Total cost of job = $147.51 Duration of job = 5 hours Price of parts = $32.50 Overhead rate = 55% Hourly labor rate = _____.

[tex]a_1=2;\ a_2=-6;\ a_3=18;\ a_4=-54;\ a_5=162;\ ...[/tex]

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

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{-6}{2}=-3[/tex]

Therefore [tex]\boxed{a_1=2;\qquad a_n=-3a_{n-1}}[/tex]

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

The exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=2(-3)^{n-1}=2(3)^n(3)^{-1}=2(3)^n\left(\dfrac{1}{3}\right)\\\\\boxed{a_n=\dfrac{2}{3}\left(-3)^n}[/tex]

Answer:

A

Step-by-step explanation:

We find the ratio by dividing two y-values from 2 consecutive x values (1 unit apart). Notice that in the table, all x-values are 1 unit apart. We can choose any pair of consecutive points.

Let's choose: (2,-4) and (1,-2). We divide -4/-2=+2.

Answer A.

Answer:

B) -2/√5

Step-by-step explanation:

see attached

Answer:

1/2 is the slope of the line

Step-by-step explanation:

To find slope, use the following equation

slope (m) = (y₂ - y₁)/(x₂ - x₁)

First, set each coordinate. Let:

(x₁ , y₁) = (8 , -6)

(x₂ , y₂) = (4 , -8)

Plug in the corresponding numbers for the corresponding variables.

m = (y₂ - y₁)/(x₂ - x₁)

m = (-8 - (-6))/(4 - 8)

Simplify. Note that two negative signs would result in a positive sign.

m = (-8 + 6)/(4 - 8)

Combine like terms.

m = -2/-4

Simplify. Divide common factors from both the numerator and denominator.

m = (-2/-4)/(-2/-2) = 1/2

1/2 is the slope of the line

~

Answer:

a=21, b=24, c=27

Step-by-step explanation:

a= side 1, b= side 2, c= side 3

a+b+c=72

a/b=7/8 and b/c=8/9 (proportion it)

then cross multiply to get 8a=7b and 9b=8c---> divide to get a=7/8b and c=9/8b

put that into the first equation--> 7/8b+8/8b+9/8b=72

add the fractions to get 24/8b=72 (24/8 equals 3) so 3b=72 (divide to get b=24)

then fill that in to the above equations (8a=7b, 9b=8c)

8a=7(24) and 9(24)=8c---> 8a=168 and 8c=216

divide all that and get a=21 and c=27

with all the measurements, you can check the proportion to make sure it works (7:8:9-->21:24:27)

if you multiple 7, 8, and 9 by 3 then you get the numbers found so it works

The sides of the triangle in question, which are in a 7:8:9 ratio, are 21 cm, 24 cm, and 27 cm respectively when the perimeter is 72 cm.

The subject of this question is Mathematics, specifically related to the concept of ratios and the calculation of triangle side lengths. The triangle in question has sides in the ratio of 7:8:9. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is 72 cm. This means that the total ratio units (7+8+9 = 24 units) represent 72 cm in real lengths.

To find out how much each ratio unit represents, we divide the total perimeter by the total units. This gives us 72 cm / 24 units = 3 cm/unit. This means that each ratio unit represents 3 cm. Thus, the lengths of the sides following the 7:8:9 ratio would be 7*3=21 cm, 8*3=24 cm, and 9*3=27 cm respectively.

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Answer:

The area of the given rectangle is 51

Step-by-step explanation:

First we have to find the coordinates of the vertices of the rectangle.

Then the length and breadth of it using distance formula.

The distance d between points (x₁ , y₁) and (x₂ , y₂) is given by

[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

Finally calculate the area of rectangle using the formula,

Area of rectangle = Length * Breadth

From the given graph, we get the coordinates of the rectangle as

A(2,4) , B(-2,3) , C(1,-9) , D(5,-8)

Breadth, AB = [tex]\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}[/tex]

Length, BC = [tex]\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}[/tex]

Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51

∴ The area of the given rectangle is 51

Answer:

51

Step-by-step explanation:

Hi there! :)

Answer:

The answer is B) 17/30

Step-by-step explanation:

In order to find your answer you need to subtract 1/3 from 9/10:

9/10 - 1/3 = chocolate left

Since theses fractions do not have the same denominators (bottom number), the key here is to rewrite both of the fractions so that they have the same denominator:

The denominator is going to be a common multiple of "10" and "3". Ideally it's going to be the least common multiple of "10" and "3".

Let's start with the larger of the two denominators, which is "10". You have to go through its multiples and and see when we get to one that's divisible perfectly by 3.

So 10 is not divisible perfectly by 3, neither is 20. 30 on the other hand is divisible perfectly by 3. 30 is three times 10.

So you can rewrite both of these fractions as something over 30.

1/3 = ?/30

To get from 3 to 30, we have to multiply by 10. So if you multiply the denominator by 10, if you don't want to change the value of the fraction, you have to multiply the numerator (top number) by 10 also.

1/3 = 10/30

Same thing with the other fraction:

9/10 = ?/30 → 3 × 10 = 30 / SO, you need to multiply the numerator by three also → 9 × 3 = 27

9/10 = 27/30

Now that your fractions both have the same denominator, you can subtract the numerators together and put the answer on 30.

27/30 - 10/30 = ?

27 - 10 = 17 → 17/30

Since the fraction is simplified, you are now done.

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:105

Step-by-step explanation:

the question says it prints 75 pages in 5 minutes.

to find out how much it prints in 7 minutes you must find how much it prints in 1 minute.

1 minute=75/5=15

it prints 15 pages in 1 minute.

15*7=105 pages.

so it prints 105 pages in 7 minutes.

please mark brainliest if it helps and please like.

welcome!

Answer:

105 pages

Step-by-step explanation:

It prints 75/5 = 15  pages per minute.

So in 7 minutes 15*7 = 105 pages are printed.

Answer:

x=3

Step-by-step explanation:

Since this is an isosceles trapezoid

The angles at the top have to equal each other

112 = 30x + 11y

The sides also have to equal each other.

12 = 2x+3y

Divide each side by 3

12/3 = 2x/3 + 3y/3

4 = 2/3 x +y

Subtract 2/3 x from each side

4 -2/3 x =y

Substitute this into the first equation

112 = 30x + 11y

112 = 30x +11(4-2/3x)

112 = 30x +44 -22/3 x

Subtract 44 from each side

112-44 = 30x +44-44 -22/3 x

68 = 30x -22/3 x

Get a common denominator on the right of 3

68 = 90/3x -22/3 x

68 = 68/3 x

Multiply each side by 3/68

68 * 3/68 = 68/3 * 3/68 x

3 =x

Answer:

Δ ABC is the required triangle.

Step-by-step explanation:

Since the person is standing at the top of tower.

let the height of tower be 'h' and 'b' be the distance from base of tower to the point where keys are dropped.

Consider, ABC be the right angled triangle with AB be the tower and A be the point where person is standing and C denotes the point where keys dropped finally.

Alpha (α) be the angle at which keys is dropped.

BC denotes the distance from foot of tower to the keys.

Answer:

The population of the town at the end of 2017 was 65,550.

Step-by-step explanation:

The population of the town was 60,000 in the beginning of 2016.

In 2016, the total population is increased by 15%.

[tex]60,000\times\frac{15}{100}=9000[/tex]

Therefore the population is increased by 9000 and the population of the town at the end of 2016 was

[tex]60,000+9000=69,000[/tex]

In 2017, the total population is decreased by 5%.

[tex]69,000\times\frac{5}{100}=3450[/tex]

Therefore the population is decreased by 3450 and the population of the town at the end of 2017 was

[tex]69,000-3450=65,500[/tex]

Therefore the population of the town at the end of 2017 was 65,550.

Answer:

The answer for fraction part is 6/7

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Answer:

[tex]\frac{13}{20}[/tex] of the group's video games is either at Jeromes house or Marios  house.

Step-by-step explanation:

Given the statement: Jerome has 1/4 of the group's video games at his house.

