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3 years ago

The diagram shows a sector OAPB of a circle, centre O.

Mathematics

1 answer:

Iteru [2.4K]3 years ago

5 0

Answer:

4.44 cm²

Step-by-step explanation:

If the diagram attached below is required to complete the question,

Applying,

Area of the shaded segment(A) = Area of the sector- area of the triangle

A = (πr²∅/360)-(r²sin∅/)2................ Equation 1

Where r = radius of the circle, ∅ = angle at the center of the circle,π = pie

From the question,

Given: r = 5.4 cm, ∅ = 72°

Constant: π = 3.14

Substitute these values into equation 1

A = (3.14×5.4²×72/360)-(5.4²/2×sin72)

A = 18.31-13.87

A = 4.44 cm²

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Find the vertex of the parabola f(x)=x2-6x+13

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Rewrite in standard form using (h,k) to find the vertex.
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3 years ago

Find x, y, and z x = 39 x = 29 y = 61 y = 29 z = 61 z = 29

nikdorinn [45]

answer:

x = 29

y = 29

z = 61

step-by-step explanation:

all angles in a triangle must equal 180 degrees.

we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.

the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.

so to figure out y,

we must add 61+90 and then subtract the sum of that from 180.

so, 61+90 = 150 and 180-151 = 29

therefore,

we can conclude that y = 29

now, to determine the degrees of x and z we do the same thing.

we already know one angle equals 90 degrees.

180-90 = 90

that concludes that x and z must have a sum of 90.

if we use our choices,

39+61 = 100 (no)

39+29 = 68 (no)

29+61 = 90 (CORRECT)

29+29 = 28 (no)

therefore, x = 29 and z = 61

so, in total :

x = 29

y = 29

z = 61

hope this helps :)

-audrey <3

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2 years ago

Find the measure of each angle indicated

Alenkinab [10]

The measure of the angle is 150 degrees.

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3 years ago

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two

Oliga [24]

Let

x-------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of the rectangle is equal to

$A=x*y$

The area of the two congruent right triangles is equal to the area of the rectangle

$A=2*44=88\ in^{2}$

$88=x*y$ -------> equation A

$y=x-3$ -----> equation B

Substitute equation B in equation A

$x*[x-3]=88$

$x^{2} -3x-88=0$ --------> equation that can be used to solve for the length of the rectangle

Using a graph tool-------> solve the quadratic equation

see the attached figure

The solution is

$x=11\ in$ -----> the length of the rectangle

Find the value of y

$88=11*y$

$y=8\ in$ ----> the width of the rectangle

Statements

case A) The area of the rectangle is $88$ square inches

The statement is True

See the procedure

Case B) The equation $x*[x-3]=44$ can be used to solve for the dimensions of the triangle

The statement is False

Because, the equation $x*[x-3]=88$ can be used to solve for the dimensions of the triangle

case C) The equation $x^{2} -3x-88=0$ can be used to solve for the length of the rectangle

The statement is True

see the procedure

case D)The triangle has a base of $11$ inches and a height of $8$ inches

The statement is True

Because, the base of the triangle is equal to the length of the rectangle and the height of the triangle is equal to the width of the rectangle

case E) The rectangle has a width of $4$ inches

The statement is False

See the procedure

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3 years ago

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If your total grocery store purchase is $19.83, and he gives the cashier $50.00, how much change will I get?

scZoUnD [109]

Answer:

50 - 19.83 = $30.17

Step-by-step explanation:

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2 years ago