Find two numbers whose sum 7500 and whose product is the maximum value.
(Round your answer to the nearest whole number.)
Blank = 1
Blank = 2

Answers

Answer 1

The two numbers whose sum is 7500 and whose product  is a maximum value are 3750 and 3750.

Let the two numbers be x and y.

Since their sum equals 7500,

x + y = 7500  (1)

Their product f(x,y) = xy  (2)

We desire to maximize the product.

From (1), x = 7500 - y

Substituting x into (2), we have

f(x,y) = xy

f(x,y) = (7500 - y)y

f(y) = 7500y - y²

To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.

So, df(y)/dy = d(7500y - y²)/dy

f'(y)/dy = d(7500y)/dy - dy²/dy

f'(y)/dy = 7500 - 2y

Equating it to zero, we have

7500 - 2y = 0

7500 = 2y

y = 7500/2

y = 3750

To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.

So, f"(y) = d(7500 - 2y)dy

f"(y) = 0 - 2

f"(y) = -2 < 0.

So, y = 3750 gives a maximum for f(y) = f(x, y)

Since x = 7500 - y

Substituing y = 3750 into the equation, we have

x = 7500 - 3750

x = 3750

So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.

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Answer:

x = 35°

Step-by-step explanation:

These are corresponding angles. When a transversal crosses 2 parallel lines, 4 angles are created at each intersection, and each pair of corresponding angles between those are congruent.

These angles are congruent, so you can set them equal to each other:

[tex]2x+20=3x-15[/tex]

Then, just solve for x:

[tex]20=x-15\\35=x\\x=35[/tex]

You can check that by plugging it back into both:

[tex]2x+20=3x-15\\2(35)+20=3(35)-15\\70+20=105-15\\90=90[/tex]

Answer:

x = 35

Step-by-step explanation:

The angles shown are corresponding angles

Corresponding angles are congruent ( equal to each other )

This means that 2x + 20 should equal 3x - 15

Note that we've just created an equation that we can use to solve for x

We know use that equation to solve for x

2x + 20 = 3x - 15

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And we are done!

Question

Each data point on the scatter plot represents last month’s necklace and earring sales, in thousands of dollars, at one of the fourteen locations in a nationwide jewelry store chain. The correlation coefficient between necklace sales and earring sales is 0.98.


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Answer:

25cm^2

Step-by-step explanation:

A square has 4 equal sides so each side will be 20/4 = 5cm

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Answer:

94)=154°

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g
is −12
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1
2
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−12
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·
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Answers

Answer:

g

is −12

-

1

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Answer:

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Step-by-step explanation:

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Answers

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Answer:

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Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

Explanation:

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Answers

Given the perimeter of the parallelogram in the image below is 60, the value of GH will be: 23.

Recall:

Perimeter of a parallelogram = 2(a + b), where a is the side length and b is the base length.Opposite sides of a parallelogram are equal.

Given the parallelogram as shown in the diagram below, where:

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Answer:

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Answer:

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Answers

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Answers

The current depth of the hole is at least 20 feet below ground level.

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Step-by-step explanation:

You want to be able to withdraw $30,000 from your account each year for 15 years after you retire. If you expect to retire in 25 years and your account earns 6.4% interest while saving for retirement and 5.6% interest while retired:
Round your answers to the nearest cent as needed.

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d) How much did you receive in payments during retirement?


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Answer:

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Step-by-step explanation:

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Third one hope that helps :)

Based on the graph, what is true about polygon ABCD?

a. The polygon is a hexagon
b. The area of the polygon is 96 square units
c. The perimeter is 20 unit
d. Side AD is congruent to side DC

Answers

Answer:

B

Step-by-step explanation:

The Width of the Rectangle (read Polygon) is 8 units and the Length of the Rectangle is 12 units.

The area of the polygon is 96 square units. Therefore, the correct answer is option C.

From the given graph, we have polygon ABCD.

From the graph, we have AB=DC=12 units and BC=AD=8 units.

Here, the given polygon is rectangle.

Area of a rectangle = Length×Breadth

Now, area of a rectangle = 12×8

= 96 square units

Perimeter of a rectangle = 2(Length+Breadth)

= 2(12+8)

= 2(20)

= 40 units

Therefore, the correct answer is option C.

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#SPJ4

Question
A triangle with area 40 square inches has a height that is four less than six times the width. Find the width and height of the
triangle

Answers

Answer:

width is 4

height is 20

Step-by-step explanation:

Area=½ width × height

let the width be x

height will be 6x - 4

40 = ½ × x × (6x - 4)

40 = 2/2 × 3x² - 2x

40 = 3x² - 2x

3x² - 2x - 40 = 0

3x² -12x + 10x - 40 = 0

3x(x-4) + 10(x-4) = 0

(3x + 10)(x - 4) = 0

x = -10/3 or 4

dimension cannot be negative

x is 4

6x-4= 6(4) - 4

24 - 4

20

which expression are of -48xyz+24xy+40xyz
A4
B24
C3X
D8Y
E2XY
F6XY
GXYZ

Answers

Answer:

I'm GUESSING you want to know which are possible FACTORS of the equation. - 48xyz + 24xy + 40xyz

IF so,

THEN

A) 4         as 48, 24, and 40 divide evenly by 4

              4(-12xyz + 6xy + 10xyz)

D) 8Y      as 48, 24, and 40 divide evenly by 8 and each term has a Y

               8y(-6xz + 3x + 5xz)

E) 2XY     as 48, 24, and 40 divide evenly by 2 and each term has a XY

                2xy(-24z + 12 + 20z)



Which term has the definition "A relationship in which two variables change at the same rate

Answers

positive correlation

(i believe thats what it is)

Can someone check my answer?? PLEASE-

The length of a rectangle is six more than the width. If the perimeter of the rectangle is 40 ft, find the length of the rectangle.

A. 13 ft (what I think) ****

B. 7 ft

C. 23 ft

D. 17 ft

Answers

Answer:

the length of the rectangle is 13 ft.

Step-by-step explanation:

width of a rectangle x ft

length of a rectangle x+6 ft

the perimeter of the rectangle is 40 ft,

2(x+x+6) = 40

2x+6 = 20

2x = 14

x = 7

So the length of the rectangle is x+6 = 7+6 = 13 ft

congrats you're right (≧▽≦)!!

Answer:

The correct answer ia A)13 ft

Step-by-step explanation:

hope this helps

In AJKL, j = 75 cm, k = 23 cm and

Answers

Answer:

The length of side j is 11.85cm

Step-by-step explanation:

Given that

In triangle JKL,

Side k=LJ=3.7cm

To find side j=KL:

By using sine rule,

We can write as

Using property of triangle,

Thus,

The length of side j is 11.85cm

Which type of correlation does this scatterplot show?

Answers

Positive correlation. Y varies directly with x. Meaning as x increases or decreases, Y will behave the same as x.

Four squirrels have 30 berries each. But before they start watching, two more squirrels join the group. They share the berries equally amongst themselves. How many berries will each squirrel get to eat?

Answers

Answer:

5

Step-by-step explanation:

4+2=6

30 berrys so you do 30/6=5

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