Use the diagram to find the measure of the given angle.

Given angle: PRQ

Answer:

Mean Absolute Deviation = 3.

Step-by-step explanation:

The mean = (2 + 9 + 1 + 7 + 8 + 9) / 6

= 36/6

= 6.

Subtract  6 from each  number:

2 - 6 = -4 Absolute value = 4

9 - 6 = 3

1 - 6 = -5 Absolute value = 5

7 - 6 = 1

8 - 6 = 2

9 - 6 = 3

Total = 4 + 3 + 5 + 1 + 2 + 3 = 18

Mean Absolute Deviation = 18 / 6 = 3.

Answer:

B: 3

Step-by-step explanation:

First you will take the numbers and add them. The equation would be 2 + 9 + 1 + 7 + 8 + 9. That equals 36.

Then, you may divide that by 6 (how many numbers there were) and that is your mean (also 6).

Next, you find the how far each number is from the mean using absolutes. Those values are 4, 3, 5, 1, 2, and 3.

Finally, add those together to get 18, then divide by how many numbers there were (6) that to get the mean absolute deviation (3).

Hope this helped! :)

Answer:

C and D

Step-by-step explanation:

The fourth quadrant is where all the points are in the form (positive, negative).

The center and radius of [tex](x-h)^2+(y-k)^2=r^2[/tex] is (h,k) and r, respectively.

Let's look at the centers and the radius of each of these choices:

A) This one has center (4,-2) and radius [tex]\sqrt{32} \approx 5.7[/tex].

If you add 5.7 to -2 you get a positive number and we needed it negative.

Not this choice; moving on.

B) This one has center (-3,2) and radius [tex]\sqrt{25}=5[/tex].

The center is not even in quadrant 4; moving on.

C) This one has a center (3,-4) and radius 1.

Add 1 to 3 you get 4.

Subtract 1 from 3 you get 2.

Those x's are positive so that looks good so far.

Add 1 to -4 you get -3.

Subtract 1 from -4 you get -5.

Those y's are negative so that looks good.

This circle is in quadrant 4 and doesn't go outside it.

D) This one has center (5,-7) and radius 4.

Add 4 to 5 you get 9.

Subtract 4 from 5 you get 1.

Positive x's is good.

Add 4 to -7 you get -3.

Subtract 4 from -7 you get -11.

Those are negative so that looks good.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex], [tex](x-5)^{2} +(y+7)^{2} =16[/tex] lie completely within the fourth quadrant.

Quadrant IV: The fourth quadrant is in the bottom right corner of the plane. In this coordinate X has positive values and y has negative values.

According to the question

We have to find the circles lie completely within the fourth quadrant.

Observing the below graph, These two circle lie  completely within the fourth quadrant.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex]

[tex](x-5)^{2} +(y+7)^{2} =16[/tex]

These circles lie bottom right corner of the plane.

From the given graphs below Option C and D lie completely within the fourth quadrant.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex], [tex](x-5)^{2} +(y+7)^{2} =16[/tex] lie completely within the fourth quadrant.

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Answer:

No solution

Step-by-step explanation:

-3x + 3y = 4

-x + y = 3

Solve the equation for x:

Move the variable to the right side and change its sign

-x + y = 3

-x = 3 - y

Change the signs on both sides of the equation

-x = 3 - y

x = -3 + y

Substitute the given value of x into the equation -3x + 3y = 4

-3x + 3y = 4

x = -3 + y

-3(-3+y)+3y=4

Solve the equation for y

-3(-3+y)+3y=4

y = 0

There is no solution for y.

And since there's no solution for y, the system has no solution.

Answer:

[tex] \sqrt{37} [/tex]

or 6.08276253

Answer:

(1,1)

Step-by-step explanation:

We have the following system:

[tex]y=x^2-x+1[/tex]

[tex]y=x[/tex]

We are going to plug the 2nd equation into the 1st eqaution giving us:

[tex]x=x^2-x+1[/tex]

Now time to solve [tex]x=x^2-x+1[/tex].

[tex]x=x^2-x+1[/tex]

Subtract x on both sides:

[tex]0=x^2-2x+1[/tex]

Now this actually not too bad.  This a perfect square trinomial.  That is it is of the form [tex]a^2x^2+2abx+b^2[/tex] which equals [tex](ax+b)^2[/tex].

So solving [tex]0=x^2-2x+1[/tex] is equivalent to solving [tex]0=(x-1)^2[/tex]

In order to solve  [tex]0=(x-1)^2[/tex], we just need to know when x-1=0 which is at x=1.  I got by adding 1 on both sides of x-1=0

Now remember y=x means we have the solution (1,1).

Okay, I'm going to leave all of this algebra here.  I'm going to graph this without a graphing calculator.

[tex]y=x[/tex] is a line with slope 1 and y-intercept 0.

[tex]y=x^2-x+1[/tex] is a parabola.  The vertex isn't obvious to me right now without the algebra but I do know the parabola is open up because the coefficient of x^2 being positive.

So let's find the vertex.

I'm going to start with the x-coordinate which is -b/(2a).

Compare [tex]x^2-x+1[/tex] to [tex]ax^2+bx+c[/tex] and you should see that [tex]a=1,b=-1,c=1[/tex].

So [tex]-\frac{b}{2a}=-\frac{-1}{2(1)}=\frac{1}{2}[/tex]

So the vertex occurs when the x-coordinate is 1/2.

To find the correspond y-value just use the equation that relations x and y.

That is use [tex]x^2-x+1[/tex].

Replace x with 1/2.

[tex](\frac{1}{2})^2-(\frac{1}{2})+1[/tex]

[tex]\frac{1}{4}-\frac{1}{2}+1[/tex]

Find a common denominator.

[tex]\frac{1}{4}-\frac{2}{4}+\frac{4}{4}[/tex]

[tex]\frac{1-2+4}{4}[/tex]

[tex]\frac{3}{4}[/tex]

So the vertex is at (1/2,3/4) and the parabola is open up.

When you plug in 0 into [tex]x^2-x+1[/tex] you get [tex]0^2-0+1=1[/tex] so the ordered pair (0,1) is on the parabola.

Using symmetry about the line x=1/2 we know that (1,1) is also on this graph.

Let's use this information to produce a graph now.

Now our answer appears to be (1,1) in the graph.

We can check this answer by plugging in (1,1) into our system and see if both equations check out:

[tex]y=x[/tex]  gives us 1=1 which is true.  So we are good there.

[tex]y=x^2-x+1[/tex] gives us [tex]1=1^2-1+1[/tex] which is true. So we are good there.

The work for showing [tex]1=1^2-1+1[/tex].

[tex]1^2-1+1[/tex]

[tex]1-1+1[/tex]

[tex]0+1[/tex]

1

So the point (1,1) checks out for both of our equations which means it is a common point amongst the equations given.

Answer:

She need a interest rate of 6.25%

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=16\ years\\ P=\£8,000\\ A=\£8,000*2=\£16,000\\r=?[/tex]

substitute in the formula above  and solve for r

[tex]16,000=8,000(1+16r)[/tex]

[tex]16r=2-1[/tex]

[tex]r=1/16[/tex]

[tex]r=0.0625[/tex]

Convert to percentage

[tex]r=0.0625*100=6.25\%[/tex]

Answer:

[tex]\large\boxed{x=3\dfrac{3}{4}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3}{4x}=\dfrac{1}{5}\qquad\text{cross multiply}\\\\(4x)(1)=(3)(5)\\\\4x=15\qquad\text{divide both sides by 4}\\\\x=\dfrac{15}{4}\\\\x=3\dfrac{3}{4}[/tex]

Answer:

its 4/15 because u will get the answer i got 100% for that

Answer:

2.5

Step-by-step explanation:

The positive factors of 12 are 1,2,3,4,6,12

The positive prime factors of 12 are 2 and 3.

(Primes are integer numbers only divisible by themselves and one.)

The arithmetic mean or average of 2 and 3 is (2+3)/2.

(2+3)/2=5/2=2.5

Answer:

-6 goes inside ( ) since G(-6)=10.

Step-by-step explanation:

It looks like you are looking for a number such that when you put in the ( ) of G(  ) you get 10 as a result.

So let's say you are trying to solve G(b)=10 for b.

Well G(x)=-3x-8 so G(b)=-3b-8.

I just replaced all the x's with b's to find G(b).

Now we are trying to solve G(b)=10 for b.

G(b)=10

-3b-8=10

Add 8 on both sides:

-3b=10+8

Simplify:

-3b=18

Divide both sides by -3:

  b=18/-3

Simplify:

  b=-6

So G(-6)=10!

Check:

-3(-6)-8

18-8

10

G(-6)=10 is confirmed.

-6 goes inside the G( )=10.

answer g(-6)=−3x−8=10

Answer:

[tex]-\frac{25}{3}[/tex]

Step-by-step explanation:

To isolate for x, start by multiplying both sides by 2.5.

[tex]\frac{25}{3} =-x[/tex]

Next, divide both sides by -1.

[tex]\frac{-25}{3} =x[/tex]

Answer:

x = -25/3

Step-by-step explanation:

10/3 = x / (-5/2)

Multiply each side by (-5/2) to isolate x

-(5/2) * 10/3 = -5/2 * (x / (-5/2))

-50/6 = x

Divide the top and bottom by 2 on the left hand side

-25/3 =x

Changing to a mixed number ( if required)

3 goes into 25  8 times ( 3*8=24)   with 1 left over(25-24=1)

x = -8 1/3

Answer:

We can find the answer to your question by using a computational tool or any similar software

The equation is

-8/2*y - 8 = 5/y + 4 -7y + 8/y^2 - 18

-4*y + (- 8-4 + 18) = 5/y  -7y + 8/y^2

-4*y + 6 = 5/y  -7y + 8/y^2

-4*y + 7y + 6 = 5/y  + 8/y^2

3y + 6 = 5/y  + 8/y^2

We multiply by y^2

3y^3 + 6y^2 = 5y  + 8

3y^3 + 6y^2 -5y - 8 = 0

See image below for result of the equation

Answer:

9*4

Step-by-step explanation:

We can Factor out a 9 from each term

9 + 27

9 (1+3)

9 (4)

9*4

Answer:

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Step-by-step explanation:

The given complex number equation is:

[tex]\frac{1-2i}{2+i}+\frac{4-i}{3+2i}=x+yi[/tex]

We simplify the LHS and compare with the RHS

We collect LCD on the left to get:

[tex]\frac{(1-2i)(3+2i)+(4-i)(2+i)}{(2+i)(3+2i)}=x+yi[/tex]

[tex]\frac{3+2i-6i+4+8+4i-2i+1}{6+4i+3i-2}=x+yi[/tex]

Simplify to get:

[tex]\frac{16-2i}{4+7i}=x+yi[/tex]

Rationalize the LHS:

[tex]\frac{(16-2i)(4-7i)}{(4+7i)(4-7i)}=x+yi[/tex]

Expand the numerator using the distributive property and the denominator using difference  of two squares.

[tex]\frac{64-112i-8i-14}{16+49}=x+yi[/tex]

Simplify to get:

[tex]\frac{50-120i}{65}=x+yi[/tex]

[tex]\frac{10-24i}{13}=x+yi[/tex]

[tex]\frac{10}{13}-\frac{24}{13}i=x+yi[/tex]

By comparing real parts and imaginary parts; we have;

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Answer:

A strong positive correlation

Step-by-step explanation:

A strong correlation when the correlation coefficient is close to 1 or -1. If the correlation coefficient is close to positive 1, then it is a positive strong correlation coefficient. If the correlation coefficient is close to negative 1, then it is a negative strong correlation coefficient.

Answer:

The r-value indicate A strong positive correlation

Step-by -step-explanation:

The following information should be considered:

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(9x^2 + 8x) – (2x^2 + 3x)

Subtract like terms:

9x^2 - 2x^2 = 7x^2

8x - 3x = 5x

The difference is 7x^2 + 5x

Answer:

A) x² + 7x - 9

Step-by-step explanation:

Deduct\Add each like-term to arrive at your answer.

Answer:

* cos 211.7 not equal the other values

Step-by-step explanation:

* Lets revise the angles in the four quadrant

- If the angle in the first quadrant is Ф, then the equivalent angles to

 it in the other three quadrant are

# 180° - Ф ⇒ 2nd quadrant (sin only +ve)

# 180° + Ф ⇒ 3rd quadrant (tan only +ve)

# 360° - Ф ⇒ 4th quadrant (cos only +ve)

# -Ф ⇒ 4th quadrant (cos only +ve)

# -180 + Ф ⇒ 3rd quadrant (tan only +ve)

# -180 - Ф ⇒ 2nd quadrant (sin only +ve)

# -360 + Ф ⇒ 1st quadrant (all are +ve)

* Lets solve the problem

∵ Ф = 31.7°

∵ cos 31.7 = +ve value

∵ 180° + Ф° = 180° + 31.7° = 211.7°

∵ cos (180° + Ф°) = - cos Ф° ⇒ cos (180° + Ф°) in the 3rd quadrant is

  same value as cos Ф but with -ve sign

∴ cos 211.7° = - cos 31.7°

∴ cos 31.7° ≠ cos 211.7°

∵ 360° - Ф° = 360° - 31.7° = 328.3°

∵ cos (360° - Ф°) = cos Ф° ⇒ cos (360° - Ф°) in the 4th quadrant has the

  same value and sign with cos Ф°

∴ cos 328.3° = cos 31.7°

∴ cos 31.7° = cos 328.3°

∵ -391.7° + 360° = -31.7° ⇒ more then clockwise turn by 31.7°

∵ cos (-Ф°) = cos Ф° ⇒ cos (-Ф°) in the 4th quadrant has the same value

  and sign with cos Ф°

∴ cos (-31.7°) = cos 31.7°

∴ cos 31.7° = cos (-390.7°)

