A parabola can be represented by the equation y2 = 12x. which equation represents the directrix?

The complete question is:

Create a matrix for this linear system:

what is the solution of the system?

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]

and z = r

A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.

Given:

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

By applying two more row operations, we get

[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]

simplifying the above matrix, we get

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]

[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and

z = r

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Answer:

t ≥ 36

Step-by-step explanation:

took a while but i had to try a lot of the numbers. hope it helped, mark me brainleist.

The inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

We know that t is the time,  in minutes, since Marcel plugged in the phone and the tablet.

For phone:-

Initial battery charge = 13%.

Rate of charging = 2% points in 3 minutes = 2/3 % in 1 minute.

Thus, the total charge on the phone after t minutes = 13% + t(2/3)%.

For tablet:-

Initial battery charge = 25%.

Rate of charging = 1% points in 3 minutes = 1/3 % in 1 minute.

Thus, the total charge on the tablet after t minutes = 25% + t(1/3)%.

We are asked to complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.

Since the phone is required to have at least as much battery charge as the tablet, we can show this as:

The total charge on the phone after t minutes ≥ The total charge on the tablet after t minutes,

or, 13% + t(2/3)% ≥ 25% + t(1/3)%,

or, t(2/3)% - t(1/3)% ≥ 25% - 13%,

or, t(1/3)% ≥ 12%,

or, t ≥ 12%/(1/3)%,

or, t ≥ 36.

Thus, the inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

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The pair of the line together that could be perpendicular to RS and should be considered will be EA and FG.

It should be noted that in terms of elementary geometry, two geometric objects should be considered as perpendicular when they intersect at a right angle.

In such a case, a line is treated to be perpendicular to another line in the case when the two lines intersect at a right angle.

Therefore, based on the information, the pair of the line together that could be perpendicular to RS and should be EA and FG.

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Answer:

110 degrees

Step-by-step explanation:

to find the angle x, we need to use the formula to find the 50 degree angle:

(y - x) / 2 = 50

y is 210

(210 - x) /2 = 50

210-x = 100

x = 110 degrees

Question The price of a sofa is Sx. A man buys the sofa on hire purchase according to the following terms:

a downpayment of 25 % and the remaining to be paid in monthly instalments over 30 months at a

simple interest rate of 12 % per annum. Given that his monthly instalment is $52, find the value of x.

The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.

A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right cylinder.

Volume of the cylinder = [tex]\pi r^{2}h[/tex]

Rate of change of height is  [tex]\frac{dh}{dt}[/tex] = ?

At any time t,

Volume, V =  [tex]\pi r^{2}h[/tex]

Since r does not change with time, then r is a constant, so,

V =  [tex]\pi (6)^{2}h[/tex]

V = [tex]36\pi h[/tex]

Differentiate both sides with respect to time t,

[tex]\frac{dV}{dt} = 36\pi \frac{dh}{dt}[/tex] -------------(i)

Since [tex]\frac{dV}{dt}[/tex]is given as 4[tex]\pi[/tex] cu.in. per min,

[tex]4\pi = 36\pi \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{4\pi }{36\pi }[/tex]

[tex]\frac{dh}{dt} = \frac{1 }{9 }[/tex] in/min.

Hence, The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.

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Based on the fact that the identical darts were thrown at four identical dartboards and Ben took a list, the number of different lists possible is 5 lists.

If all the darts hit on dartboard then the list would be:

= 0004

If one dart hit a dartboard and three hit one dartboard the list would be:

= 0031

If two darts hit two boards:

= 0022

If two darts hit one board, 1 dart two others:
= 0211

If all darts hit separate boards;

= 1111

This means that 5 lists are possible to Ben.

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Based on the given parameters, the number of filet mignon the restaurant served is 14

From the question, the given parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

This means that the proportion of filet mignon is

filet mignon = 100%- Salmon filets

This gives

filet mignon = 100%- 80%

Evaluate the difference

filet mignon = 20%

The number of filet mignon is calculated as:

filet mignon = 20% * Dinner specials

Substitute the known values in the above equation

filet mignon = 20% * 70

Express 20% as decimal

filet mignon = 0.20 * 70

Evaluate the product

filet mignon = 14

Hence, the number of filet mignon the restaurant served is 14

So, the complete parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

filet mignon = 14

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Answer:

7/14, so 50%

Step-by-step explanation:

Answer:

  BD = √97 cm ≈ 9.849 cm

Step-by-step explanation:

Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...

  AB = 4 cm

  AD = 9 cm

The sides are related to the diagonals by the Pythagorean theorem.

The Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:

  AB² +AD² = BD²

  4² +9² = BD² = 16 +81 . . . . . evaluating the squares

  BD = √97 . . . . . take the square root

The length of BD is √97 cm, about 9.849 cm.

The volume of the similar triangular prism is:  1,280 cm³.

Volume of a right triangular prism = 0.5 × b × h × altitude, where:

b is the base length of the triangular base

h is the height of the triangular base

Find the of the first triangular prism

Base length of the triangular base (b) = 4 cm

Height of the triangular base (h) = 4 cm

Altitude of the prism = 20 cm

Volume of the first triangular prism = 0.5 × 4 × 4 × 20 = 160 cm³.

Volume of the first prism/Volume of the second prism = (leg of first prism)³/(leg of second prism)³

160/Volume of the second prism = (4)³/(8)³

160/Volume of the second prism = 64/512

160/Volume of the second prism = 0.125

Volume of the second prism = 1,280 cm³.

Thus, applying the volume formula for a right triangular prism, the volume of the given similar prism is calculated as: 1,280 cm³.

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The answer is B.

To obtain A'B'C'D' from ABCD, we can clearly see that it has been shifted 2 units right and 3 units down.

The line of best-fit that represents the relationship between velocity and time is:

v = 2.19t + 6.7.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v) are given as follows:

(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).

Hence, inserting these points into a calculator, the equation is given by:

v = 2.19t + 6.7.

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The smaller number, x from the inequality x + 2x + 6 < 50 is x < 14.67

x + 2x + 6 < 50

3x + 6 < 50

3x < 50 - 6

3x < 44

x < 44/3

x < 14.6666666666666

Approximately,

x < 14.67

Therefore, the smaller number, x is approximately x < 14.67

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The purpose of statistical inference population based upon information obtained from the sample.

statistical inference uses sample data to make estimates of or draw conclusions about one or more characteristics of a population.

The purpose of statistical inference is to estimate this sample to sample variation or uncertainty. Understanding how much our results may differ if we did the study again, or how uncertain our findings are, allows us to take this uncertainty into account when drawing conclusions. It allows us to provide a plausible range of values for the true value of something in the population, such as the mean, or size of an effect, and it allows us to make statements about whether our study provides evidence to reject a hypothesis.

We have four ideas for using the statistical inference.

1. Estimating uncertainty.

2. Confidence intervals.

3. Hypothesis tests.

4. Connections with other material.

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The given question is not complete.

The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.

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The lateral surface area of a right circular cone is 234.09 [tex]cm^2[/tex]

Given that volume = [tex]320cm^3[/tex]

Radius = 8cm

we know that

The volume of the right circular cone = [tex]V = \frac{\pi r^2h}{3}[/tex]

[tex]320 = \frac{22 \times 8^2h}{3 \times 7}[/tex]

after solving the equation we get

h =  4.77cm

now, the lateral surface area of the cone = [tex]A = \pi \times r \times \sqrt{h^2 + r^2}[/tex]

now putting the values in the above equation

[tex]A = \pi \times 8 \times \sqrt{4.77^2 + 8^2}[/tex]

A = 234.09 [tex]cm^2[/tex]

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Answer:

b=67.5°

Step-by-step explanation:

hope it helps!!!

Applying the SAS congruence theorem and the definition of angle bisector, the complete proof is shown in the image attached below.

The SAS theorem (side-angle-side theorem) state that two triangles are congruent to each other if they have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

A line segment that divides an angle into two equal parts is referred to as an angle bisector.

From the proof given, we know that;

m∠DEK = 2(m∠DEF)

m∠DEK = 2(44) = 88°

With the given information and using the reflexive property, we know that triangles DEF and KEF have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

Therefore, ΔDEF ≅ ΔKEF based on the SAS congruence theorem. Because they are congruent triangles, DF = KF based on the CPCTC theorem.

Then, KF = 1/2(DK) = 1/2(16) = 8.

The complete proof is show in the image attached below.

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Answer:  $34.32

Step-by-step explanation: We first calculate the price of the dress that was on sale. 30% of 35 is 35/10 x3. This is equal to 3.5x3 which is 7+3.5 = 10.5 We subtract this from 35 to get $24.5. So, the dress cost $24.5. Next 1/2 of 17 is 8.5. In total, the items cost $24.5+$8.5 = $33. Then, there is a 4% sales tax we have to add on to 33. 1% of 33 is 33/100 which is 0.33. This time 4 is 1.32. 33+1.32 is 34.32.

