A rectangular pen is built with one side against a barn it 2500 m of fencing are used for the other three sides of the pen what dimensions maximize the area of the pen?

Answer:

(-3, 1)    (Answer H)

Step-by-step explanation:

f(x) = x^2 + 6x +10 can be rewritten by "completing the square" as

f(x) = (x + 3)^2 + 1, and by comparing this to y = (x - h)^2 + k, we see that h is -3, k is 1, so the vertex, (h, k), is at (-3, 1)    (Answer H)

Answer:

x = 100°

Step-by-step explanation:

x = 100° because the two angles are corresponding.

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Answer:

n o

Step-by-step explanation:

Answer:

Add 5 to both sides.

Step-by-step explanation:

3.7 = x + (-5)

3.7 + 5 = x + ( -5) + 5

5 cancels on the right

8.7 = x

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3.7=x+(-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 3.7=x-5

Add 5 to both sides of an equation, we get

3.7+5=x-5+5

x=8.7

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

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Answer:

Solution : (- 9, - 3)

Step-by-step explanation:

Approach 1 : Imagine that this point (3, - 9) is rotated 90 degrees clockwise. We know that this point lies in the fourth quadrant, so if it is rotated 90 degrees, you can imagine the x - coordinate will be greater than the y - coordinate, if you take their absolute value(s). Remember that the new coordinates will also lie in the third quadrant. Based on these requirements we have the resulting point (- 9, - 3) or option c.

________________________________________

Approach 2 : There is another approach to this, a more exact approach.

Rotation of axis, θ : (x, y) --> (X, Y)

X = xcos(θ) + ysin(θ),

Y = - xsin(θ) + ycos(θ)

Here θ = 90 degrees. Substitute and solve for the exact coordinates.

X = 3cos(90) + - 9sin(90) = 3cos(90) - 9sin(90) = 3 * 0 - 9 * 1 = - 9,

Y = - 3sin(90) + - 9cos(90) = - 3sin(90) - 9cos(90) = - 3 * 1 - 9 * 0 = - 3

As you can see our solution is the same, (- 9, - 3), or option c.

The ordered pair (3,4) in relation to origin is plotted as:

3 spaces to the right and 4 spaces up

When two items are written inside parantheses and are separated by a comma, they create an ordered pair. For instance, the ordered pair (x, y) indicates an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables or constants, have distinct names depending on the context in which they are used. In an ordered pair, the element order is somewhat significant. It implies that (x, y) may not always be equivalent to (y, x).

In coordinate geometry, a point's location on the coordinate plane with respect to the origin is represented as an ordered pair. Two perpendicular intersecting lines, one of which is the x-axis and the other is the vertical line, together constitute a coordinate plane (y-axis).

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The classification of the compounds according to their functional class: A | Aldehyde

B | Alcohol

C | Ketone

D | Amine

Compound A contains a carbonyl group (C=O) bonded to two alkyl groups (R-). This is the general structure of an aldehyde. Aldehydes are characterized by their strong, sweet odor.

They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound B contains an oxygen atom (O) bonded to two alkyl groups (R-). This is the general structure of an alcohol. Alcohols are characterized by their ability to dissolve other polar compounds, such as water. They are also used in a variety of products, such as solvents, cleaners, and fuels.

Compound C contains a carbonyl group (C=O) bonded to a propyl group (CH3CH2CH2-) and an amino group (NH2). This is the general structure of a ketone.

Ketones are characterized by their strong, sweet odor. They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound D contains a nitrogen atom (N) bonded to three alkyl groups (R-). This is the general structure of an amine. Amines are characterized by their basic properties. They are also used in a variety of products, such as pharmaceuticals, plastics, and fertilizers.

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Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.

So, ∠P = ∠E and ∠Q = ∠F.

Hence, we can write: DP/DE = DQ/DF= PQ/EF.

The above expression is written as

DP/DE = DQ/DF=BC/EF.

It means that PQ = BC.

Hence, the triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ.

Thus, by using the AAA criterion for similarity of the triangle, we can say that

∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer:

9/8

Step-by-step explanation:

divide 3/4 by 2/3

use the KCF method

so your gonna get 3/4 divided 2/3 then change the division to multiplcation and then flip the 2/3 to 3/2

now multiply across: 3/4 × 3/2=9/8

Answer: The second answer.

Step-by-step explanation:

Answer:

The value of x is 7.

