Determine the next three terms in the following sequence: 2, 3, 5, 8, ____, ____, ____,... a. 13, 19, 26 b. 12, 17, 23 c. 12, 16, 20 d. 13, 17, 23 Please select the best answer from the choices provided A B C D

Option: D is the correct answer.

  D.    The slope of is 3, and passes through O.

It is given that:

AB is dilated by a scale factor of 3 to form AB .

Also, the line AB pass through the origin.

So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:

[tex]Slope=\dfrac{y-0}{x-0}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]

( Since, it is given the slope of AB is 3 )

Now , if AB is dilated to A'B' by a scale factor of 3 then

(0,0) → (0,0)

and

(x,y) → (3x,3y)

i.e. (0,0) and (3x,3y) will lie on A'B'.

Hence, the slope of line A'B' is given by:

[tex]Slope=\dfrac{3y-0}{3x-0}\\\\i.e.\\\\Slope=\dfrac{3y}{3x}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]

Hence, both have the same slope.

                The answer is :  Option: D

Answer:

Step-by-step explanation:

Answer: 0.44444444444....

Step-by-step explanation: 4/9 is the same as 4 ÷ 9. 9 does not divide into 4, so we add a 0 and bring down a 0 to get 9 divided by 40. 9 can be multiplied by 4 to get 36, 40 - 36 = 4, bring down another 0, 9 can be multiplied by 4 to get 36, 40 - 36 = 4.... this is a never ending decimal.

Answer:

f(x) = -38

Step-by-step explanation:

well f(x) is the same thing as y so just write it as y so its easier to understand.

y = -2x -13

take the x value they give you which in this case is 5 and plug it in to the x in your equation.

y = -2(5) -13

now just use a calculator or something and find that

y = -25 - 13

and finally

y = -38

now just change y back to f(x) if needed

hope this helps :)

Answer:

If the python has the area x sq. ft, they all have the area [tex]\dfrac{5x}{2}+538\ sq. ft.[/tex]

Step-by-step explanation:

Let x sq. ft be the area the python has.

1. If the anaconda has 538 more square feet than the python, then the anaconda has (x+538) sq. ft.

2. If the python has twice as many square feet as the rattlesnake, then the rattlesnake has the area  [tex]\dfrac{x}{2}\ sq. ft.[/tex]

In total they have the area  

[tex]x+(x+538)+\dfrac{x}{2}=\dfrac{5x}{2}+538\ sq. ft.[/tex]

As an improper fraction, the simplified answer would be 9/7 after you divide both top and bottom by 10

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

If you need a mixed number, then 9/7 converts to 1 & 2/7 because

9/7 = 1 remainder 2

If you had 9 cookies and 7 friends, then each friend gets 1 whole cookie, and there will be 2 left over.

Answer:

The answer would be 9/7 as improper, but if you want the mixed number it would be 2 2/7. Glad I could help let me know if I can do anything else

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

given sin x ≈ 0.2588, then

x = [tex]sin^{-1}[/tex](0.2588) ≈ 15°

using the cofunction identity

cos x = sin(90 - x)

the complement of 15° is 90° - 15° = 75°, hence

cos 75° = sin(90 - 75)° = sin15° ≈ 0.2588

Answer:

It will take 10 hours.

Step-by-step explanation:

We know distance = rate * time

Sally's rate = 55

Jim's rate = 65

We want Jim to be 100 miles ahead of Sally

The time will always be the same.

d =Sally's distance

Sally

d = 55t

Jim

d+100 = 65 t

We know have 2 equations with 2 unknowns.  Substitute d= 55t into Jim's equations

55t + 100 = 65t

Subtract 55t from both sides.

