3.) mr. smith’s class sold wrapping paper for $3.50 each and mr. davis’ class sold magazines for $2.75 each. together, the classes sold 72 items and earned $222 for their school. a. write and solve a system of equations that model the problem. show all your work. Need answer ASAP!!!!!

Answer:

rational number

Step-by-step explanation:

Answer:

It's a rational. You can convert this to a simplified fraction

An irrational number is a number which cannot be expressed in a ratio of two integers. In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero. While an irrational number cannot be written in a fraction.

Answer:

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step

That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step.Because this is the correct way to do simplify the rational expression. And also because Nadine made a blender mistake in her operations in step

Step-by-step explanation:

Given that Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4

Their expression can be written as below

[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]

Nadine's first step is to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction

That is [tex]\frac{r^{20}s^{12}}{r^{-32}s^8}[/tex]

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4

That is [tex]r^{-13}s^{-1}[/tex]

Now simplify the given expression to check whose step is correct:

[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]

[tex]=(r^{-5}s^{-3}r^{-8}s^{2})^{-4}[/tex] ( using the property [tex]\frac{1}{a^m}=a^{-m}[/tex] )

[tex]=(r^{-5-8}s^{-3+2})^{-4}[/tex]

[tex]=(r^{-13}s^{-1})^{-4}[/tex]

Therefore [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex]

Therefore Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step.

That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step .Because this is the correct way to do simplify the rational expression.And also because Nadine made a blender mistake in her operations in step

The solution to the system of linear equations 4x - 2y = 8 and y = (3/2)x - 2 is x = 4 and y = 4, found by substituting y in the first equation with the expression from the second equation and solving for x.

The student is asking to solve a system of linear equations. The equations provided are:

4x - 2y = 8

y = (3/2)x - 2

We will solve this system using substitution since the second equation is already solved for y. Here are the steps:

Substitute y in the first equation with the expression from the second equation: 4x - 2((3/2)x - 2) = 8.

Simplify the equation: 4x - 3x + 4 = 8.

Solve the simplified equation for x: x + 4 = 8, which leads to x = 4.

Substitute x back into the second equation to find y: y = (3/2)4 - 2.

Calculate the value of y: y = 6 - 2, which leads to y = 4.

The solution to the system of equations is x = 4 and y = 4.

Answer:

Therefore,

The Length is longer than Width by 2 units.

[tex]Length=Width+2[/tex]

Step-by-step explanation:

Given:

Let the vertices of a Rectangle be  

A ( -7 , 6)

B ( 3 , 6)

C ( 3 , -6)

D ( -7 ,-6)

To Find:

Relation between Length and Width = ?

Solution:

First we will find the Length and Width of Rectangle by Distance Formula ,

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((3-(-7))^{2}+(6-6)^{2} )}[/tex]

[tex]l(AB) = \sqrt{((10)^{2}+(0)^{2} )}\\l(AB)=\sqrt{100}=10\ unit[/tex]

Similarly for BC we will have,

[tex]l(BC) = \sqrt{((3-3)^{2}+(-6-6)^{2} )}\\l(BC)=\sqrt{144}=12\ unit[/tex]

Now

Length = 12 units.

Width = 10 units.

Therefore,

Let Length be denoted by "L" and Width by "W" then

[tex]Length=Width+2=10+2=12\\\\\therefore L=W+2[/tex]

Therefore,

The Length is longer than Width by 2 units.

[tex]Length=Width+2[/tex]

Answer:

f^-1 (x)=1/5x-11/5

Step-by-step explanation:

y=5x+11

x=5y+11

5y=x-11

y=1/5x-11/5

Final answer:

The correct inequality to represent the number of situps Lyle can do, if 57 is more than he can do, is D. x < 57, indicating that Lyle can do fewer than 57 situps.

Explanation:

The inequality that represents the number of situps Lyle can do, given that the number 57 is more than the number of situps Lyle can do, is x < 57. This is because if 57 is more than what Lyle can do, then Lyle can do any number of situps that is less than 57.

