Solve the system
x+2y=-11
3y=x+1

Answer:

d

Step-by-step explanation:

Answer:

\(k(x) = (x + 1) (4x + 16)\\\)

Step-by-step explanation:

The equation of a parabola given roots \(x_1\) and \(x_2\) is
\(y = a( x - x_1)(x - x_2)\)

where a is a constant

The x-intercepts of a parabola will be the roots of the quadratic equation to the parabola since k(x) = 0 at these points

The x-intercepts are (-1, 0) and (-4, 0)

Therefore the equation of the parabola is of the form
\(k(x) = a ( x - (-1) ) ( x - (-4) )\)

\(= a( x+ 1) (x + 4)\)

To find a, find a point (x, y) through which the parabola passes and plug this value into the above equation to solve for a

We see that the parabola passes through (-5, 16) and (0, 16). The latter point is also the y-intercept of the parabola

This means k(x) = 16 at x = 0

Plugging (0, 16) into the equation gives

\(k(x) = a(x + 1) ( x + 4)\)

\(a(x + 1) ( x+ 4) = k(x)\)

\(a(0 + 1) (0 + 4) = 16\)

\(a \cdot 1 \cdot 4 = 16\)

\(4a = 16\)

\(a = 16/4 = 4\)

Equation of the parabola is

\(k(x) = 4 (x + 1) (x + 4)\)

which can be rewritten as

The probability of a person choosing a card from the second row is 50%.

The probability of an event occurring can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. In this case, there are four possible rows that the card could be chosen from, and each row has the same number of cards. Therefore, the probability of the card being chosen from any one row is 1/4, or 25%.

However, the question specifies that the person is choosing a card from the second row. Since there are two rows with 10 cards, the probability of the card being chosen from the second row is 2/4, or 50%.

It is important to note that this is just a theoretical probability. In reality, the probability of the card being chosen from any one row may be slightly different, depending on how the cards are arranged. For example, if the cards are arranged in a stack, the person may be more likely to choose a card from the top row. However, in the absence of any other information, the probability of the card being chosen from the second row is 50%.

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The probability that no digit appears more than twice is 0.648.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

We will choose each digit of 5-digit numbers at random from digits 0,1,2,..,9.

We have to compute the probability that no digit appears more than twice.

So, we have to form a five-digit number say "abcde".

Now, for 'a' we have 10 choices.

For 'b' we have again 10 choices because a digit can appear at most two.

For 'c' we have 9 choices because the digit in 'a' can not be chosen as a digit can appear at most two.

For 'd' we have again 9 choices by a similar argument.

Finally, for 'e' we have 8 choices because the digit chosen previously can not be repeated more than twice.

The total number of such 5-digit numbers is = 10*10*9*9*8 = 64800.

Now, a total number of 5-digit numbers = 10*10*10*10*10 = 100000.

Hence, the probability that no digit appears more than twice is given by,

= 64800/ 100000

= 0.648

Hence, the probability that no digit appears more than twice is 0.648.

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The statement suggests that there is likely to be an interaction between nitrogen (N) and phosphorus (P), which are two fertilizer ingredients used to achieve optimum levels in plant growth. However, without further context or specific details, it is uncertain to determine the nature and extent of this interaction.

In agriculture and plant nutrition, both nitrogen and phosphorus are essential elements for plant growth and development. They play crucial roles in various physiological processes and are often supplied through fertilizers to optimize crop yields. The interaction between nitrogen and phosphorus can have significant implications for plant growth and nutrient utilization.

The ratio of nitrogen to phosphorus in the soil can affect nutrient uptake, plant growth, and overall productivity. Different plant species and soil conditions may exhibit varying responses to the interaction between these two fertilizer ingredients. Factors such as soil type, pH, organic matter content, and crop-specific nutrient requirements further contribute to the complexity of this interaction. To fully understand and assess the interaction between nitrogen and phosphorus, detailed research and experimentation specific to the particular context are necessary.

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Answer:

Option A

Step-by-step explanation:

angle a and angle are equal since the vertical lines are parallel and horizontal lines are not and a, b, c are corresponding angles

An equation which has an extraneous solution is: C. √x = -5.

In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that isn't a direct solution (root) of the original equation.

This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that aren't solutions to the original equation as shown below:

Taking the fifth root of both sides of the equation, we have:

\(\sqrt[5]{x} = -2\\\\(\sqrt[5]{x})^5 = -2^5\\\\\)

x = -32.

Taking the cubic root of both sides of the equation, we have:

∛(x + 1) = 10

[∛(x + 1)]³ = 10³

x + 1 = 1000

x = 1000 - 1

x = 999.

Taking the fourth root of both sides of the equation, we have:

\(\sqrt[4]{x-5} =3\\\\(\sqrt[4]{x-5})^4 =3^4\)

x - 5 = 81

x = 81 + 5

x = 86.

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Step-by-step explanation:

The equation is y = 50x.

Answer:

170.25

Step-by-step explanation:

use pythagoras theorem to find the missing side, then find the an angle using the sine rule. at this point you will only have one angle left. using the law that sum of all angles of a triangle add up to 180⁰, you can do 180⁰- ( [the angle you found by the sine rule] + 90⁰) hope this wasn't too complicated :)

i did (b) as an example attatched (2 photos bc it couldn't fit it all)

The limit of lim (x − 9)/ (x² − 81)  using the l'Hospital's Rule is 1/18.

                  x→9

We can directly substitute the value 9 in the given limit expression.

We get,

lim (x − 9)/ (x² − 81) = (9 - 9)/(9^2 - 81)

= 0/0

The given limit is in indeterminate form. We can apply L'Hospital's rule here.

