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kolbaska11 [484]
3 years ago
8

A bag contains purple marbles and white marbles, 34 in total. The number of purple marbles is 1 less than 4 times the number of

white marbles. How many purple marbles are there?
Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
3 0

There are 27 purple marbles

Step-by-step explanation:

Let p be the purple marbles

and

w be the white marbles

Then according to given statements

p+w = 34\ \ \ Eqn\ 1\\p = 4w-1\ \ \ Eqn 2

Putting p = 4w-1 in equation 1

4w-1 +w = 34

Adding one on both sides

5w-1+1 = 34+1\\5w = 35

Dividing both sides by 5

\frac{5w}{5} = \frac{35}{5}\\w = 7

Putting w = 7 in equation 2

p = 4(7)-1\\p = 28-1\\p = 27

Hence,

There are 27 purple marbles

Keywords: Linear equation

Learn more about linear equations at:

  • brainly.com/question/2116906
  • brainly.com/question/2131336

#LearnwithBrainly

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Answer:

The perimeter is 8 cm.

Yes, the perimeter of a square is directly proportional to its side length.

Step-by-step explanation:

Given:

The side length of the square is, a=2\ cm

The perimeter of a square is the sum of all of its side lengths. The perimeter of a square of side length 'a' is given as:

P=a+a+a+a=4a

Plug in a=2\ cm and find perimeter, 'P'. This gives,

P=4\times 2=8\ cm

Therefore, the perimeter is 8 cm.

Now, two quantities are directly proportional only if their ratio is a constant.

Let us find the ratio of 'P' and 'a'.

We have, P=4a

Dividing both sides by 'a', we get:

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Therefore, the ratio of perimeter and side length is a constant. Hence, these are directly proportional quantities.

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3 years ago
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Step-by-step explanation:

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A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a
Komok [63]

Answer:

a) 64 feet

b)  3 seconds

Step-by-step explanation:

a)

The maximum height of h=h(t) can be bound by finding the y-coordinate of the vertex of y=-16x^2+32x+48.

Compare this equation to y=ax^2+bx+c to find the values of a,b,\text{ and } c.

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The x-coordinate of the vertex can be found by evaluating:

\frac{-b}{2a}=\frac{-32}{2(-16)

\frac{-b}{2a}=\frac{-32}{-32}

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y=-16(1)^2+32(1)+48

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y=16+48

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So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

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I'm going to divide both sides by -16:

0=t^2-2t-3

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

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The second equation can be solved by subtracting 1 on both sides: t=-1.

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