which of the following is equivalent to 2 stretching below? (14-9i)+(2+3i)..​

A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).

In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;

f(x) = −x² + 2x - 15

f(x) = −2x + 2

0 = −2x + 2

2x = 2

x = 2/2

x = 1

For the maximum value of function 2, we have:

f(1) = −(1)² + 2(1) - 15

f(1) = -14

For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.

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Solution :

a). The researcher in the experiment recruited 12 adults wo are healthy to conduct the study. So the individuals are the "healthy adults".

The treatment is the "reading technology" and the response variable in the experiment is the time taken to get a deep sleep.

b). Here, in this research study every participant are randomly assigned to the treatment, i.e. the e-book or the print book at night. So we can say that a true experimental research design has been made to conduct this experiment.

c). It is very important to select the e-reader night or the print book at random order for the participant in order to reduce bias and also to remove any effect of the confounding variable.

The randomization of the participants means the random assignment of the treatments.

The answer to all parts is shown below.

a. To combine the two chemicals, we need to add them together. Therefore, the rational expression for C(z) is:

C(z) = C₁(z) + C₂(z)

C₁(z) = z / (z + 1)

C₂(z) = 2 / (z - 3)

Combining the two chemicals, we have:

C(z) = C₁(z) + C₂(z)

= z / (z + 1) + 2 / (z - 3)

b. To find the simplified equation of V(x), we substitute the expressions for C(z) and H(x) into the formula:

V(x) = C(x) + C₂(x) H(x)

= (z / (z + 1) + 2 / (z - 3)) (x³ - x) / x

Simplifying further, we have:

V(x) = (z(x³ - x) + 2x (z - 3)) / ((z + 1) x)

c. To find the volume when a specific number of units are produced, we substitute the value into the equation V(x) and simplify.

Let's calculate the volume for 50, 100, and 1000 units:

For z = 50:

V(x) = (50 (x³ - x) + 2x (50 - 3)) / ((50 + 1) x)

For z = 100:

V(x) = (100 (x³ - x) + 2x (100 - 3)) / ((100 + 1) x)

For z = 1000:

V(x) = (1000 (x³- x) + 2x (1000 - 3)) / ((1000 + 1) x)

d. To find the number of units needed to achieve a volume of 3000 c³, we set V(x) equal to 3000 and solve for x:

3000 = (z (x³ - x) + 2x (z - 3)) / ((z + 1) x)

Solving this equation for x will give us the number of units needed to produce a volume of 3000 c³.

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Answer: -6

Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.

\(3-9\)

\(3+(-9)\)

\(=\fbox{-6}\)

\(3+(-9)\) on a number line:

Answer:

a= 14

b= 111

Step-by-step explanation:

just took it

The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.

Area = length × width

Area = 11.2 cm × 5.1 cm

Calculating the product, we get:

Area = 57.12 cm²

Therefore, the area of the rectangle is 57.12 cm².

The correct answer is: 57.12 cm².

It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.

So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

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About 0.46

0.46(6+26)=>15

Answer: 3/-4

The slope is measured in terms of rise over run. Rise is how many units you go up or down from the point (0, 0). Run is how many units you go left to right from the point where rise left off.  For this question, we go up 3 and to the left 4. SO that's a 3 on top and a -4 on the bottom.

The table shows increases (+) and decreases (-) in the lake level for the given period. By doing a cummulative addition, it would be easy to tell what the level was eventually.

We shall take the initial level of water to be x feet. The cummulative addition is now shown below;

Initial level + changes in subsequent levels

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer:

20gallons

Step-by-step explanation:

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The factors in the expression 7z⁴ - 5 + 10(y³ + 2) are 10 and y³ + 2

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

7z⁴-5+10(y³+2)

Express properly

So, we have the following representation

7z⁴ - 5 + 10(y³ + 2)

Consider an expression given as

a + b + cd

We have

Terms = a, b and cd

Factors = c and d

Using the above as a guide, we have the following:

The factors in the expression are 10 and y³ + 2

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Complete question

Which of these is a factor in this expression- 7z^4-5+10(y^3+2). Choices- A- 7z^4-5, B- 10(y^3+2) C = -5+10(y^3+2) D= (y^3+2)

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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a. The marginal profit function Py is Py = -30x + 47y - 915 and

b. Change in profit if price increase by 1 cent is 831 cents.

To find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.

Given:

P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)

a. Marginal profit function Px:

To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:

Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)

Simplifying further:

Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y

Combining like terms:

Px = 355 - 3x - 2y

b. Marginal profit function Py:

Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:

Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)

Simplifying further:

Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225

Combining like terms:

Py = -30x + 47y - 915

This is the profit function Py.

b. Estimating the daily change in profit:

To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.

Given initial prices:

First brand price (x) = 70 cents

Second brand price (y) = 73 cents

To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:

Px(70, 73) = 355 - 3(70) - 2(73)

          = 355 - 210 - 146

          = -1

Py(70, 73) = -30(70) + 47(73) - 915

          = -2100 + 3431 - 915

          = 416

The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:

Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2

               ≈ -1 * 1 + 416 * 2

               ≈ -1 + 832

               ≈ 831 cents

Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.

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Using the rules of indices to evaluate the expressions given, that with a value of 1 is (3² * 3⁵)/3¹⁰

1.)

\(7^{-6} \times 7^{5} = 7^{-6+5} = 7^{-1} = \frac{1}{7}\)

2.)

10³/10² = 10¹ = 10

3.)

(5⁶)²/5⁸ = 5¹²/5⁸ = 5⁴ = 625

4.)

(3² * 3⁵)/3¹⁰ = 3¹⁰/3¹⁰ = 3⁰ = 1

Therefore, the expression which has a value of 1 is the option D

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============================================================

Explanation:

The order of a matrix is a way of describing its size. Specifically, the order is represented in the form \(m \times n\), where,

The rows are laid out horizontally, and the columns are vertical.

In this case, we have 5 rows and 3 columns. Therefore, the answer is 5 x 3. The order is important because a 5 x 3 matrix is different from a 3 x 5 matrix.

The batch 3,5,7,9,11 represents items in set A which are the sums that are odd. For instance, rolling a 2 and a 3 leads to 2+3 = 5 which is an odd number sum.

The batch 4,8,12 represents the sums that are divisible by 4, ie they are multiples of 4. For instance: 2+6 = 8 is a multiple of 4.

The notation A U B means "A union B". Set union has us combine the two sets together to form one single set as indicated above. We toss out any duplicate entries. In this case, there are no duplicates because sets A and B have nothing in common. This means sets A and B are disjoint or mutually exclusive. If an item is in set A, then it cannot be in set B, and vice versa.

Optionally you can sort the items from smallest to largest getting A U B = {3,4,5,7,8,9,11,12}, but I chose to list 3,5,7,9,11 first to show that those items all belonged originally to set A, and kept 4,8,12 separate as well.

The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).

Given the expression in the question;

(x² + 7x) / (9 - x²)

To simplify, first factor out x form x² + 7x

(x × x + 7 × x) / (9 - x²)

Factor out x

x (x + 7) / (9 - x²)

Next, simplify the denominator

x (x + 7) / (9 - x²)

Rewrite 9 as 3²

x (x + 7) / (3² - x²)

Now, since both terms are perfect squares

a² - b² = (a + b)(a - b)

Hence,

x(x + 7) / ( 3 + x )( 3 - x )

Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).

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Answer:

A

Step-by-step explanation:

11.

a.

The y-intercept is given by:

The y-intercept is:

The y-intercept represents the initial amount of money in the inactive account

b.

The decay rate is 0.02 or 2% it means that each year the amount of money in the account is decreased by 2%

Answer:

it is 74389

Step-by-step explanation:

you do 74 + 094904

Answer:

A packet of nuts costs $2.70

Step-by-step explanation:

Let C represent the cost of a bar of chocolate and P represent the cost of a packet of nuts

4 bars of chocolate will cost $4C

1 packet of nuts costs $P

Total price Sandra paid is $11.50

This can be represented using

4C + P = 11.50    (1)

A bar of chocolate costs $0.50 less than a packet of nuts. So

P - C =0.50  

-C + P = 0.50   (2)

Multiply eq (2) by 4 to get

-4C + 4P = 4 x 0.50

-4C + 4P = 2   (3)

