The gardening store sells clay flower pots, which hold 2 litres of dirt, and ceramic flower pots, which hold 7 litres. Tara bought 35 flower pots, which will hold a total of 150 litres of dirt. How many of each flower pot did she buy?

Answer:

2.$9.25  3.11

Step-by-step explanation:

For the first question virtually you could just go through each one and determine how they would fit. But what I did for both is determine the change in the first column (5 in #2 3 in #3) Then subtract the second change from the first in the second column (185-138.75 and 132-99) you come up with a rate of change like (46.25 and 33) then using that number dividing by the change from the first column (46.25/5=9.25 and 33/3=11) And to check applying all of that to the other changes.

Answer:

Step-by-step explanation:

abc = 1

We have to prove that,

[tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]

We take left hand side of the given equation and solve it,

[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}[/tex]

Since, abc = 1,

[tex]\frac{1}{c}=ab[/tex] and c = [tex]\frac{1}{ab}[/tex]

By substituting these values in the expression,

[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}[/tex]

                                       [tex]=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}[/tex]

                                       [tex]=\frac{1+b+ab}{1+b+ab}[/tex]

                                       [tex]=1[/tex]

Which equal to the right hand side of the equation.

Hence, [tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]

Answer:

y=1/2x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or kx

The value of the constant k is equal to the value of the slope m

In this problem we have the point (8,4)

Find the value of k

y/x=k------> substitute the value of x and y

4/8=k

k=1/2

The equation is equal to

y=1/2x

Answer:

2nd option

Step-by-step explanation:

the domain is from 0 to infinity

we count 0 because

f(0)=1 (just look in the graph)

so

[tex]x \geq 0[/tex]

which is the 2nd option

Answer: x < 2

-3x + 7 > 1

<=> -3x > - 6

<=> x < -6/-3

<=> x < 2

Step-by-step explanation:

Answer:

36%

Step-by-step explanation:

Jeans: 14

Shorts: 9

Capris: 2

Total number of students = Number of Jeans + Number of Shorts + Number of Capris

Total number of students = 14 + 9 + 2 = 25

% of students wearing shorts = Number of shorts / Total number of students * 100

% of students wearing shorts = 9 / 25    * 100 = 0.36  * 100 = 36%

Answer:

tanx + cotx =  [tex]\frac{1}{sinxcosx}[/tex]

Step-by-step explanation:

Explanation

Take R.H.S   = [tex]\frac{1}{sinxcosx}[/tex]

            =      [tex]\frac{sin^{2}x+cos^{2}x }{sinxcosx}[/tex]

          =      [tex]\frac{sin^{2}x }{sinx cosx} + \frac{cos^{2} x}{sinxcosx}[/tex]

        = [tex]\frac{sinx}{cosx} + \frac{cosx}{sinx}[/tex]

        = tanx + cotx

tanx + cotx =  [tex]\frac{1}{sinxcosx}[/tex]

Answer:

Step-by-step explanation:

Diagonal is 60 inches, height is 24 inches so

60^2 = 24^2 + width^2

6.25 inches

Step-by-step explanation:

P * h = k, where k is a real constant.

Answer:

(i) ∠ABH = 14.46⁰

(ii) The length of AH = 4.6 m

Step-by-step explanation:

From the image uploaded;

Consider △ABC;

the length of b is calculated by applying Pythagoras theorem as follows;

b² = c² - a²

b² = (13.2)² - (6.9)²

b² = 126.63

b = √126.63

b = 11.25 m

Also, ∠ABC is calculated as;

[tex]Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o[/tex]

Consider △CBH, ∠CBH is calculated as;

∠CBH = 90⁰ - 46⁰ = 44⁰

(i) ∠ABH will be calculated as;

∠ABH = θ

θ + 44⁰ = ∠ABC

θ + 44⁰ = 58.46⁰

θ = 58.46⁰  - 44⁰

θ = 14.46⁰

Thus, ∠ABH = 14.46⁰

(ii) The length of AH

length HC is calculated as;

[tex]tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m[/tex]

length of AH = CA - HC

x = b - HC

x = 11.25 - 6.66

x = 4.6 m

length of AH = 4.6 m

Answer:

2.8125 mile

Step-by-step explanation:

hope its right

Given:

The function is

[tex]f(x)=-5x-7[/tex]

To find:

The rate of change of the given function.

Solution:

We have,

[tex]f(x)=-5x-7[/tex]        ...(i)

It is a linear function because the degree or power of x in this function is 1.

Slope of a linear function is always constant.

The slope intercept form of a linear function is

[tex]f(x)=mx+b[/tex]      ...(ii)

where, m is slope and b is y-intercept.

On comparing (i) and (ii), we get

[tex]m=-5[/tex]

It means, the function has a constant rate of change, decreasing for all x at a rate of 5.

Therefore, the correct option is D.

Answer:

Answer is in photo

Step-by-step explanation:

Answer:

2/3-3/2

Step-by-step explanation:

Answer:

C y = 7x +19

Step-by-step explanation:

There are 19 gallons in the water tank and 7 gallons are added when you take x amount of minutes, which gives you y.

