What number is being factored in this factor tree?





A. 34
B. 68
C. 136
D. 272

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.

Learn more about product of two numbers here:

https://brainly.com/question/15607519

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[tex]9 \: + \: 7 \: = \boxed{16}[/tex]

USE CALCULATOR...

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[tex] \mathfrak{JazmineChoi}[/tex]

STAN TREASURE

Answer:

y= [tex]\frac{3}{2}[/tex]x -1

Step-by-step explanation:

To find slope I first found the two points on the graph which were (0, -1) and (2, 2). Then I used rise over run to find the slope the point went up 3 units and to the right two units.

then to find the y intercept I found a pint of the graph where the line had passed through the y-intercept line on the graph which just so happened to be -1.

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Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

Answer:

y = 3/2 - 1

Step-by-step explanation:

First let's take two coordinates in the line.

( 2 , 2 )     ( 0 , -1)

You can use y = m x + c to find the equation of the line.

Here,

m → slope

c  → y - intercept

( 2 , 2 )                ( 0 , -1)

 ↑  ↑                    ↑  ↑

( x1 , y1 )            ( x2 , y2 )

First let's find the slope of the line.

m = ( y1 - y2) / ( x1 - x2)

m = ( 2 - (-1) ) / (2 - 0 )

m = ( 2 + 1 ) / 2

m = 3 / 2

Now let's find the y - intercept of the line.

For that, let's use ( 0 , -1 ) coordinate

y = m x + c

y = 3/2 × 0 - 1

y = 0 - 1

y = ( - 1 )

Therefore, the equation of the line is,

y = 3/2x - 1

Hope this helps you :-)

Answer:

QR is equal to 5 since 13 is 5 less that 18. So since 13 was already taken, that leaves 5

Answer:

I don't know sorry

Answer:

22.5 degrees

Step-by-step explanation:

Complementary angles add up to be 90 degrees. You can model the simple equation [tex]x+3x=90[/tex] where is x is the small angle and 3x is the large angle.

[tex]4x=90\\x=22.5[/tex]

the smaller angle is 22.5 degrees

Answer is -4

Step-by-step explanation:

8x-4< -36

8x < -36+4 (move [- 4] to the other side to find x)

8x < -32

8x < -4

Answer:

x < -4

Step-by-step explanation:

8x - 4 < -36

+4           +4 (Add 4 on both sides)

8x < -32

/8      /8        (Divide by 8 on both sides)

x < -4

Answer:

Step-by-step explanation:

Answer:

4 Hours

Step-by-step explanation:

2 1/6 = 13/6

1 5/6 = 11/6

13/6+11/6= 24/6

Simplify 24/6 which will give you 4

Answer:

A, B and C

Step-by-step explanation:

They all can mirror to overlap perfectly with the other side of the shape.

D and E can not

I hope this helps :)

Answer:

A    C     B

Step-by-step explanation:

those are the right answers i just did it hope it helps

Answer:

con que?

Step-by-step explanation:

Step-by-step explanation:

the answer is shown in the photo

Answer:

i) 5y

Ii) 5y-3

iii) 5y×6

Iv)

Answer:

60

Step-by-step explanation:

Answer:

9) 21

10) 70

11) 34

12) 31

13) 50

14) 31

15) 137

16) 101

Step-by-step explanation:

9)

20+40=60

60 + b =180 ( sum of the interior angles on a triangle is 180 )

b = 180 - 60

b = 120

39 + c + ? = 180 ( sum of the interior angles on a triangle is 180 ) c =120 ( vertically opposite angles are equal )

39 + 120 + ? = 180

159 + ? = 180

? = 180 - 159

? = 21

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10)

60 + 65 + b = 180 ( sum of the interior angles on a triangle is 180 )

125 + b = 180

b = 180 - 125

b = 55

50 + b + c = 180 ( sum of the angels on a straight line is 180 )

50 + 55 + c = 180

105 + c = 180

c = 180 - 105

c = 75

35 + c + ? = 180

35 + 75 + ? = 180

110 + ? = 180

? = 180 - 110

? = 70

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11)

84 + 36 + b = 180 ( sum of the interior angles on a triangle is 180 )

