Alita is on the track team and loves to run. On
Monday, she ran 3.5 miles in 25 minutes. If she
runs at the same pace on Tuesday, how many
miles can she run in 40 minutes?

Answer:

Option (C) is correct.

Step-by-step explanation:

Given that z = 0.3(cos(31°) + i sin(31°)) and 20(cos(18°) + i sin(18°)).

The product of both the complex number is

zw = [0.3(cos(31°) + i sin(31°))] x [20(cos(18°) + i sin(18°))]

=(0.3x20)[cos(31°) x cos(18°) + cos(31°) x i sin(18°) + i sin(31°) x cos(31°)+ i sin(31°) x i sin(18°)]

Here, (0.3x20)=6, is the magnitude of zw, which is stretching of 0.3 by 20.

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}+ i² sin(31°)x sin(18°)]

As i²= -1, So

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)} - sin(31°)x sin(18°)]

=6[{cos(31°) x cos(18°)- sin(31°)x sin(18°)} + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}]

As cosAcosB - sin A sin B = cos (A+B) and cosAsinB + sin A sos B = sin (A+B), so

zw=6[cos(31°+18°) + i{sin(31°+18°)]

Note that, initially the argument of z is 31° and after rotation of 18° in counterclockwise direction, the argument od zw is 31°+18°= 49°. i.e

zw=6(cos(49°) + isin(49°)).

So, zw can be determined by stretching z by a factor of 20, then rotating by 18° counterclockwise.

Hence, option (C) is correct.

Answer:

C: Stretch z by a factor of 20, then rotate 18° counterclockwise.

Step-by-step explanation:

Took the quiz.

Answer:

12.17secs

Step-by-step explanation:

Given the equation that models the height as y=-16x^2+187x+93

The rocket will hit the groung at y = 0

The equation becomes;

0 =-16x^2+187x+93

16x^2-187x-93 = 0

Factorize

x = 187±√187²-4(16)(-93)/2(16)

x = 187±√34,969+5952/32

x = 187±√40,921/32

x = 187±202.29/32

x = 187+202.29/32

x = 389.29/32

x = 12.17secs

Hence the required time that t will take is 12.17secs

Answer:

=2

hope it helps!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09

The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.

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The equation will be:

t = b - 2

And we can see that:

Here we have two variables:

t = taner's age

b = age of Tanner's brother.

The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.

The dependent variable depends on the other, on this case, Tanner's age.

Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:

t = b - 2

That is the equation.

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The inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

What is the inverse of a function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1."

We have,
Functions are shown in the picture.
To find the inverse of a function plug in the place of f(x)→x and x→f(x) ⁻¹
f(x) ⁻¹ = 3(x + 17)/2

Similarly,
f(x) = x - 10
f(x) ⁻¹ = x + 10
f(x) = ∛2x
f(x) ⁻¹ = x³/2
f(x) = x/5
f(x) ⁻¹ = 5x

Hence, the inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

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Answer:

=2,400,000

Step-by-step explanation:

=30,000 x 80

=2,400,000

Answer:

x - 16 = -3

Step-by-step explanation:

x - 16 = -3  Add 16 to both sides of the equation

x = 13

It was 13 degrees at noon

Answer:

i) 104 °F

ii) 343 °K

Step-by-step explanation:

We have the relationship between temperature in degrees Fahrenheit(y) and degrees Kelvin(x) as:

\(y\:=\:\dfrac{9}{5}\left(x-273\right)+32\)

i) When temperature in Kelvin is 313°K, the equivalent temperature in °F is:
\(\begin{aligned}y &= \dfrac{9}{5}(313-273) + 32\\& = \dfrac{9}{5}(40) + 32\\&= 9 \cdot 8 + 32\\\\&= 72 + 32\\\\& = 104^\circ F\end{aligned}\\\)

So at 313°K, the equivalent temperature is 104°F

\(====================================\)

ii) We are given the temperature in degrees Fahrenheit and asked to find the temperature in degrees Kelvin

We have the equation for temperature conversion from °K to °F  as:
\(y\:=\:\dfrac{9}{5}\left(x-273\right)+32\)

Let's manipulate this equation so that x is given in terms of y

Here x = degrees Kelvin and y = degrees Fahrenheit

Given y = 158°F, just plug in this value into the equation for x giving
\(\begin{aligned}x &= \dfrac{5}{9}(158 - 32) + 273\\& = \dfrac{5}{9}(126) + 273\\&= 70 + 273\\&= 343\end{aligned}\)

Therefore temperature in °K for temperature 158°F = 342 °K

Answer:

292° 24' 36"

Step-by-step explanation:

d = int(292.41°) = 292°

m = int((292.41° - 292°) × 60) = 24'

s = (292.41° - 292° - 24'/60) × 3600 = 36"

292.41°

= 292° 24' 36"

Answer:

292 degrees 24 minutes and 36 seconds:

292° 24' 36"

Step-by-step explanation:

There are 60 minutes in a degree and 60 seconds in a minute.

so 0.41 degrees = 0.41 * 60 = 24.6 minutes

and 0.6 of a minute = 0.6 * 60 = 36 seconds.

dy/dx = 0 when x = - 2, and x = 2/3 is not possible.

dy/dx = 0 when x = - 1, and x = 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

y = x³ - 6x² - 15x - 7

Differentiating w.r.t x.

[ d\(x^n\)/dx = n\(x^{n - 1}\) ]

[ dc/dx = 0 ]

dy/dx = dx³/dx - 6dx²/dx - 15dx/dx - d7/dx

dy/dx = 3\(x^{3 - 1}\)dx/dx - 6 x 2\(x^{2-1}\)dx/dx - 15 - 0

dy/dx = 3x² - 12x - 15

Now,

dy/dx = 0

3x² - 12x - 15 = 0

3(x² - 4x - 5) = 0

x² - 4x - 5 = 0

x² - (5 - 1)x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x - 5) (x + 1) = 0

x - 5 = 0

x = 5 _____(1)

x + 1 = 0

x = -1 _____(2)

Now,

For x = 2,

dy/dx = 3x² - 12x - 15

dy/dx = 3 x 4 + 24 - 15

dy/dx = 12 - 24 - 15

dy/dx = 12 - 39

dy/dx = -27 _____(3)

For x = 2/3,

dy/dx = 3x² - 12x - 15

dy/dx = 3 x 4/9 + 24 x 2/3 - 15

dy/dx = 4/3 + 16 - 15

dy/dx = 4/3 + 1

dy/dx = 7/3 _____(4)

From (1), (2), (3), and (4)

dy/dx = 0 when x = - 2 and x = 2/3 is not possible.

Thus,

dy/dx = 0 when x = - 1, and x = 5.

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Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

An isosceles triangle is also equilateral if and only if the length of the third side is equal to the length of the two equal sides.

An isosceles triangle is a triangle that has two sides of equal length. An equilateral triangle is a triangle that has three sides of equal length. Therefore, an isosceles triangle can only be equilateral if all three sides of the triangle are equal in length.

In other words, an isosceles triangle is also equilateral if and only if the length of the third side is equal to the length of the two equal sides.

For example, a triangle with side lengths 5, 5, and 5 is both an isosceles triangle and an equilateral triangle. However, a triangle with side lengths 3, 4, and 5 is an isosceles triangle, but it is not equilateral because the length of the third side (5) is not equal to the length of the two equal sides (3).

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Using a binomial probability calculator, we can find the probability of getting 35 or more sales for 1000 telephone solicitations based on the given 3% chance of a sale.

To find the probability of getting 35 or more sales for 1000 telephone solicitations, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

n is the total number of trials,

k is the number of successful outcomes,

p is the probability of success in a single trial, and

(1 - p) is the probability of failure in a single trial.

In this case, we want to find the probability of getting 35 or more sales, so we need to calculate the sum of probabilities for all values of k from 35 to 1000.

Let's calculate it using the binomial probability formula:

P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 1000)

Since calculating this directly would involve a large number of calculations, we can use a cumulative binomial probability table, statistical software, or a calculator to find the probability.

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The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).

The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:

\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)

where EBIT is earnings before interest and taxes.

Calculate EBIT by subtracting interest expense from operating income:

EBIT = Operating Income - Interest Expense

We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.

EBIT = Interest Expense / (1 - Tax Rate)

= \(\$165,000 / (1 - 0)\)

= \(\$165,000\)

Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by  \(\$69,000\).

Therefore:

\(\triangle Working Capital = \$69,000\)

Now, we can calculate OCF:

OCF = EBIT + Depreciation - Taxes + Δ Working Capital

=\(\$165,000 + 0 - 0 +\ $69,000\)

=\(\$234,000\)

Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .

To calculate the net income for Griffin's Goat Farm, we can use the following formula:

Net Income = EBIT - Interest Expense - Taxes

where EBIT is earnings before interest and taxes. We can calculate EBIT as:

EBIT = Sales - Costs - Depreciation

= \(\$686,000 - \$332,000 - \$65,000\)

=\(\$289,000\)

Next, we need to calculate taxes. We are given a tax rate of 24%, so:

Taxes = Tax Rate x (EBIT - Depreciation)

= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)

Now, we can calculate net income:

Net Income = EBIT - Interest Expense - Taxes

= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)

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Answer:

b

Step-by-step explanation:

Answer: Coordinates: (1,3) length RS: 3 length RT: 2 ST: 3.6

Step-by-step explanation:

a^2+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

3.6=c

Answer:

228573

Step-by-step explanation:

a = 219 (first term)

an = 2018 (last term)

Sn->Sum of n terms

Sn=n/2(a + an)         [Where n is no. of terms] -> eq 1

To find number of terms,

an = a + (n-1)d     [d->Common Difference] -> eq 2

d= 226-219 = 7

=> d=7

Substituting in eq 2,

2018 = 219 + (n-1)(7)

1799 = (n-1)(7)

1799 = 7n-7

1799 = 7(n-1)

1799/7 = n-1

257 = n-1

n=258

Substituting values in eq 1,

Sn = 258/2(219+2018)

    = 129(2237)

    = 228573

Answer:

y-8

Step-by-step explanation:

Answer:

$5

Step-by-step explanation:

0.2 * $25 = $5

I hope this helped, please mark Brainliest, thank you!!

Answer:

I hope This will Help u.. Plz mark me as Brilliant please

Step-by-step explanation:

Before you get started, take this readiness quiz.

Simplify: 

If you missed this problem, review (Figure).

Solve Equations with Constants on Both Sides

In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.

Our strategy will involve choosing one side of the equation to be the “variable side”, and the other side of the equation to be the “constant side.” Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.

By doing this, we will transform the equation that began with variables and constants on both sides into the form  We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.

Solve: 

Solution

In this equation, the variable is found only on the left side. It makes sense to call the left side the “variable” side. Therefore, the right side will be the “constant” side. We will write the labels above the equation to help us remember what goes where.



Since the left side is the “”, or variable side, the 8 is out of place. We must “undo” adding 8 by subtracting 8, and to keep the equality we must subtract 8 from both sides.

Use the Subtraction Property of Equality.Simplify.Now all the variables are on the left and the constant on the right.

The equation looks like those you learned to solve earlier.Use the Division Property of Equality.Simplify.Check:Let .

Solve: 



Solve: 



Solve: 

Solution

Notice, the variable is only on the left side of the equation, so we will call this side the “variable” side, and the right side will be the “constant” side. Since the left side is the “variable” side, the 9 is out of place. It is subtracted from the , so to “undo” subtraction, add 9 to both sides. Remember, whatever you do to the left, you must do to the right.

Answer:

Division property of equality

Step-by-step explanation:

\( - 2m = 40\)

\(m = - 20\)

Answer:

a) (-25)(4)

Step-by-step explanation:

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations. In this case,

withdrew means no longer there which means subtracted.

Then, times mean multiply.

Therefore, -minus twenty-five times (x) four

combine them and it equals (-25)(4)

Given:

The height of the projectile shooting up into the air is given as,

Required:

The time t required for the projectile to return to its starting position.

Explanation:

When the projectile starts from its initial position and comes back to the same position then the height becomes zero.

Equating the given equation to zero.

Calculating the roots of the given quadratic equation.

On simplifying further,

Therefore,

At t = 0 seconds, the projectile was shot into the air. After 8 seconds the projectile returned back to its original position.

Answer:

Thus the time taken by projectile to return back to its starting position is 8 seconds.

Answer:

The answer is D or Triangle TUV is dilated by a scale factor of 9 and then translated 2 units right and 1 unit down to form triangle T"U"V" . I just took the test and I hope I helped : )

Step-by-step explanation:

Answer:

Here is the complete magic square:

-3 4 -1

2 0 -2

1 -4 3

Every row, column, and long diagonal adds to 0.

Determine the area's length and width, both in feet, to compute the square footage (abbreviated sq. ft.). To find the square feet, multiply the length by the breadth. Here is a fundamental formula you can use: Area in square feet equals length in feet times width in feet.

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Solving the provided question, we cans say that the quadratic equation is \(y= -0.5x^2 +1 6x +20\\\) the factors are x = 0.985 so, Wesley's claim is correct.

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

\(y= -0.5x^2 +1 6x +20\\\)

on solving it we get the factors

x = 0.985 and x = -2

on putting x = 0.985 we have

y = 175 feet

so, Wesley's claim is correct.

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