Find the equation of a parabola with a focus at (–2,–3) and a directrix at y = –5.

A)

y = 1∕4(x + 2)2 – 4

B)

y = –1∕16(x + 2)2 – 4

C)

y = 1∕4(x – 2)2 – 4

D)

y = 1∕4(x + 2)2 – 8

Answer:

First we convert the sentence to an equation so:

[tex] \frac{3}{4} x = 24[/tex]

Now to isolate x divide by the recuprical of 3 over 4 which is 4/3

[tex] \frac{3}{4} \times \frac{4}{3} = 24 \times \frac{4}{3} [/tex]

24x4= 96 and 3 remains.

[tex]x = \frac{96}{3} [/tex]

Now we can simplify by 3 and we will get the final answer which is

[tex]x = 32[/tex]

Answer:

12

Step-by-step explanation:

480 tomatoes/40 baskets = 12 per basket

Answer:

  c.

Step-by-step explanation:

You want a linear combination of the given 3×3 matrices.

We observe that the answer choices are different in most corresponding terms, so we only need to find the value of one term in order to choose the correct answer.

The expression applied to the matrices is applied to corresponding terms of the matrices. That is, for ...

  [tex]C = -2A +7B[/tex]

you will have ...

  [tex]c_{11}=-2a_{11}+7b_{11}\\\\c_{11}=-2(4)+7(7)=-8+49\\\\c_{11}=41[/tex]

This matches choice c.

__

Additional comment

Many graphing calculators and all spreadsheets can do the necessary calculations to help you find the desired result matrix.

Answer:

190 cm²

Step-by-step explanation:

     Area of one regular hexagon is given. Multiply 23 *2 and it will give the area of two regular hexagons.

There are 6 rectangles. Find the area of one rectangle and multiply it by 6.

 Area of regular hexagon = 23 cm²

Area of rectangle = length * width

                             = 8 * 3

                             = 24 cm²

      Area of the regular hexagon prism = 2* area of regular hexagon + 6*area of rectangle.

                                                                 = 2*23 + 6*24

                                                                 = 46 + 144

                                                                 = 190 cm²

Answer:

21.5

Step-by-step explanation:

geometric progression formula: [tex]A_{n}[/tex]=A*[tex]r^{n-1}[/tex]

where An is nth term

A is first term

r is common ratio

given [tex]A_{99}[/tex] = 48

A=12

we find r

48=12 *[tex]r^{99-1}[/tex]

48/12=[tex]r^{98}[/tex]

[tex]\sqrt[98]{4}[/tex]=r

r=1.014

so to find 50th term

[tex]A_{50}[/tex]=12*[tex]1.012^{50-1}[/tex]

[tex]A_{50}[/tex]=21.53

The solution of the inequalities is x < - 3 / 2 or x > 48 / 5

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Inequality expression always have the symbols <, >, ≤ and ≥.

Therefore, let's solve the inequalities.

12x + 7 < - 11 or 5x - 8 > 40

12x + 7 < - 11

subtract 7 from both sides of the inequalities.

12x + 7 - 7 < - 11 - 7

12x < - 18

divide both sides by 12

x < - 18 / 12

x < - 3 / 2

5x - 8 > 40

add 8 to both sides of the inequalities

5x - 8 + 8 > 40 + 8

5x > 48

divide both sides by 5

x > 48  / 5

x > 48 / 5

Therefore,

x < - 3 / 2 or x > 48 / 5

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The ordered pair (13, 41) simply means a daily usage fee of $41 would be charged to use the Body for Life gym for 13 days.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Based on the information provided, a linear equation which models the situation is given by:

y = 2x + 15

For the ordered pair (13, 41), we have:

y = 2x + 15

y = 2(13) + 15

y = 26 + 15

y = $41.

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Answer:

  B. The graph of K has a greater y-intercept

  D. The graph of J has a greater slope.

Step-by-step explanation:

Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.

The y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.

We see from the equation for function K that the constant is 8. This is the value of y when x=0.

Function K has the greater y-intercept (8 vs. 2).

The slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.

The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.

Function J has the greater slope (5 vs. 3).

Additional comment

Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.

The solution to the initial value problem in this problem is given as follows:

[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]

The initial value problem is given as follows:

y''-4y'-5y = 0.

The first step is finding the roots of the characteristic equation, which is given as follows:

r² - 4r - 5.

The equation can be factored as follows:

r² - 4r - 5 = (r - 5)(r + 1).

Applying the inverse Factor Theorem, the roots are given as follows:

These roots are real, hence the format of the solution is given as follows:

[tex]y = Ae^{5x} + Be^{-x}[/tex]

Considering the initial condition at x = 1, we have that:

Ae^(5) + Be^(-1) = 0

Considering the initial condition of the derivative at x = 1, we have that:

5Ae^(5) - Be^(-1) = 2.

Adding the two equations, the condition A is obtained as follows:

6Ae^(5) = 2.

A = 2/(6e^5)

A = 0.0022.

Hence the condition B is:

B = -0.0022e^(5)/e^(-1)

B = -0.8853.

