Wren and Jenni are reading the same book. Wren is on page 12 and reads 3 pages every night. Jenni is on page 7 and reads 4 pages every night. After how many nights will they have read the same number of pages? How many pages will that be?

Answer:

Step-by-step explanation:

Given the line L1 as y = 2x perpendicular to an unknown line L2 passing through the point P = (1, 2), we are to find the equation of line L2. to find the equation of the line L2, we will use the point-slope equation of a line expressed as y-y₀ = m(x-x₀)

m is the slope of the unknown line

(x₀, y₀) is the given point.

First is to get the slope of the known line:

comparing the line L1: y = 2x with the standard equation of the line y = mx+c, it can be seen that m = 2

Then we will calculate the slope of the required line.

Since L1 is perpendicular to L2, the product of their slope will be -1 i.e

mm₁ = -1 where m₁ is the slope of the required line L2.

Given m =2

m₁ = -1/m

m₁ = -1/2

Finally we will calculate the equation of line L2 by substituting the slope of line L2 and the point in the point slope equation above;

y-y₀ = m(x-x₀)

Given (x₀, y₀) = (1,2) and m₁ = -1/2

y-2 = -1/2(x-1)

open the parenthesis

y-2 = -x/2+1/2

multiply through by 2:

2y-4 = -x+1

2y+x = 1+4

2y+x = 5

Hence the equation of the line L2 is 2y+x = 5

The solutions of the equation of the graph is -4 and 2.

An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.

We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.

In the given graph the point of intersection of the two equations are at x = -4 and x = 2.

Hence, the solutions of the equation of the graph is -4 and 2.

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The complete question is:

Step-by-step explanation:

everything can be found in the picture

Given:

Complex numbers are 2 and 8.

Required:

We need to find the sum of the complex numbers.

Explanation:

The given complex can bw\e written as follows.

Final answer:

The set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} belong to a function

[y = f(x)] considering the pairs are in the order of (x, y).

As per the question statement, we are provided with a set of ordered pairs: {(-2, 4), (0, 2), (-1, 3), (4, -2)}.

We are required to determine if the pairs in the set satisfy a function or not.

To solve this question, let us consider each pair in the form of (x, y) and then, we will have to find out a relation between x and y that will satisfy all the ordered pairs. If we are able to find out one such common relation or pattern, we will determine our ordered pairs as inputs and outputs of the same function, otherwise not.

We can say that, \([(-2)(-1)+2]=4,\)

\([(0)(-1)+2]=(0+2)=2,[(-1)(-1)+3]=1+2)=3,\\\)

And, \([4*(-1)]+2=[(-4)+2]=(-2)\)

That is, all our ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} satisfy the function [y = f(x) = {x(-1) + 2}], being in the order of (x, y).

Therefore, the set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} are the inputs and outputs of the function [y = f(x) = {x(-1) + 2}].

       (b = q).

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The correct statements regarding the dilation to the triangle are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The resulting image is a larger or smaller version of the original object, depending on whether the scale factor is greater than or less than 1, respectively.

The ratio of the perimeter is equals to the scale factor, while the ratio of the areas is equals to the square of the scale factor.

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Answer:

The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

\(Cost = 51.275\)

Step-by-step explanation:

The given parameters can be summarized as:

\(\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}\)

Where: x = Soybeans and y = Oats.

So, the system of equations are:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

\(Cost = 21x + 7y\)

The best way to solve this, is using graph

Plot the following equations on a graph, and get the points of intersection:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

From the attached graph, we have:

\((x_1,y_1) = (1.636,2.545)\)

\((x_2,y_2) = (1.775,1.575)\)

\((x_3,y_3) = (2.023,1.256)\)

Substitute each of the values of x's and y's in the cost function to get the minimum cost:

\(Cost = 21x + 7y\)

\((x_1,y_1) = (1.636,2.545)\)

\(Cost = 21 * 1.636 + 7 * 2.545\)

\(Cost = 52.171\)

\((x_2,y_2) = (1.775,1.575)\)

\(Cost = 21 * 1.775 + 7 * 1.575\)

\(Cost = 48.3\)

\((x_3,y_3) = (2.023,1.256)\)

\(Cost = 21 * 2.023 + 7 * 1.256\)

\(Cost = 51.275\)

The values of x and y that gives the minimum cost is:

\((x_2,y_2) = (1.775,1.575)\)

and the minimum cost is:

\(Cost = 48.3\)

Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

Answer:

\(M.E=0.046\)

Step-by-step explanation:

From the question we are told that:

Sample size \(n=300\)

No. of rental \(x=111\)

Confidence Interval \(CI=0.90\ \alpha=0.10\)

Probability of rental

\(P(x)=\frac{111}{300}\)

\(P(x)=0.370\)

Generally the equation for Margin of Error is mathematically given by

\(M.E=Z_c*\sqrt{\frac{P(1-P)}{n}}\)

\(M.E=1.645*\sqrt{\frac{0.370(1-0.370)}{300}}\)

\(M.E=0.046\)

The misleading about the data shown on the figure is the clas width

From the question, we have the following parameters that can be used in our computation:

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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The solution of the integral by variable change is equal to (1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3).

