I need help ASAP!!!!!!!

The sum of two positive numbers is 120. The product of those numbers will be maximum if both numbers are equal to 60 and the maximum value is 3600.

Suppose we have a function f(x). At the extreme point (maximum/minimum), it holds:

      f ' (x) = 0

In the given problem, let the two numbers be a and b. Then,

a + b = 120 or

a = 120 - b   (equation 1)

f(b) = a x b = (120 - b) x b

f(b) = -b² + 120b

At the maximum point, the derivative with respect to b is zero,

f ' (b) = 0

-2b + 120 = 0

b = 120 / 2 = 60

Substitute b = 60 to equation 1,

a = 120 - 60 = 60

Hence, the two numbers that give maximal value of the product is 60 and 60. The product is 60 x 60 = 3600.

We can conclude that the maximum value of the product of those two numbers is 3600.

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Answer:23

Step-by-step explanation:

Answer:

Im guessing it would be a positive change

Step-by-step explanation:

part a had the cost of $100,000 while part b had the cost of $210,000

therefore, part b increased $110,000 from 2000 to 2008.

this is my guess.

The value of h(x) = -40x2 – 52x + 18. Option (b) is correct.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is defined as a function.

Given functions

f(x) = -5x − 9

g(x) = 8x − 4

we have to determine which equation defines function h

f(x) = -5x − 9

g(x) = 8x – 4

(f x g) (x) = (-5x –9)(8x – 4)

(f x g) (x) = -40x2 + 20x – 72x + 36

(f x g) (x) = -40x2 – 52x + 18

Therefore the value of  h(x) = -40x2 – 52x + 18. Option (b) is correct.

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The exponential form is  [tex]10^\frac{3}{2}= \sqrt{1000}[/tex].

Given expression is [tex](\sqrt{10})^3[/tex]

We know that

[tex](\sqrt{x})^n = x^\frac{n}{2}[/tex]

Therefore, [tex](\sqrt[]{10})^3 = 10^\frac{3}{2}[/tex]

Now, let's simplify the exponential form of this expression.

We know that [tex]a^\frac{m}{n} = nth root of a^m[/tex]

Therefore,

[tex]10^\frac{3}{2} =(\sqrt{10})^3[/tex]

[tex]10^\frac{3}{2}= \sqrt{1000}[/tex]

 Hence, the exponential form of the expression [tex](\sqrt{10})^3[/tex] is [tex]10^\frac{3}{2}= \sqrt{1000}[/tex] which simplifies to [tex]10^\frac{3}{2}[/tex].

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let length of one piece = x

length of other piece = 236-x

one piece is three times the length of the other

x=3(236-x)

x=708-3x

4x=708

x=177

so first piece is 177 inches long and second piece is (236-177)= 59 inches long

Answer:

first piece is 177 inches long and second piece is (236-177)= 59 inches long

Step-by-step explanation:

x=3(236-x)

x=708-3x

4x=708

x=177

Answer:

m = 180d -20

Step-by-step explanation:

m = miles

d = days

After 25 minutes will both aquariums contain the same amount of water.

Given:

Aquarium a contains 4. 6 gallons of water. Louise will begin filling aquarium a at a rate of 1. 2 gallons per minute. Aquarium b contains 54. 6 gallons of water. Isaac will begin draining aquarium b at a rate of 0. 8 gallon per minute.

Let y be the minutes

A(y) = 4.6 + 1.2y

B(x) = 54.6 - 0.8y

Same amount of water:

A(x) = B(x)

4.6 + 1.2y = 54.6 - 0.8y

1.2y + 0.8 y = 54.6 - 4.6

2y = 50

divide by 2 on both sides

2y/2 = 50/2

y = 25 minutes.

Therefore after 25 minutes will both aquariums contain the same amount of water.

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Answer:

Below

Step-by-step explanation:

k =  280 / 5 = Php 56 /hr

          money earned =  k x       where x = # of hours

     For 8 hours :    money earned =   56 * 8  = Php 448

Using the long division method, we have divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4) then the remainder is −55 and quotient is x^2−3x+15.

We have to divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4)

In general, long division of two integers without any variables is performed in the same way as long division of a polynomial by a binomial:

Divide the polynomial's highest degree term by the binomial's highest degree term. Over the division line, type the outcome.

Subtract the resulting binomial from the polynomial after multiplying this result by the divisor.

x+4) [tex]x^3+x^2[/tex] +3x+5 (x^2−3x+15

    −([tex]x^3+4x^2[/tex])

−−−−−−−−−−−−−−−−−−−

             −3[tex]x^2[/tex] +3x

           −(−3[tex]x^2[/tex] −12)

−−−−−−−−−−−−−−−−−−−

                         15x+5

                      −(15x+60)

−−−−−−−−−−−−−−−−−−−

                               −55

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Answer:

x=12

Step-by-step explanation:

turn into and equation because angles in a triangle add up to 180°

so

6x-19+3x+7+84=180

collect like terms

9x+72=180

solve to find 'x'

9x=108

x=12

Answer:

2\3

Step-by-step explanation:

Hope this helps!!