To represent this relationship mathematically, we use the inequality sign '<'. Thus, the correct option from the provided choices is D. x < 57. This means Lyle can do 56, 55, 54, etc., situps, but not 57 or any number greater than 57.

Answer:

4x+9=3q

Step-by-step explanation:

-3(2x-3)+10x=3q

-6x+9+10x=3q

4x+9=3q

Answer:

q = 4/3x + 3

Step-by-step explanation:

-3(2x-3)+10x=3q

Multiply the -3 at the beginning by (2x - 3), the parenthesis

-6x + 9 + 10x = 3q

Now combine the like terms (add x's and variables separately)

(-6x + 10x) + 9 = 3q

4x + 9 = 3q

Divide both sides of the equation by 3

(4x + 9) ÷ 3 = q

4x/3 + 9/3 = q

Simplify

q = 4/3x + 3

Hope this helps :)

Answer:

1. 9 pi, 2. 121 pi

Step-by-step explanation:

The formula for circumference is pi d. So for the first question the radius would be three. The you do pi r ^2 for area so 3 times pi squared. Which is 9 pi. For the second you will do the same thing you will do 22 pi divided by 2 which is 11 pi then you will square 11pi and get 121 pi

Answer:

B.

Step-by-step explanation:

1000 meters in a kilometer and 60 minutes in a hour. 1000/60= 16.6666

(rounds to 20)

Final answer:

Charles' running speed of 12 kilometers per hour is equivalent to 200 meters per minute when converted, which corresponds to option D.

Explanation:

Charles runs at a rate of 12 kilometers per hour, and the question asks us to convert this speed to meters per minute. First, we need to convert kilometers to meters. One kilometer is equivalent to 1,000 meters.

So, Charles' speed in meters per hour is:

12 km/hr × 1,000 m/km = 12,000 m/hr

To convert this speed from meters per hour to meters per minute, we divide by 60 minutes, since there are 60 minutes in one hour:

12,000 m/hr ÷ 60 min/hr = 200 m/min

Therefore, Charles' speed is 200 meters per minute, which corresponds to option D.

The ladder reaches 40 feet up the wall.

41 squared (1681) minus 9 squared (81) is 1600. 40 is the square root of 1600.

The required distance between the top of the ladder and the ground is 40 feet.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,

We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the wall "x", and let's call the length of the ladder "y".

According to the problem statement, we know that the ladder is 41 feet long and that the base of the ladder is 9 feet from the base of the apartment building.

y = 41 feet

x = 9 feet

We can use the Pythagorean theorem to solve for the distance between the top of the ladder and the ground. The Pythagorean theorem tells us that:

y² = x² + z²

where "z" is the distance between the top of the ladder and the ground. Plugging in the values we know,

(41 feet)² = (9 feet)² + z²

1681  = 81 + z²

1600 = z²

z = 40 feet

Therefore, the distance between the top of the ladder and the ground is 40 feet.

Learn more about Pythagorean triplets here:

brainly.com/question/22160915

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Answer:

Domain: (-oo, oo)

Range: (-4,oo)

Horizontal asymptote: y=-4

Answer:

The domain is all Real numbers.

The range is all real values > -4.

Step-by-step explanation:

The asymptote is y = -4.

After calculating the cost per hawk for each company, Company C offers the best buy at $2.71 per hawk.

The goal is to find out which company offers the best buy for the plush toy hawks. To do so, we'll calculate the cost per hawk from each company and compare them.

Company C offers the lowest cost per hawk at $2.71, thus they have the best buy.

Answer:

Simple Interest =$5600 (Principal and Interest)

Compound Interest = $5624.32 (Principal and Interest)

Step-by-step explanation:

Using Simple interest, use the formulae, Principal X Rate X Time

= 5000*4%*3

= $600 Interest

Principal plus Interest = $5600

Using compound Interest, use the formulae P(1+r)^n

P means Principal

R means rate

N means number of years

= 500(1+4%)^3

= $5624.32 (Principal with Interest)

Answer:

x = 1

Step-by-step explanation:

If you graph this, you will see that you will get a line that is straight up and down (or perpendicular to the x axis).  No matter what y is, x will always be 1.  

