Please put a picture

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

$\fbox {Pythagorean equation:}$ 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).

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

Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term s

vesna_86 [32]

(1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2)

In adding polynomials, make sure that each term is grouped together.

1.3t³ + 0.4t² - 24t
 + 0.6t² - 18t + 8
1.3t³ + 1.0t² - 42t + 8

In a polynomial equation, arrangement of each term is dependent on the exponential number. It should be from the highest exponent to the lowest.

4 0

3 years ago

Read 2 more answers

Need answers before 8pm!!

GaryK [48]

We have similar triangles so

12/x = (12+78)/(x+13)

We can skip some algebra by doing the ratio on the pieces. We'll show it works at the end.

12/x = 78/13

x = 12(13)/78 = 2

We check

12/2 = 6

(12+78)/(2+13) = 90/15 = 6, good

Answer: x=2

8 0

3 years ago

2248/98 as a mix fraction?

Anarel [89]

The answer is 22 46/49
Answer:
= 2248/1 ÷ 98/1

= (2248 × 1) / (98 × 1)

= 2248/98

= 1124/49

= 22 46/49

3 0

3 years ago

Tim works for a company his normal rate of pay is 10 per hour on Friday Tim worked 4 hours overtime his overtime pay is 1 1/2 ti

Flauer [41]

Answer:

60 .

Step-by-step explanation:

Normal pay for 4 hours = 10 * 4 = 40.

Overtime for 4 hours = 40 * 1 1/2

= 60.

5 0

3 years ago