use lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. let the sides of the rectangle be x and y and let f and g represent the area (a) and perimeter (p), respectively. find the following.

Answer: y=2x-5

Step-by-step explanation:

6x-3y=15

6x-6x-3y=-6x+15

-3y=-6x+15

-(3y=6x-15)

3y=6x-15

3y/3=(6x-15)/3

y=6x/3-15/3

y=2x-5

The allocation for product defined and product not defined are

PD(product defined)

PND

This is further explained below.

Generally, the rule for matrix multiplication

no. of columns for the first matrix should be equal to no. of rows in the second matrix" that is if

1st matrix has =m * n

2nd has =k *l

Therefore

m=l

L=2*2,  M=4*2,

The matrix is defined as the row and the column tally

M=4*2 and L=2*2

The matrix is not defined as a row and the column do not tally

In conclusion, Q=2*1, and P=2*2 equal so the product is defined.

P=2 *2,M=4 *2,  equal so product is defined.

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Answer:

3.6*10³

Step-by-step explanation:

Jack cannot add the powers of 10 because they are in addition. We can apply the exponent rule only when they are in multiplication.

[tex]\sf 6 *10^2 + 3*10^3= 6*100 + 3*1000\\[/tex]                          

                         = 600 + 3000

                         = 3600

                          [tex]\sf = 3.6 * 10^3[/tex]

An expression, in terms of n, for the nth term of this arithmetic sequence is aₙ = 23 - 4n.

An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ = a₁ + (n - 1)d

Where:

For the second term, we have:

a₂ = a₃ - d

a₂ = 11 - (-4)

a₂ = 11 + 4

a₂ = 15.

For the first term, we have:

a₁ = 4 + second term

a₁ = 4 + 15

a₁ = 19

Substituting the given parameters into the formula, we have;

aₙ = a₁ + (n - 1)d

aₙ = 19 + (n - 1)(-4)

aₙ = 19 - 4n + 4

aₙ = 23 - 4n

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Answer:

The slope is -1/3.

Step-by-step explanation:

When you count the rise/run, which is how much it goes up/down and left/right, you get -4/12. Simplify -4/12 and you'll get -1/3.

Answer:

6,12,24,48,96

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x+ 6[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 24x + 4y = 24[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 4y =24 - 24x [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ 24}{4} - \frac{24x}{4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x + 6[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -6 and y - intercept = +6

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The angle postulate that best defined angles CAB and CAD is; Supplementary Angles

We know that there are different angle postulates such as Corresponding angles, complementary angles, supplementary angles and others.

Now, in this case we want to find the angle theorem that best describes angles CAB and CAD. Now, from the given image, it is clear that both angles form a straight line and we know that the sum of angles on a straight line equals 180 degrees.

Since both angles sum up to 180 degrees and we know that these angles are defined as supplementary angles which are linear pairs.

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Answer: I am going to assume that 1/4 is 1 over 4 ( a fraction ) and that it is the same for 1/64

A) 0.00390625

B)     0.015625^4  <------( Here is the equation. when i put it in a calculator it was too long. here is the answer that gave me: 5.96046448 e-8 )

Answer: x^2 + y^2 - 4x + 18y = 76 = 0

The center of the circle given is (2, 9)

radius = r

The equation of a circle for a given point is

(x - h)^2 + (y - k)^2 = r^2

Where h = 2, and y = 9

(x - 2)^2 + (y - 9)^2 = 3^2

Expand the parentheses

(x - 2) (x - 2) + (y - 9) (y - 9) = 9

(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2

= x^2 - 4x + 4

(x - 2) (x - 2) = x^2 - 4x + 4

(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9

= y^2 - 18y + 81

(y - 9) (y - 9)= y^2 - 18y + 81

Therefore, the equation becomes

x^2 - 4x + 4 + y^2 - 18y + 81 = 9

Re-arrange the equation

x^2 + y^2 - 4x - 18y + 4 + 81 = 9

x^2 + y^2 - 4x - 18y = 9 - 81 - 4

x^2 + y^2 - 4x - 18y = -76

x^2 + y^2 - 4x - 18y + 76 = 0

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Answer:

The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0

Step-by-step explanation:

Answer:

54 + (7x + 1) + 90 = 180° (sum of angles in triangle=180)

7x = 35

x = 5

Answer:

x = 5

Step-by-step explanation:

This question deals with a right-angled triangle. The sum of the angles in a  triangle is equal to 180 degrees. A right angle is equal to 90 degrees which means that the other two angles must equal to 90 degrees as well.

Form the equation.

( 7x + 1 ) + 54 + 90 = 180;

Subtract 90 from both sides.

7x + 1 + 54 + 90 - 90 = 180 - 90;

7x + 1 + 54 = 90;

Simplify left-hand side.

7x + 55 = 90;

Subtract 55 from both sides.

7x + 55 - 55 = 90 - 55;

7x = 35;

Divide both sides by 7.

x = 35 / 7;

x = 5;

yes thank you very muchGiven: Measure of angle D E G equals 51 degrees. Measure of angle G E F equals 39 degrees. Prove: Triangle D E F is a right triangle. Art: A right angle triangle D E F. Angle D E F is a right angle. Point G is on segment D F, and segment E G is drawn.

The value of x is -0.004624

[tex]log_{3} (x)+log_{x} (3)=2.5[/tex]

[tex]log_{3} (x)+\frac{log_{3} (3)}{log_{3} (x)} =2.5[/tex]

Let z= [tex]log_{3} (x)[/tex]

[tex]z+\frac{1}{z} = 2.5[/tex]

[tex]3z^{2} + z-2.5z=0[/tex]

z= -0.166

[tex]log_{3} (x)=-0.166[/tex]

x = -0.004624

What is a log?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of a mistake or when the base is irrelevant, as, in big O notation, the logarithm of x to base b is written as loga (x), logb x, or even without the explicit base, log x.

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Step-by-step explanation:

5,15 can accord to be an sciencetistic teachers, the 15,11 which means you can appear to combine them together and be an 100 then you do the abcd and boom

Answer:

i will answer in 2050 my bad

i just need the points rq

Step-by-step explanation:

n/a

Answer:

I don't see any answer options, and the equation doesn't look correct.

I'll assume the equation is meant to be:

Step-by-step explanation:

(2x/5 - 9) = 9

2x/5  = 18

2x  = 90

x = 45

if the modified equation is correct.

Answer:

26 + 5x = y

Step-by-step explanation:

hope this helped

have a good day ^^

The solution to the given inequality expression is g <3

Inequality are expressions not separated by an equal sign. They are separated by a less than, greater than, less than or equal to and greater than or equal to.

Given the linear equation below:

g + 3 < 6

We are determine the unknown variable "g"

First, we need to subtract 3 from both sides to have;

g + 3 - 3 <  6-3

g < 6 - 3

g < 3

Hence the solution to the given inequality expression is g < 3

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Answer:

see explanation

Step-by-step explanation:

f(3) means what is the value of f(x) when x = 3

substitute x = 3 into f(x)

f(3) = 10(3) + 13 = 30 + 13 = 43

similarly for x = - 8

f(- 8) = 10(- 8) + 13 = - 80 + 13 = - 67

given f(x) = 10x + 13 and f(x) = 53 , equate the right sides

10x + 13 = 53 ( subtract 13 from both sides )

10x = 40 ( divide both sides by 10 )

x = 4

Answer: 35N

Step-by-step explanation:

Cross multiply and divide to find the missing value

Answer: 35N :)))))))))))))))))))))))))))))

Equation of the line is y = -(1/3)x+5

The figure shows a straight line of which two points and thereby the slope can be found out.

Equation of a line is in the slope-intercept form is,

y = mx +c,

where m is the slope of the line and c is the y-intercept of the line.

From the figure, two points on the line are, (0,5) and (3,4).

Then slope = (4-5)/(3-0)

                  = -1/3

Now y-intercept, c is the y-co-ordinate when x = 0.

From the figure, when x = 0, y = 5

So y-intercept, c = 5.

Thus the equation of the line is, y = -(1/3)x+5

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I can buy 75 latex balloons and 50 mylar balloons.

This is a problem from an algebraic equation. We can solve this problem by following a few steps.

We need 125 balloons. Let's assume we have to purchase x latex balloons.

So, mylar balloons are ( 125 - x ).

Our total budget is $32.50.

The cost of x latex balloons is ($.10 × x) = $.10x , as the latex balloons cost $.10 each.

The cost of ( 125- x)  mylar balloons is $[( 125- x) × 0.50] , as the mylar balloons cost $.50 each.

So the total cost is,

$[( 125- x) × 0.50] + $.10x  = 32.50

Now, we have to solve this equation, Let's simplify it.

62.50 - 0.50x + .10x = 32.50

Or, 62.50 - 0.40x = 32.50

Or, -0.40x =  32.50 - 62.50       [ deduce 62.50 from both side ]

Or, -0.40x =  -30                 [ we should devide both sides 0.40 ]

Or, x = 30/0.40 = 75

So, the number of latex balloons is 75. Therefore, the number of remaining mylar balloons is ( 125 - 75) = 50

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Answer:

i think is (a)

because i zay do

Step-by-step explanation:

anyways...... i want more pictures of math problems

Answer:

1b) in first image

1c) in second image

The equation of line is y = -9.

These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.

Given that,

(1, -9) = ( [tex]x_{1}, y_{1}[/tex])

(-3, -9) = [tex](x_{2},y_{2})[/tex]

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         = [tex]\frac{-9+9}{-3-1}[/tex]

Slope = 0

Then the equation of line

[tex]y-y_{1} = m(x-x_{1})[/tex]

y+9 = 0

y = -9

Hence, The equation of line is y = -9.

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Answer:

x = 7 degrees

Step-by-step explanation:

Angle CDB = 49 degrees (corresponding angles triangle ABD congruent to triangle CBD)

Angle CDB = 49 degrees = 7x

7x = 49 degrees

x = 7 degrees

Given:

The geometric sequence is

To find the common ratio,

Hence the common ratio, r is 14/35.

Answer:

Is y3 supposed to be y^3?  Is so, the answer is 1.  

Step-by-step explanation:

If the equation is correct as written, 3y = 1, then y = 1/3

y^3 = 1

This can also be written as y^2*y = 1

1.  If y = -1, then y^2y would be (1)*(-1) = -1

2. If y = 1, then (1)^3 * (1) = 1  This works.

3.  If y = ±1, then -1 is a possible answer and -1 does not work as per #1

4.  3^3 = 27

INFORMATION:

We have the next rhombus

And we must find the measure of

Knowing that DB = 10, BC = 13, and m∠WAD = 25°

STEP BY STEP EXPLANATION:

To find all measures, we need to use properties or the rhombus:

- DA: To find DA we need to know that all sides of the rhombus are equal. So, if BC measures 13, then DA measures 13 too.

- BW: To find BW we need to know that in a rhombus, diagonals bisect each other at right angles. That means, diagonals intersect in the middle. So, if DB = 10, then BW will be half of BD. BW = 10/2 = 5.

- WC: We can find it as one of the legs of the right triangle formed by BW, BC and WC. Where, BC is the hypotenuse.

So, WC = 12.

- Angle BAC: To find this angle, we need to use that the interior triangles formed in the interior of the rhombus are congruent. So, angle BAC is congruent with the angle DAC. Then, BAC = 25°.

ANSWER:

DA = 13

BW = 5

WC = 12

BAC = 25 degrees