120 + b = 180

b = 180 - 120

b = 60

86 + b + ? = 180 ( sum of the interior angles on a triangle is 180 )

86 + 60 + ? = 180

146 + ? = 180

? = 180 - 146

? = 34

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12)

35 + 23 + b = 180 ( sum of the interior angles on a triangle is 180 )

58 + b = 180

b = 180 - 58

b = 122

27 + c + ? = 180 ( sum of the interior angles on a triangle is 180 ) c =122 ( vertically opposite angles are equal )

27 + 122 + ? = 180

149 + ? = 180

? = 180 - 149

? =31

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13)

115 + b = 180 ( sum of the angels on a straight line is 180 )

b = 180 - 115

b = 65

65 + 90 + c = 180 ( sum of the angels on a straight line is 180 )

155 + c = 180

c = 180 - 155

c = 25

155 + d = 180 ( sum of the angels on a straight line is 180 )

d = 180 - 155

d = 25

c + d + e = 180 ( sum of the interior angles on a triangle is 180 )

25 + 25 + e = 180

50 + e = 180

e = 180 - 50

e = 130

e + ? = 180 ( sum of the angels on a straight line is 180 )

130 + ? = 180

? = 180 - 130

? = 50

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14)

35 + 20 + b = 180 ( sum of the interior angles on a triangle is 180 )

55 + b = 180

b = 180 - 55

b = 125

156 + c = 180 ( sum of the angels on a straight line is 180 )

c = 180 - 156

c = 24

c + e + ? = 180 ( sum of the interior angles on a triangle is 180 ) e= 125 ( vertically opposite angles are equal )

24 + 125 + ? = 180

149 + ? = 180

? = 180 - 149

? = 31

________________________________________________________________________________________

15)

b = 45 ( vertically opposite angles are equal )

b + 60 + c = 180 ( sum of the interior angles on a triangle is 180 )

45 + 60 + c = 180

105 + c = 180

c = 180 - 105

c = 75

68 + 75 + e = 180 ( sum of the angels on a straight line is 180 )

143 + e = 180

e = 180 - 143

e = 37

100 + 37 + j = 180 ( sum of the interior angles on a triangle is 180 )

137 + j = 180

j = 180 - 137

j = 43

j + ? = 180 ( sum of the angels on a straight line is 180 )

43 + ? = 180

? = 180 - 43

? = 137

________________________________________________________________________________________

16)

b = 75 ( vertically opposite angles are equal )

c = 45 ( vertically opposite angles are equal )

b + c + e = 180 ( sum of the interior angles on a triangle is 180 )

75 + 45 + e = 180

120 + e = 180

e = 180 - 120

e = 60

e + 79 + j = 180 ( sum of the angels on a straight line is 180 )

60 + 79 + j = 180

139 + j = 180

j = 180 - 139

j = 41

j + 60 + s = 180 ( sum of the interior angles on a triangle is 180 )

41 + 60 + s = 180

101 + s = 180

s = 180 - 101

s = 79

s + ? = 180 ( sum of the angels on a straight line is 180 )

79 + ? = 180

? = 180 - 79

? = 101

________________________________________________________________________________________

hope this helps☆☆☆

it took soooo long to do btw ⊙•⊙

Answer:

14.4

Step-by-step explanation:

1.8 added 8 times = 1.8 * 8

1.8 * 8

use distributive property

1.8 = 1 + 0.8

1.8 * 8 = (1+0.8) * 8

          = 1*8 + 0.8*8

anything multiplied by 1 equals itself

1*8 + 0.8*8 = 8 + 0.8 * 8

0.8 = 8/10

0.8 * 8 = (8/10) * 8

           = 64/10

            = 6.4

8 + 0.8 * 8 = 8 + 6.4 = 14.4 as our answer

Answer:

A. x²- 4x+ 1

option A is the answer

Answer:

i dont know how to do it231

Step-by-step explanation:

1123234

Answer:

Step-by-step explanation:

The system of equations can be written ...

  x + y = 36

  x = 2y

__

The system can be solve by substituting for x:

  (2y) +y = 36

  y = 12 . . . . . . divide by 3

  x = 2(12) = 24

There are 24 pairs of Nikes and 12 pairs of Adidas.

Answer:

Step-by-step explanation:

d = √((9 -(-2))² + (5 - 2)²)

d = √(11² + 3²)

d = √130

d = 11.401754250...

d = 11.4 units

Answer:

11.4 to the nearest tenth.

Step-by-step explanation:

Distance = sqrt((5-2)^2 + (9-(-2))^2)

= sqrt(3^2 + 11^2)

= sqrt 130

= 11.402

Answer:

1) x > -2

2) x < -1

Step-by-step explanation:

1) 2(x - 2) + 7 > -1

2x - 4 + 7 > -1

2x + 3 > -1

2x > -4

x > -2

2) 5 - 4x > 9

-4x > 4

x < -1

Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x-13-(7*x^14)=0

Equation at the end of step 1

 (4x - 13) -  7x14  =

Pulling out like terms

3.1     Pull out like factors :

  -7x14 + 4x - 13  =   -1 • (7x14 - 4x + 13)

Equation at the end of step

 -7x14 + 4x - 13  = 0

Equations of order 5 or higher:

4.1     Solve   -7x14+4x-13 = 0

Answer:

x=3

Step-by-step explanation:

What u should always do is look at the letters of the triangles given:

It will tell u that:

[tex] \frac{tu}{dc} = \frac{uv}{cb} [/tex]

Now we once again just sub in the values:

[tex] \frac{12}{9} = \frac{20}{4x + 3} [/tex]

we can simplify the fraction on the right

[tex] \frac{4}{3} = \frac{20}{4x + 3} [/tex]

And now we cross multiply

3×20=4(4x+3)

60=16x+12

60-12=16x

48=16x

Therefore :

x=3

Answer:

[tex]\sqrt 10y[/tex]

Step-by-step explanation:

10*[tex]\sqrt{y}[/tex] is [tex]\sqrt 10y[/tex]

[tex]\sqrt{100y}[/tex]

Step-by-step explanation:

Recall that

[tex]10 = \sqrt{100}[/tex]

So we can write our original expression as

[tex]10\sqrt{y} = \sqrt{100}\sqrt{y}[/tex]

[tex]\;\;\;\;\;\;\;\;\;=\sqrt{100y}[/tex]

I assume a is a constant. If tan(x) = exp(at) (where exp(x) means eˣ), then differentiating both sides with respect to t gives

sec²(x) dx/dt = a exp(at)

Recall that

sec²(x) = 1 + tan²(x)

Then we have

(1 + tan²(x)) dx/dt = a exp(at)

(1 + exp(2at)) dx/dt = a exp(at)

dx/dt = a exp(at) / (1 + exp(2at))

If exp(y) = 1 + exp(2at), then differentiating with respect to t yields

exp(y) dy/dt = 2a exp(2at)

(1 + exp(2at)) dy/dt = 2a exp(2at)

dy/dt = 2a exp(2at) / (1 + exp(2at))

By the chain rule,

dy/dx = dy/dt • dt/dx = (dy/dt) / (dx/dt)

Then the first derivative is

dy/dx = (2a exp(2at) / (1 + exp(2at))) / (a exp(at) / (1 + exp(2at))

dy/dx = (2a exp(2at)) / (a exp(at))

dy/dx = 2 exp(at)

Since dy/dx is a function of t, if we differentiate dy/dx with respect to x, we have to use the chain rule again. Suppose we write

dy/dx = f(t)

By the chain rule, the derivative is

d²y/dx² = df/dx

d²y/dx² = df/dt • dt/dx

d²y/dx² = (df/dt) / (dx/dt)

d²y/dx² = 2a exp(at) / (a exp(at) / (1 + exp(2at)))

d²y/dx² = 2 (1 + exp(2at))

Answer:

x=9

Step-by-step explanation:

since the triangles are similar, the sides are all in proportion. This means that:

[tex] \frac{uw}{eg} = \frac{uv}{fg} [/tex]

Now we can just sub in the sides:

[tex] \frac{91}{13} = \frac{56}{x - 1} [/tex]

simplify the first fraction

[tex] \frac{7}{1} = \frac{56}{x - 1} [/tex]

Now we can cross multiply

56=7(x-1)

56=7x-7

63=7x

Therefore:

×=9