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oksano4ka [1.4K]
1 year ago
9

Fiona wrote the linear equation y = x – 5. When Henry wrote his equation, they discovered that his equation had all the same sol

utions as Fiona’s. Which equation could be Henry’s?
Mathematics
2 answers:
Oliga [24]1 year ago
7 0
His equation could be written in quadratic form, which is ax^2+bx=c                     


AVprozaik [17]1 year ago
6 0

Answer with Step-by-step explanation:

Fiona wrote the linear equation y = x – 5.

Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s.

Henry's equation could be any equation which is a constant multiple of Fiona's equation.

i.e. it could be

2y=2(x-5)

i.e. 2y=2x-10

Hence, Henry's equation could be:

2y=2x-10

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A coordinate plane with a straight line with a positive slope. The line starts at (0, 0) and passes through points labeled A at
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1...2....0.5 are the answers

Step-by-step explanation:

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A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at
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Answer:

dx/dt  =  0,04 m/sec

Step-by-step explanation:

Area of the circle is:

A(c) =π*x²      where   x is a radius of the circle

Applying differentiation in relation to time we get:

dA(c)/dt   =  π*2*x* dx/dt    

In this equation we know:

dA(c)/dt  = 0,5 m²/sec

And are looking for dx/dt then

0,5  = 2*π*x*dx/dt    when the area of the sheet is 12 m²  (1)

When  A(c) = 12 m²      x = ??

A(c)  =  12  =  π*x²      ⇒    12  =  3.14* x²    ⇒  12/3.14  =  x²

x²  = 3,82     ⇒   x  = √3,82    ⇒  x = 1,954 m

Finally plugging ths value in equation (1)

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The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its la
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Answer:

x = 31 hundred dolars   and      

y = 91/2 = 45.5 hundred dolars

Step-by-step explanation:

Given

R(x) = (40−8x+5y)*x + (50+9x−7y)*y

C(x) = (40−8x+5y)*10 + (50+9x−7y)*29

We can use the equation

P(x) = R(x) - C(x)

where

P(x) is the profit

R(x) is the revenue

and C(x) is the costs

In order to maximize the telephone company's profit, we apply

P'(x) = R(x)' - C(x)' = 0

⇒ R(x)' = ((40−8x+5y)*x + (50+9x−7y)*y)' = (40x-8x²+14xy+50y-7y²)'

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⇒ P'(x) = -8x²-7y²-141x+203y+14xy-1850

The first-order partial derivatives of these functions are

Px(x,y) = -16x-141+14y

Py(x,y) = -14y+203+14x

Setting these equal to zero and solving we obtain:

-16x+14y-141 = 0

14x-14y+203=0

we get the solution

x = 31     and       y = 91/2 = 45.5

Finally, the company should produce  3100  units of the first system, and  4550 units of the second system.

8 0
2 years ago
Fredrick and Kate have 1713 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for b
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Answer:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used.

Step-by-step explanation:

Fredrick and Kate have 17 1/3 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for banana bread that calls for 1 5/8 cups of flour. Kate has a recipe that calls for 1 3/4 cups of flour. Select all the statements that are true about the recipes.

1. Fredrick's recipe will make 10 whole loaves.

2. Kate's recipe will make 11 whole loaves.

3. There will be less flour left over if Frederick's recipe is used.

4. There will be less flour left over if Kate's recipe is used.

5. More loaves of bread can be made using Frederick's recipe than Kate's recipe.

Solution:

Total cups of flour = 17 1/3

Fredrick recipe = 1 5/8 cups of flour

Kate = 1 3/4 cups of flour

Number of banana bread made with Fredrick's recipe = Total flour / flour per Fredrick's recipe

= 17 1/3 ÷ 1 5/8

= 52/3 ÷ 13/8

=52/3 × 8/13

= 416 / 39

= 10.67 loaves of banana bread

Number of banana bread made with Kate's recipe = Total flour / flour per Kate's recipe

= 17 1/3 ÷ 1 3/4

= 52/3 ÷ 7/4

= 52/3 × 4/7

= 216 / 21

= 10.29 loaves of banana bread

The true statements are:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used

5 0
2 years ago
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