Answer: 13 units

Step-by-step explanation:Given that Point C is the midpoint of AB and point B is between points A and D. If AD = 17 and BD = 9

According to definition midpoint, AC = CB

According to definition of segment addition postulate, AD = AB + BD

AB = AD - BD

AB = 17 - 9

AB = 8

Again, AB = AC + CB

Therefore, CB = AB/2

CB = 8/2 = 4

Now, CD = CB + BD = 4 + 9

CD = 13 units

Hence, length of CD = 13 units

The congruency postulates for the given triangles are;

1) ASA Congruency postulate.

2) SSS congruency postulate.

3) AAS congruency postulate.

4) SAS Congruency postulate.

5) Triangles are not congruent

There are different triangle congruency postulates such as AAS, ASA, SSS, SAS, RHS.

1) We are given 2 corresponding angles and the included congruent side and as such, the congruency rule here is ASA Congruency postulate.

2) We are given 3 corresponding congruent sides for both given triangles and as such we can say that the triangle congruence postulate here is SSS congruency postulate.

3) We are given 2 corresponding angles and the non-included congruent side and as such, the congruency rule here is AAS Congruency postulate.

4) We are given two congruent sides and the include congruent angle and as such the congruency rule here is SAS Congruency postulate.

5) We are given three congruent angles but there is no mention of any of the sides being congruent and as such the triangles are not congruent.

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Answer:

I believe it would be 4.9 inches

Step-by-step explanation:

14.7 divided by 3

Answer: 4.9 inches

Step-by-step explanation: 14.7 divided by 3 is 4.9

Answer:a) No, the first support starts at (0,0) and the 2nd one starts at (2,1)

b) No, first one ends at (2,1) 2nd one ends at (6,3)

c) No, 2 ( 0 to 2) does not equal 4 ( 2 to 6)

d) No, 1 ( 0 to 1) does not equal 2  (1 to 3)

e) Yes, this is the slope of the diagonal line: 1/2

MARK BRAINILEST I GOT SO CONFUSED BUT I UNDERSTAND NOW.... Peace Out?

Step-by-step explanation:

Reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.

transformations that do not result in mapping (a,-a) to (a, a) when a > 0. are

reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2

Hence reflection in the x-axis and translation 2a units up, translation a units up, followed by a reflection in the line y = a translation a units up, followed by a reflection in the line y = 2

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The vertices of the figure after geometric translations are (11, 5), (5, 4), and (9, 7).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The vertices are D(2,8), F(1,2) and G(4,6).

Points become after reflection:

D'(8, 2), F'(2, 1), G'(6, 4)

After applying translation:

D''(8+3, 2+3) = (11, 5)

F''(2+3, 1+3) = (5, 4)

G''(6+3, 4+3) = (9, 7)

Thus, the vertices of the figure after geometric translations are (11, 5), (5, 4), and (9, 7).

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A function's domain is defined as the set of all possible input values. The domain here is 0 ≤ x ≤ 500 because the input value is x.

Given;

Let x be the overall number of cartons produced in a single day. due to the factory's daily production limit of 500 cartons.

Let P(x) denote the revenue generated by the sale of x cartons. Since a carton costs $25, the following follows;

P(x) = 25x

P(0) = 25(0) = 0 for x = 0

P(500) = 25(500) = 12500 when x = 500

The following are possible values for P(x);

0 ≤ P(x) ≤ 12500

Therefore, the collection of all potential input values is referred to as a function's domain. Since the input value in this instance is x, the domain is 0 ≤ x ≤ 500

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The equation that describes Joe’s monthly income is I = 500 + 20n. This function is Linear and discrete.

Joe makes each month = $500

The extra income per account he solicits = $20

No. of accounts he solicits = n

Income, I = 500 + 20n

It's a linear and discrete function.

A linear function in mathematics is one that has either one or two variables and no exponents. On a graph, it creates a straight line.

When the domain and range of a function are discrete sets of values rather than intervals, the function is said to be discrete.

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Step-by-step explanation:

2² - 12z +c

4 -12z + c

c = -4+12z

As a result, the tunnel is 13.83 feet high, 5 feet from the edge.

An ellipse is an oval curve on a plane that contains two fixed points called foci. The sum of the distances between the two foci from each point on the ellipse is constant at all points.

Since the tunnel has an arch that is semi-elliptical, we can put the ellipse's center at the center of its 60-foot width.

What is an ellipse?

An ellipse is a two-dimensional shape that is defined by its axes in geometry. When a plane intersects a cone at an angle to its base, it creates an ellipse. It focuses on two things. For each point in the curve, the sum of the two distances to the focal point remains constant.

What are an ellipse and an example?

An ellipse is the locus of points whose sum of their distances from its two foci is constant and has an eccentricity of less than one. The two-dimensional egg shape and the running tracking in a sports stadium are simple examples of the ellipse in our everyday lives.

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The length of the third side of the triangle is 2√14 units.

