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2 years ago

Sophia's mom spent on party bags and ice cream for her birthday party.

Mathematics

1 answer:

Katen [24]2 years ago

5 0

Answer & Step-by-step explanation:

i = 2

b = 150

---------------------------------------------------------------------------------------------------------------

The equations:

i= b-148

b= i+148

b-i = 148

I am not really sure which equation you want, but I hope this helps!!!

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Chad earned $30 for raking leaves. He has also earned money by doing chores for 6 weeks. Altogether, he has earned $120. How muc

galben [10]

You know that he makes $90 for doing chores, dividing that by 6 and you get that each week he earns $15 for chores.

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2 years ago

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

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3 years ago

Assume that price is an integer variable whose value is the price (in US currency) in cents of an item. Assuming the item is pai

cestrela7 [59]

Answer:

$Change = (Paid*100) - Price$

Step-by-step explanation:

First of all we need to know the relation between 1 dollar and 1 cent in order to express everything in the units required in the question.

We know that $1 dollar = 100 cents$ , so the amount paid for the item with single dollars has to be multiplied by 100 to express its value in cents.

$Paid_{cents}=Paid_{dollars}*100$

Now that we have everything in cents, we can make the subtraction:

$Change_{cents} = Paid_{cents} -Price_{cents}$

Replacing the value in cents we get:

$Change = (Paid*100) - Price$

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3 years ago

Construct a triangle with side lengths 6,6 and 6. what are the angle measures of a triangle

Ann [662]

Answer:

60 degrees

Step-by-step explanation:

Hello! The side lengths of this triangle are all the same, so this is an equilateral triangle. These types of triangles have equal angles. A triangle equals 180 degrees so divide that by three. Each angle in this triangle is 60 degrees. Hope this helps :)

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2 years ago

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Passes through (-4, -5), slope = 3/4

ra1l [238]

Answer:

Step-by-step explanation:

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