To sell 300 notebooks and 120 pens quickly, a store decided to create two types of gift sets. one set is to include 2 notebooks and 1 pen, and the other will consist of 1 pen and 3 notebooks. the first set will be sold for $8, while the second will be sold for $11.50. it is unprofitable to sell more than 20 of any gift set. how many gift sets of each type must the store sell to obtain the biggest possible income?

Answer: y=6/7x-1

Step-by-step explanation:

I am assuming you want a line formula in y=mx+b

slope (y2-y1)/(x2-x1) = -7+13/-7+14 = 6/7

y+7=6/7(x+7)

y+7 = 6/7x+6

y=6/7x-1

[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]

Answer:

g(26)

Step-by-step explanation:

substitute -3 for x.

g(x)=3[tex]x^{2}[/tex]-1

[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]

The number of gallons of water in the bathtub is a function of time. Therefore, it is true.

The graph shows a curve that lets you find the number of gallons of water given any value of t betweeh 0 and 30 plus.

Hence, the number of gallons of time indeed is a function of time, in the interval shown by the graph.

The answer is true, because each t value is paired with exactly one number of gallons".

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Answer:

A

Step-by-step explanation:

Answer:

-21.4

Step-by-step explanation:

0.15x + 0.2(0.15-5-x) = 0.1

0.15x + 0.03 - 1 - 0.2x = 0.1

0.15x - 0.2x = 0.1 -0.03 + 1

-0.05x = 1.07

0.05x = -1.07

x = -21.4

This rule is applied to triangles to determine the unknown sides and angles. The value of x from the diagram is 11.78m

This rule is applied to triangles to determine the unknown sides and angles.

Given the following parameter

Opposite = 5m

Adjacent = x

angle = 23 degrees

According to the theorem of tangents

tan23 = opposite/adjacent

tan23 = 5/x
x = 5/tan23

x = 11.78m

Hence the value of x from the diagram is 11.78m

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Using the given information, the unit rate is 0.0645 miles/minute

From the question, we are to determine the unit rate

From the given information,

Daniel runs 40/5 miles in 124 minutes

That is,

Distance = 40/5 miles = 8 miles  

Time = 124 minutes

Using the formula,

Rate = Distance / Time

Rate = 8 miles / 124 minutes

Rate = 0.0645 miles/minute

Hence, the unit rate is 0.0645 miles/minute

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The unit rate is 0.0645 miles/minute

We have calculated the rate

From the question, we are to determine the unit rate

From the given information,

Daniel runs 40/5 miles in 124 minutes

Distance = 40/5 miles

Distance = 8 miles  

Time = 124 minutes

Rate = Distance / Time

Rate = 8 miles / 124 minutes

Rate = 0.0645 miles/minute

Hence, the unit rate is 0.0645 miles/minute

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The expression which is equivalent to the given expression is     [tex]\frac{27 m^{5}}{n}[/tex]

From the question, we are to determine the expression which is equivalent to the given expression

The given expression is

[tex]\frac{(3m^{2}n)^{3} }{mn^{4} }[/tex]

Clearing the brackets, we get

[tex]\frac{3^{3} m^{2(3)}n^{3} }{mn^{4} }[/tex]

Simplifying, we get

[tex]\frac{27 m^{6}n^{3} }{mn^{4} }[/tex]

Then,

[tex]27 m^{6-1}n^{3-4}[/tex]

[tex]27 m^{5}n^{-1}[/tex]

= [tex]\frac{27 m^{5}}{n}[/tex]

Hence, the expression which is equivalent to the given expression is     [tex]\frac{27 m^{5}}{n}[/tex]

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The number of the cows is 63 and the number of the horses is 37.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The number of horses and cows will be calculated by forming the expression from the given data in the question. So the two expressions are as follows.

h  +  c  = 100

500h  +  200c  =  31000

Solving the above two equations by substitution method:-

h  =  100  -  c

Put the value of h in the second equation:-

500 ( 100 - c ) + 200c = 31000

50000 - 500c  + 200c =  31000

50000 - 300c  =  31000

50000 - 31000 = 300c

c  =  19000 / 300

c = 63

Put the value of c in the first equation we will get the number of the horses.

h  + c  =  100

h  +  63  =  100

h  =  100-67  =  37

Therefore the number of the cows is 63 and the number of the horses is 37.

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Answer:  £ 3675.79

Step-by-step explanation:

A = P(1 + r)^t

A = final amount = x

P = initial principal balance = 3200

r = interest rate = 0.02

t = number of years elapsed = 7

x = 3200(1.02)^7

x = 3200 * 1.14868567

x = 3675.79414

x = 3675.79

Answer:

Option D --->  y=5x

Step-by-step explanation:

When a line is directly proportional it means it crosses the origin so has a y- and x-intercept of 0.

So if we use the format y=mx+c, it will work but our c value will be 0 as I explained above .

To work out the gradient we simply take 2 points (0,0) and (1,5)) on the graph and use the gradient formula :

m = change in y ÷ change in x

m = 5÷1

m = 5

Therefore our direct proportion equation will be y=5x

Hope this helped and have a good day

Answer:

Step-by-step explanation:

The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.

  a(b +c) = ab +ac . . . . expression of the distributive property

__

When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.

Below, we have written each expression using two different common factors.

  27x +24x = x(27 +24) = 3x(9 +8)

__

  0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)

_____

Additional comment

Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.

The Euclidean Algorithm can also be useful for finding common factors.

