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3 years ago

Oder the Decimals below from least to greatest. 2.09 2.9 2.19 2.009 2.901

Mathematics

2 answers:

ehidna [41]3 years ago

7 0

Here's the order:
2.009,2.09,2.19,2.9,2.901
(what i think)

Katen [24]3 years ago

5 0

2.009 2.09 2.19 2.9 2.901

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The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio

kap26 [50]

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

the translation

∵ The general form of the quadratic function is

f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

(h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right

by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left

by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up

by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down

by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)² ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

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3 years ago

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Lisa’s grades on four exams were 80, 92, 86, and 78. What is the lowest grade she can receive on the next exam to have an averag

Andre45 [30]

Answer: It is 86 because it says lowest and greater than

85 so there is your answer have a nice day

Step-by-step explanation:

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3 years ago

HELLLLLPPPPPPPPPP FASTTTTTTT<br><br> -(8x-3)59

vagabundo [1.1K]

Answer:

-472x+ 177

Step-by-step explanation:

-(8x-3)59

-59(8x-3)

-59*8x-(-59)*3

-59*8x+59*3

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3 years ago

A chocolate manufacturing company produces two types of chocolate: A and B. Ingredients required for manufacturing the products

Karolina [17]

Answer:

The maximum profit is when they make 10 units of A and 2 units of B.

Step-by-step explanation:

Let x is units of milk

Let y units of cacao

Given that :

The company's production plant has a total of 22 units of milk and 46 units of cacao available.

2x + y ≤ 22 (2 unit of milk for each of A and 1 for B; 22 units available)

4x + 3y ≤46 (4 unit of milk for each of A and 3 for B; 46 units available

Graph the constraint equations and find the point of intersection to determine the feasibility region.

The intersection point (algebraically, or from the graph) is (10, 2)

The objective function for the problem is the total profit, which is $6.2 per unit for A and $4.2 per unit for B: 6.2x + 4.2y.

Hence, we substitute (10, 2) into the above function:

6.2*10 + 4.2*2 = 70.4

The maximum profit is when they make 10 units of A and 2 units of B.

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3 years ago

What would prove that the two triangles are<br> congruent?

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The lines on the sides!

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3 years ago

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