como dividir ? ? . . .. . . .. . . .. . .. . . .. .

Answer:

[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]

[tex](n + \frac{5}{4})^2[/tex]

Step-by-step explanation:

Given

[tex]n^2 + \frac{5}{2}n[/tex]

Required

(a) Make a perfect square trinomial

(b) Write as binomial square

Solving (a)

Let the missing part of the expression be k;

This gives

[tex]n^2 + \frac{5}{2}n + k[/tex]

To solve for k, we need to square half the coefficient of n;

i.e. Since the coefficient of n is [tex]\frac{5}{2}[/tex], then

[tex]k = (\frac{1}{2} * \frac{5}{2})^2[/tex]

[tex]k = (\frac{5}{4})^2[/tex]

[tex]k = \frac{25}{16}[/tex]

Hence;

[tex]n^2 + \frac{5}{2}n + k[/tex] = [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]

Solving (b)

[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]

Expand [tex]\frac{5}{2}n[/tex]

[tex]n^2 + \frac{5}{4}n+ \frac{5}{4}n + \frac{25}{16}[/tex]

Factorize

[tex]n(n + \frac{5}{4})+ \frac{5}{4}(n + \frac{5}{4})[/tex]

[tex](n + \frac{5}{4})(n + \frac{5}{4})[/tex]

[tex](n + \frac{5}{4})^2[/tex]

Hence:

[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex] = [tex](n + \frac{5}{4})^2[/tex]

Answer:

500

Step-by-step explanation:

Answer:

it is 500

Step-by-step explanation:

it is 500 because if you take the 5 and multiply it by the 1 you get one then all you do after you do that is add the zeros at the end.

Answer:

Answer:

160°

Step-by-step explanation:

If you add or subtract a full 360° rotation (or multiple of 360°) you get the same rotation.

Add 360° to -200°:

-200 + 360 = 160

Answer:

The lower limit is  75.04

The upper  limit is  78.96

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]n = 25[/tex]

   The sample mean is  [tex]\= x = 77[/tex]

    The standard deviation is  [tex]\sigma = 5[/tex]

Given that the confidence level is 95%  then the level of significance is mathematically represented as

        [tex]\alpha = (100 - 95)\%[/tex]

         [tex]\alpha = 0.05[/tex]

The critical value for  [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is  

     [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>   [tex]E = 1.96* \frac{5 }{\sqrt{25} }[/tex]

=>    [tex]E = 1.96[/tex]

The 95% confidence interval is mathematically represented as

        [tex]\= x -E < \mu < \= x +E[/tex]

=>   [tex]77 - 1.96 < \mu < 77 + 1.96[/tex]

=>   [tex]75.04 < \mu < 78.96[/tex]

At the point of the least cost of fencing the cost function has a zero

derivative.

Reasons:

Shape of the pen = Rectangular

Area of the pen = 24 yd²

Cost of material on one side of the fence = $6 per yard

Cost of material on the remaining three sides = $3 per yard

Required:

The least cost of fencing the pen

Solution:

The least cost is a minimum value of the cost function

Let L represent the length of the fence and let W represent the width of the fence

We have;

The perimeter of the fence = 2·L + 2·W

The area of the pen, A = L × W = 24

One of the length, L, of the fence costs $6 per yard and the other length L,

of the opposite side costs $3 per yard.

The cost of fencing, C  3 × 2·W + 3 × L + 6 × L = 6·W + 9·L

C = 6·W + 9·L

[tex]\displaystyle W = \mathbf{\frac{24}{L}}[/tex]

Which gives;

[tex]\displaystyle C = 6 \cdot \frac{24}{L} + 9 \cdot L = \frac{144}{L} + 9 \cdot L = \mathbf{\frac{144 + 9 \cdot L^2}{L}}[/tex]

The shape of the above function is concave upwards.

At the minimum value, we have;

[tex]\displaystyle \frac{dC_{min}}{dL} = \frac{d}{dL} \left(\frac{144}{L} + 9 \cdot L\right) = 9 - \frac{144}{L^2} = 0[/tex]

Which gives;

[tex]\displaystyle \frac{144}{L^2} = 9[/tex]

[tex]\displaystyle \frac{144}{9} = L^2[/tex]

By symmetric property, we have;

[tex]\displaystyle L^2 = \frac{144}{9}[/tex]

[tex]\displaystyle L = \sqrt{ \frac{144}{9}} = \frac{12}{3} = 4[/tex]

The length of the fence that gives the least cost, L = 4 yards

[tex]\displaystyle At \ L = 4, \ W = \frac{24}{4} = 6[/tex]

The width of the fence at least cost, W = 6 yards

Cost, C = 6·W + 9·L

Least cost, [tex]C_{min}[/tex] = 6 × 6 + 9 × 4 = 72

The least cost of the fencing, [tex]C_{min}[/tex] = $72.00

Learn more about the minimum values of a function here:

