Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Answers

Answer 1

The correct answer is 58 viable solutions.

To model the given situation, we need to define variables, create inequalities, and then solve the system of inequalities.

Let x = the number of pens, and y = the number of pencils.

Given information:

- The total number of writing utensils must be less than or equal to 25.

- The number of pencils must be greater than or equal to the square of (3 less than the number of pens).

Step 1: Create the first inequality for the total number of writing utensils.

x + y ≤ 25

Step 2: Create the second inequality for the condition on the number of pencils.

y ≥ (x - 3)^2

Step 3: Solve the system of inequalities.

We can substitute different values of x into the second inequality to find the corresponding values of y.

For x = 1, y ≥ (-2)^2 = 4

For x = 2, y ≥ (-1)^2 = 1

For x = 3, y ≥ 0^2 = 0

For x = 4, y ≥ 1^2 = 1

For x = 5, y ≥ 2^2 = 4

...

Substituting these values into the first inequality, we get:

1 + y ≤ 25 (y ≥ 4)

2 + y ≤ 25 (y ≥ 1)

3 + y ≤ 25 (y ≥ 0)

4 + y ≤ 25 (y ≥ 1)

5 + y ≤ 25 (y ≥ 4)

...

Therefore, the viable solutions are:

(x, y) = (3, 0), (3, 1), (3, 2), ..., (3, 22)

(x, y) = (4, 1), (4, 2), ..., (4, 21)

(x, y) = (5, 4), (5, 5), ..., (5, 20)

There are a total of 22 + 20 + 16 = 58 viable solutions.

Related Questions

What is 1 1/2 subtracted from the sum of 4 2/3 and 5 2/5

Answers

Hi there!

First, we need to add 4 2/3 and 5 2/5.

We should begin with converting the fractions into improper fractions.
4 2/3 + 5 2/5
= 14/3 + 27/5

Now, we find the common denominator.
= 70/15 + 71/15

We can add:
= 141/15

And simplify.
= 9 2/5

Finally, we subtract 1 1/2 from 9 2/5.
9 2/5 - 1 1/2
= 47/5 - 3/2
= 94/10 - 15/10
= 79/10
= 7 9/10

Your answer is 7 9/10.

Hope this helps!

7 9/10 is the correct answer. I use the wonderful world of google to help me with questions like that one

How many straight edges does a nonagon have?

Answers

More specifically, a square is a regular quadrilateral, or four-sided shape. It has four equal sides and four right angles, each measuring 90 degrees. A regular nonagon is a nine-sided shape with equal sides and equal angles of 140 degrees each.

I need help what is 80% Of 5.00

Answers

To find a percent of a number, convert the percent to a decimal and multiply by the number.

80% of 5.00 =

= 80% * 5.00

= 0.80 * 5.00

= 4.00

480 x 5
100= 4 its four lil bro

Question 19 makes no sense

Answers

Think: To write the equation of a line in slope-intercept form y=mx+b, you must have the slope (m) and the y-intercept (b).

g(0)= -6 tells us that the y-intercept is (0, -6). Thus, b= -6.

(0,-6) and (15,-9) are points on the line. Find the slope of the line. It is:
-9-(-6)
m = ------------- = -3/15 = -1/5
15-0

Thus, the equation of the line in question is y=(-1/5)x - 6.

Important that you understand that g(0)=-6 is also represented by (0,-6), and that -6 is the y-intercept.

a rectangular field has sides with the length of 120 yards in 62 yards to the nearest tenth of a yard find the length of the diagonal of the field

Answers

The Pythagorean theorem is used for this
.. diagonal = √(120² +62²) = √18244 ≈ 135.1 . . . . yards

How do you do 3.)and 3.a)

Answers

1 cm : 15 yd
Multiply this proportion by 5
5 cm : 75 yd

Multiply the original proportion by 8
8 cm : 120 yd

a) The dimensions of the field are 75 yd by 120 yd.

b) The area is (75 yd)*(120 yd) = 9000 yd^2.

select all the equations that represent a linear equation

Answers

1st, 2nd, 4th. hope this helps

The length of the shorter side of a parallelogram is 29 cm. Perpendicular line segment, which goes through the point of intersection of the diagonals to the longer side divides this longer side into two segments: 33 cm and 12 cm. What is the area of the parallelogram?

Answers

A = 900[tex] cm^{2} [/tex]

The area of a parallelogram can be found by taking its base (b) and multiplying by the height (h). The base has the measure of 33 +12 = 45 cm. Now, you just need to find the height of the parallelogram. The height can be found by using the pythagorean theorem ([tex] a^{2} + b^{2} = c^{2} [/tex].

So, when simplified the height of the parallelogram will be found from [tex] \sqrt{ 29^{2} - 21^{2}} [/tex]

The height is 20 cm. The base is 45 cm. 45 x 20 = 900.

The area of the parallelogram is approximately [tex]$ 1216.35 $[/tex] square centimeters, with a longer side of 45 cm and height 27.03 cm.

To find the area of the parallelogram given the dimensions and conditions described, we can follow these steps:

1. Identify Key Dimensions:

- The shorter side [tex]$ a = 29 $[/tex] cm.

- The longer side is divided into two segments: 33 cm and 12 cm. Therefore, the longer side [tex]$ b = 33 + 12 = 45 $[/tex] cm.

2. Determine the Height Corresponding to the Longer Side:

- We need to find the height [tex]$ h $[/tex] of the parallelogram with respect to the longer side [tex]$ b = 45 $[/tex] cm.

3. Utilize the Perpendicular Segment Information:

- The perpendicular from the point of intersection of the diagonals to the longer side divides it into two segments: 33 cm and 12 cm.

- This perpendicular segment represents the height [tex]$ h $[/tex] from the base to the opposite side.

4. Use Geometric Properties of the Parallelogram:

- In a parallelogram, the point of intersection of the diagonals divides each diagonal into two equal segments.

- Since the perpendicular divides the longer side into two segments, we can use these to find the height [tex]$ h $[/tex].

Given that the point of intersection of the diagonals and the perpendicular segment splits the longer side into two segments (33 cm and 12 cm), we note that this splitting essentially occurs at the mid-point of the segments because the diagonals bisect each other.

5. Calculate the Area:

- The area [tex]$ A $[/tex] of a parallelogram is given by the formula:

[tex]\[ A = \text{base} \times \text{height} \][/tex]

- Here, the base is the longer side [tex]$ b = 45 $[/tex] cm, and the height [tex]$ h $[/tex] needs to be calculated using the right triangle formed by the height and the segments.

6. Determine Height Using Right Triangle:

- We use the properties of the right triangle formed by the height and the segments:

[tex]\[ h^2 + \left(\frac{33 - 12}{2}\right)^2 = 29^2 \][/tex]

- This simplifies to:

[tex]\[ h^2 + 10.5^2 = 29^2 \][/tex]

[tex]\[ h^2 + 110.25 = 841 \][/tex]

[tex]\[ h^2 = 841 - 110.25 \][/tex]

[tex]\[ h^2 = 730.75 \][/tex]

[tex]\[ h = \sqrt{730.75} \][/tex]

[tex]\[ h \approx 27.03 \text{ cm} \][/tex]

7. Calculate the Area:

- Now that we have [tex]$ h \approx 27.03 $[/tex] cm, the area [tex]$ A $[/tex] of the parallelogram is:

[tex]\[ A = b \times h = 45 \times 27.03 \approx 1216.35 \text{ cm}^2 \][/tex]

Therefore, the area of the parallelogram is approximately [tex]$ 1216.35 \text{ cm}^2 $[/tex].

Help please ppl Guys

Answers

The area of a triangle is BH/2 (base x height / 2).
Base = 9
Height = 5

9*5 = 45;
45 / 2 = 22.5

Your area is 22.5 ft

I hope this helps!

HEEEEEEEEEEEEEEEEEELPPPPPPPP

Answers

Answer:
y = 2x - 4

Explanation:
The general form of the slope-intercept equation is:
y = mx + c
where:
m is the slope
c is the y-intercept

We are given that the slope = 2
Therefore, the equation of the line becomes:
y = 2x + c

Now, we will need to get the value of c.
We are given that (7,10) belongs to the line. This means that this points satisfies the equation of the line. So, we will substitute with this point in the equation and solve for c as follows:
y = 2x + c
10 = 2(7) + c
10 = 14 + c
c = 10 - 14
c = -4

Based on the above, the equation of the line is:
y = 2x - 4

Hope this helps :)

what is the area of a triangle with a base of 8 yards and a height of 3 yards

Answers

Given:
Triangle base: 8 yards
Triangle height: 3 yards

The area of a triangle is solved using this formula:

Area = (height * base) / 2

Using the given data:

Area of a triangle = (3 yards * 8 yards)/2
Area of a triangle = 24 square yards / 2
Area of a triangle = 12 square yards.

The area of the given triangle is 12 square yards.

The volume of a cube is 1,953.125 centimeters cubed. Find the length of the sides.

Answers

It will be [12.5] I think. Tell me if it is right

A regular room at the Great Wolf Lodge is $229.99. You have a discount code to get 20% off of the room rate. The sales tax on the hotel rooms is 13%. Find the total cost of the room.
Please explain how to do it. I don't understand how to do it.

Answers

229.99*.20 = $46 off
229.99-46 = $183.99
$183.99*.13 =$23.92 sales tax added
183.99+23.92 = $207.91

We'll start with our initial price- $229.99.

First, we'll want to apply our discount code, as you wouldn't want to discount something after taxes. To apply the discount, we will start by multiplying our percent by the original price.

Multiplying by a percent is easy! All we need to do is put the percent over 100, divide the fraction, and our decimal is the value.

[tex] \frac{20}{100}= \frac{1}{5} =0.2[/tex]

Now that we know our percent can be represented as "0.2," we will multiply 0.2 by our original price.

[tex]229.99*0.2= 45.998[/tex]

As our unit is money, we will round to the nearest hundredth. When we round to the nearest hundredth here, we can see that 20% of 229.99 is $46.00.

We aren't done calculating the discount yet, though! We still need to subtract the "46" from our original price, since we are only getting 20% off, not only paying 20%.

[tex]229.99-46.00=183.99[/tex]

Now that we have our discounted price, we need to add the sales tax to it. Again, we'll need to find our sales tax's value as a decimal.

[tex] \frac{13}{100} =0.13[/tex]

This time, we will multiply the discounted price by "1.13." The first "1" represents the discounted price, and the ".13" afterwards represents the cost of the sales tax.

[tex]183.99*1.13=207.9087[/tex]

Again, we'll need to round to the nearest hundredth, so our "207.9087" becomes "207.91."

With all of the logic above in mind, we can conclude that the cost of the room, after the discount and the sales tax, is $207.91.

Sid is $300 in debt. He needs to get the debt down to no more than $100 within the next 8 months. If he pays the same amount each month, what is the minimum he must pay off each month to manage this?

Answers

$25 per month, that will bring it down to $100

$25 a month for 8 months will bring his debt down to $100

What is -5/12 + (-1/4) + 3/12 as a fraction

Answers

so first get everything with a common denominator
(-5/12) + (-3/12) + (3/12)
the (-3/12) and (3/12) cancel out and you are left with
(-5/12)

Please help with any of those

Answers

the volume = 1943.9

hope this helps!

The volume of the cylinder is 1942.88 inches cubed.

First you find the area of the base(circle) and multiply it by the 3D object's height.

Krystal puts three pencils in order from longest to shortest what is a fast way to order the same pencils from shortest to longest

Answers

Swap the shortest and longest pencil's places. You don't have to move the middle pencil.

Simply swap the first and last pencil in the order.

audras parents are both in their forties. the sum of their ages is ninety -two. the product of their ages is 2,107. how old is audras oldest parent?

Answers

Audra's parents are 49 and 43 so the age of his/her oldest parent is 49.
49 + 43 = 92
49 x 43 = 2,107
:)

Answer: Hello there!

Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.

we know that:

x + y = 92

x*y = 2107

now we have a system of equations that we need to solve:

the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:

x = 92 - y

now we can replace it in the second equation and find the value of y.

x*y = 2107

y*(92 - y) = 2107

92y - y^2 = 2107

now we need to solve a cuadratic equation!

-y^2 + 92y - 2107 = 0

using the Bhaskara formula, we get:

[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]

so we have two solutions:

y = (-92 + 6)/(-3) = 43

y = (-92 - 6)/(-2) = 49

because y is the oldest one, we need to take the biggest solution, this is y = 49.

so the oldest parent has 49 years.

if you want to find the age of the other parent, replace this in the first equation:

y + x = 92

49 + x = 92

x = 92 - 49 = 43

If a store orders a total of 55 of flour, how many 25-pound bags does the store order

Answers

5. It would be 4, except they need 55, and that 5 extra makes it 5

The store would only have 2 25-pound bags of flour

Christopher just found beautiful yarn for 20% off at his favorite yarn store. He can make one scarf from 2/3 of a ball of yarn. If Christopher buys 12 balls of yarn, how many scarves can he make?

Answers

Answer:

Step-by-step explanation:

if 2/3 is used by one scarf, then we can divide 2/3 into 12

12/1 × 2/3

12/1 ×3/2= 36/2

36/2= 16

Christopher can create a total of 12 scarves with the 12 balls of yarn he buys, based on the ratio of 2/3 of a ball needed for one scarf.

Christopher can make scarves from yarn, where it takes 2/3 of a ball of yarn to make one scarf. If he buys 12 balls of yarn, we need to calculate the total number of scarves he can make.

Let's find out how many scarves he can create with 12 balls:

Firstly, determine how many scarf units are in one ball of yarn. Since it takes 2/3 of a ball to make a scarf, 1 ball equals 1.5 scarf units (since 1 / (2/3) = 1.5).Next, multiply the number of scarf units in one ball by the total number of balls. 1.5 scarf units per ball \\times 12 balls = 18 scarf units.Finally, since each scarf uses 2/3 of a ball, we divide the total number of scarf units by 1.5 to get the number of scarves. 18 scarf units / 1.5 = 12 scarves.

Therefore, Christopher can make 12 scarves with 12 balls of yarn.

how do you simplify equations? im having trouble w math. help

Answers

Depending on the equation, you can simplify it by:

1. Removing parentheses by multiplying factors.

2. Using exponent rules to remove parentheses in terms with exponents.

3. Combining like terms by adding coefficients.

4. Combining the constants.

5. Adding, subtracting, multiplying or dividing both sides of an equation.

A great way to simplify equations is by dividing to the smallest it can go. It sound complicated but it gets easier. The cymath website can show you how to simplify for further help :)

Brainliest? I would like to move up a rank!

Select all that apply.

A point located at (5, -2) undergoes two transformations. Its image is located at (-5, 2). What were the transformations?

The point was reflected over the y-axis and translated up 4 units.
The point was translated right 10 units and reflected over the x-axis.
The point was translated left 10 units and up 4 units.
The point was reflected over the y-axis and translated down 4 units.

Answers

The point was reflected over the y-axis and translated up 4 units, because when it was reflected over the y-axis, the coordinates became (-5, -2), and after getting translated up 4 units, the coordinates became (-5,2).

The point was reflected over the y -axis and translated up 4 units.

What is Transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have,

A point located at (5, -2) undergoes two transformations.

Its image is located at (-5, 2).

The point was reflected over the y-axis and translated up 4 units, as shown by the coordinates becoming (-5, -2), respectively, when the point was reflected over the y-axis and (-5,2).

So, The point was reflected over the y -axis and translated up 4 units.

Learn more about transformation here:

https://brainly.com/question/29035527

#SPJ3

What is 6.9-(-5)+4.1

Answers

here. the answer is 16

find the length of the base indicated for each trapezoid

Answers

Final answer:

To find the base of a trapezoid, you can view the trapezoid as two right triangles joined together. The base of the trapezoid is the sum of the bases of these triangles. Depending on the orientations of the sides of the trapezoid and the height, you might need to use the Pythagorean theorem.

Explanation:

The question asks to find the length of the base for a given trapezoid. In order to do this, we can use concepts from geometry and trigonometry. Consider the trapezoid as two right triangles back to back. The base of the trapezoid is the sum of the bases of the two right triangles.

For example, if you have a trapezoid with sides A and B, and the height is H, you can use these sides and the trigonometric principles to calculate the lengths of the bases. If side A or B is not perpendicular to the base, you would need to use the Pythagorean theorem. That formula is A^2+B^2=C^2, where C is the hypotenuse of the right triangle formed.

In case, the sides A and B are perpendicular to the base, the lengths of the bases would simply be side A + side B. This would give you the total length of the base of the trapezoid.

Learn more about Trapezoid Base Length here:

https://brainly.com/question/31380175

#SPJ12

What prime factor(s) will make the lcm of 9 and 15

Answers

9/3 = 3
15/3 = 5

LCM = 3

The LCM of 9 and 15 are 3

You can verify the zeroes of a function y=x^2+6x-7 by using a graph and finding where the graph ..........

Answers

... intersects the x-axis. The x-coordinates of the points of intersection are the zeros.

Who can help me with number 1

Answers

You are going to want to cross multiply this, so 5/9 would multiply with 1 and 2/3 would be multiplied by x. Now you have 5/9 = 2/3x. You would divide 2/3 on both sides and get 5/6. 5/6 is your answer.

Multiply the denominator by 3/2. The denominator is the bottom fraction

5
---
9
===
2 * 3
-- --
3 2
What this does is get rid of the fraction on the bottom. But you also have to multiply the 5/9 by 3/4

5/9 * 3/2
When you do this you get
15/18 Both can be divided by 3
5/3 <<<<< answer
1 2/3 <<<< answer
1.66666 <<<< answer

Figure PQRS is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure P′Q′R′S′:
Which statement best compares the lengths of the sides of the two figures?

Length of PQ = Length of P′Q′
Length of PQ = Length of R′S′
Length of RS = Length of P′Q′
Length of RS = Length of Q′R′

Answers

i believe that the answer is length of PQ = length of P′Q′ since they are the same sides on both shapes

Answer:

A. Length of PQ = Length of P′Q′

Step-by-step explanation:

We are given,

Figure PQRS is rotated by 180° counter-clockwise about the origin to obtain P'Q'R'S'.

Since, we know that, 'Rotation' is a transformation that turns the figure around a fixed point to a certain degree.

We get that, rotation does not affect the length of the figure.

So, the length of PQ = length of P'Q' and length of RS = length of R'S'

Thus, according to the options, we get that option A i.e. Length of PQ = Length of P′Q′ is correct.

Can i please have urgent help! 60 POINTS

Answers

(7/3 *3sqrt27-2)*1/5 +sqrt(81)

answer = 10

= (7/3 x 3 - 2) x 1/5 + 9
= 5 x 1/5 + 9
= 1 + 9
= 10

answer
10

Kevin works as a salesperson at a store that specializes in custom made computers. He earns a base pay of 325$ per week and a commission on his sales. If Kevin earned a total of $1125 last week, how much of it was commissions

Answers

Answer:
Kevin made $800 in commissions last week.

Explanation:
Since we know that he only makes money in two ways, by base salary and commission, we know that added together they equal his whole pay.

Therefore we can set up the following equation and solve for his commission amount.
Total Pay = Base Pay + Commissions.
1125 = 325 + Commissions.
800 = Comissions.

Answer:

$800

Step-by-step explanation:

Kevin earns a base pay = $325 /week

He also make some extra earning in the form of commission. Let this extra earning be “$X”

Thus, Base pay + Extra earning through commission = $1125 -------------Equation (A)

Substituting the values in equation A, we get –

$325 + $X = $1125

$X = $1125 - $325

= $ 800

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