According to the question,

We have the following information:

Note that the complete question will be related to the right angled triangle with hypotenuse 15 units and perpendicular 13 units.

(More to know: Pythagoras theorem can only be used in right-angled triangle.)

We can use the Pythagoras theorem to find the base of the right-angled triangle.

Let's denote the base with b, perpendicular with p and hypotenuse with h.

[tex]b^{2} = h^{2}- p^{2}[/tex]

[tex]b^{2} = 15^{2} -13^{2}[/tex]

[tex]b^{2} }[/tex] = 225-169

b = √56

b = 2√14 units

Hence, the length of the third side of the triangle is 2√14 units.

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Answer:

y=6 x=3

Step-by-step explanation:

−2(−7x−y=−27)

1(−14x+10y=18)

14x+2y=54

−14x+10y=18

12y=72

y=6

−7x−y=−27

−7x−6=−27

−7x=−21

x=3

the given numbers in standard form can be expressed as :

1. 1.5 × [tex]10^-10[/tex]

2. 4 × [tex]10^1 ^3[/tex]

3. 5 × [tex]10^-^2^1[/tex]

Standard form refers to any number that can be expressed as a decimal number and falls within the range of 1.0 and 10.0 when multiplied by a power of 10. The standard form of 123,000,000 is 1.23 108 because, if you look closely, 1.23 is a decimal number between 1.0 and 10.0.

1. The given numbers are (5x10^-4)x(3x10^-5)

On multiplying the natural numbers first we get :

15 × [tex]10^{-9}[/tex]

1.5 × [tex]10^-10[/tex]

2. The given numbers are  (2.8x10^9) and (7x10^5)

on dividing them we get

0.4 ×[tex]10^1 ^4[/tex]

4 × [tex]10^- ^1[/tex] ×[tex]10^1 ^4[/tex]

4 × [tex]10^1 ^3[/tex]

3. The given numbers are (2x10^-14) divided by (4x10^-6)

Thus after dividing the natural numbers we will get

0.5 ×[tex]10^- ^2 ^0[/tex]

On further simplifying we get

5 × [tex]10^ -^1[/tex] ×[tex]10^- ^2 ^0[/tex]

5 × [tex]10^-^2^1[/tex]

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Answer:

3034 grams

Step-by-step explanation:

to find one serving divide the total grams by grams per serving:

106200/35

=3034.28571429=3034(rounded to nearest whole number)

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a local ice skating rink wishes to determine the age of its customers.  then 10% of lottery winners are 70 years or older

Age____ Freq__R/freq____ Cumm Rel Freq

[20,29]___3____ 0.1________ 0.1

[30,39]__ 10__ 0.3333_____ 0.4333

[40,49]__ 2__ 0.0667______ 0.5

[50,59]__ 7 __0.2333 _____0.7333

[60,69]__ 4 ___0.1333 ____0.8666

[70,79]___ 3 ____0.1 ______0.9666

[80,89]___ 1 ___0.0333 ____0.9999

A.) What is the frequency of lottery winners of age between 19 and 40?

Frequency = (3 + 10) = 13 winners

B.) What percentage of lottery winners are 70 years or older?

From the relative frequency table = 0.1 (3/30) = (0.1 * 100%) = 10%

complete question is

Given the frequency distribution for the data, Age Frequency Relative Frequency Cumulative Relative Frequency [20,29] 3 0.1 0.1 [30,39] 10 0.3333 0.4333 [40,49] 2 0.0667 0.5 [50,59] 7 0.2333 0.7333 [60,69] 4 0.1333 0.8666 [70,79] 3 0.1 0.9666 [80,89] 1 0.0333 0.9999 What is the frequency of lottery winners of age between 19 and 40? What percentage of lottery winners are 70 years or older?

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Answer: 86 86/91 or 7912/91

Work: So you multiply 3/4x by what is in the parenthesis like this: 3/4x*5/6-3/4x*4/23. and you get 5/8x-3/23x=43. And then you simplify to get 91/184x=43 then u multiply both sides by 184 to get rid of the fraction. and you get 91x=7912. then you divide both sides by 91 and you get x=7912/91 or 86 86/91

The measures of the following angles are:

∠6 = 124°,  ∠2 =124°,  ∠3 = 124° ∠5 = 56°,  ∠7 = 124° ∠1 = 56°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

∠4 = 56° ( corresponding angles are equal)

∠1 =∠4 ( vertically opposite angles are equal)

∠1 = 56°

∠7 + 56° = 180 ( angles on a straight line sum up to 180°)

∠7 = 180 - 56

∠7 = 124°

∠7 = ∠6 ( vertically opposite angle are equal)

∠6 = 124°

∠3 = ∠6 ( alternate angles are equal)

∠3 = 124°

∠2 = ∠3 ( vertically opposite angle)

∠2 = 124°

∠5 = 56° ( vertically opposite angles)

The unknown angles are: ∠1 = 56° ∠2 = 124°, ∠3 = 124°, ∠4 = 56°, ∠5 = 56°, ∠6 = 124° ∠7 = 124°

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