55t-55t + 100 = 65t-55t

100 = 10t

divide each side by 10

100/10 = 10t/10

10 = t

Answer:

It will take exactly 10 hours

Step-by-step explanation:

Answer:

Each student would get 4 inches of ribbon

Step-by-step explanation:

Mrs. Barkley has 75 inches of ribbon and is splitting it between 18 students so you would divide 75 by 18. When you divide you get 4.166666... etc. So the answer would be 4

Each of the 18 students in Mrs. Barkley's class will receive 50 inches of ribbon when 75 feet of ribbon are divided equally among them.

The student has asked how many inches of ribbon each student will get if Mrs. Barkley has 75 feet of ribbon and splits it equally among 18 students. To solve this problem, we first need to convert feet to inches because there are 12 inches in a foot. Then we divide the total inches of ribbon by the number of students.

Total length of ribbon for each student= 75/18

The total length of ribbon for each student≈4.1667

So, each student will receive approximately 4.1667 feet of ribbon.

To find out how many inches this is, we'll convert this value to inches. Since 1 foot is equal to 12 inches, we can multiply the total length of the ribbon for each student by 12:

The total length of ribbon for each student (in inches)=4.1667×12

The total length of ribbon for each student (in inches)≈49.9999

Therefore, each student will receive approximately 50 inches of ribbon.

Answer:

the area of this trapezoid= 81 square inches

Step-by-step explanation:

To find area of trapezoid , we use formula

[tex]Area = \frac{a+b}{2} * h[/tex]

Where a,b are the base of the trapezoid

h is the height of the trapezoid

Here a= 3 in

b = 15 in

h = 9 in

Plug in all the values in the formula

[tex]Area = \frac{a+b}{2} * h[/tex]

[tex]Area = \frac{3+15}{2} * 9[/tex]

[tex]Area = \frac{18}{2} * 9[/tex]

Area = 9 * 9 = 81

the area of this trapezoid= 81 square inches

Answer:

The answer is 1/6.

In each square yard, Norah would spread 1 / 6 ton of stone.

Given that,
Norah has 2/3 tons of stone to spread equally in 4 square yards, how many tons of stone will be spread in each square yard is ot be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Quantity if Stone = 2/3 ton
Area = 4 square yards
Quantity per yard = [2/3] / 4= 1 / 6

Thus, in each square yard, Norah would spread 1 / 6 ton of stone.

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[tex]-1.8w+3.96=(-0.36)(5w)+(-0.36)(11)\\\\=\boxed{-0.36(5w+11)}[/tex]

Answer:

7.25252525

Step-by-step explanation:

Irrational numbers are numbers that never end, therefore 7.25 is an irrational number. also, none of the other ones are never ending

Answer:

9r

Step-by-step explanation:

Simplify:

4r + 9r - 11r + 7r

13r - 11r + 7r

2r + 7r

9r

The answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.

Given that,

Based on the above information, the calculation is as follows:

= 4r + 9r - 11r + 7r

= 20r - 11r

= 9r

Therefore we can conclude that the answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.

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The center of the circle described by the equation x^2 + (y+4)^2 = 64 is at the point (0,-4), and the radius is 8.

In the context of a circle, the general equation form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Looking at your given equation x^2 + (y+4)^2 = 64, it is in this general format.

Here, the value of a is 0 (as there is no number being subtracted from x) and b is -4 (the y coordinate has been shifted 4 units down). Therefore, the center of the circle is at point (0,-4).

For the radius, since r^2 = 64, the radius r will be the square root of 64 which is 8.

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Answer:

Angle ABC is 22 degrees

Angle BAC is 68 degrees

======================================

Work Shown:

Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.

The three angles A, B, C add up to 180 degrees. This is true for any triangle.

A+B+C = 180

(6x+8) + (2x+2) + 90 = 180 ... substitution

6x+8 + 2x+2 + 90 = 180

8x+100 = 180

8x+100-100 = 180-100 ... subtract 100 from both sides

8x = 80

8x/8 = 80/8 ... divide both sides by 8

x = 10

If x = 10, then angle BAC is

angle BAC = 6x+8

angle BAC = 6*10+8

angle BAC = 60+8

angle BAC = 68

Use x = 10 to find angle ABC as well

angle ABC = 2x+2

angle ABC = 2*10+2

angle ABC = 20+2

angle ABC = 22

The three angles of this triangle are A = 68, B = 22, C = 90

As a check, the three angles must add to 180

A+B+C = 180

68+22+90 = 180

180 = 180

Answers are confirmed

Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.

Answer:

1225

Step-by-step explanation:

a loss of 20% represents 80% ( 100 - 20) of the cost price

100% represents the cost price

To find the cost price divide the selling price by 80 to find 1% and multiply by 100 to find cost price

cost price = [tex]\frac{980}{80}[/tex] × 100 = 1225

[tex]\sqrt[5]3+\sqrt{12}+\sqrt{32}=\sqrt[5]3+\sqrt{4\cdot3}+\sqrt{16\cdot2}=\sqrt[5]3+\sqrt4\cdot\sqrt3+\sqrt{16}\cdot\sqrt2\\\\=\boxed{\sqrt[5]3+2\sqrt3+4\sqrt2}[/tex]

Answer:

B

Step-by-step explanation:

To get to to triangle Y'X'Z', you need to move triangle YXZ 3 units to the right (+3), and 1 unit down (-1). So (x+3,y-1)

Answer:

b

Step-by-step explanation:

Answer:

A. y = -(-x) +7 = x + 7

D. y = 0.05x + 10

Answer:

25

Step-by-step explanation:

We must find the difference between 3 1/12 and 2 1/3. So we can first subtract 3 from 2 and we earn 1 whole number. Next we must subtract  1/12 and 1/3. This is the same as 3/36-12/36, which is -9/36 or -1/4. Since we can't have -1/4 we must subtract 1/4 from 1 and earn 3/4 as our answer.

Hope this helps! <3

Answer:

1,12/ Not a solution

2,10/ solution

4,5/ solution

6,10/ not a solution

12,8/ not a solution

18,6/ not a solution

Step-by-step explanation:

all you have to do is put it into the equation.

for example:

1,12

1x1+12x3= $37

1x1+12x1.5= 19lbs

This is not a solution because he can carry it but doesn't have the money to buy it.

Answer:

(1,12)=no solution

(2,10)=Solution

(4,5)=Solution

(6,10)=no solution

(12,8)=no solution

(18,6)=no solution

Step-by-step explanation:

You have to add the money and pounds each together. For example, the equation you would set up would be, for money: 1(1)=1 and the jars 3(12)=36. Together, it equals 37, which would be over the total amount that Tyler may buy. If you do all of these to show your work, then the answers are the ones shown above.

Answer:

Option B is correct

For [tex]n\geq 1[/tex] , the function for the given sequence is defined as; [tex]f[n] = 4 +3n[/tex]

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.

An explicit formula for this arithmetic sequence given by;

[tex]a_n = a+(n-1)d[/tex] where a represents first term

Since, the given sequences; 7 , 10 , 13 , 16 and 19

⇒ common difference(d) = 3 and a = 7

Since.

10 -7 = 3

13- 10 = 3  ....

The function which defined this sequence is;

[tex]f[n]=a_n = 7 +(n-1)(3)[/tex]

using distributive property:

[tex]f[n] = 7 + 3n -3[/tex]

[tex]f[n] = 4 +3n[/tex]

therefore, the function for the given sequence for all integers [tex]n\geq 1[/tex] is;  [tex]f[n] = 4 +3n[/tex]

The correct option is D) f(n) = 4 + 3n.

Step-by-step explanation:

Given :

Arithmetic Sequence -- 7,10,13,16,19

Solution :

The explicit formula of arithmetic sequence is given by,

[tex]T_n = a+(n-1)d[/tex] ------- (1)

where, common difference (d) = 10 - 7 = 3

first term (a) = 7

So from equation (1),

[tex]T_n = 7+(n-1)3 = 7+3n-3[/tex]

[tex]T_n = 4 + 3n[/tex]

Therefore, the correct option is D) f(n) = 4 + 3n.