An example is 1 minute.

Y = 7(1) + 19

y = 7 + 19

y = 26

You have to remember that there are 19 gallons already in the tank and that 1 minute has passed, which means 7 gallons have been added. Thus there are 26 gallons in the water tank.

Hope this helps. :)

Answer:

I think the answer is A hopefully this helps

Answer:yes he is correct

Step-by-step explanation: if you go on a certain site and you put in the equation, you press enter then it will pop up with what you want to do. Press graph, then you can compare the graphs and if it is the same you know it is correct

9514 1404 393

Answer:

  see attached (7 dimes, 5 nickels)

Step-by-step explanation:

The inequalities are plotted in the attachment. The solution shown is ...

  (x, y) = (7, 5)

7 dimes and 5 nickels are 12 coins worth $0.90. This is the maximum number of coins, worth more than $0.85.

9514 1404 393

Answer:

  both C and D are correct

Step-by-step explanation:

The diagram shows that x is the total of $40 and 20% of $40.

Description A would be represented by the difference of $40 and 20% of $40, not the sum.

Description B would be represented by 20% of $40, not the sum of that and $40.

Both descriptions C and D are properly represented in the diagram.

Answer:

0.95

Step-by-step explanation:

[tex]Correlation \ coefficient \ (r) = \dfrac{covaraince \ between \ X \ and \ Y }{SD_X \times SD_Y }[/tex]

[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{10^{1/2} \times 25^{1/2} }[/tex]

[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{3.162 \times 5 }[/tex]

[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{15.81 }[/tex]

[tex]Correlation \ coefficient \ (r) \simeq 0.95[/tex]

Answer:

The answer is 11

Step-by-step explanation:

so substitute 3 for x, then your equation would be 3^2 + 2

3^2 is 9

9 + 2 = 11

Answer:

Tn = 2n+4

T20 = 44

Step-by-step explanation:

Given Sn = n²+ 5 n-6

Tn = Sn - Sn-1

Sn-1 = (n-1)² + 5(n-1) - 6

Tn = n²+ 5n-6 - ((n-1)² + 5(n-1) - 6))

Tn = n²+ 5n-6-(n²-2n+1+5n-5-6)

Tn = n²+ 5n-6-n²+2n-1-5n+5+6

Tn = 2n-7+11

Tn = 2n+4

Get the general term is 2n+4

To get the 20th term;

T20 = 2(20) + 4

T20 = 40+4

T20 = 44

Hence the 20th term of the sequence is 44

Answer:

14n

Step-by-step explanation:

just rearrange the number with the variable

Answer:

y = -1 !!!!!!!!!!! :)))))))))))))

Answer:

y=-1

Step-by-step explanation:

symmetry is where it is the same on both sides, so that would be the line between the top and bottom point and because they are up and down it is a y whereas if it were side to side it would be x. it is on the left side which are negatives and it is one over to the left making it y=-1

Answer:

38

Step-by-step explanation:

Simplifying

6 + -5x + -3x = 38

Combine like terms: -5x + -3x = -8x

6 + -8x = 38

Solving

6 + -8x = 38

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -8x = 38 + -6

Combine like terms: 6 + -6 = 0

0 + -8x = 38 + -6

-8x = 38 + -6

Combine like terms: 38 + -6 = 32

-8x = 32

Divide each side by '-8'.

x = -4

Simplifying

x = -4

Answer:

I think the answer is 14.5x-132

Step-by-step explanation:

6.5x+3x+5x=14.5x

38+10-180=-132

=14.5x-132

Answer:

6.93 lbs.

Step-by-step explanation:

The weight on the moon is approximately 16.5% of what you would weigh on Earth. Using this information, we can say that 16.5% of 42 lbs would equal how much the object would weigh on the moon.

I prefer to convert percentages the decimal way, so let's do it that way. 16.5% is 0.165 as a decimal, so now all we have to do is multiply 0.165 by 42 (since we are saying 16.5% of 42 lbs), and we get 6.93 lbs.

Hope this helps! :)

Answer:

sorry i only know the number 2.

so the answer is the first one...

Answer:

153.16

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = ???

μ is the population mean = 140

σ is the population standard deviation = 8

Top 5% means the score is in the 95th percentile

The z score of 95th percentile = 1.645

1.645 = x - 140/8

Cross Multiply

1.645 × 8 = x - 140

13.16 = x - 140

x = 13.16 + 140

x = 153.16

Therefore, the minimum score needed to be in the top 5% of the scores on the test is 153.16

Answer:

y = - [tex]\frac{2}{3}[/tex] x - 7

Step-by-step explanation:

A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

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

~~~~~~~~~~~~~

( - 6, - 3 )

( - 3, - 5 )

m = [tex]\frac{-5+3}{-3+6}[/tex] = - [tex]\frac{2}{3}[/tex]

y + 5 = - [tex]\frac{2}{3}[/tex] ( x + 3)

y + 5 = - [tex]\frac{2}{3}[/tex] x - 2

y = - [tex]\frac{2}{3}[/tex] x - 7