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2 years ago

Evaluate the expression: 2/3-1/4+(-5/6)

Mathematics

1 answer:

Aliun [14]2 years ago

3 0

Answer:

$\\ \frac{2}{3} - \frac{1}{4} + \frac{( - 5)}{6}$

$\\ = \frac{2}{3} - \frac{1}{4} - \frac{5}{6}$

$\\ = \frac{8 - 3 - 10}{12}$

$\\ = \frac{8 - 13}{12}$

$\\ = \frac{ - 5}{12}$

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For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perim

Marina86 [1]

Area of the shaded region $$=36(\pi -2)$ square cm

Perimeter of the shaded region $=6 (\pi + 2\sqrt 2)$ cm

Solution:

Radius of the quarter of circle = 12 cm

Area of the shaded region = Area of quarter of circle – Area of the triangle

$$=\frac{1}{4} \pi r^2 - \frac{1}{2} bh$

$$=\frac{1}{4} \pi \times 12^2 - \frac{1}{2} \times 12 \times 12$

$$=36\pi -72$

$$=36(\pi -2)$ square cm.

Area of the shaded region $$=36(\pi -2)$ square cm

Using Pythagoras theorem,

$AC^2=AB^2+BC^2$

$AC^2=12^2+12^2$

$AC^2=288$

Taking square root on both sides of the equation, we get

$AC= 12\sqrt 2$ cm

Perimeter of the quadrant of a circle = $\frac{1}{4} \times 2\pi r$

$$=\frac{1}{4} \times 2 \times \pi \times 12$

$$=6 \pi$ cm

Perimeter of the shaded region = $6 \pi + 12\sqrt 2$ cm

$=6 (\pi + 2\sqrt 2)$ cm

Hence area of the shaded region $$=36(\pi -2)$ square cm

Perimeter of the shaded region $=6 (\pi + 2\sqrt 2)$ cm

6 0

2 years ago

Write a verbal sentence to represent each equation.<br> 8+3x=5

gladu [14]

Answer:

eight plus three times a number

Step-by-step explanation:

I think I'm wrong I don't know I'm not really the master at this (but feel free to do tell me if I'm wrong)

7 0

2 years ago

Read 2 more answers

I need fast help with step by step<br> <img src="https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_1%20%7B%5Cfrac%7B3x-1%7D%7Bx%2B1%7D

Ganezh [65]

Answer:

1.38 to the nearest hundredth.

Step-by-step explanation:

Dividing:

x + 1 ) 3x - 1 ( 3

3x + 3

-4

so (3x - 1) / (x + 1) = 3 - 4 / x+ 1

Integral of (3 - 4 / x+1 ) = 3x - 4 ln(x + 1)

Between limits of 1 and 2 we have:

(3(2) - 4 ln 3) - (3 - 4 ln2)

= 1.6056 - 0.2274

= 1.3782.

5 0

3 years ago

The height of a triangle is 2 less than 5 times it's base. If the base of the triangle is x feet, and the area of the triangle i

____ [38]

Answer:

Area A = 12 = 1/2 × x × (5x-2)

5x^2 - 2x -24 = 0

Solution;

Base x = 2.4

Height h = 10 ft

Step-by-step explanation:

Given;

base of the triangle is x feet;

Base = x

The height of a triangle is 2 less than 5 times it's base;

Height = 5x - 2

the area of the triangle is 12 square feet;

Area A = 12 ft^2

The area of a triangle is;

Area A = 1/2 × base × height

Substituting the base and height;;

Area A = 1/2 × x × (5x-2)

Area A = 1/2 × (5x^2 - 2x)

Area A = 12

12 = 1/2 × (5x^2 - 2x)

Multiply through by 2.

24 = (5x^2 - 2x)

5x^2 - 2x -24 = 0

Solving the simultaneous equation;

x = 2.4 or -2

Since the base cannot be negative;

x = 2.4 ft

Height h = 5x -2 = 5(2.4) - 2 = 12 - 2 = 10 ft

Base x = 2.4

Height h = 10 ft

6 0

2 years ago

Marvin is buying a watch from his brother

I am Lyosha [343]

Answer:

$30 down

and 10 installments of $10 each

Step-by-step explanation:

paying $30 down means the left price to divide into installments is : 130-30 = 100

since he will pay the rest in equal installments, we divide by the number of installments to get how much each one will be :

100/10 = $10

3 0

3 years ago