Find the common ratio 2,2/3,2/9,2/27,2/81

The answer to the given word problem is as follows. From the calculations: Johanna purchased

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation.

The calculations is given as follows:

Step 1 -  First, let's define the variables to represent the unknowns.

Let p = number of pens

Let n = number of notebooks

Let h = number of highlighters

p + n + h = 17 ......................... 1  (purchased 17 items)

.5p + 4n + 1.5h = 41.5 ...................2 (total cost $41.50)

n = h+3  ................................3 (3 more notebooks than highlighters)

Step 2...............Solve for P in equation 1

P = 17 - n - h..................4

Recall that in equation 3,

n = h + 2

If we make n the subject of the expression, we have:

n = h+ 3

Substituting that into equation 4, we have

p = 17 - (h+3) - h
p = 17 -2h - 3 ..................5

Going back to equation 2, let's substitute n with h+3 and replace p with 17 -2h - 3

.5(17 -2h - 3) + 4 (h+3) + 1.5h = 41.5

To remove all decimals, we can multiply all with 10 to get:

5(170-20h -30) + 40(10h +30) + 15h = 415

Expand all brackets and we have:

850 - 100h - 150 + 400h + 1200 + 15h = 415

Collect like terms

-100h + 400h + 15h = 415-850+150-1200

315h = -1485

h = -1485/315

h = -4.71

Since a physical item cannot be negative, we utilize the absolute value which is:

h = 4.71

h [tex]\approx[/tex] 5 highlighter

Recall that

n = h + 3

Hence

n = 5 +3 = 8 notebooks

Recall that

p + n + h = 17

Hence we have

p + 8 + 5 = 17

p = 17 -8 - 5

p = 17 - 13
P = 4 pens.

Hence Johanna purchased

4 pens, 8 notebooks and 5 highlighters.

Learn more about Word Problems:
https://brainly.com/question/13818690
#SPJ1

The correct equation that is balanced using the given numbers once is;

5(-1 + (-3)) = (7 * -4) + 8

There are different properties of Algebra such as;

Commutative Property of Addition or multiplication

Associative Property of Addition or multiplication

Distributive Property

Now, from the given numbers, it will be best to use only a positive digit outside the bracket on the left hand side to make it easy to balance on the right hand side. Thus, for the left hand side we will try;

5(-1 + (-3))

When that is solved we will get -20

Now, to balance that on the right hand side , we will have;

(7 * -4) + 8

Read more about Algebra Properties at; https://brainly.com/question/11131460

#SPJ1

1.

(a) 2π - 9

= 2 x 3.142 - 9 = 6.284 - 9

= -2.716

This will be closest to the letter C on the number line.

(b) [tex]\sqrt{3}[/tex]

= 1.732

This will be closest to the letter T on the number line.

(c) [tex]\sqrt[3]{9}[/tex] - 8

= 3-8

= -5

This will be closest to the letter S on the number line.

To learn more about Real numbers, refer to:

https://brainly.com/question/551408

#SPJ13

Answer:

1

Step-by-step explanation:

The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.

Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Equation of line is y = 2/3x + 2

The equation of the image is y = 3x - 4

In this question, we have been given a line y = 3x + 2 is reflected in the line y = -1.

We need to find the equation of the image.

The reflected line must be parallel to the line y = 3x + 2

So, the slope of the image must be equal to the slope of the line y = 3x + 2

The y-intercept of the line y = 3x + 2 is (0, 2)

The distance between point (0, 2) and the line y = -1 is 3 units.

