Which fraction is equivalent to<br> ?<br> -3/2

The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

$\fbox {Pythagorean equation:}$ <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

$H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17$

H = 17

If we decrease the base and the height by 2 centimeters, we have

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

$H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3$

$H' \approx 14.3$

So, the hypotenuse decreases $H - H' \approx 17 - 14.3 = 2.7$

3 0

3 years ago

What is the sales of volume V, of a particular product with a net income of $5000 given a sales price of $40, a variable cost of

iVinArrow [24]

Answer:

The sales of volume V, of a particular product with a net income of $5000 given a sales price of $40, a variable cost of $15?and $1000 in fixed cost is 240

Step-by-step explanation:

Given:

Net income= $5000

sales price= $40

variable cost =$15 and $1000

To Find:

sales of volume V=?

Solution:

We Know that

$\text {Income}=40 * x$

Where x= number of units sold

Similarily,

$\text { Net Income }=40 \mathrm{x}-\text { VARIABLE } \cos \mathrm{T} * \mathrm{x}-1000$

Substituting the known values,

$\text { Net Income }=40 \mathrm{x}-\text{VARIABLE COST} * \mathrm{x}-1000$

$5000=40 \mathrm{x}-15 * \mathrm{x}-1000$

Sloving the equation,

$5000=40 \mathrm{x}-15 \mathrm{x}-1000$

$5000=25 \mathrm{x}-1000$

$5000+1000=25 \mathrm{x}$

$6000=25 \mathrm{x}$

$x=\frac{6000}{25}$

$x=240$

5 0

3 years ago

The graph of 2x-3=12 crosses the x axis

vovangra [49]

Where is crosses the x axis is the x intercept
it is also when y=0
so set y to zero
2x-3y=12
2x-3(0)=12
2x-0=12
2x=12
divide by 2
x=6
t
the y intercept=6 or (6,0)

3 0

4 years ago

Read 2 more answers

Garth is giving 10 of the action figures from his collection to his brother. If a represents the number of action figures Garth

lawyer [7]

The answer is “a-10”
have a great dayyy!!! :)

4 0

3 years ago

Numbers 11,12,13 and 14

leonid [27]

Answer:

11. ×8; ×27; ÷8

12. ÷16; ÷256; ×16

13. ×8

14. ×4

Step-by-step explanation:

11. g(x) =5x³

g₁ = 5x₁³

g₂ = 5x₂³

g₂/g₁ = (x₂/x₁)³

a. x is doubled. g₂/g₁ = (2x₁/x₁)³ = 2³ = 8

If x is doubled, g is multiplied by eight.

b. If x is tripled, g₂/g₁ = (3x₁/x₁)³ = 3³ = 27

If x is tripled, g is multiplied by 27.

c. If x is halved, g₂/g₁ = (½x₁/x₁)³ = (½)³ = ⅛

If x is halved, g is divided by 8.

12. ƒ(x) = 3/x⁴

f₁ = 1/x₁⁴

f₂ = 1/x₂⁴

f₂/f₁ = (x₁/x₂)⁴

a. x is doubled. f₂/f₁ = (x₁/2x₁)⁴ = (½)⁴ = 1/16

If x is doubled, f is divided by 16.

b. If x is quadrupled, f₂/f₁ = (x₁/4x₁)⁴= (¼)⁴ = 1/256

If x is tripled, f is divided by 256.

c. If x is halved, f₂/f₁ = [x₁/(½x₁)]⁴ = 2⁴ = 16

If x is halved, f is multiplied by 16.

13. V = ⁴/₃πr³

V₁ = ⁴/₃πr₁³

V₂ = ⁴/₃πr₂³

V₂/V₁ = (r₂/r₁)³

r is doubled. V₂/V₁ = (2r₁/r₁)³ = 2³ = 8

The volume of the sphere is multiplied by 8.

14. V = πr²h

V₁ = πr₁²h

V₂ = πr₂²h

If r is doubled and h stays the same, V₂/V₁ = (2r₁/r₁)² = 2² = 4

The volume of the cylinder is quadrupled.

6 0

3 years ago

Which fraction is equivalent to ? -3/2