Maximize: z = 3x + y
subject to: x-y≤9 3x + 5y ≤45 x≥0, y≥0​

The resulting equation is the x-coordinate of the point of local extrema of a quadratic function.

To find the local extrema of a polynomial function f(x), we apply the equation f'(x) = 0. We are given the basic form of a quadratic equation. The equation is given below.

f(x) = ax² + bx + c

We need to find the differentiation of the above equation.

f'(x) = 2ax + b

Now, we will equate the obtained equation to zero and solve for the value of the variable "x".

f'(x) = 0

2ax + b = 0

2ax = -b

x = -b/2a

This resulting equation is familiar from algebra/pre-calculus. This is the x-coordinate of the point of local extrema of a quadratic function.

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Answer:

1. 5√7

2. (√15)/6

Step-by-step explanation:

1. √175

= √(25) * √(7)

= 5√7

2. √(5/12)

= (√5)/(√12)

= (√5)/(√(4) * √(3))

= (√5)/(2√3)

Radicals can't be in the denominator:

(√5)/(2√3)

(√5 * 2√3)/(2√3 * 2√3)

(2√15)/12

(√15)/6

Answer:

-1.25

Step-by-step explanation:

m=

[tex]y2 - y1 \div x2 - x1[/tex]

3- (-2)÷ -1-3

5/-4

m=-1.25

A linear function will have the form f(x) = mx + b.

f(0)=7 means the point (0,7) is on this line.

f(3)=1 means the point (3,1) is on the line as well.

Using those two points, we can find the slope:

   m = (1-7)/(3-0) = -6/3 = -2

Since we were given f(0)=7, we also know the y-intercept.

So our function is f(x) = -2x+7

Answer:

  30 m

Step-by-step explanation:

Given a trapezium with area 756 m², height 28 m, and one base of length 24 m, you want to know the length of the other base.

The formula for the area of a trapezium is ...

  A = 1/2(b1 +b2)h

Using the given values, we have ...

  756 = 1/2(24 +b2)(28)

  54 = 24 +b2 . . . . . . . . . . . divide by 14

  30 = b2 . . . . . . . . . . . . subtract 24

The measure of the other parallel side is 30 m.

Answer:

acute angle - UVW

obtuse angle - VWX

right angle - UYX

Answer:

2   6    12   20,000

6   18   36   60,000

Step-by-step explanation:

The bottom number is 3 times the top number.

The standard form of the quadratic function y=ax² + bx + c = a (x - h)² + k

By definition, quadratic function is a function in the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.

ax² + bx + c = a (x² - 2xh + h²) + kax² + bx + c

= ax² - 2ah x + (ah² + k)

Comparing the coefficients of x on both sides,b = -2ah ⇒ h = -b/2a .............................................(i)

Comparing the constants on both sides,c = ah² + kc = a (-b/2a)² + k (From (1))

c = b²/(4a) + kk = c - (b²/4a)k = (4ac - b²) / (4a)

Therefore, we can use the formulas h = -b/2a and k = (4ac - b²) / (4a) to convert the standard form to its vertex form.

the vertex form of the parabola is  y = a (x - h)² + k

The standard form of the parabola is y = ax² + bx + c

The standard form of the quadratic function y=ax²+bx+c is x=-b± [tex]\frac{\sqrt{b^{2}- } 4ac}{2a}[/tex]

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By evaluating f(x) in x = 0 we will see that the value is 1, then we will get:

f²⁰²³(0) = 1²⁰²³ = 1

Remember that 1 is the identity of the multiplication, this means that any number times 1, is equal to the same number.

Then, for any real value n, we know that:

1ⁿ = 1

Now we have the function:

f(x) = 1/(1 + x²)

Evaluating in x = 0, we get:

f(0) = 1/(1 + 0²) = 1

Now we can apply the exponent n = 2023 we will get:

f²⁰²³(0) = 1²⁰²³ = 1

The answer is 1.

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The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

​f(x) = 1 / 2+3x and point P = (2 , 1/8)

f(x+h) = 1/(2 + 3a + 3h)

f(a) = 1/(2 + 3a)

m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h

After simplifying:

m(tan) = -3/[(2+3a)(2+3a+3h)]

h = 0

m(tan) = -3/(2+3a)²

The equation of the line:

y - 1/8 = [-3/(2+3a)²](x - 2)

Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).

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Using the two points on the graph, Sandra can prove that her speed was constant using: Slope (m) = (18 - 6) / (3 - 1).

The slope of a graph is the ratio of the vertical distance along the line to the horizontal distance across the line, which is given as, m = change in y / change in x.

For a proportional graph, the slope is always constant, for whichever points we choose to use on the line.