Step-by-step explanation:

First, you have to make the left side into 1 fraction by making the denormintor the same and make it into simplest form :

\( \frac{x}{3} + \frac{x}{6} \)

\( = \frac{x \times 2}{3 \times 2} + \frac{x}{6} \)

\( = \frac{2x}{6} + \frac{x}{6} \)

\( = \frac{2x + x}{6} \)

\( = \frac{3x}{6} \)

\( = \frac{x}{2} \)

Next you have to multiply both sides by 2 in order to make x the subject :

\( \frac{x}{2} = \frac{7}{2} \)

\( \frac{x}{2} \times 2 = \frac{7}{2} \times 2\)

\(x = 7\)

The formula for finding the standard deviation for a binomial distribution is σ2=npq. f.

What means binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution.

For each random variable X, the binomial distribution formula is given by;

P(x:n,p) = nCx px (q)n-x

Where,

n = the number of experiments

x = 0, 1, 2, 3, 4, …

p = Probability of Success in a single experiment

q = Probability of Failure in a single experiment = 1 – p

formula for finding standard deviation of a binomial distribution is npq. f.

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Answer:

-11y+19

Step-by-step explanation:

-2y+(-9y)+14+5=-11y+19

Answer:

-11y+19

Step-by-step explanation:

-2y-9y+14+5

-11y+14+5

-11y+19

Hope this helps!

The equivalent expressions to 5x + 30x - 15x are given as follows:

A) 5x(1 + 6 - 3).

B) 5(x + 6x - 3x).

C) (5 + 30 - 15)x.

Equivalent expressions are expressions that have the same result when they are simplified as much as possible.

The expression for this problem is given as follows:

5x + 30x - 15x

Combining the like terms, the result is given as follows:

35x - 15x = 20x.

Hence the equivalent expressions are given as follows:

A) 5x(1 + 6 - 3) = 5x + 30x - 15x = 20x.

B) 5(x + 6x - 3x) = 5x + 30x - 15x = 20x.

C) (5 + 30 - 15)x = 5x + 30x - 15x = 20x.

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Answer:

One solution

Step-by-step explanation:

The probability that a selected day of a leap year falls in April is 0.082

We know that the probability is the likelihood that an event is going to occur.

The formula for probability is:

Probability = number of favorable outcomes / total number of outcomes.

Normally in a year there are 365 days and in the month of February there are 28 days but during a leap year there are 366 days in the year and 29 days in the month of February.

We need to find the probability that a randomly selected day of a leap year (with 366 possible days) is in April.

Number of days in the month of April = 30

So, the probability that a selected day of a leap year is in April would be,

P = 30 / 366

P = 0.082

Therefore, the probability that a selected day of a leap year falls in April is 0.082

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The trigonometric or polar form of a complex number expresses the number in terms of its magnitude and argument. The complex number z = 1 in trigonometric form (polar form) is written as z = 1(cos(0) + i sin(0)), where theta = 0 radians.

The complex number z = 1 can be written in polar form as z = cos(0) + i sin(0), where cos(0) = 1 and sin(0) = 0. Therefore, the magnitude of z is 1, and the argument of z, denoted by theta, is 0 radians since it lies on the positive real axis.

Hence, the trigonometric form of z is z = 1(cos(0) + i sin(0)) = 1(cos(0) + i sin(0)), where 0 <= theta < 2pi. This representation is useful for performing operations on complex numbers, such as multiplication and division, since the operations can be carried out using the magnitude and argument of the numbers.

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Answer: the number of votes each candidate received

Step-by-step explanation:

The number of votes each candidates received is best displayed by histogram.

" Histogram is a bar representation of a statistical data which plots all the frequency of the given class interval."

According to the question,

Option A and C does  not show any class interval.

Option D is based on daily basis , so it will not represent histogram in a best way.

Option B represents candidates verses number of votes, it is the best data to represent histogram.

Hence, we conclude that Option B is correct.

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Answer:

1 7/12

Step-by-step explanation:

5/6 + 3/4

Put in common denominators

10/12 + 9/12 = 19/12

Simplify

19/12 = 1 7/12

Answer:

62/78*( 1 6/8)

= 31/39*( 1 6/8)

= 31/29*( 1 3/4 )

= 31/39* 7/4

Multiply the numerator together and the denominator together

= 217/156

Step-by-step explanation:

LIKE IT PLS AND 5 STARS

Answer:

i think 7

Step-by-step explanation:

you cant go diagonal and count it as one unit. however doing stairs up to the second point gets you 7 units

Approximately 38% of deaths among 16 to 19 year-olds are related to motor vehicles.

According to the Centers for Disease Control and Prevention (CDC), motor vehicle crashes are the leading cause of death for teenagers in the United States.

In 2019, a total of 2,375 teenagers aged 16-19 years died in motor vehicle crashes, and an additional 258,000 were treated in emergency departments for injuries sustained in motor vehicle crashes.

These deaths accounted for 62% of all deaths among teenagers aged 16-19 years.

Therefore, around 38% of fatalities among individuals aged 16 to 19 are connected to automobiles.

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The expanded form of 5x³y²z⁴ without exponents is 5x * x * x * y * y * z * z * z * z.

The expressions rewritten using a single exponent are:

a) a⁵b⁵

b) \(y^{2+12}\)

c) (x³)⁴

d)\(y^{12-1}\)

To write 5x³y²z⁴ in expanded form without exponents, we simply write out each variable the number of times indicated by its exponent. So, we have 5x * x * x * y * y * z * z * z * z.

Rewriting the expressions using a single exponent:

a) The expression a⁵b⁵ represents a to the power of 5 multiplied by b to the power of 5.

b) The expression y² * y¹² can be simplified by adding the exponents, giving us \(y^{2+12}\), which is y¹⁴.

c) The expression (x³)⁴ represents x³ raised to the power of 4, which simplifies to \(x^{3*4}\) or x¹².

d) The expression y¹² ÷ y can be written as \(y^{12-1}\) since division corresponds to subtracting the exponents.

Therefore, \(y^{12-1}\) simplifies to y¹¹.

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This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

Amount is a numerical value that refers to the total sum of money or other type of payment due. It is used to quantify the size of a transaction, the cost of goods or services, or any other type of financial transaction. Amounts can be expressed in a variety of different currencies, and they can be negative (owing) or positive (owed).

To calculate the amount of work required to pump all the water from the rectangular swimming pool into a drain at the top edge, we must first calculate the volume of the water in the pool. Volume is calculated by multiplying the length, width, and depth of the pool, which in this case is 20 ft x 20 ft x 8 ft = 3,200 cubic ft. Since the pool is filled to 1 ft below the top, the volume of water is 3,200 ft3 - 20 ft3 = 3,180 ft3.

Next, we must calculate the weight of the water, which is the volume multiplied by the weight density of water (62.4 lb/ft3). The weight of the water in the pool is 3,180 ft3 x 62.4 lb/ft3 = 197,952 lbs.

Finally, to calculate the amount of work required to pump the water from the pool into a drain at the top edge, we must multiply the weight of the water (197,952 lbs) by the height of the drain (8 ft). This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

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Step-by-step explanation:

-5x+2y= 4         <==== Multiply entire equation by -3 to get:

15x-6y = -12  

2x+3y= 6          <====  Multiply entire equation by 2 to get :

4x+6y = 12    Add the two underlined equations to eliminate 'y'

19x = 0     so x = 0

sub in x = 0 into any of the equations to find:  y = 2

(0,2)

Answer:

51380000 mg

Step-by-step explanation:

10 - 3 = 7

7.34 x 7 = 51.38

1 kg = 1000000 mg

51.38 x 1000000 = 51380000

When \(7.34 \times 10^{-3} kg\) is converted to milligrams the result is 7340 mg.

Given, that kilograms to be converted to milligrams.

Multiplication: It is the basic mathematical operation among subtraction, division and addition. Multiplication follows associative and distributive property.

Exponential multiplication:

a) \(10^{-3} = \frac{1}{1000}\)

b) \(10^3 = 1000\)

Conversion factors:

1 Kg = 1000 grams

1 Gram = 100 milligrams

1 kg = 1000000 mg

Apply unitary method to convert Kg to mg.

1 kg = 1000000 mg

Multiply both sides by  \(7.34 \times 10^{-3} kg\)

\(7.34 \times 10^{-3} kg\) × 1 = \(7.34 \times 10^{-3} kg\) × 1000000

Here the kilograms is converted to equivalent milligrams.

\(7.34 \times 10^{-3} kg\) = 7340 milligrams

Thus the total milligrams in \(7.34 \times 10^{-3} kg\) are 7340 .

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Answer: 7 minutes and 30 seconds

Step-by-step explanation:

Answer:

It will take 7.5 mins.

Step-by-step explanation:

2 gallons - 3 mins

1 gallon - 3/2 mins

5 gallons - 3/2 x 5 = 7.5/

Solved using unitary method

Answer:

I personally have no idea how to do this but quizlet might have the answer

Sorry hope this helps though

Step-by-step explanation: