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2 years ago

The PTO is hosting a donut and coffee day at the shcool. Each box of donuts and costs $9.00 and each cup of

Mathematics

1 answer:

vodka [1.7K]2 years ago

3 0

Answer:

The school where the donut and coffee day will take place.

The number of boxes of donuts the PTO bought.

The number of cups of coffee the PTO bought.

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Which of the following sets of lengths can Sean use to make a right triangle?

Aleks [24]

Answer:

{8 cm, 15 cm, 17 cm}

Step-by-step explanation:

we know that

The length sides of a right triangle must satisfy the Pythagoras Theorem

$c^2=a^2+b^2$

where

c is the greater side (the hypotenuse)

a and b are the legs (perpendicular sides)

Verify each case

case 1) we have

{5 cm, 15 cm, 18 cm}

substitute in the formula

$18^2=5^2+15^2$

$324=250$ ----> is not true

therefore

Sean cannot make a right triangle with this set of lengths

case 2) we have

{6 cm, 12 cm, 16 cm}

substitute in the formula

$16^2=8^2+12^2$

$256=208$ ----> is not true

therefore

Sean cannot make a right triangle with this set of lengths

case 3) we have

{5 cm, 13 cm, 15 cm}

substitute in the formula

$15^2=5^2+13^2$

$225=194$ ----> is not true

therefore

Sean cannot make a right triangle with this set of lengths

case 4) we have

{8 cm, 15 cm, 17 cm}

substitute in the formula

$17^2=8^2+15^2$

$289=289$ ----> is true

therefore

Sean can make a right triangle with this set of lengths

6 0

2 years ago

Can yall help me with this tell me your answer step by step plz

Ludmilka [50]

He will have 30 % in 2 years which is 30.00 dollars

6 0

2 years ago

Read 2 more answers

Please please help me no links

Slav-nsk [51]

pretty sure it’s 108 because each angle of a pentagon is 108

4 0

3 years ago

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x

nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

$f_x=8x$

$f_y=4y$

$g_x=3$

$g_y=3$

Setting up the Lagrange multiplier equations:

$f_x=\lambda g_x$

⇒ 8x = 3λ .....................(1)

$f_y=\lambda g_y$

⇒ 4y = 3λ ......................(2)

constraint: 3x + 3y = 108 .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728 ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944 ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0

1 year ago

Answer choices are: x=20 x=22 x=10 x=11

Vlada [557]

The answer would be 22

6 0

2 years ago