Hence the solution is:

[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]

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The number of chocolate bars, c, the sports club must sell in order to reach their goal is 80

An inequality refers to a statement that has two quantities in which one is specifically less than (or greater than) another. Symbols of inequality includes:

Let

The inequality that represent the situation is given by

3c ≥ 240

c ≥ 240/3

c ≥ 80

Therefore, all real whole numbers greater than or equal to 80 is the number of chocolate bars, c, the sports club must sell in order to reach their goal.

The shaded area to the right of the solid line c = 80 is the graph which represent the inequality.

Complete question:

A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3c > 240. Which graph represents this inequality?

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Answer:

Answer and explanation in image

Step-by-step explanation:

The annual percentage growth rate is 5.9%

The doubling time of an investment of $10000 is 12 years

The compound interest caluclated annually can be given by

A=P(1 + r/n)^nt

where A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

20000 = 10000(1 + r)¹²

2⁻¹² = 1 + r

r = 1.059 - 1

r = 0.059

Rate of inetrest = 5.9%

Therefore, the annual percentage growth rate is 5.9%

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The value of x is 1.1913

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

5[tex]x^5[/tex] = 9+3

5[tex]x^5[/tex] =12

[tex]x^5[/tex]=12/5

Take 5th root on both sides

[tex]x=\sqrt[^5]{12/5}[/tex]

x= 1.1913

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Answer:

Step-by-step explanation:

The average rate of change between two points is the slope of the line between those points.

The points are:

The slope is:

The points are:

The slope is:

Answer:

[tex]\textsf{Average rate of change of the golf ball}=\dfrac{9}{2}\; \sf m/s[/tex]

[tex]\textsf{Average rate of change of the baseball}=\dfrac{9}{4}\; \sf m/s[/tex]

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\boxed{\dfrac{f(b)-f(a)}{b-a}}[/tex]

To find the average rate of change from 3 to 7 seconds:

Therefore, use the formula:

[tex]\implies \dfrac{f(7)-f(3)}{7-3}[/tex]

Golf Ball

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&14\\\cline{1-2} 7&32\\\cline{1-2} 9&24\\\cline{1-2} 12&2\\\cline{1-2}\end{array}[/tex]

From inspection of the table:

Substitute these values into the formula to find the average rate of change of the golf ball from 3 seconds to 7 seconds:

[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{32-14}{7-3}=\dfrac{9}{2}\; \sf m/s[/tex]

Baseball

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&6\\\cline{1-2} 7&15\\\cline{1-2} 9&13\\\cline{1-2} 12&0\\\cline{1-2}\end{array}[/tex]

From inspection of the table:

Substitute these values into the formula to find the average rate of change of the baseball from 3 seconds to 7 seconds:

[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{15-6}{7-3}=\dfrac{9}{4}\; \sf m/s[/tex]

Answer:its  10,00 more than it so one

Step-by-step explanation:

10^4=10,000

10,000x4=40,000

10000x5=50,000

Answer:

1 × 10^4

Step-by-step explanation:

5 × 10 ^ 4 = 5 × 10000

= 50,000

4 × 10 ^ 4 = 4 × 10000

= 40,000

Therefore; 50,000 - 40,000

= 10,000 or 1 × 10 ^ 4

Hence 5 × 10^4 is bigger than 4 ×10^4 by

1 × 10^4

Answer:

C) 20

Step-by-step explanation:

The absolute value of -20 is 20, because absolute value just keeps the same number, but makes positive.

Hope this helped!

Answer:

Equation:

50t + 100 = P

Table:

T             P

0          100

1           150

2           200

3           250

4            300

Step-by-step explanation:

$100 - starting value because it is the initial studio use fee

50t - since 50 dollars is the hourly fee, you have to multiply it by t (time)

The three geometric mean between 2 and 512 are

The first term = 2

Consider the common ratio as r

Then the second term = 2r

The third term = [tex]2r^2[/tex]

The fourth term is = [tex]2r^3[/tex]

The fifth term is given that 512

The fifth term = [tex]2r^4[/tex]

Then the equation will be

[tex]2r^4[/tex] = 512

[tex]r^4[/tex] = 512 / 2

[tex]r^4[/tex] = 256

r = ±4

When r = 4

The three geometric mean between 2 and 512 are

2r = 2×4 = 8

[tex]2r^2[/tex] = 2×4×4 = 32

[tex]2r^3[/tex] = 2×4×4×4 = 128

When r = -4

The three geometric mean between 2 and 512 are

2r = 2×-4 = -8

[tex]2r^2[/tex] = 2×-4×-4 = 32

[tex]2r^3[/tex] = 2×-4×-4×-4 = -128

Hence, the three geometric mean between 2 and 512 are

The complete question is :

Find the three geometric means between 2 and 512.

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Answer:

a = 108°

b = 72°

c = 48°

d = 48°

Step-by-step explanation:

• ∠a and the 72° angle are on a straight line. Therefore they add up to 180°:

∠a + 72° = 180°

⇒ ∠a = 180 - 72°

⇒ ∠a = 108°

• ∠b and the 72° angle are corresponding angles (the angles make an F-shape). Therefore, they are equal:

∠b = 72°

• ∠d and the 48° angle are alternate angles (the angles make a z-shape). Therefore they are equal:

∠d = 48°

• ∠c and ∠d are vertically opposite angles. Therefore, they are equal:

∠c = ∠d

⇒ ∠c = 48°

Considering a discrete distribution modeling the situation, it is found that:

a) The expected value of each $1 bet in roulette is of: -$0.988.

b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

The total number of outcomes for the three-number bet is of:

10 x 10 x 10 = 1000.

As three numbers are taken, and for each number, there are 10 possible outcomes.

Hence the probability of winning is of:

p = 1/1000.

As there is only one correct sequence.

The probability of losing is of:

p = 1 - 1/1000 = 999/1000.

Considering a payout of $11 for a $1 bet, the distribution of earnings is presented as follows:

Hence the expected value of a $1 bet is calculated as follows:

E(X) = 11/1000 - 999/1000 = -$0.988.

Which means that you are expected to lose approximately 99 cents for every dollar that you bet.

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The sample size will be needed to estimate the mean time to spoilage with an accuracy of one day is 166

The formula for the margin of error is given as

[tex]E = Z*\frac{sd}{\sqrt{n} }[/tex]

The standard deviation is given as sd = 5 days

We have to find the critical value of Z at the confidence level of 99 %

This value is given as 2.576

E = 1 day because the accuracy has been said to be within one day.

We have to insert the values in the formula that we have here

[tex]1 = 2.576*\frac{5}{\sqrt{n} }[/tex]

√n = 12.88

square both sides to get rid of the square root sign

n = 12.88²

n = 165.89

n ~ 166

The sample size would be 166

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Answer:

Nepali=17 English=18

Step-by-step explanation:

first in Nepali,

The suitable for blank is 2099.43 approximately.

Let the principle be P.

Time (t) = 19 years and 6 months = 19.5 years

Compound is semiannually.

Rate of Interest (r) = 4.5%

Amount will be (A) = $5000

So, suitable equation is given by,

[tex]A=P\left(1+\frac{r}{200}\right)^2t\\5000=P\left(1+\frac{4.5}{200}\right)^{2\times19.5}=P\left(1+\frac{9}{400}\right)^{39}\\\\P\approx2099.43[/tex]

Hence the suitable for the blank is 2099.43.

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Answer:

[tex] \huge{ \bold{y = 45x + 94}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is represented by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = 45

In order to find c we substitute the point (0,94) into the equation y = mx + c

That's

[tex]94 = 45(0) + c \\ 94 = 0 + c \\ c = 94[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = 45x + 94}[/tex]

Hope this helps you

The recursive equation for the nth term is aₙ = -4aₙ₋₁

The definition of the functions is given as

a₂ = 2

a₅ = -384

Sequence type = Geometric sequence

The nth term of a geometric sequence is represented as

aₙ = arⁿ⁻¹

So, we have

a₂ = ar = 6

a₅ = ar⁴ = -384

Divide the equations

r³ = -384/6

Evaluate

r³ = -64

Take the cube roots

r = -4

The recursive equation for the nth term is represented as

aₙ = aₙ₋₁ * r

So, we have

aₙ = -4aₙ₋₁

Hence, the equation is aₙ = -4aₙ₋₁

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Assuming Pod wrote that N could be equal to -18, Pod is correct.

A quadratic equation is an equation with a variable to the second power as its highest power term.

The Standard Form of a Quadratic Equation:

ax² + bx + c = 0

where:

x² + 7x - 18 = (x + 9)(x - 2) . . . . . g = 9, h = -2

There are no integer factors of 13 that add to give 7. 13 is prime, so the sum of its integer factors is 1+13 = 14.

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Suppose that the equations of line [tex]C[/tex] and [tex]D[/tex] are as follows;

If these two lines are parallel to each other, the following equality must be satisfied.

In summary, the slope of the two lines must be equal to each other.

We know the equation of line [tex]C[/tex]. Then let us form the equation of line [tex]D[/tex].

We must find the variable [tex]c_{1}[/tex] by placing the given point [tex](-3,-1).[/tex]

If we write it in slope-intercept form, the correct answer will be as follows;

Answer:

+8 or -8

Step-by-step explanation:

Both can be the qrt of 64 because   -8 * -8 = + 64

The y-intercept is (0, 400), which represents the amount of money the radio station originally had. The x-intercept is (8, 0), which represents the number of weeks it will take for the radio station to have $0 left.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Similarly, the x-intercept can be defined as the point at which the graph of any function crosses the x-coordinate and the value of "y" is equal to zero (0).

For the y-intercept, x = 0 and we have the following:

y = 400 - 50x

y = 400 - 50(0)

y = 400.

For the x-intercept, y = 0 and we have the following:

y = 400 - 50x

0 = 400 - 50x

50x = 400

x = 400/50

x = 8.

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