A client has asked you to put together a quote for converting their Oast House.

Determine whether a triangle can be formed with the given side lengths.

choli [55]

We can use triangle inequality to prove it. What this rule is, it's basically if u add up 2 sides of the triangle, the length must be longer than the third side, check all 3 sides, and if all sides matches with the rule, a triangle is possible.

5 0

4 years ago

If you half the resistance does it double the current?

Inessa05 [86]

Answer:

Yes if the voltage is kept constant

Step-by-step explanation:

V=IR

6 0

3 years ago

Read 2 more answers

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

What is the sum of the first 10 terms in the sequence 1, 3/2, 9/4, 27/8, 81/16

Julli [10]

Answer:

This is GP and number of terms is 10 first term is 1 ratio is 3/2

Step-by-step explanation:

Using the formula u get sum as 113.33 (didn't calculate in fraction)

5 0

3 years ago

The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation

labwork [276]

Answer:

Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.

We know that radius is half of diameter.

$\text{Radius = }\dfrac{\text{Diameter}}{2}$

$\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}$

The equation for circle given the center and radius, can be represented as:

$(x-a)^{2}+ (y-b)^{2} = r^{2}$

Where (a,b) is the co-ordinate of center and r is the radius.

Let us consider the following formula:

$(p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq$

$(x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0$

Hence, Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

4 0

3 years ago