The edges of a cube measures 3 1/2 inches each. What is the volume of the cube, in cubic inches

Vadim26 [7]

Fifteen increased by a number

4 0

3 years ago

Suppose we have a right triangle with legs of length a and b and hypotenuse of length c. Suppose b=3 and c=5. Then a= , For the

ANTONII [103]

Answer:

Length of right-angle triangle 'a' = 4

b)

$sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$

$cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$

$tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$

Step-by-step explanation:

Step(i):-

Given b = 3 and hypotenuse c = 5

Given ΔABC is a right angle triangle

By using pythagoras theorem

c² = a² + b²

⇒ a² = c² - b²

⇒ a² = 5²-3²

=25 - 9

a² = 16

⇒ a = √16 = 4

The sides of right angle triangle a = 4 ,b = 3 and c = 5

Step(ii):-

$sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$

$cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$

$tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$

7 0

3 years ago

Stephen & Richard share a lottery win of £2950 in the ratio 2 : 3. Stephen then shares his part between himself, his wife &a

horsena [70]

Answer:

Stephen's wife got £354 more than his son.

Step-by-step explanation:

Given:

Amount of Lottery = £2950

Now Given:

Stephen & Richard share a lottery amount in the ratio 2 : 3

Let the common factor between them be 'x'.

So we can say that;

$2x+3x=2950\\\\5x = 2950$

Dividing both side by 5 we get;

$\frac{5x}{5}=\frac{2950}{5}\\\\x = 590$

So we can say that;

Stephen share would be = $2x =2\times 590 = \£1180$

Now Given:

Stephen then shares his part between himself, his wife & their son in the ratio 3 : 5 : 2.

Let the common factor between them be 'y'.

So we can say that;

$3y+5y+2y=1180\\\\10y=1180$

Dividing both side by 10 we get;

$\frac{10y}{10}=\frac{1180}{10}\\\\y=118$

So Stephen's wife share = $5y = 5\times 118= \£590$

And Stephen's son share = $2y=2\times118 =\£236$

Now we need to find how much more her wife got then her son.

To find how much more her wife got than her son we will subtract Stephen's son share from Stephen's wife share.

framing in equation form we get;

Amount more her wife got than her son = $590-236 = \£354$

Hence Stephen's wife got £354 more than his son.

3 0

3 years ago

What is the rate of change of the linear relationship modeled in the table (-2,5) (-1,4) (0,3) (1,2)

poizon [28]

The rate of change of the linear relationship is -1.

Explanation:

It is given that there is a linear relationship between all these points, these points lie on a straight line.

The equation to find the slope passing through two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the points $(-2,5)$ and $(-1,4)$ , we get,

$\begin{aligned}m &=\frac{4-5}{-1+2} \\&=\frac{-1}{1} \\&=-1\end{aligned}$

Thus, the slope is -1.

Thus, the rate of change of the linear relationship is -1.

8 0

4 years ago

Find the least number must be added to 4015 to make it a perfect square. also,find the square root of the perfect square so obta

Vladimir [108]

To solve this, I used guess and check.

I started by finding 60²=3600 and 70²=4900. 70² is too much, so I then did 65²=4,225.

After 65², I did 62²=3,844. I knew that was pretty close, so I did 64. 64²=4,096 and 63²=3,969. So, 64² was it.

4,096-4015=81

So, you would need to add 81 to 4015 in order to receive a perfect square, which is 64²(4,096).

7 0

3 years ago