In this problem we find the definition of an integral, whose solution must be found by variable change, that is, a kind of algebraic substitution. First, write the complete expression:

∫ [x / √(2 · x + 3)] dx

Second, use algebraic substitution to simplify the expression:

u = 2 · x + 3

x = (u - 3) / 2

dx = du / 2

(1 / 2) ∫  [(u - 3) / (2 · √u)] du

(1 / 4) ∫ [(u - 3) / √u] du

(1 / 4) ∫√u du - (3 / 4) ∫ du / √u

Third, solve the integral:

(1 / 6) · √u³ - (3 / 2) · √u

Fourth, revert the algebraic substitution:

(1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3)

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1) Given that the sum of all probabilities must be equal to 1, and there are 6 plums, 14 clementines, and 12 nectarines we can tell there are 14+12+6 objects:

14+12+6= 32 this is our subspace.

2) So let's find first the probability of that teacher picking a nectarine:

But notice, we don't want to know that we want the probability of not picking a nectarine so let's subtract that from 1 and write it this way:

3) We want to find the probability of the Complementary set to that:

Note that we simplified this.

What does that even say

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

He made a mistake in step 2

Step-by-step explanation:

-3x does not equal 6 it clearly states it equals 1

Answer:

Step-by-step explanation:

c^2=28.2 + 42.1

SOLVE FOR A

A=logc (703/20), c ≠ 1 and C > 0

SOLVE FOR C

{ c = - (700/20) 1/a, A ≠ 0 and Numberator (A) bmod 2 = 0 and denominatior (A)bmod 2=1 SOOOOOOO a ≠ 0

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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9514 1404 393

Answer:

  0.09 per inch

Step-by-step explanation:

There are 12 inches in a foot, so 15 feet is 15×12 = 180 inches.

The cost per inch is found by dividing the cost by the number of inches.

  cost per inch = 16.20/180 = 0.09

The cost per inch of electrical wire is 0.09.

Answer:

you would change it 4 times a year

Step-by-step explanation:

if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4

Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

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Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity

hello

the answer to the question is:

x³ - 3x² + 3x - 1 > (3/2)x(x - 1)² ---->

(x - 1)³ > (3/2)x(x - 1)² ----> x - 1 > (3/2)x ---->

(1/2)x < - 1 ----> x < 2

because it's value will always be same

Answer:

This value doesn't depend on x or y

It'll be the same things always

The equation of the directrix is y = -5

The equation is given as:

(x -1)^2 = 12(y + 2)

Express 12 as a product of 4 and 3

(x -1)^2 = 4 * 3(y + 2)

The parabola is represented as:

(x -h)^2 = 4p(y - k)

Where the directrix is

y = k - p

By comparison, we have:

k = -2 and p = 3

So, we have:

y = -2 - 3

Evaluate

y = -5

Hence, the equation of the directrix is y = -5

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The relation between the probability of its complement is that their sum is 1.

Complement in probability theory is an essential concept that helps us understand the likelihood of an event not occurring. It is a mathematical term that refers to the opposite or negation of an event.

Complement refers to the probability of an event not occurring, given the probability of it occurring. It is often denoted as the complement of an event A and is represented by A’.

The complement of an event A is defined as the set of all outcomes in the sample space that are not in A.

The probability of the complement of A is equal to the probability of all the outcomes in the sample space that are not in A.

The most important properties of the complement of an event is that the probability of an event and its complement always add up to 1. This is known as the law of complementary probability, and is expressed as:

P(A) + P(A’) = 1

This means that if we know the probability of an event occurring, we can easily calculate the probability of its complement by subtracting the probability of the event from 1.

For example, if the probability of event A is 0.7, then the probability of its complement, A’, is 1 – 0.7 = 0.3.

Hence the relation between the probability of its complement is that their sum is 1.

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Wdym by definition Answer:

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-2 and 12 are 14 whole numbers apart.

14/2 = 7

12 - 7 = 5

This isn't the most technical way to do this problem, but its easy and correct.

The statement which correctly represents the graph of g (x) given that g (x) = -3 f (x) is; g (x) is a dilation of the graph of f (x) with a scale factor of 3 and followed by a reflection over the x-axis.

It follows from the task content that the statement which correctly represents the graph of g (x) be determined given that; g (x) = -3 f (x).

Recall that given a function; f (x), the graph of -f(x) represents a reflection of the graph of f (x) over the x-axis.

Also, given a function; f (x) ; the function k f(x) represents a dilation of the graph of f(x) by a scale factor of k.

On this note, since the g (x) = -3 f (x), it follows that;

g (x) is a dilation of the graph of f (x) with a scale factor of 3 and followed by a reflection over the x-axis.

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The linear function that shows the proportional relationship between the distance and time is d = 100t

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

From the table given, we can find the slope of the function by using the formula

m = y₂ - y₁ / x₂ - x₁

m = 300 - 200 / 3 - 2

m = 100

To find the y - intercept,

y = mx + c

300 = 100(3) + c

300 = 300 + c

c = 300 - 300

c = 0

The equation that shows the relationship is

d = 100t

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Answer:

a - b > 0, Yes

Step-by-step explanation:

for the interval to exist,

a - b > b - a

2a - 2b > 0

a > b

if a > b then

b - a < 0 and a - b > 0 Hence upper limit of the interval will be positive and lower limit will be negative.

Interval will include 0.

Hopefully this answer helped you!!!

Answer:

y=(2/9)x-(4/3)

Step-by-step explanation:

12y=(8x-48)/3

multiply by 3 on both sides

36y=8x-48

divide by 36 on both sides

y=(8/36)x-(48/36)

simplify fractions

y=(2/9)x-(4/3)

The Relative Maximum will be (7, 50) and minimum is (12, 0).

We have the graph showing average low temperatures in international falls minnesota.

From the graph the maximum y coordinate is 50.

So, the Relative Maximum will be (7, 50).

and, the minimum y coordinate is 0.

So, the Relative minimum is (12, 0)

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