* cos 211.7 not equal the other values

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{y}=0.64\to\dfrac{x}{y}=\dfrac{64}{100}\\\\25<y<100\Rightarrow\dfrac{x}{y}=\dfrac{64:2}{100:2}\\\\\dfrac{x}{y}=\dfrac{32}{50}\to x=32[/tex]

Answer:

y=2.4

Step-by-step explanation:

9y-2+y=5y+10

(combine like terms)

10y-2=5y+10

(subtract 5y from both sides)

5y-2=10

(add 2 to both sides)

5y=12

(divide both sides by 5)

y=2.4

Answer:

C. $6 per hour.

Step-by-step explanation:

Pick a convenient point on the graph. The rate of change  is the

y coordinate /  x coordinate.

So we pick the point near the top right corner where y = 30 and x = 5 which gives us the answer 30/5 = 6.

The rate of change shown in the graph is option B that is $3 per hour.

The rate of change in a line is the difference between vertical values divided by horizontal values. It is also known as slope. It can be calculated as under:

Rate of change= y2-y1/x2-x1

To calculate the rate of change we need to first select two points which are in the given graph are (0,0) and (1,3)

Rate of change is equal to (3-0)/(1-0)

=3/1

means $ 3 is paid for 1 hour.

Hence the rate of change in the given graph is $3 per hour.

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Answer:

Part 1) [tex](x+4)(x-1)(x-2)(x-4)[/tex]

The related polynomial equation has a total of four roots, all four roots are real

Part 2) [tex](x+1)(x-1)(x+2)^{2}[/tex]

The related polynomial equation has a total of four roots, all four roots are real and one root has a multiplicity of 2

Part 3) [tex](x+3)(x-4)(x-(2-i))(x+(2-i))[/tex]

The related polynomial equation has a total of four roots, two roots are complex and two roots are real

Part 4) [tex](x+i)(x-i)(x+2)^{2}[/tex]

The related polynomial equation has a total of four roots, two roots are complex and one root is real  with a a multiplicity of 2

Step-by-step explanation:

we know that

The Fundamental Theorem of Algebra  states that:  Any polynomial of degree n has n roots

so

Part 1) we have

[tex](x+4)(x-1)(x-2)(x-4)[/tex]

The roots of this polynomial are

x=-4, x=1,x=2,x=4

therefore

The related polynomial equation has a total of four roots, all four roots are real

Part 2) we have

[tex](x+1)(x-1)(x+2)^{2}[/tex]

The roots of this polynomial are

x=-1, x=1,x=-2,x=-2

therefore    

The related polynomial equation has a total of four roots, all four roots are real and one root has a multiplicity of 2

Part 3) we have

[tex](x+3)(x-4)(x-(2-i))(x+(2-i))[/tex]

The roots of this polynomial are

x=-3, x=4,x=(2-i),x=-(2-i)

therefore    

The related polynomial equation has a total of four roots, two roots are complex and two roots are real

Part 4) we have

[tex](x+i)(x-i)(x+2)^{2}[/tex]

The roots of this polynomial are

x=-i, x=i,x=-2,x=-2

therefore    

The related polynomial equation has a total of four roots, two roots are complex and one root is real  with a a multiplicity of 2

Answer:

C. 60,000

Step-by-step explanation:

Given

Three times as many bought tickets

24,000 * 3 = 72,000

one-sixth of them cancelled their tickets

72,000 * 1/6 = 12,000

Subtract

72,000 - 12,000 = 60,000

Answer

60,000 people are attending this week

This week, 60,000 fans are attending the football match.

To find the number of fans attending the football match this week, we need to start with the number of fans who bought tickets. This week, three times as many fans bought tickets as last week, so there were 3 * 24,000 = 72,000 fans who bought tickets. However, one-sixth of them cancelled their tickets, which means 1/6 * 72,000 = 12,000 fans cancelled. Therefore, the number of fans attending the match this week is 72,000 - 12,000 = 60,000.