Given two points on the line that Sandra chose, (3, 18) and (1, 6), therefore:

Slope (m) = change in y / change in x

Slope (m) = (18 - 6) / (3 - 1)

Slope (m) = 12/2

Slope (m) = 6

Therefore, to show her speed, which is the slope of the line, is constant, she can use the equation below:

Slope (m) = (18 - 6) / (3 - 1).

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Answer:

i got 48000

Step-by-step explanation:

20x40x60

when solving volume you multiply the length times width times height.

The difference of the given algebraic expressions is -2x²+12x+13.

The given algebraic expressions are -2x²+5x+10 and -7x-3.

To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.

The subtraction of given expressions is as follows

-2x²+5x+10-(-7x-3)

= -2x²+5x+10+7x+3

= -2x²+12x+13

Hence, the difference of the given algebraic expressions is -2x²+12x+13.

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The linear function that models the puppy's growth is written as: y = 3x + 3.

The values we need to find before we can write he linear function that models a situation, are:

The linear function would be expressed as y = mx + b, which is in the slope-intercept form.

The table of the puppy's growth that Shayla is tracking is shown below. Using two points on the table, say, (0, 3) and (1, 6):

Slope (m) = change in y / change in x = (6 - 3)/(1 - 0)

Slope (m) = 3/1 = 3

Substitute m = 3 and (0, 3) into y = mx + b to find b:

3 = 3(0) + b

3 = 0 + b

3 = b

b = 3

To write the linear function, substitute m = 3 and b = 3 into the equation, y = mx + b:

y = 3x + 3

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Answer: A

Step-by-step explanation: FLVS question the answer is A

The volume of the largest box that can be made from the rectangular cardboard obtained by using the value of the derivative of the function for the volume at the extremum point is 18 cubic feet

An extremum of a function is the point where the value of the function is a maximum or a minimum.

The side length of the cut out squares = x

The width of the rectangular cardboard = 5 feet

The length of the rectangular cardboard = 8 feet  

The length of the side of the cut square = 8 - 2·x

Width of the side of the cut square = 5 - 2·x

Height of the cut square = x

Volume of the cut square, V = (8 - 2·x) × (5 - 2·x) × x = 4·x³ - 26·x² + 40·x

When the volume of the box is largest, we have;[tex]V' = \dfrac{d}{dx} \left(4\cdot x^3 - 26\cdot x^2 + 40\cdot x\right) = 12\cdot x^2 - 52\cdot x + 40=0[/tex]

12·x² - 52·x + 40 = 0

3·x² - 13·x + 10 = 0

Which gives;

(3·x - 10)·(x - 1) = 0

The dimensions of the cut square that gives the maximum volume are therefore;

x = 1 or x = 10/3

When x = 10/3, we have;

V = (8 - 2×(10/3)) × (5 - 2×(10/3)) × (10/3) ≈ -200/27 < 0

When x = 1, we have;

V = (8 - 2×1) × (5 - 2×1) × 1 = 18

The value of x that gives the maximum volume is therefore, x = 1

The dimensions of the box that give the maximum volume are therefore;

Height = x = 1

Length = 8 - 2×1 = 6

Width = 5 - 2 × 1 = 3

The dimensions of the box that gives the maximum volume are;

Height = 1 ft

Length = 6 ft

Width = 3 ft

The volume of the largest box that can be formed is 18 cubic feet

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The simplest form is 4xy

From the question, we have

xy + 3xy = 4xy

The simplest form is 4xy.

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer: 14 is the ancer

Step-by-step explanation:

Answer:

its 14

Step-by-step explanation:

Answer:

21y-7/11

Step-by-step explanation:

First you would multiply everything outside of the prhthises to the inside. Second multiply 7 times 3y that would equal 21y. Third multiply 7 times - 1/11    that would equal to 21y-7/11

There are 9216 more white squares than black squares in the 47th term with it's an odd number of 97

The terms are generated with the square of odd numbers with the black squares being the addition of the odd number and one subtracted from it.

For the 47th term:

Given that the first term is consists of 25 squares with 9 black and 16 white squares

first term has odd number 5

the square of 5; 5² = 25

black squares = 5 + (5-1) = 9

white squares = 25 - 9 = 16

Therefore, for the 47th term:

47th term has odd number 97

the square of 97; 97² = 9409

black squares = 97 + (97-1) = 193

white squares = 9409 - 193 = 9216

Hence, the 47th term has an odd number 97 with 9216 more black squares than the white squares,

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The corresponding values of F1 and F2 in the ordered pairs are 77 degrees Fahrenheit and -22 degrees Fahrenheit

Given: the equation F=9/5C+32 and ordered pairs: (25, F1), (−30, F2)

In order to convert the given values to degrees Fahrenheit, substitute the given values into the equation to get F1 and F2 respectively:

For (25, F1):

F = 9/5 C+32      (put C= 25 in the equation)

F1 = 9/5(25) + 32

F1 = 45 +22

F1 = 77 degrees Fahrenheit

For (−30, F2):

F = 9/5 C+32       (put C= -30 in the equation)

F2 = 9/5(-30) + 32

F2 = -54 + 32

F2 = -22 degrees Fahrenheit

Therefore, the values of F1 and F2 are 77 degrees Fahrenheit and -22 degrees Fahrenheit respectively

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Answer:

Step-by-step explanation: 32=v + 27

V= 5

how:

32-27=5

v=5

I don"t know what you meant for at the bottom, if that is included please explain what you mean.

Answer:

5

Step-by-step explanation:

32 = v + 27

Subtract 27 from both sides and make v the subject.

32 - 27 = v

5 = v

The auxiliary function used in the composition between the two functions f(x) and g(x) is equal to linear function g(x) = x + 3.

Herein we find the result of a composition between two functions, where the variable x of the parent function f(x) is substituted by the auxiliary function g(x). The composition between the two functions is defined below:

h(x) = f ° g (x) = f [g (x)]

If we know that the parent function f(x) = x⁵, then the auxiliary function within the composition is the linear function g(x) = x + 3.

The statement is poorly formatted, the correct form is shown below: The function h(x) = (x + 3)⁵ can be expressed in the form f[g(x)] where f(x) = x⁵ and g(x) is defined below.

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The elements of set (AnB)' = {1,2,3,5,6,7,8,9,10} and The elements of A'uB' = {1,2,3,5,6,7,8,9,10}

The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. For example, if A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).

Therefore if U={1,2,3,5,6,7,8,9,10} and A={4,8,9,10} B= {2,3,4,6,7} then,

(AnB) = {4}

(AnB)' = {1,2,3,5,6,7,8,9,10}

A' = {1,2,3,5,6,7} and B' = {1,5,8,9,10}

therefore A'uB'= {1,2,3,5,6,7,8,9,10}

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Answer:

I 728.Two beetles sit at the verticesAandHof a cubeABCDEFGHwith edge length40√110 units. The beetles start moving simultaneously alongACandHFwiththe speed of the first beetle twice that of the other one.....ADCBEFGH✈s✈s. . . . . . . . . . . . . . . . . . . . . . . . ......................................................................What will be the shortest distance between the beetles?29.In the diagram,4PQRhas an area of 960 square units. The pointsS,TandUare the midpoints of the sidesQR,RPandPQ, respectively, and the linesPS,QTandRUintersect atW.......PQRSUTNMLW✓✓✼. . . . . . . . . . . . . . .....................The pointsL,MandNlie onPS,QTandRU, respectively, such thatPL:LS= 1 : 1,QM:MT= 1 : 2 andRN:NU= 5 : 4.What is the area, in square units, of4LMN?30.A 40×40 white square is divided into 1×1 squares by lines parallel to its sides.Some of these 1×1 squares are coloured red so that each of the 1×1 squares,regardless of whether it is coloured red or not, shares a side with at most one redsquare (not counting itself). What is the largest possible number of red squares?

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

A ≈ 2.88×108km²

Step-by-step explanation:

A= 4 π r² = 4·π· 47902 ≈ 2.88324×10 power 8 km²

The volume of the cube is 1/125b⁹

From the question, we understand that

Shape = Cube

Side length = 1/5b³

Rewrite the side length as

a = 1/5b³

The volume of a cube can be expressed as V = a³

where a is the length of any side

And v is the volume

Substitute the known values in the above equation So, we have the following equation

V = (1/5b³)³

Evaluate

V = 1/125b⁹

Hence, the volume is V = 1/125b⁹

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Answer:

I hope this will be helpful for you.

0 (zero)

Step-by-step explanation:

[tex]{ \blue{ \sf{ {5}^{ - 3} \times {2}^{4} \times {5}^{3} \times {2}^{ - 5}}}} [/tex]

Arrange the like terms in order

[tex]{ \blue{ \sf{ {5}^{ - 3} \times {5}^{3} \times {2}^{4} \times {2}^{ - 5}}}} [/tex]

This is in the form of [tex]{ \red{ \sf{ {a}^{m} \times {a}^{n} = {a}^{m + n}}}} [/tex]

[tex]{ \blue{ \sf{ {5}^{ - 3 + 3} \times {2}^{4 + ( - 5)}}}} [/tex]

[tex]{ \blue{ \sf{ {5}^{0} \times {2}^{4 - 5}}}} [/tex]

[tex] { \blue{ \sf{0 \times {2}^{ - 1}}}} [/tex]

[tex]{ = \blue{ \sf{0}}}[/tex]

Any number which is multiplied with zero is zero itself.

Answer:

66 inches

Step-by-step explanation:

60 + .1(60)

60 + 6

66

Answer:

66 inches

Step-by-step explanation:

60 x .10 = 6

60 +6 =66