The perimeter of rectangle is 25.13 feet

Solution:

Given that,

width of a rectangle = [tex]4\frac{1}{6} \text{ feet }[/tex]

Convert the mixed fraction to improper fraction

[tex]\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}[/tex]

Therefore,

[tex]\text{width of rectangle } = \frac{25}{6} \text{ feet }[/tex]

Area of rectangle = 35 feet

The area of rectangle is given by formula:

[tex]area = length \times width[/tex]

Substituting the given values, we get

[tex]35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}[/tex]

Thus we get,

[tex]\text{length of rectangle } = \frac{42}{5} \text{ feet }[/tex]

The perimeter of rectangle is given as:

perimeter = 2(length + width)

[tex]perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13[/tex]

Thus perimeter of rectangle is 25.13 feet

The calculated cosine of the angle U is 8/17

How to determine the cosine of the angle U

From the question, we have the following parameters that can be used in our computation:

The triangle

By definition:

The cosine of the angle is calculated using

cos(U) = VW/UW

Where

VW = 8 and UW = 17

Substitute the known values into the equation

cos(U) = 8/17

Hence, the cosine of the angle U is 8/17

Answer:

c

Step-by-step explanation:

Answer:

y = 3x +2

Step-by-step explanation:

The first answer

The value of b is -12

Solution:

The given equation, b (b + 12) = 0

On distributing the b inside the parentheses we get,

[tex]\Rightarrow\bold{ b\times b+b\times12=0}[/tex]

[tex]\bold{\Rightarrow b^{2}+12b=0}[/tex]

[tex]\bold{\Rightarrow b^{2}=-12b}[/tex]

[tex]\bold{\Rightarrow 1=\frac{-12b}{b^2}}[/tex]

[tex]\bold{\Rightarrow 1=\frac{-12}{b}}[/tex]

[tex]\bold{\Rightarrow b=-12}[/tex]

Steps to use distributive property to solve an equation:

For fractions:

Answer:

The correct answer is A. Jim is better positioned to invest in bonds because he makes less and has longer before his investment matures.

Step-by-step explanation:

Jim is better positioned to invest in bonds for two reasons:

1. He can invest and take advantage of long-term bonds, between 12 and 20 years of term of maturity, that are those that usually have the highest interest rate. His goal is to invest and save for his daughter's college education, that is a newborn.

2. The real interest rates are rising. It means the bonds interest rates are clearly above the inflation rate in the country where Jim and his family live, having a better return for his investment.

Steps to solve:

-3(x + 5) = -9

~Distributive Property

-3x - 15 = -9

~Add 15 to both sides

-3x - 15 + 15 = -9 + 15

~Simplify

-3x = 6

~Divide -3 to both sides

-3x/-3 = 6/-3

~Simplify

x = -2

Best of Luck!

Answer:

x= -2

Step-by-step explanation:

First, distribute the 3 into the parenthesis.

(-3)x+ (-3)5= -9

Then, multiply.

-3x-15= -9            *The negative makes it into becoming subtraction.

Now, add 15 to both sides since that's the opposite of subtraction.

-3x-15= -9

   +15  +15

Then, divide by 3 to both sides to isolate the variable.

-3x= 6

-3   -3

x= -2

g(x) = x²

g(4) = 4² = 16

g(f(4)) = (f(4))² = (4-7)² = (-3)² = 9

Answer:

e

Step-by-step explanation:

because the lines are less scattered and they all are going straight up. they are also higher then all of the other ones.

Answer:

11/4

Step-by-step explanation:

Answer: The top one

Step-by-step explanation:

Because there can only be one input for one output. (X’s can’t repeat)

Answer:

13

Step-by-step explanation:

x + 6 = ?

[Replace x with 7]

7 + 6 = 13

Answer:

75

Step-by-step explanation:

6 and 4 are alternate interior angles meaning they have the same value

Answer:

29

Step-by-step explanation:

Look at image