5. A fan has three thin blades that spin to
produce a breeze. The diameter of the fan is
16 inches.
a. Determine the length of an arc between
two consecutive fan blades.
b. What is the area of each sector formed
by the radii passing through the center of
consecutive fan blades?
c. What is the angular velocity if the tip of
each blade in the fan moves 8m radians
in 2 seconds?

Answer:

15) Ellen is 12 years old.

16) Don't know what value you are looking for but x=(17/4) while y=(7/4) since the set of equations is 2x-2y=5 and x+y=6.

Step-by-step explanation:

15) Ellen (E) is currently twice as old as Maria (M).

Twice means to multiply by 2.

E=2M is therefore the equation for this part of the problem.

In 6 years, Maria (M) will be 2/3 as old as Ellen (E).  Keep in my Maria as aged 6 years (M+6) and Ellen as aged 6 years (E+6):

M+6=(2/3)(E+6).

So we have this system to solve:

E=2M

M+6=(2/3)(E+6).

I'm going to replace the E in the second equation with 2M since the first equation says E=2M:

M+6=(2/3)(E+6) with E=2M:

M+6=(2/3)(2M+6)

Distribute:

M+6=(4/3)M+(12/3)

Reducing 12/3 to 4:

M+6=(4/3)M+4

Subtract 4 on both sides:

M+2=(4/3)M

Subtract M on both sides:

2=(4/3)M-M

Find a common denominator:  

2=(4/3)M-(3/3)M

Combine like terms:

2=(1/3)M

Multiply both sides by the reciprocal of 1/3 which is 3:

3(2)=3(1/3)M

6=1M

6=M

M=6

Maria is six years old.

Recall E=2M.

So if M=6, then E=2(6)=12.

So currently E is twice as old as M since 6(2)=12.

In six years, M will be 12 which E will be 18.

M (12) is two-thirds as old as E (18) since 12=2/3(18)

16)

2x-2y=5

 x + y=6

Your question doesn't state which value it is looking for.

Anyways I'm going to solve the system for the point (x,y) and then you can decide which part of this answer to use.

I'm going to solve this system by elimination.  Each equation already has the same form: ax+by=c. I just need a column with the variables to be opposite or the same.

I'm going to multiply both sides of equation 2 by 2:

2x-2y=5

2x+2y=12

Now I have opposites in a column: -2y and 2y.

When you add opposites you get 0 so this is what you want to use elimination.

We are going to add the equations now:

2x-2y=5

2x+2y=12

------------------Adding!

4x+0y=17

4x      =17

Divide both sides by 4:

 x      =17/4

Now if x=17/4 and x+y=6, then we have that (17/4)+y=6.

Subtracting 17/4 on both sides gives us y=6-(17/4).

Finding a common denominaotr gives us y=(24/4)-(17/4).

Simplifying this gives us y=(7/4).

The point of intersection (the solution) is (17/4 ,  7/4)

The question is about solving two mathematical problems. The first problem is about ages, where Ellen is found to be 12 years old and Maria is six years old. The second problem is solving a linear equation system where the solution is x = 5 and y = 1.

Let's denote Maria's age as X and Ellen's age as Y. According to the problem, Ellen is twice as old as Maria, so that we can write Y = 2X. Maria will be 2/3 as old as Ellen in six years, so we can write another equation as X + 6 = 2/3 * (Y + 6). Now, we solve these equations. Substituting Y = 2X into the second equation, we get X + 6 = 2/3 * (2X + 6). Solving this, we find X = 6, so Maria is 6. Substituting X = 6 into Y = 2X, we find Y = 12, so Ellen is 12 years old.

For the second part of the problem, we solve the system of equations 2x - 2y = 5 and x + y = 6. One way is to take the second equation and solve for x: x = 6 - y. Substituting this into the first equation, we get 2*(6-y) - 2y = 5. Solving this simplifies to y = 1. Then, covering y = 1 into x + y = 6, we find x = 5.

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Answer:

2160°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 14, hence

sum = 180° × 12 = 2160°

Answer:0.035

Step-by-step explanation:

I used a calculator and put in 15 / 4 and got 0.035

Charlie should divide the 15 cents into four bags with 1 cent, 2 cents, 4 cents, and 7 cents respectively. Using combinations of these bags, he can pay any amount between 1 cent and 15 cents without opening them.

The question asks us to figure out how Charlie can divide 15 cents among four small bags so he can use these bags to pay any amount between 1 cent and 15 cents without opening them.

To solve this, we need to think about the binary representation of numbers, because each bag can either be used or not used in each transaction, similar to how a binary '1' or '0' can represent 'on' or 'off'.

Therefore, he should put the amounts that correspond to the powers of 2 in three of the bags: 1 cent, 2 cents, and 4 cents, and in the last bag, we put the sum of these three, which is 7 cents.

This way, he can make any amount up to 15 cents:

Answer:

The correct option is B

Step-by-step explanation:

The equation of a line in point-slope form is:

y-y1 = m(x-x1)

where m is the slope and (x1,y1) a point on the line

here m=2 and (x1,y1)=(2,3)

substitute these values into the equation.

y-3 =2(x-2)

Thus the correct opttion is B....

Answer:

(-inf, 3)

Step-by-step explanation:

-13x > - 39

Multiply by -1/13, and flip the inequality.

x < 3

Answer:

[tex]\huge\boxed{x<3}[/tex]

Step-by-step explanation:

Multiply -1 both sides.

[tex]\displaystyle (-13x)(-1)<-39(-1)[/tex]

Solve.

[tex]\displaystyle 13x<39[/tex]

Divide by 13 both sides.

[tex]\displaystyle\frac{13x}{13}<\frac{39}{13}[/tex]

Simplify, to find the answer.

[tex]\displaystyle 39\div13=3[/tex]

[tex]\displaystyle x<3[/tex], which is our answer.

Answer:

The correct answer is option C.

Step-by-step explanation:

Weight of George = 14 pounds

Weight of Igor = 6 pounds

Difference between weight of cats :

= 14 pounds - 6 pounds = 8 pounds

This means that George is 8 pounds more in weight than Igor.

Answer:

The answer is 3x^2+7x+2

Step-by-step explanation:

Multiply each term of the second bracket with the first bracket.

We can write:

(x+2)(3x+1)= 3x(x+2)+1(x+2)

By multiplying the terms we get:

=3x^2+6x+x+2

Now simplify by combining like terms:

=3x^2+7x+2

Thus the answer is 3x^2+7x+2....

Answer:

3x² + 7x + 2

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(3x + 1) + 2(3x + 1) ← distribute both parenthesis

= 3x² + x + 6x + 2 ← collect like terms

= 3x² + 7x + 2

The solution is, It would take 6 hours, to visit his aunt who lives.

What is speed?

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

here, we have,

given that,

Paul wants to visit his aunt who lives 300 miles away from his house. He drives his car at about 50 miles/hour.

If x represents the time spent driving.

then, we get,

An equation for that could be:

50x = 300 (X is how long it would take)

So, 50 mph• X (time spent) = 300 miles

now, we have,

50x = 300

or, x = 300/50

or, x = 6

Hence, The solution is, It would take 6 hours, to visit his aunt who lives.

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Step-by-step explanation:

Olivia is correct.  Each O is opposite of the angle θ, and each A is adjacent.

Paula's first triangle was correct.  But on the second triangle, she reversed the O and A.

Answer:

-2

Step-by-step explanation:

The rate of change is

roc = f(x2) - f(x1)

        ---------------

         x2 -x1

x2 is the last point or 15

x1 is the first point or 10

f(15) = 10 from the graph

f(10) = 20 from the graph

roc = f(15) - f(10)

        ---------------

         15-10

roc = 10 - 20

        ---------------

         15-10

roc = -10

        --------

            5

roc = -2

A. X=0 Y=5

Those 2 equations are a system. You answer is the value of x and y.

