PLSSSSS HELP ME I WILL GIVE BRAINLIEST!!!!!!

Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th

Sati [7]

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is $\frac{1}{t}$

∵ The rate of Mary is $\frac{1}{t+3}$

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by $\frac{1}{2}$ (their rate together)

∴ $\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}$

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ $\frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}$

- Add the two fractions in the left hand side

∴ $\frac{t+3+t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{2t+3}{t^{2}+3t}=\frac{1}{2}$

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

OR

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

8 0

3 years ago

Solve for x:<br> 3x – 2(6 - x) = 7x + 2(5 + x) – 6

MAVERICK [17]

Answer:

-4

Step-by-step explanation:

3x-2(6-x)=7x+2(5+x)-6

First, distribute.

3x+ −12+ 2x = 7x + 10 + 2x −6

Combine like terms on each side.

5x − 12= 9x + 4

To solve for x, pick a side to solve. I will solve the right x.

5x - 12 = 9x + 4

-5x -5x

-12 = 4x + 4

Subtract 4 to isolate the variable.

-16 = 4x

Divide 4.

-4 = x

4 0

2 years ago

11. For a math homework assignment, Karla found the

riadik2000 [5.3K]

Answer:

Option C. 12 by 15

Step-by-step explanation:

Let the length be L

Let the width be w

Area of rectangle = L x w

Perimeter of rectangular = 2 (L + w)

From the question given,

A = 180

P = 54

180 = L x w (1)

54 = 2(L + w) (2)

From equation (2),

54 = 2(L + w)

Divide both side by the 2

54/2 = L + w

27 = L + w

L = 27 — w (3)

Substituting the value of L into equation (1), we have:

180 = L x w

180 = w(27 — w)

180 = 27w — w^2

Rearrange the expression

w^2 — 27w + 180 = 0 (4)

Solving by factorization method:

Multiply the first term (i.e w^2) with the last term (i.e 180). This gives 180w^2. Now find two factors of 180w^2, such that their sum will result to the second (i.e —27w). These factors are —12w and —15w.

Now, substitute these factors (—12w and —15w) into equation (4)

w^2 — 27w + 180 = 0

w^2 — 12w —15w + 180 = 0

w(w — 12) — 15(w — 12) =0

(w — 12) (w — 15) = 0

w = 12 or w = 15.

Substituting the value of w into equation (3)

L = 27 — w

When w = 12

L = 27 — 12 = 15

When w = 15

L = 27 — 15 = 12

Since the length is longer than the width, the length is 15 and the width is 12.

Therefore the dimensions is 12 x 15

6 0

3 years ago

What is the degree of the polynomial -2x3y2+6x4?

ser-zykov [4K]

The degree of the polynomial is 4

4 0

3 years ago

Between which two ordered pairs does the graph of f(x) = one-halfx2 + x – 9 cross the negative x-axis?

Doss [256]

None of Option are correct

Step-by-step explanation:

The Given function is f(x) = y = $\frac{1}{2} x^{2} + x -9$

Here, f(x) is quadratic function and it asked that when function cross the Negative X-axis.

If any function cross the X-axis then, Point of intersection will have y component as zero.

Therefore, f(x) = y = $\frac{1}{2} x^{2} + x -9$

y = $\frac{1}{2} x^{2} + x -9 = 0$

Solving quadratric equation,

Comparing with $ax^{2} + bx + c= 0$

We get a= $\frac{1}{2}$ , b=1, c=(-9)

Since,

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$x=\frac{- 1+\sqrt{(1)^{2}-4(\frac{1}{2})(-9) }}{2(\frac{1}{2})}$

$x=\frac{-1+\sqrt{1+(2)(9)}}{1}$

$x=\frac{-1+\sqrt{19}}{1}$

$x=-1+\sqrt{19}and x=-1-\sqrt{19}$

Thus, None of option are correct.

Verification.....

A) (–6, 0) and (–5, 0) give quadratic function : y = $x^{2} + 11x +30$

B) (–4, 0) and (–3, 0) give quadratic function : y = $x^{2} + 7x +12$

C) (–3, 0) and (–2, 0) give quadraric function : y = $x^{2} + 5x +6$

D) (–2, 0) and (–1, 0) give quadratic function : y = $x^{2} + 3x +2$

3 0

3 years ago

Read 2 more answers