The radius of circle C is 6 units and the measure of central angle ACB is StartFraction pi Over 2 EndFraction radians. What is the approximate area of the entire circle? square units What is the approximate area of the entire sector created by central angle ACB? square units What is the approximate area of the shaded region only? square units

Answer:

a) Angle 1 = Value in degree = 95°

b)Angle 2 = Value in degree = 77°

c) Angle 3 = Value in degree = 85°

d) Angle 4 = Value in degree = 103°

Step-by-step explanation:

We use circle theorems to solve for this above question.

a) Angle 1 = Value in degree = 95°

Inscribed Angle is 1/2 of an Intercepted Arc

From the diagram, Angle 1 intersects at Arc B and Arc C

This means Angle 1 = (B + C)/ 2 =

Arc B = 100°

Arc C = 90°

Angle 1. = (100° + 90°)/ 2 = 190/ 2 = 95°

b)Angle 2 = Value in degree = 77°

From the diagram, Angle 2 intersects at Arc C and Arc D

Inscribed Angle is 1/2 of an Intercepted Arc

This means Angle 1 = (C+ D)/ 2

C = 90°

D = 64°

Angle 1. = (90° + 64°)/ 2 = 154/ 2 = 77°

c) Angle 3 = Value in degree = 85°

From the diagram, we can see that Angle 1 is opposite Angle 3, hence,

Opposite angles are supplementary which means their addition = 180°

Mathematically:.Angle 1 + Angle 3 = 180°

Angle 1 = 95°

95° + Angle 3 = 180°

Angle 3 = 180° - 95° = 85°

d) Angle 4 = Value in degree = 103°

From the diagram, we can see that Angle 2 is opposite Angle 4,

Hence,

Opposite angles are supplementary which means their addition = 180°

Mathematically:.Angle 2 + Angle 4 = 180°

Angle 2 = 77°

77° + Angle 3 = 180°

Angle 4 = 180° - 77° = 103°

Answer:

D) $0 Per Month.

Step-by-step explanation:

In January, Mr. Sanders spent $50 on gas. In May, Mr. Sanders spent $50 on gas. The amount that he spent on gas did not change from January to May, so the rate of change between January and May is D) $0 Per Month.

Hope this helps!

Answer:

-2

Step-by-step explanation:

8--2=8+2=10

7+-2=7-2=5

5x2=10.

Answer: A

Step-by-step explanation:

The equation given is y=1/2x-3. The y-intercept is the contant. It does not have any variable attached to it. The y-intercept is -3.

Answer:

A. -3

Step-by-step explanation:

The y intercept of a equation will always be the one that's has no variable beside it

Example: y=2x+5

In this equation, 5 is your y intercept

And 2 is your slope

Hope this helps!

Answer:

153.938 meters

Step-by-step explanation:

The area of a circle is Pi * (Radius)^2. The radius is the diameter/2.

14/2=7

Pi * (7)^2

153.938 m

Answer:

Step-by-step explanation:

[tex]d =14\\Area = \pi \times r^2\\r = d/2\\r = 14/2\\r= 7\\A = 22/7 \times 7^2\\\frac{22}{7} \times 49\\Simplify\\\frac{22}{1} \times 7\\Area =154[/tex]

[tex]A =\frac{1}{4} \pi \times d^2\\A = \frac{1}{4} \times \frac{22}{7} \times14^2\\A = 1/4\times22/7\times196\\A = 154cm^2[/tex]

Answer:

sin30° and cos60°

Step-by-step explanation:

We can see that we can use multiply trig identities to solve for r:

sin30° = r/20

r = 20sin30°

cos60° = r/20

r = 20cos60°

Answer:

no

Step-by-step explanation:

Since 4² + 8² = 10² is a false statement, 4, 8, 10 is not a Pythagorean Triple.

Answer:

a > 8

Step-by-step explanation:

a-3>5

Add 3 to each side

a-3+3>5+3

a > 8

Answer:

a > 8

Step-by-step explanation:

a - 3 > 5

Add 3 on both parts.

a - 3 + 3 > 5 + 3

The a variable must be on one side.

a > 8

Answer:

25 students are in the class.

Step-by-step explanation:

There are 3/5 girls, and there are 10 boys, so there are 2/5 boys. 5/5 is the whole class, so here is how we would solve it: 2/5=10  3/5=15, 10+15=25.  Hope this helps!

Find the age of the mammal hide to the nearest

The answer is 3425.

Be safe!

-Eli

:))

An: The person above is wrong the answer is actually 2744.

Step-by-step explanation:

Answer:

brainliest appreciated

Step-by-step explanation:

270- 216 = 54

so ...the percentage becomes

54/270 × 100 = 20%

Answer:

I think the answer is 33 I'm not sure but that is what I got

Answer:

They made 0 gain/loss.

Step-by-step explanation:

0 - 9 = -9

3 x 3 = 9

-9 + 9 = 0

Please tell me if I'm wrong.

Answer:

Option (E)

Step-by-step explanation:

Expression given in the attachment,

[tex]x-\frac{15}{x}=2[/tex]

By multiplying with x on both the sides of the given equation,

x² - 15 = 2x

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x(x - 5) + 3(x - 5) = 0

(x + 3)(x - 5) = 0

(x + 3) = 0

x = -3

And (x - 5) = 0

x = 5

Therefore, x = -3, 5 are the solutions of the given equation.

Option (E) will be the answer.

Answer:

[tex] \pm \frac{3}{7} [/tex]

Step-by-step explanation:

[tex] \huge \sqrt{ \frac{9}{49} } = \pm \frac{3}{7} \\ [/tex]

Answer: B ¥58,110

Step-by-step explanation:

$1 = ¥116.22

$500 = ?