Answer:

10

Step-by-step explanation:

look at the y axis for the answer to a question like this

Answer:

There are 25 hostel rooms.

Step-by-step explanation:

We simply need to add up the height of each bar.

3+5+8+6+2+1=25 hostel rooms

The weather that is most likely to occur where Richard is is rain shower.

Weather is the state of the atmosphere of a particular place over a short period of time. There is low atmospheric pressure, so it is likely that it would rain. This is because when the  atmospheric pressure is low, it is likely that it would rain.

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Answer:

Rain shower is most likely to occur where Richard is. (Option c)

• The air pressure is lower than the normal and that's why it suggests that the rainfall will happen in that place because rainfall generally occurs in the place where the low pressure is formed.

• And,the temperature is above than the freezing point of the water so there are no chances of the snowfall in that place.

• That's why rainfall is the most probable thing that will happen in that place.

Step-by-step explanation:

Step-by-step explanation:

x = -2-y

3(-2-y) +3y =6

-6-3y +3y=6

у=0

O=-x-2

х=-2

Answer: 1

Step-by-step explanation:

Answer:

Real and unequal

Answer:

The quadratic has two equal roots like d if it is perfect square and we may write: (x − d) 2 = x 2 − 2 d x + d 2 Then: Δ = 4 d 2 − 4 d 2 = 0 That is the discriminant is zero when the quadratic is perfect square.

Step-by-step explanation:

Answer:

I think A sorry if wrong

Step-by-step explanation:

have a good day

Answer:

A

Step-by-step explanation:

A cube has 6 square faces

given surface area = 54 mm² , then

area of one face = 54 mm² ÷ 6 = 9 mm²

the area (A) of a square is calculated as

A = s² ( s is the side length ) , so

s² = 9 ( take square root of both sides )

s = [tex]\sqrt{9}[/tex] = 3 mm

By solving the two quadratic equations we found the values (0,-1).

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equations are;-

The two equations are solved by equating them and finding the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

6x ( x+1 ) = 0

6x  = 0 so x = 0

( x+1 ) = 0 so x = -1

Therefore solving the two quadratic equations we found the values (0,-1).

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Answer:

G 33%

Step-by-step explanation:

17/52 = 0.32692307692

0.32692307692 is about 33 %

Have a nice day! :)

Answer:

Hello! Your answer is 1/2

Step-by-step explanation:

there are six cubes and three of them are shaded. That is half of the parallelograms.

So 1/4 wouldn't make sense because there are three shaded out of six.

1/6 doesn't make sense because since there is six in total for it to be 1/6 there needs to be 1 shaded out of six.

And finally 1/3 doesn't make sense because 1/3 would have to be two out of six shaded.

Have a wonderful day/night/afternoon and good luck my friend!

Answer:

  (c)  Triangle Z Y X is similar to triangle C B A

Step-by-step explanation:

Triangles are similar when corresponding sides have the same ratio. Corresponding sides will have corresponding end point vertices. The similarity statement lists corresponding vertices in the same order.

__

The side lengths, smallest to largest, for the two triangles are ...

And for the other triangle, ...

The points joining the each side to the next one longer, in order for the two triangles, are ...

  Y, X, Z  and  B, A, C

The vertices corresponding to ZYX in the same order are CBA.

  triangle ZYX is similar to triangle CBA

Answer:

The answer is C

Step-by-step explanation:

Step-by-step explanation:

separate the question into two inequalities then solve individually to derive at an answer then merge the two answers as one.

remember that < or > are open sets while <= or >= are closed set.

Answer:

11 years

Step-by-step explanation:

7200  -  80x  =  5000  +  120x
-5000 + 80x    -5000 + 80x
           2200 = 200x
                  11 = x

Answer:

[tex]BC=x=(13;+\infty)[/tex]

Step-by-step explanation:

Existence of Triangle            

[tex]x-(2x-24) < x-2 < x+(2x-24)\\[/tex]

                   [tex]13 < x > 11[/tex]

  [tex]x=(13;+\infty)[/tex]

Answer: 2(2x-1)

Range terms

Distribute

Subtract the numbers

Parallelogram is the most precise classification for the quadrilateral shown in the graph below.

This is a quadrilateral which has two pairs of parallel sides and the area is usually measured using base × height.

The opposite sides and angles are equal which is why parallelogram was chosen as the most appropriate choice.

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The slope of the graph is 745 and the y-intercept of the graph is 500

The following three points are from the graph: (2, 1990) (5, 4225) (9, 7205)

Find the slope and y-intercept

The points are given as:

(2, 1990) (5, 4225) (9, 7205)

The slope is calculated using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m = (4225 - 1990)/(5 - 2)

Evaluate

m = 745

Hence, the slope of the graph is 745

In (a), we have

m = 745

To calculate the y-intercept, we use the following points

(x1 , y1) = (0,y)

Recall that:

m = (y2 - y1)/(x2 - x1)

So, we have:

745 = (4225 - y)/(5 - 0)

Evaluate the difference

745 = (4225 - y)/(5)

Multiply both sides by 5

3725 = 4225 - y

Solve for y

y = 500

Hence, the y-intercept of the graph is 500

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Answer:

(3x - 5 = -x + 3) x = 2

Step-by-step explanation:

3x - 5 = -x + 3

3x = -x + (3 +5)

3x=-x + 8

(3x + x ) = 8

4x = 8

4/8 =2

x = 2

Answer:

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