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Answer:

3

Step-by-step explanation:

Answer:

Greater than 4

Answer:

The probability is 0.0643 to 4 decimal places

Step-by-step explanation:

To calculate this probability, we find the z-score

Mathematically;

z-score = (x-mean)/SD

where in the question;

x = 46.3

mean = 55.1

SD = 5.8

Plugging these values, we have;

z-score = (46.3-55.1)/5.8 = -8.8/5.8 = -1.52

The probability we want to calculate is;

P(z < -1.52)

We can get this answer by using the standard normal distribution table;

Thus from the table, we have;

P(z < -1.52) = 0.064255 which is 0.0643 to 4 decimal places

Answer:

  [tex]H= 0.15x+ H[/tex]

Step-by-step explanation:

This problem requires that we produce a model that describes the daily height of the beans stalk

let us describe some variables

the daily height is H

let the initial height be h= 5 cm

and the daily increment be 15%= 0.15

and also the number of days be x

We can use the equation of straight line to model the daily height of the beans stalk

i.e

[tex]y= mx+c[/tex]

hence  the formula for the height of the beanstalk is

[tex]H= 0.15x+ H[/tex]

Answer:

y = - 14/3 +7x/3

Step-by-step explanation:

The reason for my answer is because let us move the -3y so it is before the equal sign. Let us also move 7x to the other side but make it so 14 would be to the right side of the equal sign. Now, that would mean 7x would be after 14. Our equation is now -3y=14-7x. We need to divide both sides of the equation by -3. There, we just divided -3y by 3 which equals to y. 14 divided by -3 equals to -14/3. -7x divided by -3 would equal to +7x/3. Finally, we get the answer of y = - 14/3 +7x/3.

Answer:

Step-by-step explanation:

● 7x-3y = 14

This a 1st degree equation with two variables.

● 7x-3y = 14

Substract 7x from both sides

● 7x-7x -3y = 14-7x

● -3y = 14-7x

Mulitply both sides by -1

● (-1)×(-3y) = (-1)×(14-7x)

● 3y = -14+7x

● 3y = 7x+14

Divide both sides by 3

● 3y/3 = (7x+14)/3

● y = (7/3)x + 14/3

There are infinite solutions for this equation. Keep replacing x with value and the output will change everytime.

Answer:

4

Step-by-step explanation:

there are only for sandwiches.

Answer:

The answer is $690.78

Step-by-step explanation:

bhai ap apne ap kar lo ye question

Answer:

The solution to the given expression is 1/2562890625

Step-by-step explanation:

(3⁴ × 5⁴)⁻²

Simplify the terms inside the parentheses. 3⁴ × 5⁴ is the same as 15⁴ because even though the base numbers are different, the exponents are the same which makes it similar.

(15⁴)⁻²

Now, for this step, we are going to add the exponents because when multiplying, the exponential numbers add together. So 4 × -2 = -8.

15⁻⁸

Since we can not have a negative exponent, we are going to change this into a fraction. We do this by putting this term in a fraction where 1 is the numerator and the term is the denominator.

1 / 15⁻⁸

Now, we simplify the term on the bottom.

1 / 2562890625

So, this is the solution to the problem.

In a fraction, the fraction bar means divided by. So to find the decimal form equivalent of a fraction like 1/4 you need to solve the math problem 1 dived by 4.

1 ÷ 4= 0.25

Answer:

The height of the triangle is 6.4cm

Step-by-step explanation:

- If the triangle has a side that measures 12.5cm, it means that two of its sides are equal in length.

Which is equivalent to the description of an isosceles triangle.

To find the height, use the equation of the area.

Area = (Base * height) / 2

- We know the value of the area and its shorter side that could be the base.

40cm = (12.5 cm * h) / 2

- Clearing the height would give that:

80cm / 12.5cm = h

h = 6.4cm

The height of the triangle is 12.5cm

A triangle is a plane figure with edges that are all straight with three sides and three angles.

The formula for calculating the area of a triangle is;

[tex]\mathbf{Area = \dfrac{1}{2}\times Base \times Height}[/tex]

Given that:

The area = 40 cm²

Since the diagram for the triangle is not given;

∴

Using the formula form above:

[tex]\mathbf{40.0 cm^2 = \dfrac{1}{2}\times 12.5 cm \times Height}[/tex]

[tex]\mathbf{40.0 cm^2 \times 2 = 1\times 12.5 cm \times Height}[/tex]

[tex]\mathbf{80.0 cm^2 = 12.5 cm \times Height}[/tex]

[tex]\mathbf{Height = \dfrac{80.0 cm^2}{ 12.5 cm} }[/tex]

Height of the triangle = 6.4 cm

Therefore, we can conclude that the height of the triangle = 6.4 cm

Learn more about triangles here:

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Answer:

Step-by-step explanation:

A complex number in its rectangular form is expressed as x+iy where x is the real part of the complex number and y is the imaginary because it is attached to the imaginary number i.

Given the complex number 4-5i, comparing the complex number with x+iy

4 = x and iy = -5i

Hence x = 4 and y = -5.

Since x is the real part of the complex number x+iy, hence 4 will be the real part of the complex number 4-5i based on comparison.

Answer:

From the given information, the value of n is 1. By using that information, the measure of JL is 29.

Step-by-step explanation:

For this problem, we have to not only find the value of n but, we also have to find the value of JL. We are given information in this problem.

ΔABC ≅ ΔJKL

AC = 10n + 19

JL = 9n + 20

From this information, we can conclude that AC and JL are congruent meaning they are equal in measure. So, let's set up an equation where they set equal to each other.

10n + 19 = 9n + 20

Subtract 9n from 10n.

n + 19 = 20

Subtract 19 from 20.

n = 1

So, the value of n is 1. We can use this to find the value of JL.

JL = 9(1) + 20

JL = 9 + 20

JL = 29

Answer:

JL is equal to 29

Step-by-step explanation:so JL= 29 is the answer

Answer:

Lulu= £81

Ruby=£108

Emma=£ 72

Step-by-step explanation:

Let Lulu's money be x

Let Ruby's money be y

Let Emma's money be z

The total money they went shopping with is = £261

So

x+y+z= 261

Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

Money spent by each

Lulu= 2/3x

Ruby=1/2y

Emma= 3/4z

Each of them spent the same amount of money.

2/3x= 1/2y= 3/4z

2/3x= 1/2y

x(2*2)/3 = y

4/3(x) = y

2/3x=3/4z

x(2*4)/(3*3)= z

8/9x= z

x+y+z= 261

x+4/3x+8/9x= 261

9x +12x +8x= 2349

29x= 2349

X= 81

4/3(x) = y

4/3(81) = y

108= y

8/9x= z

8/9(81)= z

72= z

Answer:

the answer is b

Step-by-step explanation:

2nd graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses.

The answer is option B.

The test to verify if a function f is the inverse of another function g is given by using the composition of the functions such as this, f(g(x))= x. Therefore, to answer your question, f(g(x))=x is saying f is the inverse of g. f(g(x))=x is saying f is the inverse of g but g is not the inverse of f, g(f(x))≠x.

Learn more about inverses here: brainly.com/question/14796161

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Answer:

x < 9

Step-by-step explanation:

Hello!

We solve inequalities the same we would solve equations. What we do to one side we have to do to the other.

5x < 45

Divide both sides by 5

x < 9

The answer is x < 9

Hope this helps!

Answer:

x<9 I hope help you Mark as Brainliest

Answer:

60 miles

Step-by-step explanation:

all you do is 1/3 + 1/3 and get 2/3. then times that by 180. You get 120. divide that by 2 because half the time she gets a ride and you get 60.

Answer:

a) The profit function is [tex]P(x) = -x^{2}+60\cdot x -100[/tex], b) The marginal profit function is [tex]P'(x) = -2\cdot x + 60[/tex].

Step-by-step explanation:

a) Let be [tex]C(x) = 30\cdot x + 100[/tex] (cost function) and [tex]R(x) = -x^{2}+90\cdot x[/tex] (revenue function), the profit function is found by subtracting the cost function from the revenue function. That is:

[tex]P(x) = R(x)-C(x)[/tex]

[tex]P(x) = -x^{2}+90\cdot x -(30\cdot x + 100)[/tex]

[tex]P(x) = -x^{2}+90\cdot x -30\cdot x -100[/tex]

[tex]P(x) = -x^{2}+60\cdot x -100[/tex]

b) The marginal profit function is the first derivative of the profit function:

[tex]P'(x) = -2\cdot x + 60[/tex]

Answer: 77

Add the three given values to get that result above.

Answer:

The expression

Y(x)= 15(v)+1.5(x)

Step-by-step explanation:

The entry fee is $15 per vehicle for up to and including 5 people, with an additional $1.50 for each person over 5.

Let the entrance fee be Y

Let the number of vehicle be V

Let X be the number of people more than 5

The expression

Y(x)= 15(v)+1.5(x)

Answer:

v (E) = √(2E/m)

Step-by-step explanation:

From the question given:

E = ½mv²

E is the kinetic energy

m is the mass of object

v is the velocity.

To find a model v(E) for the velocity of the object, we simply make V the subject of the above equation.

This can be obtained as follow:

E = ½mv²

Cross multiply

mv² = 2E

Divide both side by m

v² = 2E/m

Take the square root of both side

v = √(2E/m)

Therefore, the model v(E) for the velocity of the object is given by:

v (E) = √(2E/m)

Answer:

0 ones

7 tenths

6 hundredths

I'm sorry if I misunderstood.

Good luck though! :)

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