consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area?

Answer:

c = ab - df

Step-by-step explanation:

ab - c = df

》ab = c + df

c + df = ab

c = ab - df

Answer:  c = -fd + ab

This is the same as saying  c = ab - fd

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

Work Shown:

\(\frac{ab-c}{d} = f\\\\\\ab-c = fd\\\\\\-c = fd-ab\\\\\\c = -fd+ab\\\\\\\)

Explanation for each step:

Answer:

15%

Step-by-step explanation:

see the picture for explanation

Answer:

28%.

Step-by-step explanation:

That would be 100 * 7/25

= (100/25) * 7

= 4*7

= 28.

Answer

4 = ax - 14

18 = ax

x = 18/a or 4

Step-by-step explanation:

Answer:

\(4(a + 2) - 2(a - 8) = 24 \\ 4a + 8 - 2a + 16 = 24 \\ 2a + 24 = 24 \\ 2a = 24 - 24 \\ a = \frac{0}{2} \\ \\ a = 0\)

I hope I helped you^_^

The difference quotient of the given function is 16a + 8h + 8.

The given function is f(x) = 8x² + 8x + 1. To calculate and simplify the difference quotient, we'll use the following formula:

f(a + h) - f(a) / hLet's first calculate f(a + h) and f(a).

f(a + h) = 8(a + h)² + 8(a + h) + 1

= 8(a² + 2ah + h²) + 8a + 8h + 1

= 8a² + 16ah + 8h² + 8a + 8h + 1f(a)

= 8a² + 8a + 1

Now, let's substitute these values in the formula:

f(a + h) - f(a) / h

= [8a² + 16ah + 8h² + 8a + 8h + 1 - (8a² + 8a + 1)] / h

= [8a² + 16ah + 8h² + 8a + 8h + 1 - 8a² - 8a - 1] / h

= (16ah + 8h² + 8h) / h

= 16a + 8h + 8

So, the difference quotient of the given function is 16a + 8h + 8.

In conclusion, the difference quotient of the given function is 16a + 8h + 8.

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Answer:

I’m pretty sure it’s 23

Step-by-step explanation:

Answer:

I THINK it's 15

Step-by-step explanation:

Answer:

3%

Step-by-step explanation:

It says 21 out of 700 are defective

What we're trying to find: "21 is what % of 700"

We can divide 21/700 to get that answer

21/700 = 0.03 which is 3%

We can set a ratio also

21/700 = x/100

If we cross multiply and divide we end up with

700x = 2100

Divide both by 700 and you get 3... 3%

The function that has a range limited to only negative numbers is Square Root.

The function of this kind is known to be a kind of radical function that is said to have even index e.g. a square root.  and thus, this radicand  is one that can have a negative value for some or for the  values of x.

Note therefore, that The function that has a range limited to only negative numbers is Square Root and thus it is correct.

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Answer:

A or the first Graph

Step-by-step explanation:

My attachment proves this answer is true

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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Answer: The third choice is the answer.

Step-by-step explanation:

If the original function is x^2, then to translate it 4 units to the right you need (x - 4)^2, and if you want to translate it 9 units up you simply add +9 outside the parenthesis.

The correct option regarding the vertex of the quadratic equation is given as follows:

The maximum profit of $62.80 thousand occurs when the sales price of the tool is $21.75.

The vertex-form representation of a quadratic equation of vertex (h,k) is given as follows:

f(x) = a(x - h)² + k.

The coefficient a is the leading coefficient, and it's meaning is given as follows:

In the context of this problem, the equation is given as follows:

P(x)= −5.1(x−21.75)² + 62.80

The parameters of the vertex are as follows:

h = 21.75, k = 62.80.

The leading coefficient is negative, hence the vertex is a maximum point, and the correct option is given as follows:

The maximum profit of $62.80 thousand occurs when the sales price of the tool is $21.75.

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Answer: Sx1.25

Step-by-step explanation:

expressions dont have = sign so, pizzas times the money will determine how much money she makes per pizza sold.

Answer:

s times 1.25

Step-by-step explanation:

hope u pass have a great day

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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The normal strain experienced by each wire is 0.00578 mm.

L'AC=√300²+2²+2(300) (2) cos50°=301.734 mm

AC=AB

=(L'AC - LAC) /LAC =(301.734 - 300) /300 = 0.00578mm

Strain is the relative change in size or shape of an object that is experiencing stress. Strain can be defined as the ratio between the increase in the length of the object to the length of the initial object. In addition, strain is a measure of how far the object changes shape.

Mathematically it is written as:

Strain = ΔL/L

where:

ΔL = change in length (m)

L = initial length (m)

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The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.

The time it takes Lyle to drive to his friend's house is given by t = d/v where

Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that

Substituting the values of the variables into t, we have

t = d/v

= 720 km/80 km/h

= 9 h

So, it takes Lyle 9 hours to drive.

Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min

= 1 h + 30 min

= 1 h + 30 min/60 min × 1h

= 1 h + 0.5 h

= 1.5 h

So, the total time Lyle takes to reach his friend's house is T = t + t'

= 9 h + 1.5 h

= 10.5 h

Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.

So, Lyle must leave no later than 8:30 a.m

So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m

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∠B ≅ ∠D reason is they are interior congruent angles in triangle.

What is interior congruent angles?

When two triangles' matching sides and interior angles are of the same length, two triangles are said to be congruent. To convey congruence, we utilise the symbol. In a triangle with corresponding sides and angles, the side on one triangle matches the side on the other triangle in the same position.

In the given figure,

Δ EDC ≅ Δ BEC and Δ AED ≅ Δ AEB

Also the sides AD ≅ AB

It means that their corresponding interior angles are equal in measure.

That is ∠D and ∠B are of same measure.

Hence, ∠D ≅ ∠B and the reason is they are interior congruent angles in triangle.

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Answer:

880

Step-by-step explanation:

Answer:

880

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is a representation of the functional relation with dependent and independent variables, normally, x- independent and f(x) - dependent variable.

We can write the given function as:

The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)

The following procedures can be used by us while factoring polynomials:

Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.

Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.

Eliminate any factors that are frequent.

In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).

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Answer: the answer is SSS I hope this is what u asked for let me now if it wasn't Have a great night :)

Step-by-step explanation:

Answer:

37.68cm

Step-by-step explanation:

C=2πr=2·π·6

T(5,6) is not one of the options provided .

Let T : R2 → R2 be a linear transformation such that T(1,2) = (2, 3) and T(0, 1) = (1, 4). Then T(5, 6) is (6,-1).Linear TransformationThe term "linear transformation" refers to a transformation in which the output of the transformation is a linear combination of the input variables. The vector spaces V and W are involved in this transformation.

If T : V → W is a transformation from V to W,

we say that T is a linear transformation if for all u, v in V and all scalars c, the following hold for T (u) and T (v).

The vector (5, 6) can be represented as a linear combination of (1, 2) and (0, 1) as follows: (5,6) = 3(1,2) - (1,2).Then,T(5,6) = T(3(1,2) - (1,2))= 3T(1,2) - T(1,2)= 3(2,3) - (1,4)= (6,9) - (1,4)= (5,5)Therefore, T(5,6) is not one of the options provided, hence the correct option is (none of the above).

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Answer:

Choice 1
It is a one to one function.

Appears to be a cubic function

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

No it is 10,000

Step-by-step explanation:

100*100 is like adding 2 zeros to 100. so 1 zero would make it 1000, and 2 zeros would make it 10,000

Using the Poisson distribution, in a 1-minute interval, the probability is approximately 0.0165, and in a 3-minute interval, the probability is approximately 0.0542.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. It is characterized by a single parameter, λ (lambda), which represents the average rate of events occurring per unit of time or space. In this case, the arrival rate is given as 11.35 inquiries per minute.

a) In a 1-minute interval, we want to find the probability of exactly 15 inquiries arriving. The probability mass function of the Poisson distribution is given by P(X=k) = (e^(-λ) * λ^k) / k!, where X is the random variable representing the number of inquiries arriving. Plugging in the values, we have λ = 11.35 and k = 15. Calculating the probability, P(X=15) = \(\frac{e^{-11.35}*11.35^{15} }{15!}\). This yields approximately 0.0165.

b) In a 3-minute interval, the average number of inquiries would be 3 times the average rate, λ = 11.35 * 3 = 34.05. Using the same formula as before, we calculate P(X=15) =\(\frac{e^{-34.05}*34.05^{1}}{15!}\), which gives us approximately 0.0542.

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The equation of a straight line passing through the given point and slope is y - y1 = m(x - x1).

What is the simple definition of slope?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Let the given point be (x1,y1).

slope be m.

we know that,

Line equation passing through point is:

y - y1 = m(x - x1)

where m = slope and (x1,y1) = given point.

Therefore The equation of a straight line passing through the given point and slope is  y - y1 = m(x - x1).

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Answer: if you want to know what x is then x = -10

Step-by-step explanation:

−2(x+12)=−x−14

Use the distributive property to multiply −2 by x+12.

−2x−24=−x−14

Add x to both sides.

−2x−24+x=−14

Combine −2x and x to get −x.

−x−24=−14

Add 24 to both sides.

−x=−14+24

Add −14 and 24 to get 10.

−x=10

Multiply both sides by −1.

x=−10

here are the steps i'd take. if anything is unclear, let me know and i can explain!

-2(x+12)=-x-14

let's open the parentheses on the left side

-2x-24=-x-14

and let's move variables to one side and numbers to the other.

-x=10

let's multiply each side by -1 to get positive x

x=-10

hope i helped! good luck.