. A retailer sold 10 packs of pens in 3 days. There were 48 pens in each pack. He sold twice as many pens on Sunday than on Monday. He sold 55 pens fewer on Tuesday than on Sunday. How many pens did the retailer sell on Monday?

Answers

Answer 1

Answer:

The number of pens sold on Monday is 107 pens

Step-by-step explanation:

total pack of pen sold by the retailer in 3 days =  10 packs

total number of pens in the 10 packs = 48 x 10 = 480 pens

let the number of pens sold on Monday = x

let the number of pens sold on Sunday = y

let the number of pens sold on Tuesday = z

He sold twice as many pens on Sunday than on Monday

y = 2x ------equation (1)

He sold 55 pens fewer on Tuesday than on Sunday

y = z + 55 ------equation (2)

total number of pens sold in the three days

y + z + x = 480  ------equation (3)

from equation (1) make x the subject of the formula

x = y/2

from equation (2) make z the subject of the formula

z = y - 55

substitute the value of x, and z into equation (3)

y + y/2 + y - 55 = 480

2y + y/2 = 480 + 55

5y/2 = 535

5y = 535 x 2

5y = 1070

y = 1070 / 5

y = 214

The number of pens sold on Monday is:

x = y / 2

x = 214 / 2

x = 107 pens

Thus, the number of pens sold on Monday is 107 pens


Related Questions


Use the grouping method to factor the polynomial below x^3 -4x^2+3x-12

Answers

Answer:

x^2(x-4) + 3(x-4)

(x^2 + 3)(x-4)

Step-by-step explanation:

The inverse of f(x) is a function

Answers

Answer:

The inverse of a function may not always be a function!

The original function must be a one-to-one function to guarantee that its inverse will also be a function.

Which equation is rewritten in vertex form

Answers

Answer:

Option (2)

Step-by-step explanation:

Given expression is, y = (x + 3)² + (x + 4)²

By solving this expression,

y = x² + 6x + 9 + x² + 8x + 16

y = 2x² + 14x + 25

y = (2x² + 14x) + 25

y = 2(x² + 7x) + 25

y = 2[x² + 2(3.5x) + (3.5)² - (3.5)²] + 25

y = 2[x² + 2(3.5x) + (3.5)²] - 2(3.5)² + 25

y = 2(x + 3.5)² - 24.5 + 25

y = 2(x + 3.5)² + 0.5

[tex]y=(x+\frac{7}{2})^2+\frac{1}{2}[/tex]

Therefore, Option (2) will be the vertex form.

Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°. What is the measure of minor arc BD?

Answers

Answer:

100°

Step-by-step explanation:

From the image attached, line BC and line CD are tangents to circle A. Also, AB and AD are the radius of the circle. The tangent theorem states that the angle between a tangent and the radius is 90°. Therefore:

∠ABC and ∠ADC = 90°.

Given triangle ABC:

∠ABC + ∠BCA + ∠CAB = 180°

∠CAB = 180 - ∠ABC - ∠BCA = 180 - 90 - 40 = 50

∠CAB = 50°

From the two tangent theorem, tangents that meet at the same point have the same length. This means BC = CD, ∠ACD = ∠BCA, ∠CAB = ∠CAD.

arc BD = ∠CAB + ∠CAD = 50 + 50

arc BD = 100°

Answer:

D.

Step-by-step explanation:

Two friends can paddle a canoe at a rate of 6 km/h in still water. It takes them 1 h in total to paddle 2 km up a river and another 2 km back. Find the speed of the current, rounded to the nearest tenth.

Answers

Answer: The speed of the current is 3.5 km/h.

Step-by-step explanation:

When they move in the river, the speed of the canoe is:

Sc is the speed of the canoe and Sr is the speed of the current.

Sc + Sr (when they move in the same direction as the current)

Sc - Sr (when they move in the opposite direction as the current)

So we have that in one hour, they moved 2km and then they returned other 2km.

Now, using the relation:

Velocity*time = distance

we can write 1hour = T1 + T2 such that:

(Sc + Sr)*T1 = 2km

(Sc - Sr)*T2 = 2km

T1 + T2 = 1hour -------> T2 = 1h - T1

Sc = 6km/h.

So we can write this as two equations:

(6km/h + Sr)*T1 = 2km

(6km/h - Sr)*(1h - T1) = 2km.

Now, the first step will be isolate one of the variables in one equation, we can get:

T1 = 2km/(6km/h + Sr)

and replace it in the second equation:

(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.

Now we solve this for Sr, i will ignore the units, so it is easier to read the math.

(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2

(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)

6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0

-Sr^2 + 36 -12 -12 = 0

-Sr^2 + 12 = 0

Sr = √12 = 3.5km/h

(where we take the positive value of the square root)

The speed of the current is 3.5 km/h

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:

(6 - a)(t₁) = 2 km

t₁ = 2 / (6 - a)      (1)

(6 + a)(t₂) = 2 km

t₂ = 2 / (6 + a)   (2)

t₁ + t₂ = 1 hour

[2 / (6 - a)] + [2 / (6 + a)] = 1

12 + 2a + 12 - 2a = 36 - a²

a² - 12 = 0

a = 3.5 km/h

The speed of the current is 3.5 km/h

Find out more at: https://brainly.com/question/22610586

There are 50 sheets of drawing paper.
Larry divides the drawing paper between himself
and his younger brother John.
And Larry has 14 more sheets.
How many
sheets of drawing paper do Larry and his
brother have, respectively?​

Answers

Answer:

John has 18 pieces of paper.

Larry has 32 pieces of paper.

Step-by-step explanation:

Let [tex]l[/tex] be how many pieces of paper Larry has and [tex]j[/tex] be how many pieces of paper John has.

We get:

[tex]j+14=l[/tex]

[tex]j+l=50[/tex]

[tex]j+j+14=50\\\\2j+14=50[/tex]

Subtract 14 from both sides

[tex]2j=36[/tex]

Divide both sides by 2

[tex]j=18[/tex]

John has 18 pieces of paper.

[tex]j+14=l\\\\18+14=l\\\\l=32[/tex]

Larry has 32 pieces of paper.

The measure of angle JKL can be represented using the expression 3x + 5. Point K has three lines extending from it. One line extends to point J, another to point M, and the other to point L. Angle J K M is 45 degrees. Angle M K L is x degrees. What is the degree measure of AngleJKL? °

Answers

Answer:

its 65

Step-by-step explanation:

The measure of ∠JKL = 3 x 20 + 5 = 65 degrees.

We have three lines extending from point K such that one line extends to point J, another to point M, and the other to point L.

We have to determine the degree measure of ∠JKL .

Define Angle.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

According to the question, we have -

Measure of ∠JKL = 3x + 5

Measure of ∠JKM = 45 degrees

Measure of ∠MKL = x degrees

Refer to the image attached for more clarity. It can be seen from the image that -

∠JKL = ∠JKM + ∠MKL

3x + 5 = 45 + x

3x - x = 45 - 5

2x = 40

x = 20

Therefore, the measure of ∠JKL = 3 x 20 + 5 = 65 degrees.

To solve more questions on Angle measurements, visit the link below -

https://brainly.com/question/17107683

#SPJ6

What does y=? Also if you cant read that bright red number its 60

Answers

Answer:

y = 13.9

Step-by-step explanation:

The triangle is a 30-60-90 triangle, so x is 16 (double 8). Use the pythagorean theorum to find y. 256 - 64 =192. [tex]\sqrt{192}[/tex] is about 13.9

john has × marbles and max has twice as many.max give gives john 5 of his marbles does max now have

Answers

Answer: 2x -5

Step-by-step explanation:

Hi, to answer this question we have to write equations with the information given:

John has × marbles  

John=x

Max has twice (multiplied by 2) as many.max give gives john 5 of his marbles.

We have to multiply by 2 the number of marbles that John has (x), and subtract 5.  

Max = 2x -5

Feel free to ask for more if needed or if you did not understand something.  

How many lines of rotational symmetry does this shape have?

Answers

Answer:

14 lines shape symmetry

Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?


$ ___

Answers

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 1.50

the sum of (x-1) + (2x+ 3) is 3x-2 correct?

Answers

Answer: no , the correct answer is 3x+2

Step-by-step explanation:

Remove parentheses.

x−1+2x+3

Collect like terms.

(x+2x)+(−1+3)

Simplify.

3x+2

determine weather it is no solution many solutions or one solutions
3(6-4m)=2(9-6m)

Answers

Answer:

Many solutions

Step-by-step explanation:

solve 5kx+ 6=7kx for x

Answers

Answer:

A

x= 3/x

Step-by-step explanation:

5kx + 6 = 7kx

collect like term

5kx - 7kx = -6

-2kx = -6

minus cancel out

=> 2kx = 6

divide bothside by 2k

=> x = 6/2k

=> x = 3/k

Answer:

Step-by-step explanation:

its A just trust :)

If the perimeter of a rectangle picture frame must be less than 200 in and The width is 36 in what Must the height H of the frame be

Answers

Answer:

So since the formula for perimeter is 2(w+h)

200 = 2(w+h)

that means that

100 = w+h

100 = 36+x

x=

64 UNITS

Step-by-step explanation:

Can someone help? Thanks :D

Answers

Answer:

[tex]y\leq -x+4[/tex]

Step-by-step explanation:

The first thing that we can do is look at the equation of the line and then worry about the inequality afterwards.

This line has a y-intercept of 4 and a slope of -1.

This means that the equation of this line would be [tex]y=-x+4[/tex]

Now that we have the equation of the line, we just need to determine which inequality sign to use.

As the shaded region is BELOW the line, we will use a less than (<) sign.

As the line is fully shaded, I can only assume that it is meant to include the line, which would mean that [tex]y\leq -x+4[/tex] would be the equation for this inequality.

8. Let ABCD be a parallelogram with A on top left, B on top right, D on bottom left and C on the bottom right. Prove that opposite sides of a parallelogram are congruent.

Answers

Answer:

Step-by-step explanation:

A parallelogram is a quadrilateral with four sides.

Given parallelogram ABCD, to prove that opposite sides of the parallelogram are congruent.

Join D to B, the diagonal of the parallelogram which is also a traversal.

So that;

    <ABD = <BDC (alternate angle property)

    <BAC = <ACD (alternate angle property)

Also, diagonals;

      /AC/ = /BD/ (reflexive property)

Then;

      ΔABD = ΔCBD (Angle-Side-Angle, ASA, property)

Thus;

     /AB/ ≅ /CD/ (corresponding sides of congruent triangles are congruent)

    /BC/ ≅ /AD/  (corresponding sides of congruent triangles are congruent)

Therefore, the opposite sides of the parallelogram ABCD are congruent.

At the gym, Polina put 4 five-pound weights onto a barbell that weighed 22 pounds without any weights on it. If Polina lifted the barbell with both arms, which expression can be used to determine the weight that each arm was lifting?

[(4 × 5) ÷ 2] + 22
(4 × 5) ÷ 2 + 22
[22 + 4 × 5] ÷ 2
22 + (4 × 5) ÷ 2

Answers

Answer:

D. 22+(4×5)÷2

Step-by-step explanation:

Four 5 pound weight=(4×5)

Barbell weighed 22 pounds

={(4×5)+22}

Paulina lifted it with both arms

Both arms=2

{(4*5)+22}/2

It can be rewritten as

22+(4*5)÷2

Use the vectors v = 7i + 2j and w = –4i + j to find 10v + 3w

Answers

Answer:

v = 7i + 2j

w= - 4i + j

10v = 10(7i + 2j) = 70i + 20j

3w= 3(- 4i + j) = -12i + 3j

10v + 3w

= 70i -12i + 20j +3j

= 58i + 23j

Hope this helps.

a vegetable garden surrounding path are shaped like a square that together are 10 ft wide. The path is 3 ft wide. Find the total area of the vegetable garden and path. ​

Answers

Answer: Garden = 36 ft², Path = 64 ft²

Step-by-step explanation:

Path is 3 ft wide ON EACH SIDE of the garden

Garden + 2(Path) = 10 ft   --> Garden = 6 ft wide.

Since the garden is a square, Area = 6² = 36

Garden + 2(Path) = 10 ft

Since the Garden + Path form a square, Area = 10² = 100

Area of Garden + Area of Path = Total Area

         36             + Area of Path =      100

                              Area of Path =      64

determine whether the systems have one solution, no solution, or infinitely many solutions


3x-2y=3;6x-4y=1


3x-5y=8;5x-3y=2


3x 2y=8;4x 3y=1


3x-6y=3;2x-4y=2


3x-4y=2;6x-8y=1

Answers

Answer:

First system: no solution

Second system: one solution

Third system: one solution

Fourth system: infinite solutions

Fifth system: no solution

Step-by-step explanation:

First system: 3x-2y=3; 6x-4y=1

From the first equation: y = (3x - 3)/2

Using this value of y in the second equation:

6x - 6x + 6 = 1

6 = 1 -> System has no solution

Second system: 3x-5y=8; 5x-3y=2

From the first equation: x = (8 + 5y)/3

Using this value of x in the second equation:

5*(8 + 5y) - 9y = 6

40 + 25y - 9y = 6

16y = -34 -> y = -2.125

x = (8 - 5*2.125)/3 = -0.875

This system has one solution

Third system: 3x-2y=8; 4x-3y=1

 From the first equation: x = (8 + 2y)/3

Using this value of x in the second equation:

4*(8 + 2y) - 9y = 3

32 + 8y - 9y = 6

y = 26

x = (8 + 2*26)/3 = 20

This system has one solution

Fourth system: 3x-6y=3; 2x-4y=2

  From the first equation: x = 1 + 2y

Using this value of x in the second equation:

2*(1 + 2y) - 4y = 2

2 + 4y - 4y = 2

2 = 2

This system has infinite solutions

Fifth system: 3x-4y=2; 6x-8y=1

  From the first equation: x = (2 + 4y)/3

Using this value of x in the second equation:

2*(2 + 4y) - 8y = 1

4 + 8y - 8y = 2

4 = 2

This system has no solution

According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

Answers

Answer:

Step-by-step explanation:

You didn't give your options, but it doesn't matter. We'll find all the possibilities and then you can pick it from your list.

When I teach this in Algebra 2, I call it the "the c over d thing" and all my students know EXACTLY to what I am referring. "c" is the constant and "d" is the leading coefficient. The combination of c/d give you the possibilities of roots for the polynomial. There are no real roots that a polynomial can have other than the possibilities we find when we do the c/d thing.

Our c is a 20.  All the factors of 20 are as follows (notice that we have both the positive and negative factors):

20: ±1, ±2, ±4, ±5, ±10, ±20

Our d is a 3.  All the factors of 3 are as follows (again, both the + and the -):

3: ±1, ±3 and that's it for 3.

c/d is as follows. Make sure you put ever c over every d!!!:

c/d: ±[tex]\frac{1}{1}[/tex], ±[tex]\frac{2}{1}[/tex], ±[tex]\frac{4}{1}[/tex], ±[tex]\frac{5}{1}[/tex], ±[tex]\frac{10}{1}[/tex], ±[tex]\frac{20}{1}[/tex], ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex], ±[tex]\frac{5}{3}[/tex], ±[tex]\frac{10}{3}[/tex], ±[tex]\frac{20}{3}[/tex]

Those are all the possibilities for your roots for that polynomial. As long as the roots are real (and they won't always all be real!), there are no roots but these.

Answer:

its D on edge

Step-by-step explanation:

If 14x = 6(–4 + x), then x = ?

Answers

Answer:

Step-by-step explanation:

Expand first

-24+6x=14x

-6x on both sides

-24=8x

/x on both sides

X=-3

Answer: [tex]x=-3[/tex]

Step-by-step explanation:

You want to apply the distributive property. Or, you could just divide by 6 on both sides. Ill just apply the distributive property:

[tex]14x = -24 +6x[/tex]

Now subtract 6x from both sides to get:

[tex]8x = -24[/tex]

Divide both sides by 8 to get x = -3

A(n) _____ generally has a highly elliptical orbit. A. moon B. comet C. planet D. asteroid

Answers

Answer:

b

Step-by-step explanation:

Answer:

B comet

Step-by-step explanation:

Orbit of a Comet. Comets go around the Sun in a highly elliptical orbit. They can spend hundreds and thousands of years out in the depths of the solar system before they return to Sun at their perihelion. Like all orbiting bodies, comets follow Kepler's Laws - the closer they are to the Sun, the faster they move.

Please BRAINLIEST!

A caterer prepares three times as many pizzas as she usually prepares for a large party. The caterer usually prepares 4 pizzas. The caterer also estimates that each party guest will eat 1/3 of a pizza. Drag and drop each expression into the correct boxes to complete the explanation.
The expression that represents how many guests the pizzas can serve is (blank).
How many party guests will the pizzas serve? Drag and drop the number of guests into the box.(answer)
The pizzas can serve guests.

Answers

Answer:

So if each person eats 1/3 pizzas. And he makes 4 pizzas. There are 3 1/3s in 1 pizza. 3*4 = 12.

The answer is 12 guests

Please Answer ASAP! will give 5 star and brainliest

An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. Draw the possibility diagram of the product of the two numbers appearing on the die in each throw Use the possibility diagram to calculate the probability that the product of the two numbers is (i) A prime number (ii) Not a perfect square (iii) A multiple of 5 (iv) Less than or equal to 21 (v) Divisible by 4 or 6

Answers

Answer:

Step-by-step explanation:

Use the possibility diagram to calculate the probability that the product of the two numbers is

A prime number

Sample Space: 64

Prime Number:8

Probability: 8/64 = 1/8

Not a perfect square

Sample Space:64

Not a perfect square:56

Probability: 56/64 = 7/8

A multiple of 5  

Sample Space:64

A multiple of 5: 16

Probability: 16/64 = 1/4

Less than or equal to 21  

Sample Space:64

Less than or equal to 21:24

Probability: 24/64 = 6/16 = 3/8

Divisible by 4 or 6

Sample Space:64

Divisible by 4 or 6:32

Probability: 32/64 = 1/2

How can a triangular prism have a greater volume than a rectangular prism?

Answers

Answer:

If the triangular prism is bigger than the rectangular prism, it will have a greater volume. There are also many other reasons listed below:

Possible reasons:

If the triangular prism is bigger than the rectangular prism, it will have a greater volumeThe rectangular prism could have less width than the triangular prismThe rectangular prism could have less depth than the triangular prismThe rectangular prism could have less length than the triangular prism

Please mark Brainliest if correct.

Sorry if it is not correct.

The volume of a triangular prism is less than a rectangular prism with the same size base. A painter would need to know the surface area hope it helps

You design a tree house using a coordinate plane in which the coordinates are measured in feet. The vertices of the floor are (-2,-3),(-2,4),(5,4) and (5,-3) . Find the perimeter (in yards) and the area (in square yards).

Answers

Answer:

Step-by-step explanation:

The vertices (-2, -3) and (-2, 4) are on the same vertical line and are separated by 4 - (-3), or 7, units.  The vertices (-2, 4) and (5, 4) are on the same horizontal line (y = 4) and separated horizontally by 5 - (-2), or 7, units.  If you can picture this in your mind, you'll see a 45-45-90 isosceles triangle with leg lengths 7 (there are two such legs).

The next thing to do is to calculate the length of the hypotenuse of this triangle.  Using the Pythagorean Theorem, we get:

d = √(7² + 7²) = 7√2 ft.

The perimeter of this triangle is thus 7 ft by 7 ft by 7√2 ft, or approximately 23.9 feet, or 7.97 yd

and ...

The area of the triangular shape is A = (1/2)(base)(height), which here is

A = (1/2)(7)(7) = 49/2 ft^2, or 16.4 yd^2

the sides of a triangle are in the ratio, 4:5:7 and its perimeter is 64cm. find its area , correct to 2 decimal places

Answers

Answer:

Step-by-step explanation:

First find all the sides of the triangle:

Total parts: 4+5+7 =  16

cm per part = 64/16 = 32/8  =4cm

therefore, all measures: 16cm, 20cm, 28cm.

Answer:

since you have not specified the height, I will use any no.

= 0.16

Step-by-step explanation:

perimeter is the distance round

add the ratios; 4+7+5=16

Ratio 16= Perimeter 64cm

R.16=64cm, find all the ratios

start with ratio 4

R.16=64cm

R.4×64cm÷16=16 cm

R.5×64÷16= 20 cm

R.7×64÷16=28 cm

A=1/2× b×h

1/2×16×20= A= 160cm2

2 dp, divide

0.16

a rectangular sheet of paper dimentions 44 cm x 18 cm is rolled along its length and cylinder is formed . find voloume of cylinder so formed

Answers

Answer:

1134cm³

Step-by-step explanation:

rolled along the length means the length becomes the height of the cylinder.

length of rectangle = height of cylinder= 44 cm

breadth of rectangle = circumference of top and bottom circles = 18 cm

to find radius = 2πr = 18

2 * 22/7 *r = 18

22/7r = 18/2

22/7r = 9

r = 9*7/22

r= 63/22

Volume of cylinder formula = πr²h

= 22/7 * 63/22 * 63/22 *44

= 63 * 18

= 1134 cm³

(We cannot take it as a hollow cylinder because a rectangular sheet can only have one radius)

Hope this helps you!

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