Also,Mario has 2/5 of the group's video games at his house.

⇒ Jerome has group's video games at his house(J) = [tex]\frac{1}{4}[/tex]

and

Mario has group's video games at his house(M) = [tex]\frac{2}{5}[/tex]

To find the fraction of the group's video games is either at Jerome house or Mario house.

Between two they have = [tex]J+M[/tex] = [tex]\frac{1}{4} + \frac{2}{5} = \frac{5+8}{20} =\frac{13}{20}[/tex] of the group's video games.

The height of the Kite from the ground is √19 feet.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, A kite flying in the air has a 10-ft line attached to it and its line is pulled taut and casts a 9-ft shadow.

The line can be thought of as a hypotenuse and the shadow as the base.

So, We have to find the height of the kite.

Therefore, From the Pythagoras theorem,

Base² + Height² = Hypotenuse².

9² + Height² = 10².

Height² = 100 - 81.

Height² = 19.

Height = √19.

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x = number of messages sent or received

y = total cost per month

Plan A costs $30 per month plus $0.10 per text message. So the cost for plan A is y = 0.10*x + 30. The portion 0.10*x represents just the cost of the 10 cents per message, and then we add on the fixed cost of $30 to get the total cost.

In a similar fashion, plan B's cost is y = 60. There is no cost per message, so we don't have to include x in the picture. The cost is a flat fee, which leads to a flat horizontal line graph (as shown in the attachment below)

Our two equations are: y = 0.10x+30 and y = 60. Let's use substitution to find x

y = 0.10x + 30

60 = 0.10x + 30 ... replace y with 60 (works because y = 60)

60-30 = 0.10x

30 = 0.10x

0.10x = 30

x = 30/0.10

x = 300

If you send or receive 300 messages, then both plans will cost the same. We can see this on the graph below where the two lines cross at (300,60). Note how plugging x = 300 into the first equation simplifies to y = 60.

Answer:

C. (X-9)^9 + (y+9)^2= 16

D. (X-9)^2 + (y+5)^2= 9

Step-by-step explanation:

The formula for a circle is

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

where (h,k) is the center of the circle and r is the radius

The 4th quadrant is where x is positive and y is negative

Add r to the y coordinate of the center and if it is still negative, the circle is still completely in the 4th quadrant

A. (X-12)^2 + (y+0)^2= 72

The center is at 12,0 and the radius is sqrt(72) = 6sqrt(2)

This will be positive so it goes into the 1st quadrant

B. (X-2)^2 + (y+7)^2= 64

The center is at 2,-7  and the radius is 8

-7+8=1 so it goes into the 1st quadrant

C. (X-9)^9 + (y+9)^2= 16

The center is at 9,-9  and the radius is 4

-9+4 = -5  so it is completely in the 4th quadrant

D. (X-9)^2 + (y+5)^2= 9

The center is at 9,-5 and the radius is 3

-5+3 = -2 so it is completely in the 4th quadrant

Answer:

C and D

Step-by-step explanation:

The fourth quadrant is the bottom, right quadrant. In the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative.

For a circle to be completely within the fourth quadrant, the circle must have its center in the fourth quadrant, and the center has to be far away enough from the positive x-axis and from the negative y-axis, that no points on the circle are outside the fourth quadrant.

Choice A has center (12, 0), so it cannot be.

Choice B has center (2, -7) and radius 8. Many points will be past the axes.

Choice C has center (9, -9) and radius 4. All points will be in the fourth quadrant.

Choice D has center (9, -5) and radius 3. All points will be in the fourth quadrant.

Answer: C

Step-by-step explanation:

The general form of the equation is: g(x) = a|x - h| + k  ;

4 units left means h = 4

2 units up means k = 2

--> g(x) = |x - 4| + 2

Option: C is the correct answer.

                C.   [tex]g(x)=|x+4|+2[/tex]

The parent function f(x) is given by:

             [tex]f(x)=|x|[/tex]

Now, we know that for any parent function f(x) the transformation of the type:

 f(x) → f(x+k)

is a translation of the function f(x) k units to the right if k<0

and k units to the left if k<0

and the transformation of the type:

           f(x) → f(x)+k

is a translation of a function f(x) k units upward if k>0

and k units downward if k<0

Now here it is given that:

The function f(x) is shifted 4 units left and 2 units up.

Hence, the transformed function g(x) is given by:

[tex]g(x)=f(x+4)+2\\\\i.e.\\\\g(x)=|x+4|+2[/tex]

Answer:15

Step-by-step explanation:

Answer:

Given equation are:

[tex]y = -\frac{1}{4}x+8[/tex]                  ......[1]

[tex]-2x+8y = 4[/tex]                             .....[2]

Now, Equation of a line is in the form of y =mx+b where m is the slope of the line.

Slope[tex](m_1)[/tex] of equation of line in [1] is;

[tex]y = -\frac{1}{4}x+8[/tex]  

then;

[tex]m_1= -\frac{1}{4}[/tex]

Slope[tex](m_2)[/tex] of equation of line in [2];

[tex]-2x+8y = 4[/tex]

Add both sides 2x we get;

-2x + 8y + 2x = 2x + 4

Simplify:

8y = 2x +4

Divide both sides by 8 we get;

[tex]y = \frac{1}{4} x + \frac{1}{2}[/tex]

then;

[tex]m_2 = \frac{1}{4}[/tex]

Therefore, the given two lines are neither parallel nor perpendicular.

Answer: D) 4

Step-by-step explanation:

x⁴ - x³ - 9x² + 7x + 14 = 0

possible rational roots are: ±{1, 2, 7, 14}

Try x = -1

-1  |   1   -1   -9   7   14

   |   ↓  -1     2   7   -14

       1   -2    -7   14   0 ← remainder is 0 so x = -1 is a root

Let's try x = 2 with the factored polynomial

2  |  1   -2   -7   14

   |  ↓    2   0   -14

       1    0   -7    0  ← remainder is 0 so x = 2 is a root

Factored polynomial x² - 7 can be factored to:

(x - √7) (x + √7)

⇒ x = √7   and x = -√7

The roots are x = {-1, 2, √7, -√7) which are all real numbers.

Answer:

The number of gallons of gas Karl used is 15 gallons.

Option (C) is correct.

Step-by-step explanation:

As given

Karl drove 617.3 miles.

For each gallon of gas, the car can travel 41 miles.

i.e

1 gallons = 41 miles

[tex]1\ miles = \frac{1}{41}\ gallons[/tex]

Now find out for the  617.3 miles.

Thus

[tex]617.3\ miles = \frac{617.3}{41}\ gallons[/tex]

[tex]617.3\ miles = 15.1\ gallons[/tex]

[tex]617.3\ miles = 15\ gallons\ (Approx)[/tex]

Therefore the number of gallons of gas Karl used is 15 gallons.

Option (C) is correct.

Answer:

first answer is -10

second answer is 10

third answer is -2

fourth answer is 2

Step-by-step explanation:

Explanation to get the answers:

you plug in the b c d and a

depending on what your abc and d are will depend on how the equation goes

like for example if the equation is

a x (c) - (-d) + b

and a=5, b=8, c=10, d=15

then you plug 5 where a is

plug in 10 where c is

plug 15 where d is as a negative

and lastly plug 8 where b is

if you have a calculator/graphing calculator i would use it to help answer these equations

a graphing calculator solves it for you without doing all the extra work like you would on a regular calculator

i use the graphing calculator to help solve equations like this specific one and it works very well

i hope my answers and explanation helps you :)

Answer:

d= 10.44030651

Step-by-step explanation:

The diameter is the length  between the endpoints.  We can find it using the distance formula.

d= sqrt((x2-x1)^2+(y2-y1)^2 )

d = sqrt((-6-4)^2+ (-1-2)^2)

d = sqrt((-10)^2+(-3)^2)

d= sqrt(100+9)

d = sqrt(109)

d= 10.44030651

Hi there! :)

Answer:

B. hexagon

Step-by-step explanation:

Every hexagon tessellates. Hexagon is a plane figure having six sides.

I hope this helps you!

Have a nice day! :)

:D

-Charlie

Thank you!

Answer: hexagon

Step-by-step explanation:

We know that equilateral triangles, squares and regular hexagons are the only regular polygons that tessellate .

Hexagon is a six sided regular polygon having all its sides equal. It is one of the three regular polygons which tessellates.

Therefore, from all the given choices the correct answer would be "hexagon".

The complete statement :-Every hexagon tessellates.

Answer:

16%

Step-by-step explanation:

To find this, we have to divide the amount spent on books by the total amount, then multiply by 100:

[tex]\frac{368}{2300}  * 100 = 16[/tex]

So 16% was spent on books!

16% of last semester college costs was spent on books.

To find the percent of last semester college costs spent on books, we need to divide the amount of money spent on books by the total cost of last semester and multiply by 100 to get a percentage.

Amount spent on books: $368

Total cost of last semester: $2300

Percentage spent on books: 368/2300 * 100 = 16%

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[tex](x^{2} +8x+16)(x^{2} -8x+16)\\(x+4)^{2} (x-4)^{2} \\(x^{2}-16)^{2} \\[/tex]

it is true; just work them out, you should get what they got :))

Answer:

True.

Step-by-step explanation:

We have been given an equation [tex][x^2 + 8x + 16]\cdot [x^2- 8x+16] = (x^2-16)^2[/tex]. We are asked to determine whether our given equation is true or false.

To answer our given problem, we will simplify left side of our given equation using distributive property as:

[tex]x^2(x^2- 8x+16)+ 8x(x^2- 8x+16)+16(x^2- 8x+16)[/tex]

[tex]x^4- 8x^3+16x^2+ 8x^3-64x^2+128x+16x^2-128x+256[/tex]

Combine like terms:

[tex]x^4- 8x^3+ 8x^3+16x^2+16x^2-64x^2+128x-128x+256[/tex]

[tex]x^4-32x^2+1256[/tex]

Now, we will expand right side of our given equation using perfect square formula as:

[tex](x^2-16)^2=(x^2)^2-2(x)(16)+16^2[/tex]

[tex](x^2-16)^2=x^4-32x+256[/tex]

Since both sides of our given equation are equal, therefore, our given statement is true.

Answer: 75

Step-by-step explanation:

    [tex]2^A3^B5^{13}=20^D18^{12}[/tex]

⇒ [tex]2^A3^B5^{13}=(2^2\cdot5^1)^D(2^1\cdot3^2)^{12}[/tex]

⇒ [tex]2^A3^B5^{13}=(2^{2D}\cdot5^D)(2^{12}\cdot3^{24})[/tex]

⇒ [tex]2^A3^B5^{13}=2^{2D+12}\cdot3^{24}\cdot5^D[/tex]

Now compare the like bases:

[tex]2^A=2^{2D+12}[/tex] ⇒ A = 2D + 12

[tex]3^B=3^{24}[/tex] ⇒ B = 24

[tex]5^{13}=5^D[/tex] ⇒ D = 13

Next, let's solve for A:

A = 2D + 12

  = 2(13) + 12

  = 26 + 12

  = 38

LAST STEP: Find the sum of A, B, and D

S = A + B + D

  = 38 + 24 + 13

  = 75

Answer:

B. 315 mi.

Step-by-step explanation:

180 ÷ 4 = 45

45 x 7 = 315

or...

180 ÷ 4 = 45

45 x 3 = 135

135 + 180 = 315

I hope this helps!

Cheers, July.

The train travels option B. 315 miles in 7 hours.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Distance train travelled = 180 miles

Time taken to travel the distance = 4 hours

Speed = Distance / Time

           = 180 / 4

           = 45 miles per hour

Also, given that train travels at constant speed.

Distance = Speed × Time

Since speed is constant, the distance train travelled in 7 hours will be,

Distance = 45 × 7

               = 315 miles

Hence the distance train travelled in 7 hours is 315 miles.

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