13x+3y=15

y=5-4x

First, lets make each equation fit into y=mx+b

13x +3y=15 y=5-4x

-13x -13x y=-4x+5

3y= -13x +15

Let's use the elimination method to solve this.

y= -4x+ 5 multiply top by 3

3y=-13x+15

3y=-12x+15

3y=-13x+15 subtract the equations

0=x

Lets use the x we just found to solve for y.

y=4x+5

y=4(0)+5

y=5

Answer:

A. (1.55, 2)

Step-by-step explanation:

The formula to apply when finding the midpoint of a segment where the coordinates of the end points are given is;

[tex]midpoint=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

where (x₁,y₁) and (x₂,y₂) are the coordinates of the end points

Given;

x₁= -0.4 ,y₁=2.5,  x₂=3.5, y₂=1.5 then applying the formula for midpoint

[tex]=(\frac{-0.4+3.5}{2} ,\frac{2.5+1.5}{2} )\\\\\\=(\frac{3.1}{2} ,\frac{4.0}{2} )\\\\\\=(1.55,2.0)[/tex]

[tex]\bf tan(39^o)=\cfrac{\stackrel{opposite}{x}}{\stackrel{adjacent}{8}}\implies 8\cdot tan(39^o)=x\implies 6.48\approx x \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(39^o)}{x}=\cfrac{sin(51^o)}{8}\implies \cfrac{8\cdot sin(39^o)}{sin(51^o)}=x\implies 6.48\approx x[/tex]

one thing to bear in mind is that calculators have two modes, Degree mode and Radian mode, if your calculator is in Radian mode and you plug in tan(39), it thinks "tangent of 39 radians" and so it gives that, bearing in mind that 1 radian is about 57°.

So make if you're using degrees as the angle, make sure your calculator is in Degree mode first, thus tan(39) will mean "tangent of 39 degrees".

[tex]\bf 8\cdot tan(39~rad) \approx 28.9~\hspace{10em} \cfrac{8\cdot sin(39~rad)}{sin(51~rad)}\approx 11.5[/tex]

Answer:

The answer in the procedure

Step-by-step explanation:

we have

2x-3y=-1 ----> equation A

3x+3y=26 --> equation B

Solve the system by elimination

Adds equation A and equation B

2x-3y=-1

3x+3y=26

----------------

2x+3x=-1+26

5x=25

x=25/5

x=5

Find the value of y

substitute the value of x in equation A or equation B and solve for y

2(5)-3y=-1

10-3y=-1

3y=10+1

y=11/3

Answer:

5x=25

Step-by-step explanation:

A p e x

Answer:

D[3, 3], C[1, 4], B[0, 1], A[4, -1]

Step-by-step explanation:

Whenever you are doing a 90° clockwise rotation ABOUT THE ORIGIN, it is in the form of [y, -x], meaning you take the y and make it your x, then take your original x and put its OPPOSITE.

90° counterclockwise rotation → [-y, x]

90° clockwise rotation → [y, -x]

I hope this helps, and as always, I am joyous to assist anyone at any time.

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for third angle

∠C = 180° - (50 + 75)° = 180° - 125° = 55°

∠B = 180° - (60 + 30)° = 180° - 90° = 90°

∠A = 180° - (45 + 30)° = 180° - 75° = 105°

The required measure of the angle for the given triangles is given as ∠C  = 55°, ∠B  = 90° and ∠A = 105°

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for the third angle

∠C = 180° - (50 + 75)°
     = 180° - 125°
      = 55°

Similarly,

∠B  = 90°

∠A = 105°

Thus, the required measure of the angle for the given triangles is given as ∠C  = 55°, ∠B  = 90° and ∠A = 105°

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Answer:

The values of a and b are a = 11 , b = 7

Step-by-step explanation:

* Lets explain how to solve the problem

* In the exponential functions we have some rules

1-  In multiplication if they have same base we add  the power

# Ex: b^m  ×  b^n  =  b^(m + n) ⇒ b is the base , m and n are the powers

2- In division if they have same base we subtract  the power

# Ex: b^m  ÷  b^n =  b^(m – n) ⇒ b is the base , m and n are the powers

3- If we have power over power we multiply them

# Ex: (b^m)^n = b^(mn) ⇒ b is the base , m and n are the powers

* Lets solve the problem

∵ The equation is [tex](5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{a}y^{2}[/tex] ⇒ (1)

- At first multiply the coefficients

∵ -4 × 5 = -20

- Multiply the base x

∵ [tex](x^{7})(x^{4})=x^{7+4}=x^{11}[/tex]

- Multiply the base y

∵ [tex](y^{2})(y^{5})=y^{2+5}=y^{7}[/tex]

∴ [tex](5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{11}y^{7}[/tex] ⇒ (2)

- By comparing (1) and (2)

∴ a = 11 and b = 7

* The values of a and b are a = 11 , b = 7

Answer:

DH and HF correspond.

Step-by-step explanation:

The order matters in a congruence statement.

You are given Figure GHF=Figure EHD.

I say the order matters in a congruence statement because it tells you the parts that correspond.

Angles G and E correspond because they are both first.

Angles H and H correspond because they are both second.

Angles F and D correspond because they are both third.

The same thing works with the segments.

Segments GH and EH correspond because it goes first to second for both.

Segments HF and HD correspond because it goes second to third for both.

Segments FG and DE correspond because it goes third back to first for both.

I have named all the correspond parts for you congruence statement:

Figure GHF=Figure EHD.

So let's look at the choices.

DH and HF correspond.

Answer:

DH and HF correspond.

Step-by-step explanation:

Answer: [tex]\sqrt[3]{-62}[/tex]

Step-by-step explanation:

It is important to remember the following:

[tex]a^{(\frac{1}{n})=\sqrt[n]{a}[/tex]

In this case we have:

[tex]-62^{\frac{1}{3}[/tex]

Then, in order to simplify it, we need to rewrite it in radical form, where the index of the root will be 3 and the radicand will be -62.

Therefore, the simplified form is this:

[tex]-62^{\frac{1}{3}}=\sqrt[3]{-62}[/tex]

Answer: -4

Step-by-step explanation: I put it in Desmos calc.

Answer:

-8x+10

Step-by-step explanation:

The expression is: -2(3x+x-5)

Step 1: Using order of operations, combine like terms

-2(4x-5)

Step 2: Distribute -2 to each term in the  parentheses:

-8x+10

Hence, the simplified expression is:

-8x+10

Answer:

-8x+10

Step-by-step explanation:

on edge

Answer:

$69.50

Step-by-step explanation:

First you need to know how much wall you're going to cover.

Each wall us 12 ft by 8ft

The area of a rectangle can be computed with the formula:

A = L x W

Using the given:

A = 12ft x 8 ft

  = 96 ft²

This is the area of each wall. Since all 4 walls will be covered, you multiply the area of 1 wall by 4.

96 ft² x 4 = 384 ft²

Next we subtract the area of the windows and the door because we won't be covering that.

384 ft² - 52 ft² = 332 ft²

So the total area we are covering with wall paper is 332 ft².

To get the cost of the wallpaper needed, we just need to compute first how many bolt we will need. Divide the total area to be covered by the area of one bolt of wall paper.

332 ft² ÷ 72 ft²/bolt = 4.61 bolts ≅ 5 bolts

Then we multiply it by the price per bolt:

5 bolts x $13.90/bolt = $69.50

bearing in mind that a diagonal line from the center of a square will give us an isosceles triangle, Check the picture below.

Answer:

The area of this polygon is 98.1 yd²

Step-by-step explanation:

Check the image below.

The diagonal line from the corner of a square to the center of this one will shape an isosceles triangle.

The Pythagoras theorem give us the following formula:

A² + A² = H²

Both "A" are the sides and H is the hypotenuse, seeing the figure, the diagonal coincide with the hypotenuse and the measure is 7 yd.