= 500 x 116.22

= 58,110

Answer:

B

Step-by-step explanation:

1)

2, 5, 8, 11, 14

2)

0, 2, 8, 18, 32

3)

-6, -1, 2, 3, 10, 29

substitute the given values for x and do as the function says.

Answer:

The roots for the given equation are -8 and 3.

Step-by-step explanation:

The first thing we must do in order to find the roots is factor the equation. We can do this by first multiplying the first and last term together. Then, we find the factors of that product that multiply together to that product but also adds together to get the middle term in the equation.

x² * -24 = -24x²

-24x² = 8x * -3x

Now, we write our new equation by replacing 5x with 8x - 3x.

x² + 8x - 3x - 24

Group the first and second terms together and also group the last two terms together.

(x² + 8x) + (-3x - 24)

Factor each parentheses. You will know that you factored them correctly when the two terms in the final parentheses are the same.

x(x + 8) -3(x + 8)

Since the two terms in the parentheses are the same, hen we have correctly factored out the equation. Now, we form the equation so we can find the roots.

(x - 3)(x + 8)

Now, equal each term in the parentheses to zero.

x - 3 = 0

x + 8 = 0

Now, solve for x in each equation. The final answer for each equation will be our roots. The roots are the values of x in a quadratic equation.

x = 3

x = -8

So, the roots of this equation are {-8, 3}

Answer:

y = -7x + 499

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find slope m

m = (401 - 450)/(14 - 7)

m = -49/7

m = -7

y = -7x + b

Step 2: Find b

450 = -7(7) + b

450 = -49 + b

499 = b

Step 3: Rewrite equation

y = -7x + 499

Answer: 33 degrees

Step-by-step explanation: Angle x=angle m

Answer:

the triangle on the left is named XYZ

the triangle on the right is named MNL

therefore ∠X ≅ ∠M, ∠Y ≅∠N, and ∠Z ≅ ∠L

since ∠X = 33º, then ∠M = 33º

hope this helps :)

Answer:

x=63

z=72, y=45

Step-by-step explanation:

Angles "z+y" and "x" add up to 180°, so they are supplementary angles.

angle B=72+b+63=180⇒b=180-135=45

angle B=72+45=117

angle A+angle B=180

x+117=180

x=180-117=63

angle D+angle A=180

z=72, y=45  alternate angles (opposite angle of parallelogram are congruent)

x+z=117 = angle B

Answer: b and d

Step-by-step explanation:

On edge

Answer:

B. (7, 13/3)

Step-by-step explanation:

Since the graph doesn't show the intersecting point, we must use algebra to solve this (Substitution or elimination).

Step 1: Substitute y

1/3x + 2 = 4/3x - 5

Step 2: Isolate x

-x + 2 = -5

-x = -7

x = 7

Step 2: Find y using x

y = 1/3(7) + 2

y = 7/3 + 2

y = 13/3

Answer: 450

Step-by-step explanation:

971 = B + (T+71)

971-71 = 2 B

450 = B

Answer:

(D)[tex]3x+2 < -7$ or $3x+2 >7[/tex]

Step-by-step explanation:

Given the absolute inequality: [tex]|3x+2| >7[/tex]

When solving absolute inequalities, if the problem has a greater than sign we set up an "OR" compound inequality that looks like this:

Therefore, for the absolute inequality |3x+2| >7, we have:

[tex]3x+2 < -7$ or $3x+2 >7[/tex]

The correct option is D.

Answer:

x = 5

Step-by-step explanation:

Step 1: Write equation

-3/4 + 2/5x = 7/20x - 1/2

Step 2: Subtract 7/20x on both sides

-3/4 + 1/20x = -1/2

Step 3: Add 3/4 to both sides

1/20x = 1/4

Step 4: Divide 1/20 on both sides

x = 5

Answer: Answer: The answer is A,C,E

A: 2/5x = 7/20 x+ 1/4

C: -3/4 = -1/20 x -1/2

E: -3/4 + 1/20 x= -1/2

Step-by-step explanation:

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression. Since taking the square root is the same as raising to the power, is also an algebraic expression.

Answer:

13,-5,-35,-77,-131,-197

Step-by-step explanation:

To get from 13 to -5, you subtract 18 (or add -18)

To get from -5 to -35, you subtract 30

 To get from -35 to -77, you subtract 42

 Notice that the amount being subtracted is increasing by 12 each time.

 So the next subtraction will be 54, and the one after that will be 66.

 So the next term is -77 - 54 = -131

 And the term after that is -131 - 66 = -197

 So the sequence would be:  13,-5,-35,-77,-131,-197

Answer:

15, 36, 39

Step-by-step explanation:

Use the Pythagorean theorem.

a² + b² = c²

2² + 3² ≠ 13²

4² + 6² ≠ 10²

9² + 12² ≠ 18²

15² + 36² = 39²

Answer:

Step-by-step explanation:

[tex]Lets -test-using ;\\Pythagoras -Theorem=\\a^2+b^2=c^2\\\\(A.) 2,3,13\\2^2 +3^2 = 13^2\\13 = 169\\WRONG\\\\(B.) =4,6,10\\4^2+ 6^2 =10^2\\16+ 36 = 100\\52 = 100\\WRONG\\(C.) 9,12,18\\9^2+12^2=18^2\\225 = 324\\WRONG\\\\(D.) 15 , 36 ,39\\15^2 +36^2 = 39^2\\1521=1521\\\\CORRECT[/tex]