So, the y-intercept of the reflected line must be (0, -4)

With slope m = 3 and y-intercept (0, -4) the equation of the line would be,

y = 3x - 4

Therefore, the equation of the image is y = 3x - 4

Learn more about equation of line here:

https://brainly.com/question/24524587

#SPJ1

Answer:

Step-by-step explanation:

Answer: 145

Step-by-step explanation:

To find the total of the three numbers: 115 x 3 = 345

So the 3rd number must be 345 - 110 -90 = 145

Check the answer= 110 + 90 +145

                                         3

= 115

A and C because it asks which word is in the square and pentagon, it is the a and the c

The inequality that describes the domain is 0 ≤ x ≤ 5

The given parameters are

Size of tank = 3 gallons

Rate = 0.6 gallons per hour

The highest number of time is calculated as

Time = Size of tank/Rate

Substitute the known values in the above equation

So, we have the following equation

Time = 3/0.6

Evaluate

Time = 5

The domain is then represented as

0  ≤ x ≤ Time

This gives

0 ≤ x ≤ 5

Hence, the domain of the situation is 0  ≤ x ≤ 5

Read more about domain at

https://brainly.com/question/2264373

#SPJ1

Answer:

a) 69 b) -11

Step-by-step explanation:

-8 + 77 or 77 - 8 = 69

-21 + 10 = 11

The illness is spreading at a rate of 10% per hour -> it is spreading 1.1x faster per hour as 10% more people are infected each time.

Therefore, we can write the amount of people infected as 3 x [tex]1.1^{n}[/tex], where n is the hour. So, if n equals 1, the amount of people infected is 3 x 1.1 = 3.3 (so when this mark surpasses the 1200 limit, we round up to the nearest whole number)

It will take 1200 : 3 : 1.1 = 363.636364.. (hours)

If it's only 363 hours, the number of people infected will not have reached 1200, as we have .636364 hours left. So, it will take 364 hours.

Answer:

y=x/4

Step-by-step explanation:

if the line is perpendicular (m2)=-1/(m1)

m2=1/4

y=x/4+c

sub in 8,2

2=8/4+c

c=0

equation is therefore y=x/4

Answer:

Plane EFGH

Step-by-step explanation:

we can see that plane ABCD is on the bottom

and that plane EFGH is on the top

so if the go left and right, they will never touch that is what parallel is

any other plane will intersect or touch eventually

Answer:

1. perpendicular

2. parallel

3. neither

Step-by-step explanation:

The first set of lines are perpendicular because they intersect each other at a right angle.

The second set of lines are parallel because they never cross.

The first pair forms a 90° angle therefore the lines are perpendicular.

The second lines are straight that it's obviously clear they will never meet meaning they are parallel

the third lines are neither perpendicular nor parallel.

Answer:

-11 F

Step-by-step explanation:

So we need to just add or decrease the temperature.

-5 + 14

9 - 20

-11

Answer:

-5 + 14 = 9

9 - 20 = -11

the answer is -11°f

Based on the trend found in the data set, the x-coordinate that would yield a y-coordinate of 30 is 28

Pick two points from the data set:

(26, 31) and (64, 13)

The slope is:

= Change in y / Change in x

= ( 13 - 31) / (64 - 26)

= -18 / 38

= -9/19

The y-intercept is:

y = mx + b

13 = -9/19(64) + b

b = 43.3

The x-coordinate that gives a y-coordinate of 30 is:

30 = -9/19x + 43.3

x = 28

Find out more on trend in data set at https://brainly.com/question/24679525

#SPJ1

Suppose that $25,200 is invested in a certificate of deposit for 2 years at 11.1 % annual interest to be compounded semi-annually, compound interest will this investment earn is $5,904.8892.

Compound interest, also known as interest on the principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on principal amount plus any accumulated interest. In the finance and economics, compound interest is common.

In contrast to the simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time. The interest per period multiplied by number of periods in a year yields the simple annual interest rate. The nominal interest rate is the another term for the basic annual interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

It is known that the compound interest is given as

Compound Interest = [total amount of the principal and interest in future]-[total amount of the principal in present]

                                 =[tex]P(1+i)^{2} - P\\P(1+i)^{2} - 1\\[/tex]

where, p= principal, i= nominal annual interest, n= the number of  the compounding period

Given

P = $25,200

i= 11.1% = 0.111

n= 2

compound interest is

C = 25,200 [[tex](1+0.111)^{2}[/tex]-1]

  = $5,904.8892

The investment will earn the interest of $5,904.8892.

To know more about compound interest visit: https://brainly.com/question/15353704

#SPJ9

For Roberts the equation is:

to we can write it as slope intercept so:

Now we replace x = 5 so

So the two points are ( 0 , -5) and ( 5 , -4)

Fo Hookthe equation is:

In slope intercept is:

so we replace x = 5 so:

So the two points are: ( 0 , 0) and ( 5 , 2 )

For Elizabeth the equation is:

and slope intercept:

now we replace x = 2 so:

So the coordinates are ( 0 , 5) and ( 2, 6 )

And for Silver the equation is:

In slope intercept is:

now we replace x = 1 so:

So the coordinates are: ( 0, -3) and ( 1, 1 )

So now you can made the graph of the lines and find the message.

Answer:

the length is 99m

Step-by-step explanation:

you have to add 86 to 86 to get 172, subtract 172 from 370 then you have 198 then divide to have  99m the length.

If a case of 24 pairs of the same kind of switches cost a little more than $800. $28 per pair with tax included is not  good estimate of the price  but  $33.33 is the good estimate for the price .

Assuming that the  cost per pair is the amount of $28. Hence, cost of 24 pairs is calculated as:

Cost= $28x24

Cost  = $672.

Based on the above calculation for the cost of 25 pairs we can see that that the  24 pairs of the same kind of switches does not cost more than $800 which implies that $28 is not good estimate for the price.

Now let determine the best estimate of the price with tax included :

Cost = $800/24

Cost = $33.33

Therefore the good estimate for the price with the tax included is $33.33.

Learn more about estimated price here: https://brainly.com/question/11292014

#SPJ1

Answer:

write a semi formal letter to your father's friend

4y = x + 6 is the equation of the line using the slope value.

The steepness of a line segment is explained by the slope of the line. It is a ratio of the vertical x-axis coordinates and the y-axis coordinates. The classification of whether two lines are parallel or perpendicular depends on the slope value.

The parameters for the line segment are as follows, in accordance with the question:

The coordinate points (6, 3) and the slope of a line (1/4) are as follows: (x = 6; y = 3)

Using the line segment's standard equation now: y = mx + c

If (x, y) are coordinates, "m" is the slope, "c" is the y-intercept,

The following results are obtained by replacing the slope and y-intercept values in the formula:

y = mx + c

⇒ 3 = (1/4)(6) + c

⇒ c = 3 - 3/2 = 3/2

Consequently, c = (3/2) is the y-value. intercept's

by changing the slope value and y-intercept value in the line's equation:

y = (1/4)x + (3/2) = 4y = x +6

Consequently, 4y = x + 6 is the equation of the line using the slope value.

To learn more about the slope of a line from the given link:

https://brainly.com/question/16949303

#SPJ10

Using trigonometric functions :

From the problem, we have a hypotenuse of 22.25 cm and an angle of 31°28'

To find A, we will use the sine function :

To find B, we will use the cosine function :

The total length is the sum of A and B :

A + B = 11.615 + 18.978 = 30.59

The answer is 30.59 cm

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{7}~~ = ~~\cfrac{10}{x}\implies x^2=70\implies x=\sqrt{70}[/tex]

THE VOLUME OF A RECTANGULAR PRISM ID GIVEN BY

[tex]v = l \times b \times h \\ = ( \frac{7}{2} in) \times ( \frac{5}{2} in) \times ( \frac{3}{2} in) \\ \\ v = \frac{35}{2} {in}^{2} \times \frac{3}{2} in \\ v = \frac{105}{2} {in}^{3} \\ v = 52\times \frac{3}{2} {in}^{3} [/tex]

THE FIRST OPTION IS THE ANSWER!!

Answer: It's $12 an hour.

Step-by-step explanation: