MATHEMATICS HIGH SCHOOL

a recipe that makes 12 muffins calls for 2 1/2 cups of flour. how much flour is needed to make 18 muffins

Answers

Answer 1
Answer:

Answer:  3(3)/(4) cups of flour

=============================

Work Shown:

A = 12 muffins

B = 2.5 cups of flour

C = 18 muffins

D = x cups of flour

A/B = C/D

12/2.5 = 18/x

12x = 2.5*18

12x = 45

x = 45/12

x = 3.75

x = 3(3)/(4)

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Jill is building a wooden raised bed garden for her vegetable she wants the frame to have dimension X feet by X +3 feet if she wants the garden to have a maximum area of 50 ft.² what are the possible values of X

Answers

Answer: 0ft < X ≤ 5.73ft

Step-by-step explanation:

In this case, we have a rectangle.

For a rectangle of length L and width W, the area is:

A = L*W.

And we have:

L = X

W = X  + 3ft.

Then the area will be:

A = X*(X + 3ft) = X^2 + 3ft*X.

And we want to have a maximum area of 50ft^2.

Then we can write:

A = X^2 + 3ft*X ≤ 50ft^2

Now let's solve this for X.

Now, the first thing we can see is that both coefficients in our quadratic equation are positive, so as the absolute value of X increases, also does the whole equation.

Then makes sense start for the upper limit of X, this is when:

X^2 + 3ft*X = 50ft^2.

Now we can solve the quadratic equation:

X^2 + 3ft*X - 50ft^2 = 0

Applying the Bhaskara formula, the solutions are:

X = (-3ft +- √((3ft)^2 - 4*1*(-50ft^2)) )/(2) = (-3ft +-14.46ft )/(2)

Then we have two solutions:

X = (-3ft - 14.46ft)/2 = -8.73 ft.

X = (-3ft + 14.46ft)/2 = 5.73 ft

Because X represents a distance, it can only be positive, then we must select the option X = 5.73ft.

This is the maximum value of X, and we will have:

0ft < X ≤ 5.73ft

Where the lower limit is there because we can not have X = 0ft, as this does not have physical meaning.

7
Solve the equation x^2 - 8x + 15 = 0.

Answers

Answer:

x=5   x=3

Step-by-step explanation:

x^2 - 8x + 15 = 0

Factor

What 2 numbers multiply to 15 and add to -8

-5*-3 = 15

-5-3 = -8

(x-5)(x-3) =0

Using the zero product property

x-5 =0    x-3 =0

x=5   x=3

Answer:

x = -5

Evidence to support reasoning:

The diagram shows 2 wheels of radii 15 cm and 24 cm. Their centres, H and K, are 41 cm apart. ( Refer to the attatchment given )Help me find the lengthof the belt by providing workings. Thanks!

Answers

Hello,

1) \ncos(\widehat{HKR})= (9)/(41) ==\ \textgreater \ \widehat{HKR}=1.34948188...rad\n\nsin(\widehat{KHR})= (9)/(41) ==\ \textgreater \ \widehat{KHR}=0,22131444...rad\n\n

\widehat{QKA}=\pi-1,34948188...=1,792110769...rad\n\n$\overset{\frown}{QA}$=24*1,792110769...=43,010658459...\n\n\widehat{KHB}= (\pi)/(2)-0,22131444...=1,3494888...\n\n$\overset{\frown}{PB}$=15*1,3494888...=20,2422282\n\n

2)
|HR|=√(9^2+41^2) =41,976183723\n\n


length=2*(43,010658459+20,2422282+41,976183723)=210,458140764

3g-2+7g+8=
What is this

Answers

Answer:

10g+6 is the answer

Step-by-step explanation:

Solve each system by elimination:
10x+8y= -18
8x+8y= -24

Answers

Answer:

Step-by-step explanation:

10x + 8y = -18

-8x - 8y = 24

2x = 6

x = 3

8(3) + 8y = -24

24 + 8y = -24

8y = -48

y = -6

(3, -6)
(3,-6) would be the answer to this question

6 + V196
4
What’s the two solutions

Answers

Answer:

hi

Step-by-step explanation:
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