A² + A² = 72  

2A² = 49

A²= 49/2

A²= 24. 5

A=√24.5

A= 4.95 yd

Knowing that the diagonal ends up in the center of the square, we assume that the side of the triangle (“A” side) is the half of the side of the square, then this last one is 2A. Bearing in mind that square have all of the sides with the same measure, the four sides have a 2A size.

2A = 2(4.95) =9.9 yd

Each side of the square measures 9.9 yd

The area of a square is  

Side²= (2A)2²

(9.9)²= 98.1 yd²

The area of this polygon is 98.1 yd²

Answer:

2304

Step-by-step explanation:

The volume of the sphere is 2304π cubic units or 7238.229 cubic units if the radius is 12 units.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]

We have a radius of the sphere R = 12 units

Volume:

[tex]\rm V = \dfrac{4}{3} \pi (12)^3[/tex]

V = 2304π cubic units or

V = 7238.229 cubic units

Thus, the volume of the sphere is 2304π cubic units or 7238.229 cubic units if the radius is 12 units.

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In the word "Mathematical"

Vowels are "a", "e", "a", "i", "a" from left to right

Consonants are "m", "t", "h", "m", "t", "c", "l"

5 vowels and 7 consonants of total 12 letters

So the probability of picking a vowel is

[tex] \frac{5}{12} [/tex]

Answer:

The probability to pick a vowel is   [tex]\frac{5}{12} }[/tex]

Step-by-step explanation:

Probability = Required outcome / All possible outcome

From the question;

the word “Mathematical” is written on individual pieces of paper

We have to count the total numbers of letter present in the word

When we count properly, we have 12 total numbers of letters

The we proceed to count the numbers of vowel

Here are the vowel in the word  “Mathematical” :

a, e, a, i, a

The vowels are 5 letters

Probability = Required outcome / All possible outcome

Required outcome = 5

All possible outcome = 12

Probability =  [tex]\frac{5}{12} }[/tex]

The probability that you pick a vowel  is  [tex]\frac{5}{12} }[/tex]

Answer: 252

Step-by-step explanation:

A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

Answer:

Step-by-step explanation:

When one variable depends on another variable according to a rule it is known as function:

For example if you want an output of 2 and the input value is 4. Then you will subtract 4 from x

We have to find x f(x).

x f(x) =?

f(x) = x-4

Now input value is:  x= 3

x f(x)

3 (x-4)

3 (3-4)

3 -1

Now x= 4

x f(x)

4 (x-4)

4 (4-4)

4 0

Now x=5

x f(x)

5 (x-4)

5 (5-4)

5 1

Now x=6

x f(x)

6 (x-4)

6 (6-4)

6 2 ....

[tex]\sqrt{\dfrac{3}{15x}}=\sqrt{\dfrac{1}{5x}}=\dfrac{1}{\sqrt{5x}}=\dfrac{\sqrt{5x}}{5x}[/tex]

Slope intercept form is [tex]y=mx+b \to y=-3x+4[/tex]

Answer:

y=-3x+4

Step-by-step explanation:

Slope-intercept form is y=mx+b

where m is the slope and b is the y-intercept.

m=-3 because -3 is the slope.

b=4 because 4 is the y-intercept.

Let's plug that into y=mx+b giving us y=-3x+4.

Answer:

There is no real solutions

Step-by-step explanation:

We have to count delta:

∆=(-3)²-4*8*1=-23.

Because ∆ is less than zero, your equation has only 2 imaginary solutions.

This equation hasn't got any real solutions (because √∆ isn't real)

Answer:

There are 0 real number solutions.

Step-by-step explanation:

You can use the discriminant to find the number of real number solutions.

The discriminant equation is:

[tex] {b}^{2} - 4ac[/tex].

a=1

b=-3

c=8

If the discriminant is positive, there are 2 real number solutions. If the discriminant is negative, there are 0 real number solutions. If the discriminant is 0, there is 1 real number solution.

[tex] {( - 3)}^{2} - 4(1)(8)[/tex]

= 9 - 32

= -23

The discriminant is negative.

0 real number solutions.