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Answer:

10/14, 15/21

Step-by-step explanation:

WE are given a ratio 5/7

To find equivalent ratios it is sufficient to multiply both numerator and denominator by the same number

Let us take 2,3 for example.

When we multiply both numerator and denominator by 2, value does not change.

Hence we get equivalent fraction.

So 10/14 is one such fraction.

Next is multiply by 3

15/21 is another fraction.

y=8.5x

y= money earned

x= hours worked

The equation to find Dianna's money earned as a lifeguard is e = 8.50h.

To find Dianna's money earned, we can write an equation using the formula for calculating earnings:

Earnings=Hourly Rate × Number of Hours Worked

In this case, Dianna's hourly rate is $8.50, and let's denote the number of hours she worked as ℎ.

So, the equation to find Dianna's money earned

E=8.50×h

Where:

E represents the total earnings

8.50 represents Dianna's hourly rate

h represents the number of hours worked

This equation will give us the total amount of money Dianna earned based on the number of hours she worked.

Answer:

4 Dollars and 30 cents

Step-by-step explanation:

15.95 x 6 = 95.7

100-95.7= 4.30

Final answer:

Erin bought six shirts at $15.95 each, totaling $95.70. After paying with a $100 bill, she would receive $4.30 in change.

Explanation:

The question asks us to calculate the total cost of six shirts and then determine the change from a $100 bill. Erin bought six shirts that cost $15.95 each. To find the total cost, we multiply the price of one shirt by the number of shirts:

$15.95 × 6 = $95.70.

Next, we calculate the change Erin would receive if she paid with a $100 bill:

$100 - $95.70 = $4.30.

Therefore, Erin would receive $4.30 in change.

Answer:

100% profit of 1500

Step-by-step explanation:

One the first calculator David earns 25% profit:

25% + 1500 = 1,875

He gets a 25% on the second calculator:

1500 - 25% = 1,125

In total he receives 1125 + 1875 = 3000

Therefore he has 100% profit

Final answer:

James cuts each of the three lasagnas into five equal parts, resulting in a total of 15 pieces of lasagna.

Explanation:

When James cuts each square lasagna into pieces that are each 1/5 of the lasagna, he's effectively dividing each whole lasagna into five equal parts. Since he has three whole lasagnas, each cut into 1/5-sized pieces, the total number of pieces he would end up with can be found by multiplying the number of pieces per lasagna by the number of lasagnas.

To calculate this, you multiply 5 (the number of pieces from one lasagna) by 3 (the number of lasagnas):

Multiply the number of pieces per lasagna (5) by the number of lasagnas (3).

5 pieces/lasagna × 3 lasagnas = 15 pieces

Thus, James cuts the lasagna into 15 pieces in total.

Answer:

f(x) = 34 + 25w

Step-by-step explanation:

First, we need to find the amount he was paid over the 35 weeks:

909 - 34 = 875

35w = 875

w = 875 / 35 = 25

So every week he is paid $25

The function has to start with 34, as that is the amount already in there, and as w is multiplying by 25, this can be written as 25w

So put these two together:

f(x) = 34 + 25w

Answer:

60%

Step-by-step explanation:

Use the equation a=pw. A= Part   P= Percent. W= Whole

A= $56.49

P = x (unknown)

W= $ 89.99

Equation = 56.49=89.99x

You divide 89.99 on both sides to be equal and isolate the variable x. You would divide 56.49 by 89.99 and will get 0.627736415. You would round it to the nearest tenth , 0.6 so the percent is 60%

The percent off is 37.2263 % of the sale price.

Calculations :

                with the same whole number                     =   3350/8999

              numerator and the denominator                 =  0.372263 x  [tex]\frac{100}{100}[/tex]

               equal to 100 as a percent                             = 37.2263 %

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