x/10000

Remaining contaminant after fourth pass = 81x/10000

Total removal of contaminant,

y = x - 81x/10000

= 9919x/10000

Therefore, the original contaminants will be removed from the water sample is 99.19%.

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Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

Answer:

i got you it 10,000

Step-by-step explanation:

all you have to do is add the zeros

Answer:

Step-by-step explanation:

This is what I did to solve it:You can multiply the x+2 and the 7 and it will turn into:log5(7x+14)Then the 1 can be turned into:log55The current state of the equation is:log5(7x+14)=log55You can then cancel the "logs" out and it will leave you with:log5(7x+14)=log557x+14=5From here you just solve for x:7x−14=5−147x=−97x=−97

Answer:

D, 30%

Step-by-step explanation:

you move the decimal point twice to the right

Answer:

D. 30%

Step-by-step explanation:

This is the answer because:

1) When you convert decimals to percents, you have to remember the two main decimal places:

0.00 = The hundredths place

0.00 = The tenths place

2) Whenever there is a decimal that is in the hundredths place, it will equal a one digit percent. For example, 0.07 = 7%.

3) Whenever there is a decimal that is in the tentsh place, it will equal a two digit number. For example, 0.3 = 30%.

4) Another way to solve it is to convert the decimal to a percentage by multiplying the decimal by  100 .

Therefore, the answer is 30%.

Hope this helps! :D

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

E. 2,850 ft²

Step-by-step explanation:

Answer:

OptionE)

Step-by-step explanation:

Area of a circle = \(\pi r^{2}\)

\(3.14X30X30\)

= \(2826\)

Hence the closest is 2,850

a)The array after the while loop and afterwards is: [1, 2, 3, 4, 5, 6, 7, 8, 9]

b)The final formula for the recurrence relation is T(n) = n².

c)The T(n) is both Big O(nlogn) and Omega(nlogn),  conclude that T(n) is theta(nlogn).

Let's go through the steps of the partition function with the given array a=[4,3,5,9,6,1,2,8,7], start=0, and end=8. In each step annotate the array and show the changes in the values and the indexes H and L.

Step 1:

Original array: [4, 3, 5, 9, 6, 1, 2, 8, 7]

H = 8, L = 0

Step 2:

Swap a[H] and a[L]: [7, 3, 5, 9, 6, 1, 2, 8, 4]

Increment L: H = 8, L = 1

Step 3:

Increment L: H = 8, L = 2

Step 4:

Increment L: H = 8, L = 3

Step 5:

Increment L: H = 8, L = 4

Step 6:

Increment L: H = 8, L = 5

Step 7:

Increment L: H = 8, L = 6

Step 8:

Increment L: H = 8, L = 7

Step 9:

Swap a[H] and a[L]: [4, 3, 5, 9, 6, 1, 2, 7, 8]

Increment L: H = 7, L = 8

Step 10:

Swap a[H] and a[L]: [4, 3, 5, 7, 6, 1, 2, 9, 8]

Decrement H: H = 6, L = 8

Step 11:

Swap a[H] and a[L]: [4, 3, 5, 2, 6, 1, 7, 9, 8]

Decrement H: H = 5, L = 8

Step 12:

Swap a[H] and a[L]: [4, 3, 5, 2, 6, 1, 7, 9, 8]

Decrement H: H = 4, L = 8

Step 13:

Swap a[H] and a[L]: [4, 3, 5, 2, 6, 1, 7, 9, 8]

Decrement H: H = 3, L = 8

Step 14:

Swap a[H] and a[L]: [4, 3, 1, 2, 6, 5, 7, 9, 8]

Decrement H: H = 2, L = 8

Step 15:

Swap a[H] and a[L]: [4, 3, 1, 2, 6, 5, 7, 9, 8]

Decrement H: H = 1, L = 8

Step 16:

Swap a[H] and a[L]: [2, 3, 1, 4, 6, 5, 7, 9, 8]

Increment L: H = 1, L = 2

Step 17:

Swap a[H] and a[L]: [2, 1, 3, 4, 6, 5, 7, 9, 8]

Increment L: H = 1, L = 3

Step 18:

Swap a[H] and a[L]: [2, 1, 3, 4, 6, 5, 7, 9, 8]

Increment L: H = 1, L = 4

Step 19:

Swap a[H] and a[L]: [2, 1, 3, 4, 6, 5, 7, 9, 8]

Increment L: H = 1, L = 5

Step 20:

Swap a[H] and a[L]: [2, 1, 3, 4, 5, 6, 7, 9, 8]

Increment L: H = 1, L = 6

Step 21:

Swap a[H] and a[L]: [2, 1, 3, 4, 5, 6, 7, 9, 8]

Increment L: H = 1, L = 7

Step 22:

Swap a[H] and a[L]: [2, 1, 3, 4, 5, 6, 7, 8, 9]

Decrement H: H = 0, L = 7

Step 23:

Swap a[H] and a[L]: [1, 2, 3, 4, 5, 6, 7, 8, 9]

Increment L: H = 0, L = 8

b) To solve the recurrence relation T(n) = 3²(k-1) + 3T(3²(k-1)) for k >= 1, expand the recurrence to find a pattern and then extrapolate to the bottom level.

Let's calculate T(1), T(3), T(9), and T(27) to identify the pattern:

T(1) = 0

T(3) = 3²(3-1) + 3T(3³(3-1)) = 3² + 3T(3) = 9 + 3(0) = 9

T(9) = 3³(9-1) + 3T(3³(9-1)) = 3³ + 3T(3³) = 6561 + 3T(6561)

T(27) = 3²(27-1) + 3T(3²(27-1)) = 3³ + 3T(3²6)

We can observe that T(1) = 0, T(3) = 9, T(9) = 6561 + 3T(6561), and T(27) = 3³ + 3T(3³6).

Now, let's try to find a pattern in the values of T(1), T(3), T(9), and T(27):

T(1) = 0

T(3) = 3² + 3T(3) = 9 + 3(0) = 9

T(9) = 3³ + 3T(3³) = 6561 + 3T(6561)

T(27) = 3²6 + 3T(3²6)

From the above values, that T(3) = 3², T(9) = 3³, and T(27) = 3²6.

Based on this pattern,  generalize that T(3²) = 3²(2k) for k >= 0.

Now, let's express the formula in terms of n:

Let n = 3²k

Then, k = log base 3 of n

Therefore, T(n) = 3²(2log3(n)) = n²

c) To show that the formula in Part b, T(n) = n², is theta of nlogn, to prove that T(n) is both Big O(nlogn) and Omega(nlogn).

Big O(nlogn) proof:

We need to find a constant c and an integer N such that T(n) <= c ×nlogn for all n >= N.

Let's consider T(n) = n². choose c = 1 and N = 1.

For n >= N,

T(n) = n² <= n² ×logn (as logn >= 1 for n >= 1)

<= c × nlogn

Therefore, T(n) is Big O(nlogn).

Omega(nlogn) proof:

To find a constant c and an integer N such that T(n) >= c ×nlogn for all n >= N.

Let's consider T(n) = n². choose c = 1 and N = 1.

For n >= N,

T(n) = n >= n ×logn (as logn >= 1 for n >= 1)

>= c ×nlogn

Therefore, T(n) is Omega(nlogn).

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Answer:

the answer is negative 3/7

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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Answer:

27.6%

Step-by-step explanation:

See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%.  (8/29)*(100%) = 27.6% to the nearest tenth.

Answer:

Slope: 2

Step-by-step explanation:

The inequalities seen on Cartesian plane are - 2 · x + y > 1 and - (1 / 2) · x + y ≤ 2, respectively.

In this problem we find two graphs by inequalities on Cartesian plane, whose definitions are listed below:

Case 19:

f(x) > y

Case 20:

f(x) ≤ y

Each inequality has a function of the form:

y = m · x + b

Where:

And the slope can be determined by secant line formula:

m = Δy / Δx

Now we proceed to determine each inequality:

Case 1:

Slope

m = 4 / 2

m = 2

Intercept

b = 1

Inequality

y > 2 · x + 1

- 2 · x + y > 1

Case 2:

Slope

m = 1 / 2

Intercept

b = 2

Inequality

y ≤ (1 / 2) · x + 2

- (1 / 2) · x + y ≤ 2

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CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.

Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.

Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.

Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.

Therefore, the largest angle of an obtuse triangle is opposite the longest side.

Step 4: In triangle ABC, A=103°, a=25, and c=30.

a² = b² + c² - 2bccos(A),

a² = b² + 900 - 900 cos(103),

a² = b² + 900 + 900 cos(77),

a² > b² + 900, so a > b.

Similarly, a² > c² + 900, so a > c.

Therefore, triangle ABC satisfies a>b and a>c.

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The slope of the tangent line to the curve is given by dy/dx at t=1 is -9 - (3/√21) given the parametric equations r=/²-21 and y=3t+1.

To calculate the slope of the tangent line to the curve given by the parametric equations x = t² - 2 and y = 3t + 1, we need to find the derivative dy/dx with respect to the parameter t.

First, we can rewrite r in terms of x and y using the Pythagorean theorem:

x^2 + y^2 = 21

Substituting in our given parametric equations, we get:

x^2 + (3t+1)^2 = 21

Simplifying, we get:

x^2 + 9t^2 + 6t + 1 = 21

x^2 + 9t^2 + 6t - 20 = 0

Now, we can take the derivative of both sides with respect to t:

2x(dx/dt) + 18t + 6 = 0

Solving for dx/dt, we get:

dx/dt = (-9x - 3)/x

Evaluating this at r=√21 and y=3t+1, we get:

dx/dt = (-9√21 - 3)/(√21)

Simplifying, we get:

dx/dt = -9 - (3/√21)

Therefore, the slope of the tangent line to the curve at t=1 is -9 - (3/√21).

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To find the location of E' after the dilation, we need to apply the dilation rule to the coordinates of point E. The dilation rule states that each coordinate (x, y) is transformed to (3/2x, 3/2y).

The coordinates of point E are given as (2, 2/3). Let's apply the dilation rule to these coordinates:

x-coordinate of E' = (3/2) * x-coordinate of E = (3/2) * 2 = 3

y-coordinate of E' = (3/2) * y-coordinate of E = (3/2) * (2/3) = 1

Therefore, the coordinates of point E' are (3, 1).

None of the answer choices matches the coordinates (3, 1), so none of the given options is correct.

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True....

it's a polynomial.

Answer:

am not really sure but ig the answer is B

Step-by-step explanation:

Plz help timed test I’ll give extra points