A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
Education and Health Services - All Employees, 2000-2009
A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.

By elimination, the solution of the system of equations, 6x - 3y = 3 and 5x - 5y = 10, is (-1 , -3).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

First, simplify both equations by dividing the first equation by 3 and the second equation by 5.

6x - 3y = 3 ⇒ 2x - y = 1     (equation 1)

5x - 5y = 10 ⇒ x - y = 2     (equation 2)

Use the elimination method since subtracting the two equations will eliminate the variable y.

2x - y = 1     (equation 1)

 x - y = 2     (equation 2)

x        = -1

x = -1

Substitute the value of x to any of the two equation and solve for y.

6x - 3y = 3     (equation 1)

6(-1) - 3y = 3

-3y = 3 + 6

-3y = 9

y = -3

Hence, the solution of the system of equations is (-1 , -3).

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Answer:

n = 1

Step-by-step explanation:

[tex]\frac{8}{3}[/tex] = [tex]\frac{19}{6}[/tex] n - [tex]\frac{1}{2}[/tex] n

multiply through by 6 ( the LCM of 3, 6 and 2 ) to clear the fractions

16 = 19n - 3n

16 = 16n ( divide both sides by 16 )

1 = n

Answer: Two planes intersecting in a line

Explanation:

The wall and floor are two different planes. They meet up to form a line which is the crease between them.

A plane is a flat surface without any bends or curves to it. In theoretical terms, planes go on forever in all directions. Realistically there are limits of course. The wall or floor cannot go on forever.

Another example of two planes would be found in a book. Each page is a plane. Two adjacent pages meet up to form a line (i.e. the spine of the book is a line).

The mean height of the given sample of values is approximately 65.20.

The heights of the 15 students are as follows:

{59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73}

To find the mean (average) height of the given values, we need to add up all the heights and then divide the sum by the total number of heights:

59 + 61 + 62 + 63 + 63 + 64 + 65 + 65 + 66 + 67 + 67 + 67 + 67 + 69 + 73

= 978

So, the mean height can be calculated as:

Mean height = Total height / Number of heights = 923 / 15 = 65.2

Therefore, the mean height is approximately 65.20.

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Using the given information, the equation of the circle with center located at point (2 , 1) and passes through the point (6 , 4) is (x - 2)^2 + (y - 1)^2 = 25

Using the distance formula, get the radius of the circle by solving for the distance between the center (2 , 1) and the point (6 , 4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(6 - 2)^2 + (4 - 1)^2

radius= √16 + 9

radius = √25

radius = 5

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (2 , 1)

r = 5

(x - 2)^2 + (y - 1)^2 = 5^2

(x - 2)^2 + (y - 1)^2 = 25

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The length of seesaw will be equal to 11 feet.

It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.

We have to find out the length of seesaw.

What do you mean by midpoint of a line segment ?

The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.

As per the question ;

The midpoint of the seesaw is 13.5 feet from the swing set.

and

The swing set is 8 feet from the edge of the seesaw.

So ;

The distance from the midpoint to the edge will be ;

13.5 – 8 = 5.5.

And

The length of the seesaw will be ;

= 2× (5.5)

= 11 feet

Thus , the length of seesaw will be equal to 11 feet.

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The naive forecast for day 6 is 94.

The naive forecast for the nth period is calculated as follows.

Forecast period Yn=Yn−1​

Period Sales Naive Forecasts

1         90                   -

2         97                  90

3         92                  97

4         90                  92

5         94                  90

6                            94

Hence, the naive forecast for day 6 is 94.

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Answer:

22 :)

Step-by-step explanation:

I've attached an image to help break down the answer. (credit to cymath.com)

Hope this helps!

By using collinearity assumptions and addition and subtraction of line segments, the length of the line segment AB is 26 units.

Let A, B, D, F be points lying on the same line such that A(x) ≤ B(x) ≤ D(x) ≤ F(x), where x is the position of each point on a number line. Then, the value of the length of the line segment AB is:

AB = AD + DF - BF

AB = 26 + 8 - 8

AB = 26

Please notice that B(x) = D(x) as AB = AD.

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The Gary's score after getting stuck in the dust storm will be -35 points.

It is given in the problem that,

The points gained by Gary by jumping over a crater = 20 points

And then,

The points lost by Gary for getting stuck in a dust storm = 45 points

We need to find,

The Gary's score after getting stuck in the dust storm

As in the beginning of the game, Gary's account had 20 points but as he then stuck in the dust storm he lost 45 points, which means he has lost points more than he had. So, now Gary would have negative points left in his account in the game

= 10 - 45

= - 35

Hence, the Gary's score after getting stuck in the dust storm will be -35 points.

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The average interest rate does he pay on the total $32,000 he owes is 9. 5%

From the information given, we have that;

Given the total pay he owes as;

= $22, 000 +$ 10, 000

= $32, 000

The average interest rate is expressed as;

= sum of interest rate for college loan and car/ number of interest rate

Substitute the values

= 8 + 11/ 2

= 19/ 2

Find the quotient

= 9. 5%

Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%

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Answer:

no solution

Step-by-step explanation:

5n + 1 = 5n - 1 ( subtract 1 from both sides )

5n = 5n - 2 ( subtract 5n from both sides )

0 = - 2 ← not possible

this indicates that the equation has no solution

The two numbers which are 5 units away from zero on the number line as required in the task content are; -5 and 5.

It follows from the task content that the numbers which are 5 units away from zero on the number line be identified and plotted.

Hence, given that the numbers in discuss are represented by; x; we have;

| x - 0 | = 5

| x | = 5

Ultimately, x = ±5. where +5 is to the right and -5 is to the left of zero respectively.

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4)

The measures of the angles m∠1 and m∠2  are: m∠1 = 109 and m∠2 = 71

Linear pair angles are two angles which are adjacents and supplementary.

Given that: m∠2 and m∠1 form a linear pair

we know that the angles   and   are supplementary, which means that they add up to 180 degrees.

In order to solve for "x," we can write the following expression:

180 = (5x + 9) + (3x + 11)

8x = 180 - 20

x = [tex]\frac{160}{8}[/tex]

x = 20

Therefore, substituting, we get that the measures of the angles   and   are

m∠1 = 5(20) +9 = 109

m∠2 = 3(20) + 11 = 71

5)

the angle m∠2 = 86°

Given that m∠1 and m∠2 are vertical angles and m∠1 = (17x + 1) and m∠2 =  (20x - 14)

Vertical angles are always congruent

m∠1 = 17x + 1

m∠2 = 20x - 14

Since ∠1 and ∠2 are vertical:

m∠1 = m∠2

17x + 1  = 20x - 14

Collect like terms

20x - 17x = 1 + 14

3x = 15

Divide both sides by 3

3x / 3 = 15/3

x = 5

m∠2 =  20x  -  14

m∠2 =  20(5)  -  14

m∠2 =  100    -   14

m∠2 =   86°

6)

The value of each angle that is p=119 and q=61

In light of this, the measure of an angle is P, which is three less than the measure of angle q.

P + q = 180  ( By definition of supplementary)

p = 2q -3

Substitute the value

Then ,we get

2q - 3 + q =180

3q = 180 + 3

3q = 183

q= [tex]\frac{183}{3}[/tex]

= 61

then, if you substitute q's value, you get

p= 2(61) - 3 = 122 - 3 = 11.9

Hence, p= 119 and q= 61

7)

The value of x is 19°

Given that : ∠DBE =2x - 1

∠CBE =5x – 42  and BD is perpendicular to AC.

A right angle is formed when two lines are perpendicular.

∠DBE + ∠CBE = 90

90 = (2x - 1) + (5x - 42)

7x = 133

x = 19°

8)

The value of x and y are : x= 26° and y= 9°.

As a linear pair, (5x - 17)° + (3x - 11)° = 180°.

or, 8x - 28°= 180°

8x = 180° + 28°

Therefore, the value of x is 26°.

Now,

3x - 11°= 3×26°-11° = 67°

Again,

67°+90°+(2y+5)° = 180° { being linear pair}.

157°+2y+5° = 180°

or, 2y + 162° = 180°

or, 2y = 180° - 162°

y = [tex]\frac{18}{2}[/tex]

Therefore, the value of y is 9°.

The value of x is 26° and y is 9°.

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18/ 3x+1 is  18x²-2/ 3x²-5x - 2}  in simplest terms.

What are examples of linear equations?

18 x² - 2 / 3x² - 5x - 2

3x² - 5x - 2 = 3x² - ( 6- 1 ) x - 2 = 0

                    ⇒  3x² - 6x + x - 2 = 0

                     ⇒  3x( x - 2 ) + 1 ( x - 2) = 0

                      ⇒ ( 3x + 1 ) ( x - 2 ) = 0

put in equation -

= 18 x² - 2 /  ( 3x + 1 ) ( x - 2 )

= 18/ 3x+1

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Answer:

Step-by-step explanation:

Givens

Flight speed there = 12 feet / second

Flight speed back = 8 feet / second

Total time = 22 minutes

Time at rest = 18 minutes

Time in flight = 22 - 18 = 4 minutes

Equation

Let the time going to the flowerbed = t

12*t + 8*t + 18 = Distance travelled + time at rest.

Answer

12*t + 8*t + 18 = Distance travelled + time at rest

The equation and the solution are 2 = -8 * -x and x = 1/4, respectively

On the model, we have the following representations

[1][1]          [-1][-1][-1][-1][-1][-1][-1][-1][-x]

When represented as an equation, we have the following equation

So, we have

2 = -8 * -x

Evaluate the product in the above equation

So, we have

2 = 8x

Divide both sides of the above equation by 8

So, we have

1/4 = x

Rewrite the above expression as

x = 1/4

Hence, the equation and the solution are 2 = -8 * -x and x = 1/4, respectively

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an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.

Is a triangle capable of tessellation?

To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.

Every vertex, edge, and tile in a regular tesselation are identical.

However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).

Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.

Each vertex in the semiregular tessellations is the same.

Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)

The Octagon & square tiling (4,8,8) is a very common floor tiling.

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The arithmetic mean of two terms in an arithmetic sequence is 42 .

One term is 30 then other term is

42 = (x+30)/2

x=54

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The Slope-intercept form of the given equation is y = -3x + 18 .

An equation in Slope-intercept form is of the form

[tex]y = mx + b[/tex]

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

Now, the given equation is (y/9) + (x/3) = 2

Taking LCM on the left hand side of the equation, we get

⇒ [tex](3y+9x)/(2y) = 2[/tex]

⇒ 3y + 9x = 54

⇒ 3y = 54 - 9x

Dividing both side of the equation by 3, we get

⇒ y = [tex](54 - 9x)/3[/tex]

⇒ y = 18 - 3x

⇒ y = -3x + 18

∴ The equation y = -3x + 18 is in Slope-intercept form.

In the equation the slope is -3 and the y-intercept is 18.

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The slope of the line that contains the  points G(-4,3), H(-4,7) is not defined.

Slope of a line containing two points (a,b) and (c,d) is denoted  by

[tex]slope=\frac{d-b}{c-a}[/tex]

In the given question

The points given are G(-4,3), H(-4,7)

a=-4, b= 3  and c= -4 and d=7

Substituting the values in formula of slope we get

[tex]slope=\frac{d-b}{c-a}[/tex]

[tex]slope=\frac{7-3}{-4-(-4)}\\ \\ =\frac{4}{-4+4} \\ \\ =\frac{4}{0}[/tex]

Since the division of any number by zero is not defined .

Therefore , the slope of the line that contains the  points G(-4,3), H(-4,7) is not defined.

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Answer:

D. 52 45

Step-by-step explanation:

The 9th term of the geometric sequence can be determined by using the nth term of geometric sequence formula: an=arn-1

Geometric sequence is the series of number in which each term is determined by multiplying the common ratio with the preceding term.

In the formula, an=arn-1, a is the first term, n is the number of terms, and r is the common ratio.

The geometric sequence from the part b is 2,4,8,…

The first term a = 2

The common ratio r = 2

The number of term n = 9

Hence, to find the 9th term,

a9=2(2)9-1

a9=2(2)8

a9=512

The 9th term of the geometric sequence 2,4,8,… is 512

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Answer:

[tex]0 \leqslant c \leqslant 56[/tex]

Step-by-step explanation:

Since candy costs $7 per pound, and Kayla will buy less than 8 pounds, she will spend no more than $7 × 8, or $56.

Answer:

  g(f(x)) = 6x -9

Step-by-step explanation:

Given f(x) = 3x –5 and g(x) = 2x +1, you want to find g(f(x)).

A function is evaluated by simplifying the result of substituting the argument for the function's variable.

  g(f(x)) = 2·f(x) +1 = 2(3x -5) +1 = 6x -10 +1

  g(f(x)) = 6x -9

Answer:

2b + 9

Hope this helps :)

Step-by-step explanation:

This equation shows the statement, "Ava's sister is 9 years less than twice Ava's age b."

Answer:

where is the equal to sign????

Answer:

6n2-15=150-15

6n2-15=135

6n2=150

divied both side by 6

n2=25

sqrt both side

n=-5 or 5 bc sqrt so 2 answer

Step-by-step explanation: