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3 years ago

How much of the circle is shaded? Write your answer as a fraction in simplest form?

Mathematics

2 answers:

VladimirAG [237]3 years ago

4 0

Shaded area = 1 - Un-shaded area
S. area = 1 - (1/2 + 1/7)
S. area = 1 - (7+2) /14
S. area = 1 - 9/14
S. area = 5/14

So, your final answer is 5/14

Hope this helps!

JulijaS [17]3 years ago

3 0

Answer:

$5/14$

Step-by-step explanation:

Let

x-----> the shaded area

we know that

$x+\frac{1}{7}=\frac{1}{2}$

solve for x

Multiply by $14$ both sides

$14x+2=7$

$14x=7-2$

$14x=5$

Divide by $14$ both sides

$x=5/14$ ----> fraction irreducible

You might be interested in

What is the value of 5k + m when k = -3 and m = - -9? A. -60 B. -30 C.-24 D. -6

sladkih [1.3K]

Answer:

C. -24

Step-by-step explanation:

$5k + m \\ k = - 3 \\ m = - 9$

Plug in values into the given equation

$5( - 3) + ( - 9) \\ - 15 - 9 \\ = - 24$

6 0

3 years ago

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

3 0

3 years ago

How many ways can you arrange the letters in the word prime?

Jobisdone [24]

There are 5 letters in the word "prime"

Imagine we had 5 slots to fill. They are empty initially.
Slot 1 has 5 choices to pick from
Once we pick a letter, we have 4 choices left over for slot 2
Slot 3 will have 3 choices
Slot 4 will have 2 choices
Slot 5 will have 1 choice

We have this countdown: 5,4,3,2,1

which multiplies out to 5*4*3*2*1 = 120

There are 120 unique ways to arrange the letters. Order matters. Because order matters, this is a permutation.

7 0

3 years ago

To hang lights up on his house.Garrett place is a 14 foot ladder 4 feet from the base of the house. How high up the house will t

Mariulka [41]

This seems like a right triangle problem.

So assuming 14 feet is the hypotenuse and 4 feet is a leg of the right triangle, we can use the pythagorean theorem ( $a^{2} +b^{2} =c^{2}$ ) to solve for the height of the house, in which we shall name it x.

So, the equation is $4^{2} +x^{2} =14^{2}$ .

Solve for x:

16+x^{2}= 196

x^{2}= 196-16

x^{2}= 180

x = 6√5 feet

Hope this helps!

6 0

2 years ago

Read 2 more answers

Factor this trinomial completely.

zmey [24]

First you want to write 7x as a sum or difference: 15x-8x
Now, the expression would look like this: 10x^2+15x-8x-12
Next, factor out the 5x and -4 from the expression: 5x(2x+3)-4(2x+3)
Now, factor out the 2x+3 from the expression and you have your answer:
(2x+3)(5x-4)

4 0

3 years ago