Rose’s checking account has a balance of -$54. She makes no more withdrawals but deposits $15 per day in her account over the next 5 days. On the sixth day, she makes no deposits, but the bank charges a maintenance fee of $5. What is the balance in her account on the sixth day?

Answer:

L = B + 3  ..................(1)

L × B = 270  m²  .................(2)

on solving we get

L = 18 m, B = 15 m

Step-by-step explanation:

Let the length of the rectangle be L

and,

Width of the rectangle be 'B'

thus,

according to the question

L = B + 3  ..................(1)

And, area of the rectangle = 270 m²

also,

Area of the rectangle = L × B = 270  m²  ...........(2)

on substituting 'L' from equation 1 in equation 2, we get

( B + 3 ) × B = 270

or

B² + 3B - 270 = 0

or

B² + 18B - 15B - 270 = 0

or

B( B + 18 ) - 15(B + 18) = 0

or

( B - 15 ) × ( B + 18 ) = 0

thus, we get

B = 15 m (accepted ) and B = -18 m (neglected : since the length cannot be negative)

therefore,

From 1, we get

L = 15 + 3 = 18 m

Answer: c.(3, 25) and (7, 9)

y = –x^2 + 6x + 16 and y = –4x + 37

Plug in -4x+37 for y in first equation . It becomes

Combine like terms. add 4x  and subtract 37 on both sides

Divide the whole equation by -1 to remove negative sign from -x^2

Now factor the left hand side

(x-7)(x-3) = 0

x-7 =0  and x-3=0

x= 7  and x=3

Now we find out y using y = –4x + 37

when  x= 7 , then y=-4(7) +37 = 9

when x= 3, then y=-4(3) + 37 = 25

We write solution set as (x,y)

(7,9)  and (3,25) is our solution set

Answer:

• cylinder — 90π in³
• pyramid — 37 1/3 in³
• cone — 12.5π in³

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = Bh . . . . . where B is the base area and h is the height

The volume of a pyramid or cone is given by ...

  V = (1/3)Bh . . . . . where B is the base area and h is the height

The area of a square of side length s is ...

  A = s²

The area of a circle of radius r is ...

  A = πr²

___

Using these formulas, the volumes of these objects are ...

  cylinder: (9π in²)(10 in) = 90π in³

  square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³

  cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid

Answer:

12.5

Step-by-step explanation:

Hi Ponie

Simplify both sides of the equation

3-x/5-4-x/2=1

3+ -1/5 x+ -4+ -1/2 x =1

Combine like terms

(-1/5 x + -1/2 x)+(3+-4)=1

-7/10 x +-1=1

-7/10 x -1=1

Add 1 to both sides

-7/10 x-1+1=1+1

-7/10 x=2

Multiply both sides by 10/-7

(10/-7)*(-7/10 x )= (10/-7)*2

x= -20/7

I hope that's help and I am sorry for the late answer !

Answer:

Length of an isosceles triangle is, 3.12 m

Step-by-step explanation:

Given: Perimeter of an isosceles triangle is 15.6 m.

Let a be the length of sides and b be the base of an isosceles triangle respectively.

To find the length of the sides(a);

Isosceles triangle is a triangle with two equal sides and two equal base angles.

Perimeter of the isosceles triangle is the sum of the three sides i,e

Perimeter(P) = a +b +a = 2a +b              

also it is given that; the base is 3 m bigger than a leg.

⇒ b = 3 a

Substitute this in perimeter formula;

P = 2a +3a =5a

Substitute the value of perimeter = 15.6 m

we have;

Divide both sides by 5 we get;

Simplify;

a  = 3.12 m

Therefore, the length of the sides of an isosceles triangle is, 3.12 m

Answer:

The legs are 4.2m long.

The base is 7.2m long.

Step-by-step explanation:

x=leg

y=base

We can write two equations with the information given.

y=x+3

2x+y=15.6

We can solve this as a system of equations.

y=x+3

-(2x+y=15.6) - make the bottom equation negative.

-2x=x-12.6 - add the bottom to the top, canceling out the y.

-2x+12.6=x - add 12.6 to both sides.

12.6=3x - add 2x to both sides.

4.2=x - divide both sides by 3.

x=4.2

Now we can solve for y.

y=x+3

y=(4.2)+3 - substitute in the x.

y=7.2