Add equations (1) and (3) to eliminate the 4C term

4C + P - 4C + 4P = 11.50 + 2

P+4P = 13.50

5P = 13.50

Dividing by 5 on both sides

5P/5 = 13.50/5

P = 2.70

So a packet of nuts costs $2.70  (Answer)

To verify this is correct,

Use equation (2) to get

-C + P = 0.50

-C + 2.70 = 0.50

Add C to both sides

-C + 2.70 + C = 0.50 + C

2.70 = 0.50 + C

Subtract 0.50 from both sides

2.70-0.50 = 0.50 + C - 0.50

2.20 = C which is C= 2.20

Plug this value into equation (1)

4(2.20) + 2.70 = 8.80 + 2.70 = 11.50

So verified that answers are correct

Write the equation of a line in point slope form that goes through the points (7,-5) and (3,8)

step 1

Find the slope

m=(8+5)/(3-7)

m=13/-4

m=-13/4

step 2

write the equation in point slope form

so

y-y1=m(x-x1)

we take the point (7,-5)

substitute

If you take the point (3,8)

we have

The length of CD is approximately 27.931 meters.

To find the length of CD, we can use the concept of similar triangles and trigonometric ratios.

Let's start by drawing a diagram to visualize the situation:

      A----------B

     /           /

    /           /

   /           /

  D----------C

  |

  |

  |

  F

We are given that road AB slopes at 10.2 degrees to the horizon and road BC slopes at 6.3 degrees to the horizon. From the diagram, we can see that angle DAF is the same as the slope angle of road AB (10.2 degrees), and angle DCF is the same as the slope angle of road BC (6.3 degrees).

Now, we can set up the following trigonometric equations using the given information:

tan(10.2 degrees) = CD / AD (equation 1)

tan(6.3 degrees) = CD / BF (equation 2)

Since AD and BF are perpendicular, we can consider them as vertical heights. Let's calculate the lengths of AD and BF.

For road AB, we can use the definition of tangent:

tan(10.2 degrees) = height AB / length AB

Solving for the height AB, we have:

height AB = tan(10.2 degrees) * length AB

height AB = tan(10.2 degrees) * 800m

height AB ≈ 147.294m

Similarly, for road BC:

height BC = tan(6.3 degrees) * length BC

height BC = tan(6.3 degrees) * 300m

height BC ≈ 33.706m

Now, we can substitute these values into equations 1 and 2:

tan(10.2 degrees) = CD / 147.294m (equation 1)

tan(6.3 degrees) = CD / 33.706m (equation 2)

Solving equation 1 for CD:

CD = tan(10.2 degrees) * 147.294m

CD ≈ 27.931m

Therefore, the length of CD is approximately 27.931 meters.

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$225 was earned from the craft sales

and $40 was earned from the play.

Given, During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions.

Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.

Let the amount earned by play be x,

Now, Games earned = 0.15×500 = $75

Also, crafts earned 3×75 = $225

Now, as play earned x, then food earned 4x.

According to question,

x + 75 + 225 + 4x = 500

5x + 300 = 500

5x = 200

x = 40

So, the amount earned by Play be, $40

and the amount earned by Food be $160.

Hence, $225 was earned from the craft sales

and $40 was earned from the play.

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Answer:

-12

Step-by-step explanation:

So to start we need to know what makes a line parallel. In an equation we know that for lines to be parallel they must have the same slope(m).

Then, we  need to know the slope-intercept form of an equation. The slope intercept form is \(y=mx+b\) where \(m\) is the slope of the line and \(b\) is the y-intercept. In this problem where can see the second equation is already in this form.

Now that we know we need to find the slope, and we know that the second equation is in slope-intercept form we're going to convert the fist equation into the correct form.

To do this, we know we need to make sure \(y\) is the only thing on the left side of the equal sign. Currently, on the left side of the equal sign we have \(-\frac{1}{2} y\) so we have to divide both sides by \(-\frac{1}{2}\) to get \(y=-12x -20\)

Now that we have it converted to slope-intercept form, we are going to look for what represents the slope or \(m\) in the equation. In this case the slope would be -12, so any line with a slope of -12 will be parallel.