HELP PLEASE SOLVE ITS SLOPE!

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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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

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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Answer:

Series calculator is a free online tool that gives the summation value of the given function for the given limits.

please make my answer as brainelist

Answer:

0.282kg/m3

Step-by-step explanation:

density=mass/volume

mass=32.5kg

volume=lxbxh

volume=2.4mx60cmx80cm

convert 60cm and 80cm to m:

60cm=6m

80cm=8m

volume= 2.4mx6mx8m

volume=115.2m3

density=32.5/115.2m3

density=0.28211kg/m3

round to nearest three decimal places:

= 0.282kg/m3

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: 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

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 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:

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

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

2

−

2

x

+

1

=

x

2

−

2

x

+

1

2

=

(

x

−

1

)

2

A perfect square trinomial is the square of a binomial, so will take the form:

a

2

+

2

a

b

+

b

2

since

(

a

+

b

)

2

=

a

2

+

2

a

b

+

b

2

So a perfect square trinomial satisfies the following conditions:

(1) Two of the terms are squares.

(2) The other term is twice the product of the square roots (positive or negative) of the other two terms.

If the two square terms are

a

2

and

b

2

then the trinomial is either

(

a

+

b

)

2

or

(

a

−

b

)

2

depending on the sign of the third term.

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:

2\3

Step-by-step explanation:

Hope this helps!!

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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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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Step-by-step explanation:

2² - 12z +c

4 -12z + c

c = -4+12z

Answer:23

Step-by-step explanation:

Answer:

<8, <1, <4 are all 96

<6,<7,<3, <2 are all 84

Step-by-step explanation:

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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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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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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The constant, k is $2500 and 7 months of work will be needed to earn $17,500.

According to the question,

We have the following information:

We have a table where months and the salary in dollars is given.

Now, the salary is increasing constantly with number of months.

So, we have the following expression:

9) Amount of dollars is directly proportional to number of months.

Dollars = k*months

2500 = k*1

k = 2500

10) Now, the amount given is $17,500.

So, we have:

k*months = 17,500

Months = 17500/2500

Months = 7

Hence, the constant, k is $2500 and 7 months of work will be needed to earn $17,500.

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The first quadrant that lies between the circle x² + y² =4 is 1.09587

The graph of x² +y² = 4 is a circle of radius 2, centered at (0, 0). In polar coordinates, this equation becomes simply r = 0.

The second equation requires a bit more work. To convert it to a polar equation, we

substitute, r cos θ for x and r sin θ for y:

r²cos ²θ + r²sin ²θ

   = 2r cos Ф

⇒r² = 2r cos θ

⇒r = 2 cos θ

This is the polar equation for a circle of radius 1, centered at the point (x, y) = (1, 0). (This can be seen directly from the original equation by completing the square, which results in the equation (x − 1)²+ y² = 1.)

To describe the region between the circles in polar coordinates, we can let θ range from 0 to π/2. Our values for r should range from the smaller circle to the larger one

Recalling again that x = r cos θ and dA = rdrdθ, our integral becomes

∫ ∫ₐ  x DA  = 8/3 - π/2

We can get a rough check of this answer as follows. The area of the region D is easily computed to be π/2. The average value of the function x in the region is somewhat less than 1, since D is thicker on the left. Doing these sorts of visual estimates can be very tricky, but let’s say the average value of x in D is about 0.70. Thus

∫∫ₐ x dA ∼=π/2· 0.70 ∼= 1.09956

Since 8/3 − π/ 2∼= 1.09587, this estimate agrees quite well with our answer.

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Answer:

The answer has to be 8.999

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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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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