Differentiating both the numerator and the denominator with respect to x, we get,

lim (x − 9)/ (x² − 81) = lim (1)/(2x)

Now we can directly substitute the value of x in the above expression.

lim (x − 9)/ (x² − 81) = lim (1)/(2x) = 1/18

Therefore, the limit of the given expression is 1/18.

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Answer:

1. slope -9

y-int (0, 3)

2. slope 5

y-int (0, -7)

we don't have the tables

(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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Answer:

hot potato

Step-by-step explanation:

Answer:

1/72

Step-by-step explanation:

Probability of getting a 4 on white cube is:

P(W) · P(4) = 1/2 × 1/6 = 1/12

P(R) · P(>4) = 1/2 × 2/6 = 1/6

multiply both probabilities:  1/12 × 1/6 = 1/72

To find the third derivative y'''(4) of the function y = √x³, we need to differentiate the function three times with respect to x.

First, let's find the first derivative:

y' = d/dx (√x³)

Using the power rule and chain rule, we have:

y' = 1/2(x³)^(-1/2) * 3x²

  = 3x²/(2√x³)

  = (3x²√x)/(2x√x)

  = (3x^(2+1/2))/(2x^(1/2))

  = (3x^(5/2))/(2x^(1/2))

  = (3/2)x

Now, let's find the second derivative:

y'' = d/dx (y')

    = d/dx ((3/2)x)

    = 3/2

Finally, let's find the third derivative:

y''' = d/dx (y'')

     = d/dx (3/2)

     = 0

Therefore, y'''(4) = 0.

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Answer: 10 seconds will it take to publish the sports report if they print at the same speed.

Given that,

A printing company for newspapers is called Periodical Express. In barely 15 seconds, 450 copies of the Informer were printed! The sport report needs to be printed in 300 copies next.

We have to find how long will it take to publish the sports report if they print at the same speed.

We know that,

450 copies of the Informer were printed

450 copies times=15

1 copies time =15/450

For,

300 copies time =15/450×300

300 copies time = 10seconds

Therefore, 10 seconds will it take to publish the sports report if they print at the same speed.

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Step-by-step explanation:

Given data:

The given scale is 2 cm= 6 ft.

The given height of the tree is h= 7.8 cm.

The given scale can be written as,

The actual height of the tree is,

Thus, the actual height of the tree is 23.4 ft.

In this problem, we want to apply special right triangles.

We will take a close look at the 30-60-90 triangle:

When working with this special right triangle, we can apply the following ratio for the legs and hypotenuse:

As long as we know one of the three legs, we can find the missing legs as well.

We are given the following diagram:

It looks like we were given the hypotenuse. Using our ratio above, we see:

Let 10 be equal to the hyptonuse length from the ratio.

Solve for x by dividing by 2:

Since know a = x,

We can find b the same way:

Answer:

5x+17

Step-by-step explanation:

5 times a number, X, can be represented as 5x. If we want to add 5x and 17, we can say 5x+17.

The length of the other aircraft is 59.04ft.

To solve this problem, we simply need to find the certain percentage of the length of aircraft which is given as 144ft.

let's calculate 41% of 144

\(41\% of 144\)

This is given as

\(\frac{41}{100} = \frac{x}144}\\ 0.41 = \frac{x}{144} \\x = 0.41 * 144\\x = 59.04ft\)

The length of the plane built by the other manufacturer is 59.04 ft.

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Answer:

3%

Step-by-step explanation:

1 percent of 67,500 is 675

2 percent of 67,500 is 1,350

3 percent of 67,500 is 2,025

4 percent of 67,500 is 2,700

Answer:

3(14)+2(9) is the equation

$60 is the total cost

Tell me if im right :)

Answer:

T=60

Step-by-step explanation:

Interchange (switch) the value of x and y in "y = x + 5" as x = y + 5, subtract 5 from both sides and re-write in the form "y = f(x)" as y = x - 5.

In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).

The steps required to write the inverse of f(x) = x + 5 include the following:

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Answer:

\(14v+7=7(2v+1)\)

Step-by-step explanation:

break down the equation 14v +7

Answer:

7(2v+1)

Step-by-step explanation:

7 goes into 14 twice and into itself once so its factorised as 7(2v+1) you can do the multiplication to test it .

Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be \(900-880=20\) meters from the starting point.

The following eight symmetries represent all possible transformations that preserve the square's shape and size. Each symmetry corresponds to a unique way of manipulating the square while maintaining its original configuration.

The eight symmetries of the square with vertices at (-1,-1), (-1, 1), (1, 1), and (1, -1) are as follows:

1.Identity (E): No transformation, the square remains unchanged.

2.90-degree rotation clockwise (R90): The square is rotated 90 degrees in a clockwise direction.

3.180-degree rotation clockwise (R180): The square is rotated 180 degrees in a clockwise direction.

4.270-degree rotation clockwise (R270): The square is rotated 270 degrees in a clockwise direction.

5.Reflection about the x-axis (F1): The square is reflected across the x-axis.

6.Reflection about the y-axis (F2): The square is reflected across the y-axis.

7.Reflection about the line y = x (F3): The square is reflected across the line y = x.

8.Reflection about the line y = -x (F4): The square is reflected across the line y = -x.

The line segment AB, defined by two distinct points A and B, has only two distinct symmetries. The first symmetry is the identity transformation (E), where the line segment remains unchanged. The second symmetry is the reflection across the perpendicular bisector of AB. This reflection swaps the positions of points A and B, while preserving the length and direction of the line segment. Therefore, there are two distinct symmetries for the line segment AB: the identity transformation and the reflection across its perpendicular bisector.

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