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Rainbow [258]
3 years ago
7

Factor the polynomial completely using the

Mathematics
2 answers:
ElenaW [278]3 years ago
4 0

Answer:

(-6-2√3,0)(-6+2√3,0)

if im not mistaken

DerKrebs [107]3 years ago
4 0

Answer:(x+12)(x+12)

Step-by-step explanation:

You might be interested in
Please help me thanks :)
Lina20 [59]

Answer:

A

Step-by-step explanation:

To sovle this we must combine the numbers togther and the variables togther.

We have:

8c+6-3c-2

Lets take out the c's and combine them:

8c -3c

=

5c

Now lets take out the numbers:

6-2

=

4

Now lets put these back together and we get the expression:

5c+4

This looks like A.

Hope this helps! :D

8 0
2 years ago
Javier asks his mother how old a tree in their yard is. His mother says, "The sum of 10 and two-thirds of that tree's age, in ye
Sloan [31]

Answer:

His error is adding 10 and 2/3 before multiplying by a(age of the tree)

Step-by-step explanation:

The sum of 10 and two-thirds of that tree's age, in years, is equal to 50.

Correct equation

Sum = addition (+)

two-thirds = 2/3

The tree's age = a

10 + 2/3a = 50

2/3a = 50 - 10

2/3a = 40

a = 40 ÷ 2/3

= 40 × 3/2

= 60

a = 60 years

Javier writes the equation

(10 + two-thirds) a = 50

(10 + 2/3)a = 50

(30+2/3)a = 50

32/3a = 50

a = 50 ÷ 32/3

= 50 × 3/32

= 150/32

a = 150/32

His error is adding 10 and 2/3 before multiplying by a(age of the tree)

5 0
3 years ago
The equation of function h is h... PLEASE HELP MATH
Flura [38]

Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

There is a constant difference between each two consecutive values of x and also in y, then the table represents a linear function

The form of the linear function is m(x) = a x + b, where

  • a is the slope of the function
  • b is the y-intercept

The slope = Δm(x)/Δx

∵ At x = 8, m(x) = 2

∵ At x = 10, m(x) = 3

∴ The slope = \frac{3-2}{10-8}=\frac{1}{2}

∴ a = \frac{1}{2}

- Substitute it in the form of the function

∴ m(x) = \frac{1}{2} x + b

- To find b substitute x and m(x) in the function by (8 , 2)

∵ 2 = \frac{1}{2} (8) + b

∴ 2 = 4 + b

- Subtract 4 from both sides

∴ -2 = b

∴ m(x) = \frac{1}{2} x - 2

Now let us answer the questions

Part A:

∵ h(x) = \frac{1}{2} (x - 2)²

∴ h(4) = \frac{1}{2} (4 - 2)²

∴ h(4) = \frac{1}{2} (2)²

∴ h(4) =  \frac{1}{2}(4)

∴ h(4) = 2

∵ m(x) = \frac{1}{2} x - 2

∴ m(16) =  \frac{1}{2} (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = \frac{1}{2} (x - 2)²

∵ x = 0

∴ h(0) = \frac{1}{2} (0 - 2)²

∴ h(0) =  \frac{1}{2} (-2)² =  

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = \frac{1}{2} x - 2

∵ x = 0

∴ m(0) = \frac{1}{2} (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

- Find the distance between y = 2 and y = -2

∴ The difference between the y-intercepts of the graphs = 2 - (-2)

∴ The difference between the y-intercepts of the graphs = 4

∴ The y-intercepts are 4 units apart

Part C:

The minimum/maximum point of a quadratic function f(x) = a(x - h) + k is point (h , k)

Compare this form with the form of h(x)

∵ h = 2 and k = 0

∴ The minimum point of the graph of h(x) is (2 , 0)

∵ k is the minimum value of f(x)

∴ 0 is the minimum value of h(x)

∴ The domain of h(x) is all real numbers

∴ The range of h(x) is h(x) ≥ 2

∵ m(8) = 2

∵ m(14) = 5

∵ h(8) = \frac{1}{2} (8 - 2)² = 18

∵ h(14) = \frac{1}{2} (14 - 2)² = 72

∴ h(x) is always > m(x)

∴ m(x) can not exceed h(x) for any value of x

<em>Look to the attached graph for more understand</em>

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

7 0
3 years ago
R leaks out of a barrel so that the rate of change in the water level is proportional to the square root of the depth of the wat
Irina-Kira [14]
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
  y'(t) = k√(y(t)) . . . . for some proportionality constant k
  y(0) = 30
  y(1) = 29

We observe that a function of the form
  y(t) = a(t - b)²
will have a derivative that is proportional to y:
  y'(t) = 2a(t -b)

We can find the constants "a" and "b" from the given boundary conditions.
At t=0
  30 = a(0 -b)²
  a = 30/b²
At t=1
  29 = a(1 - b)² . . . . . . . . . substitute for t
  29 = 30(1 - b)²/b² . . . . . substitute for a
  29/30 = (1/b -1)² . . . . . . divide by 30
  1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
  b = 30 +√870 . . . . . . . . simplify

The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
5 0
3 years ago
Please someone help me!!! its urgent!
I am Lyosha [343]

Answer:

<em>12.99</em>

Step-by-step explanation:

<em>a²+b²=c²</em>

<em>a²+b²=c²√91²+√78²=c²</em>

<em>a²+b²=c²√91²+√78²=c²√8281+√6084=c²</em>

<em>a²+b²=c²√91²+√78²=c²√8281+√6084=c²91+78=c²</em>

<em>a²+b²=c²√91²+√78²=c²√8281+√6084=c²91+78=c²169=c²</em>

<em>a²+b²=c²√91²+√78²=c²√8281+√6084=c²91+78=c²169=c²c=√169</em>

<em>a²+b²=c²√91²+√78²=c²√8281+√6084=c²91+78=c²169=c²c=√169 =13</em>

8 0
2 years ago
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