Select the action you would use to solve x-3= 12. Then select the property that justifies that action.
A. Action: Add 3 to both sides.
B. Action: Multiply both sides by 3,
C. Action: Subtract 3 from both sides.
D. Property: Addition property of equality
E. Property: Multiplication property of equality
F. Property: Subtraction property of equality

Answer:

The system has one solution: (4,1)

Step-by-step explanation:

We have the equations:

1) Y = -X + 5

2) Y = X - 3

Replace the "value" of Y of the 2nd eq into the 1st eq:

(X - 3) = -X + 5

Now let's leave X alone in one side of the iquality:

X + X = 5 + 3

2X = 8

X = 8/2

X = 4

Now, having the value of X, replace it into any of the aquations, let's use the 2nd:

Y = X - 3

Y = 4 -3

Y = 1

The ONE solution of this equations system is (4,1), which is the point in the xy plane where the two lines intersect.

The following equation has:

          Unique solution (one solution i.e. (4,1) )

The system of equation is given by:

                 y= -x + 5-----------(1)

             and   y= x - 3------------(2)

Now, on substituting the value of y from equation (1) into equation (2) we have:

[tex]-x+5=x-3[/tex]

On adding x on both the sides of the equation we have:

[tex]5=x+x-3\\\\5=2x-3[/tex]

on adding 3 on both the sides of the equation we have:

[tex]2x=5+3\\\\2x=8\\\\x=\dfrac{8}{2}\\\\x=4[/tex]

Now, on putting the value of x into equation (2) we have:

[tex]y=4-3\\\\y=1[/tex]

Hence, the solution is unique (one solution )

        Also, the point of intersection of the graph of two equations is solution to the system of equations.

Answer:

The GCF for 15az and 25az is marked below.

15az = 3*5*a*z

25ab - 5*5*a*b

GCF = 5a

Step-by-step explanation:

Answers above! Hoped this helped :)

Answer:

GCF=5az.

Step-by-step explanation:

First, find a number that is the largest to be multiplied by something else to get both of these numbers. 5 is the correct number. az is also applicable, so therefore 5az is correct. you can multiply 5az by 3 to get 15az or by 5 to get 25az

Answer:

the answer is 113.1yd²

Step-by-step explanation:

Answer is provided in the image attached.

The number of students participating in the math competition, where they are divided into teams of 3, must be a multiple of 3. These numbers include 3, 6, 9, etc. Any number divisible by 3 without a remainder is possible.

To determine how many students could be participating in the math competition where teams are composed of 3 students each, we must think about multiples of 3. Since teams must be evenly divided, only a total number of students that is a multiple of 3 would be possible. The concept here is similar to the division of a group assignment among students. For instance, if five students are working on an assignment and they divide it into five equal parts, each student will do one part. In the case of the math competition, we can say that 3, 6, 9, and so on are possible numbers of students participating. Simplistically, any number that can be divided by 3 without leaving a remainder is a valid answer.

Answer:

Step-by-step explanation:

Writing a system of equations is really just writing an equation for each part of the problem.  The parts here being the calories, and number of items.  It's not asking to solve it, so I will not unless you do want me to.

First variables, let's keep it simple.  O will be onion rings and M will be mozzarella sticks.

Now, I mentioned the two parts are the calories and number of items so we'll take it one at a time.  First calories.  

The total calories will equal 800, so we know the answer to the equation.  Now, how would we relate the variables?  if you had two of each item what would the total calories be?  it may be easy to figure out,  but for our purposes we want to think of it as multiplying the calories of each by the number of each item, or in other words 40*O+60*M, where O and M equal 2.  So for the general case we use the same thing, but we know what we want So our first equation is 40*O + 60*M = 800

The second is a bit simpler.  It just wants to know the total amount of things ordered.  So we are just adding O and M together.  So this gets us O + M = 14, since there are 14 things together.  Let me know if there's still something you don't understand though.  

The system of equations is: [tex]\( x + y = 14 \)[/tex] and [tex]\( 40x + 60y = 800 \)[/tex], where \( x \) represents the number of onion rings in the combination meal and \( y \) represents the number of mozzarella sticks in the combination meal.

Let's define:
- \( x \) as the number of onion rings in the combination meal.
- \( y \) as the number of mozzarella sticks in the combination meal.

The system of equations would be:

1. [tex]\( x + y = 14 \)[/tex] (since the combination meal has a total of 14 onion rings and mozzarella sticks altogether)
2. [tex]\( 40x + 60y = 800 \)[/tex] (since each onion ring has 40 calories and each mozzarella stick has 60 calories, and together they contain 800 calories)

Answer:

100 times greater is the first 5 than the second 5 in 853,539.

Step-by-step explanation:

To find : How many times greater is the first 5 than the second 5 in 853,539?

Solution :

According to place value system,

Hundred Th.    Ten Th.   Thousand    Hundred    Tens   Ones

       8                    5                 3                5               3          9

The value of first 5 in the number 853,539 is at ten thousand place

So, The value of first 5 is 50000.

The value of second 5 in the number 853,539 is at hundred place

So, The value of second 5 is 500.

The times greater is the first 5 than the second 5 in 853,539 is

[tex]\frac{50000}{500}=100[/tex]

Therefore, 100 times greater is the first 5 than the second 5 in 853,539.

Final answer:

The first 5 in the number 853,539 is 1,000 times greater than the second 5 because it is in the ten thousands place, while the second 5 is in the tens place.

Explanation:

The question asks how many times greater is the first 5 compared to the second 5 in the number 853,539. To answer this, we compare the place values of each 5. The first 5 is in the ten thousands place while the second 5 is in the tens place.

The ten thousands place is 1,000 times greater than the tens place. Therefore, the first 5 (50,000) is 1,000 times greater than the second 5 (50).

Answer:

See explanation

Step-by-step explanation:

A dog owner records the weight of her dog. She finds that from the age of 20 weeks to the age of 48 weeks, the dog’s weight can be modelled by the equation

[tex]w = 0.92t-0.15\ \ \ (20\le t\le 48)[/tex]

where

w = weight

t = number of week from 20 weeks to 48 weeks

If we want to extend this model to the dog's weight at birth, then find the dog's weigth when it was born.

At t = 0,

[tex]w=0.92\cdot 0-0.15\\ \\w=-0.15\ kg[/tex]

We get the dog's weight -0.15 kilograms at the day the dog was born. But this is impossible, because the dog's weight cannot be negative.

The model cannot predict the dog's weight at birth due to negative values and unrealistic linear growth for early development.

The equation w = 0.92t - 0.15 describes the weight of the dog as a function of time t in weeks, specifically for the age range of 20 weeks to 48 weeks. When t is set to 20 weeks, we can calculate the weight:

w = 0.92(20) - 0.15

= 18.4 - 0.15

= 18.25 kg.

However, if we try to extend this model to predict the dog's weight at birth (t = 0 weeks), we would get:

w = 0.92(0) - 0.15

= -0.15 kg.

A negative weight is nonsensical in this context, as animals cannot have negative weight. Moreover, the biological growth of a dog does not follow a linear pattern from birth to maturity. The model is designed to represent a specific growth phase after the initial rapid growth and development that occurs in the early weeks of life.

Growth models typically start with an exponential phase during early life, which cannot be accurately captured by a linear equation.

Good evening ,

___________________

Step-by-step explanation:

AO=[tex]\sqrt{p^{2}+q^{2} }[/tex]

AB=[tex]\sqrt{( p+2q-p)^{2} + (q+2p-q)^{2}[/tex]

=[tex]\sqrt{(2q)^{2}+(2p)^{2} }[/tex]

=[tex]\sqrt{4(q^{2}+p^{2} ) }[/tex]

=[tex]2\sqrt{p^{2}+q^{2} }[/tex]

=2AO.

:)

Answer:

Step-by-step explanation:

6< 3x + 9

-3x < 9-6

-3x < 3 .( -1 )                                            

3x > 3                          

x > 3/3

x > 3

3x + 9 ≤ 18

3x ≤ 18-9

3x ≤ 9

x ≤ 9/3

x ≤  3

S = {XeIR/ 3 > x  ≤ 3 }

Not sure if the solution looks like this

Answer:

Step-by-step explanation:

Answer: [tex]48a^4[/tex]

Step-by-step explanation:

 In this case we know that the  legs of the given right triangle have these lenghts:

[tex]12a^4[/tex] and [tex]16a^4[/tex]

By definition, the sides of a right triangle are in the ratio [tex]3:4:5[/tex]

Since:

[tex]\frac{5}{4}=1.25[/tex]

We can multiply the lenght  [tex]16a^4[/tex] by 1.25 in order to find the lenght of the hypotenuse of the right triangle:

[tex](16a^4)(1.25)=20a^4[/tex]

Since the perimeter of a triangle is the sum of the lenghts of its sides, we can write the following expression for the perimeter of the given right triangle:

[tex]12a^4+16a^4+20a^4[/tex]

Simplifying, we get:

[tex]=48a^4[/tex]

The expression in the simplest form that represents the perimeter of the right triangle with legs 12a⁴  and 16a⁴ is 48a⁴

A right angle triangle has one of its angles as 90 degrees. The sides can be found using pythagoras theorem.

Therefore,

The perimeter of the right triangle is the sum of the whole sides. Therefore, let's find the hyotenuse.

c² = a² + b²

c² = (12a⁴)² + (16a⁴)²

c² = 144a⁸ + 256a⁸

c² = 400a⁸

c = √400a⁸

c = 20a⁴

Therefore, the perimeter is as follows:

perimeter = 12a⁴ + 16a⁴ + 20a⁴

perimeter = 48a⁴

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Jensen can send 4 messages for $1. This is calculated by using the concept of unit rate; first find the unit cost by dividing the total cost by the total number of messages, then divide $1 by the unit cost.

The question is asking how many text messages Jensen can send for $1 if she usually spends $18 for 72 messages. This involves a concept in mathematics called unit rate, which identifies the cost (or quantity) per one unit. First, we figure out how much it costs to send one message by dividing the total cost by the total number of messages, i.e. $18/72. This gives us a unit cost of $0.25 per message. Therefore, to find out how many messages Jensen can send with $1, we divide $1 by the unit cost, giving us 4 messages. So, Jensen can send 4 messages for $1.

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[tex]\bf \cfrac{36}{80}\implies \cfrac{~~\begin{matrix} 2\cdot 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 3\cdot 3}{2\cdot 2\cdot ~~\begin{matrix} 2\cdot 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 5}\implies \cfrac{9}{20}[/tex]

Answer:

9/20

Step-by-step explanation:

find a common factor and divide both the numerator and the denominator by that factor until there's no way to keep simplifying anymore. or use a calculator. but don't do that. you won't learn that way. im a bad teacher sorry.

Answer:

15x+100(3) ≥ $1500

x ≥ 80 pages

Step-by-step explanation:

Let x represent the number of  pages.

Manuel receives $15 per page = 15x

Plus $100 per month. Manuel would like to work for 3 months = 15x+100(3)

He wants to make at least $1500 during the summer

Thus the inequality we get is:

15x+100(3) ≥ $1500

Now solve the equation to find minimum number of pages:

15x+300 ≥ $1500

Combine the like terms:

15x ≥ 1500-300

15x ≥ $1200

Divide both sides by 15

15x ≥ $1200/15

x ≥  80 pages

Answer:

The length of a paper clip chain is directly proportional to the number of paper clips. If a chain with 65 paper clips has a length of 97.5 inches then the length of chain with 14 paper clips is 21 inches.

Solution:

Given that the length of a paper clip chain is directly proportional to the number of paper clips. Directly propotional means when the length of paper clip increases, then the number of paper clips also increases in same ratio.

Hence, by above definition, we get  

[tex]\frac{l_{1}}{l_{2}} = \frac{n_{1}}{n_{2}}[/tex]  ------- eqn 1

From question, for a chain with 65 paper clips has a length of 97.5 inches, we get  

[tex]l_{1} = 97.5 \text { and } n_{1} = 65[/tex]

Similarly, for a chain with 14 paper clips with length to be found, we get  

[tex]n_{2}=14 \text { and } l_{2} = ?[/tex]

Now by using eqn 1, we can calculate the length of 14 paper clips  is,

[tex]\frac{97.5}{65}=\frac{l_{2}}{14}[/tex]

Rearranging the terms we get,

[tex]l_{2 }= \frac{97.5 \times 14}{65}[/tex]

[tex]l_{2}=21 \text { inches }[/tex]

Hence the length of chain with 14 paper clips is 21 inches.

Answer:

to combine integers with the same sign at their sign then give their sum the same sign as the addends

Step-by-step explanation:

if you combine it with the same sign u will get a lot of negatives than postives

Answer:

4/9 * -2/3= -8/27 is the solution

Answer:

49

Step-by-step explanation:

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros.

Find the zeros by letting f(x) = 0, that is

- (x - 3)(x + 11) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 11 = 0 ⇒ x = - 11, thus

[tex]x_{vertex}[/tex] = [tex]\frac{-11+3}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4

Substitute x = - 4 into f(x) for y- value of the vertex

f(- 4) = - (- 4 - 3)(- 4 + 11) = - (- 7)(7) = 49

Answer:

18 performers

Step-by-step explanation:

I just multiplied 30 by 0.6 (the decimal form of 60 percent) and got 18

18 kids played a musical instrument

Answer:

The value of x in log x + log 3 = log 18 is 6.

Solution:

From question, given that log x + log 3 = log 18 ---- eqn 1

Let us first simplify left hand side in above equation,

We know that log m + log n = log (mn) ----- eqn 2

Adding log m and log n results in the logarithm of the product of m and n (log mn)  

By using eqn 2, log x + log 3 becomes log 3x.  

log x + log 3 = log 3x ---- eqn 3

By substituting eqn 3 in eqn 1, we get

log 3x = log 18  

Since we have log on both sides, we can cancel log and the above equation becomes,

3x = 18

[tex]x = \frac{18}{3} = 6[/tex]

Thus the value of x in log x + log3 = log18 is 6

Answer:

the answer is 6

I even toke the test as well.

it is not 6.00001

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Hold on I am doing it right now

Your answer is 75 hope this helps you

Answer:

120$ altogether

Step-by-step explanation:

There are 8 teachers and they have to pay 15 dollars so do

8×15=120

or

15+15+15+15+15+15+15+15=120

Answer:

Step-by-step explanation: 18x2+4=30

Answer:

amy is 11.

Step-by-step explanation:

in the problem it explains that brandy is 4 years younger than twice amys age. if we say that amy is 11 then we can verify the answer because 11*2 is 22-4 is 18.

hope this helps- cam:)

Answer:

-5 = a; (-5, 7)

Explanation:

-y₁ + y₂\-x₁ + x₂ = m

-7 + 5\a + 8

a + 8 = 3

- 8 - 8

_________

a = -5

Obviously, we have to set the denominator equal to three to find the value of a. Parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so -⅔ remains the same.

I am joyous to assist you anytime.

Answer:

C

Step-by-step explanation:

143.75+ tax(7.1875)= 150.9375 <-- Tennis Ball Containers

30+ tax(1.5)= 31.5 <-- Packs of Grip Tape

150.9375+31.5= 182.4375

This can be rounded up to 182.44 (which is your final answer)

Answer:

n =  1.33 repeating

Step-by-step explanation:

first you distribute the -2 by everything in the parenthesis so then you get -12 + 1- = 26 the you subtract 10 from each side which leaves you with -12 = 16 then you devide -12 by both sides and you get the decimal 1.33 repeating.

Answer:

140°

Step-by-step explanation:

The interior angles of a regular nonagon are equal.

Equate the 2 given angles and solve for x

11x - 25 = 9x + 5 ( subtract 9x from both sides )

2x - 25 = 5 ( add 25 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Substitute this value into one of the given angles

9x + 5 = (9 × 15) + 5 = 135 + 5 = 140

Thus the interior angle has a measure = 140°

The interior angle of a nonagon measure is 140°.

The given expressions are 9x+5 and 11x-25.

A regular nonagon is one in which all the 9 sides are of equal length and the 9 interior angles are of equal measure. On the other hand, when the sides of a nonagon are of unequal lengths and the angles are of different measures, it is called an irregular nonagon.

Now, equate the 2 given angles and solve for x.

That is, 11x - 25 = 9x + 5 ( subtract 9x from both sides )

⇒2x - 25 = 5 ( add 25 to both sides )

⇒2x = 30 ( divide both sides by 2 )

⇒x = 15

Substitute x = 15 value into one of the given angles

9x + 5 = (9 × 15) + 5 = 135 + 5 = 140

Therefore, the interior angle of a nonagon measure is 140°.

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Answer:

x = 5, -5

Step-by-step explanation:

Find the roots of [tex]x^{2} -25=0[/tex] by solving for x.

Add 25 to both sides

[tex]x^{2} =25[/tex]

Square root both sides

[tex]x = 5[/tex]

[tex]x=-5[/tex]

The solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The quadratic equation:

x² - 25 = 0

As we know,

a² - b² = (a + b)(a - b)

Using the above identity:

x² - 5² = 0

(x + 5)(x -  5) = 0

x + 5 = 0  

x = -5

Or

x - 5 = 0

x = 5

We can also find the solution to the equation x² - 25 = 0 using the quadratic formula.

Thus, the solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).

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Answer:

mean: 10

meidian; 9.5

Step-by-step explanation:

rasons

The mean of the movies that the students saw is, 14.67

The median of the movies that the students saw is, 15.5

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Each of 6 students reported the number of movies they saw in the past year. This is what they reported:

⇒ 16, 9, 14, 16, 18, 15

Now, The mean of the movies that the students saw is,

⇒ 16 + 9 + 14 + 16 + 18 + 15 / 6

⇒ 88 / 6

⇒ 14.67

And, We arrange the given data in ascending order,

⇒ 9, 14, 15, 16, 16, 18

Hence, The median of the movies that the students saw is,

⇒ (15 + 16) / 2

⇒ 31 / 2

⇒ 15.5

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Step-by-step explanation:

Look at the picture

a. 5k → 5

b. t = 1t → 1

c. -9t → -9

d. -j = -1j → -1