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Answer:

D. 74°

Step-by-step explanation:

∠XYZ is an inscribed angle, where its vertex is located on the circle and two intersecting chords form the vertex.

An inscribed angle is equal to HALF of the intercepted arc, which is the arc that is between the two points where the chords hit.

In this picture, the intercepted arc is the red part of the outside of the circle.

Since you are given the measurement of the intercepted arc, you can find the measure of the inscribed angle by finding half of 148°.

Therefore, the inscribed angle is 148° divided by 2, giving us 74°.

The measure of the inscribed angle, ∠XYZ, is D. 74°.

Answer:

-2

Step-by-step explanation:

6^2 = 36

5 x 6 = 30

36 - 30 - 8 = -2

For this case we must multiply the following expression:

[tex](2x-6) (3x ^ 2-4x-5)[/tex]

Applying distributive property we have:

[tex](2x) (3x ^ 2) - (2x) (4x) - (2x) (5) - (6) (3x ^ 2) + (6) (4x) + (6) (5) =[/tex]

By definition of multiplication of powers of the same base, we have to put the same base and add the exponents:

[tex]6x ^ 3-8x ^ 2-10x-18x ^ 2 + 24x + 30 =[/tex]

Adding similar terms:

[tex]6x ^ 3-26x ^ 2 + 14x + 30[/tex]

Answer:

[tex]6x ^ 3-26x ^ 2 + 14x + 30[/tex]

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (4, 2)

m = [tex]\frac{2-1}{4-2}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]\huge\boxed{\frac{1}{2}}[/tex]

We can use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope, where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are both points.

Plug in the values. [tex]\frac{2-1}{4-2}[/tex]

Subtract. [tex]\frac{1}{2}[/tex]

Answer:

y = 2 when x= 4

y=3 when x = 8

y = 4 when x=12 ....

Step-by-step explanation:

The given rule is:

y=1/4x+1

We have given the values of x. We have to find the values of y by substituting the values of x in the given rule:

y=1/4x+1

x=4

Substitute the value of x in the rule:

y=1/4 * 4+1

y=4/4 +1

By taking L.C.M of the denominator:

y= 4+4/4

y=8/4

Cancel out 8/4 by the table of 4

y= 2

y = 2 when x= 4

y=1/4x+1

x=8

Substitute the value in the given rule:

y= 1/4 * 8+1

y= 8/4 +1

By taking L.C.M we get,

y = 8+4/4

y= 12/4

Cancel out 12/4 by the table of 4

y= 3

y=3 when x = 8

Then,

y=1/4x+1

x= 12

Substitute the value in the given rule:

y = 1/4*12+1

y= 12/4+1

By taking L.C.M we get,

y=12+4/4

y=16/4

Cancel out 16/4 by the table of 4

y =4

y = 4 when x=12 ....

Answer:

Trapezoid- A.

Answer:

A. Trapezoid

Step-by-step explanation:

The proper name of this quadrilateral is a trapezoid.

The picture might look confusing because the trapezoid is upside down.

However, it still counts as a trapezoid.

Answer:

[tex]\large\boxed{A\ \cup\ B=[-5,\ 10]}[/tex]

Step-by-step explanation:

Look at the picture.

The union of two sets A and B (A ∪ B) is the set of elements which are in A, in B, or in both A and B

Answer:

(0,5)

Step-by-step explanation:

-2x+6y=30

5x+2y=10

I'm going to use elimination.

I'm choosing this method because both equations are in the same form.

They are in the form ax+by=c.  

So in order to use elimination, I need one of my columns that contain the variables to contain opposites. Neither one of my columns with the variables have that.  Example -2x and 5x are not opposites and 6y and 2y are not opposite.

I'm going to multiply both sides of equation 2 by -3.  This will help me to achieve the opposites in a column.

So the system becomes:

-2x+6y=30

-15x-6y=-30

---------------------If we add the columns you will see that the variable y get's eliminated. Let's do that.

-2x+6y=30

-15x-6y=-30

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

-17x+0y=0

-17x     =0

    x      =0

So using one of the equations (you choose; doesn't matter which one you pick) along with x=0, I'm going to find y.

I choose equation 2.

That is I choose 5x+2y=10 along with x=0 to find y.

5x  +2y=10 with x=0

5(0)+2y=10

0   +2y =10

       2y=10

         y=10/2

         y=5

The solution is (x,y)=(0,5).