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4 years ago

Can someone explain the answer and how the formula works?

Mathematics

1 answer:

zubka84 [21]4 years ago

7 0

Answer:

A = 346.185 cm²

Step-by-step explanation:

The formula given is:

A = πr²

A = Area of the object (circle).

π = 3.14

r = radius, which is 1/2 of the diameter, a straight line from one end to the other.

Set the equation, plug in the corresponding numbers to the corresponding variables:

A = (3.14)(10.5)²

Simplify. Remember to follow PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

and is the order of operation.

First, solve the exponent.

(10.5)² = 10.5 * 10.5 = 110.25

Next, multiply:

A = (3.14)(110.25)

A = 346.185 cm²

A = 346.185 cm² is your answer.

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Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$

Midpoint of given line

$= ( \frac{3 - 9}{2} , \frac{1 - 5}{2} )$

$= ( \frac{ - 6}{2} , \frac{ - 4}{2} )$

$= ( - 3 , - 2)$

Substituting (-3, -2) into the equation:

-2= -2(-3) +c

-2= 6 +c

c= -2 -6 (-6 on both sides)

c= -8

Thus, the equation of the perpendicular bisector is y= -2x -8.

5 0

3 years ago

Daisy's teacher asked her class to draw a triangle whose sides measured 2 inches, 3 inches, and 4 inches. She correctly drew the

harina [27]

Answer:

I dont think so since a triangle adds to 180 degrees

Step-by-step explanation:

but im stuck between c and d

sorry I couldnt complete;ly answer it for u!

have a nice day!

4 0

3 years ago

Can someone help!!! ASAP

vekshin1

4/5 because look at the picture

6 0

4 years ago

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Katena32 [7]

Answer:

A) A = 27.3°, B = 56.1°, C = 96.6°

Step-by-step explanation:

Use the Law of Cosines:

A = arccos [(b² + c² - a²)/(2bc)] = arccos [(13.2² + 15.8² - 7.3²)/(2*13.2*15.8)] = 27.3°
B = arccos [(a² + c² - b²)/(2ac)] = arccos [(7.3² + 15.8² - 13.2²)/(2*7.3*15.8)] = 56.1°
C = 180° - (A + B) = 180° - (27.3° + 56.1°) = 96.6°

Correct choice is A.

3 0

3 years ago

What is the zero in the quadratic function f(x)= 9x^2-54x-19?

Alex17521 [72]

Answer:

6.33... and 0.333...

Step-by-step explanation:

The quadratic formula is

$x=\frac{-b+\sqrt{b^2-4ac} }{2a}$ .

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}$

We will now solve for the plus and the minus.

The plus,,,

$x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3$

and the minus...

$x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...$

8 0

4 years ago