Answer:[tex]3r-29r^2[/tex]

Step-by-step explanation:

The following Visual Image consists with the steps

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The value of tanθ = ±∞ or tanθ = ±√(7/5)

The question is a trigonometric equation

A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.

Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.

So, 7cosec²θ - 9cot²θ = 7

using the trigonometric identity 1 + cot²θ = cosec²θ.

Substituting this into the equation, we have

7cosec²θ - 9cot²θ = 7

7(1 + cot²θ)² - 9cot²θ = 7

7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7

7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7

14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7

14cot²θ + 7cot⁴θ - 9cot²θ = 0

7cot⁴θ + 14cot²θ - 9cot²θ = 0

7cot⁴θ + 5cot²θ = 0

Factorizing out cot²θ, we have

cot²θ(7cot²θ - 5) = 0

⇒ cot²θ = 0 or 7cot²θ - 5 = 0

⇒ cotθ = ±√0 or 7cot²θ = 5

⇒ cotθ = ±0 or cot²θ = 5/7

⇒ cotθ = ±0 or cotθ = ±√(5/7)

⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)

⇒ tanθ = ±1/0 or tanθ = ±√(7/5)

⇒ tanθ = ±∞ or tanθ = ±√(7/5)

So, the value of tanθ = ±∞ or tanθ = ±√(7/5)

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Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.

Y assume we have an exponential equation of the form:

y = a*b^x + c

In this case, a is what we know as the "initial value" of the exponential.

Notice that when we evaluate in x = 0, we get:

y = a*b^0 + c

y = a + c

So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.

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Answer:

x=1990

Step-by-step explanation:

x+10=2000

x=2000-10

x=1990

Answer:

therefore x = 1990

Step-by-step explanation:

x+10 = 2000

= x = 2000-10

= x = 1990

The correct option B.

The value of the zeros of function g is -6 and 7

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

The factors are  (x − 7) and (x + 6)

On simplifying the we get:

x²+ 6x -7x -42 = 0

x² - x - 42 = 0

The factorizing these equation we get.

So the zeros are -6 and 7 , so option b is correct.

[tex]x_{1,2}=\frac{-(-1) \pm \sqrt{(-1)^{2}-4 \cdot 1 \cdot(-42)}}{2 \cdot 1}[/tex]

[tex]$$x_{1,2}=\frac{-(-1) \pm 13}{2 \cdot 1}\\[/tex]

[tex]x_1,_2[/tex] = ((1) ± 13)/2.1

[tex]x_1[/tex]    = (1+13)/2.1

[tex]x_2[/tex]     = (1 - 13)/2.1

[tex]X_1\\[/tex] = 7 , [tex]X_2[/tex] = -6

The Zeros of the function are: (7 , -6)

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Statements that describe the given function are:

To find the statements that describe the given function:

Lastly, the correct answers are:

Therefore, statements that describe the given function are:

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The complete question is given below:

Which statements describe the function f(x)=2x-5/2(x^2-1)? Check all that apply.

(A) f(x) has one real zero because it crosses the x-axis once.

(B) f(x) has two real zeros because it crosses the x-axis twice.

(C) f(x) has real zeros at 1 and –1.

(D) f(x) has a real zero at 2.5.

(E) f(x) has x-intercepts at (1, 0) and (–1, 0).

(F) f(x) crosses the x-axis when x = 1 and x = –1.

(G) f(x) has an x-intercept at (2.5, 0).

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k  is this series written in sigma notation.

What is the series written in sigma notation?

Given:

2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87

If we look at the power it is always one less the term i.e., for first term the value of k=0.

So, the series in the form of summation can be written as

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k

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Answer:

  d.  x = 5

Step-by-step explanation:

Chords that subtend congruent arcs are congruent.

Chord lengths are the same:

  AB = CD

  16x -2 = 14x +8

  2x = 10 . . . . . . add 2-14x

  x = 5 . . . . . . . . divide by 2

Answer:

Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?

The Answer Is X = 20 or x = 4

Answer:

C. 206 unit^2.

Step-by-step explanation:

Area = 2*11*5 + 2*11*3 + 2*3*5

         = 110 + 66 + 30

         =  206.