Solve the ytem of equation by the addition method.   

−4x = −4y − 12
−16x 6y = 12

The system of equation is inconsistent as these three equations does not give any solution.

In comparison to equations with two variables, a three-variable linear equation requires a little more work to solve. The extra variable is the cause of this complexity.

Even if there are various ways to solve this kind of equation, the elimination technique is still the simplest.

To solve three variable linear equations using the elimination approach, follow these steps:

1. Avoid using fractions and decimals and write all the equations in standard form.

2. Pick an appropriate variable to remove.

3. Remove the chosen variable from any two of the three equations.

4. Choose another set of the two equations, and then take the same chosen variable out.

5. For the two variables they each include, solve the two equations from stages three and four.

6. Replace the answer in fifth step.

7. Reverify by putting them again in the equation.

So according to these given Equations we have to find the value of x, y and z respectively,

-2x + 15y + z = 44

4x + 3y + 3z = 18

-3x+6y-z = 8

After solving these three equations we do not get any solutions.

Hence the system of equations is inconsistent.

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Therefore, In order to complete this activity, we must have understanding of divisibility, which leads us to discover that:

3025 is [tex]5^{2} (11)^{2}[/tex]

A number's factors, and more specifically its prime factorization, can be expressed as factor trees. There are factors for each branch of the tree. The branch comes to an end and the number is circled once the factor at the branch's end is a prime number, leaving only itself and one as potential factors.

Here,

Since divisibility is the capacity of a number to lose value, we determine that:

=> 3025/5 =605

=>  605/5=121

=> 121/11=11

=> 11/11=1

=[tex]5^{2} (11)^{2}[/tex]

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The quotient that represents the fraction 15/3 is given as follows:

5.

A fraction has the standard notation given as follows:

Fraction = x/y.

In which the terms have the technical names given as follows:

Then the quotient is obtained as the division of the numerator by the denominator.

In this problem, the fraction is given as follows:

15/3.

Then the numerator and the denominator are given as follows:

Then the quotient is given as follows:

15/3 = 5.

As the division of 15 by 3 has a result of 5.

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Answer:

15.414

Step-by-step explanation:

 3.67

x 4.20 ← the zero is your 'holding' spot so to speak

 000 ← 0 x 7, 0 x 6, 0 x 3

.7340 ← 2 x 7, 2 x 6 + 1, 2 x 3 + 1

14.6800 ← 4 x 7, 4 x 6 + 2, 4 x 3 + 2

15.414

If he wants to make $125 by working 14 hours per week, he must invest 17 hours in babysitting and -3 hours in tutoring.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Cost of tutoring=$15

Cost of babysitting=$10

Total time he can give=14 hours

Total amount he wishes to earn=$125

Let x be the time he gave to tutoring and y be the time he gave to babysitting,

x+y=14

x=14-y

15x+10y=125

15(14-y)+10y=125

210-15y+10y=125

5y=85

y=17

x=-3

He should spend 17 hours on babysitting and -3 hours on tutoring if he want to earn $125 by working 14 hours per week.

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D would give A $10 and B $5  in total amount will the friend who earned $40 give to the others .

The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by. I still provide some services to them. Definitions of quantity, lot, measure, and size Additional words for "quantity".

calculation

Let A, B, C, and D each stand in for one of the four buddies.

A made $15 in earnings.

B made $20 in revenue.

C made a profit of $25.

D made $40 in revenue.

Total earnings equal 15 plus 20 plus 25 plus 40.

$100 was earned overall.

Each friend ought to receive an equal share;

Each income is calculated as follows: total income /friends

Adding a substitute to the equation, we have;

Each income equals 100/4

$25 equals each earnings.

D would therefore become; given $40.

D = $40 - $25

D = $15

As a result, D would give A $10 and B $5.

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Answer: 26

Step-by-step explanation:

let t = thomas's age

104 = (3t) + t

104 = 4t

t = 26

Answer: 26 years old

Step-by-step explanation:

    We will write a system of equations to help us solve, let h be equal to Huilan's age and t be equal to Thomas's age.

         h = 3t

         h + t = 104

    Now, we will solve by substituting the first equation into the second.

    Then, we will simplify the equation on the left side by combining like terms and dividing both sides of the equation by 4 to isolate the variable.

         h + t = 104

         (3t) + t = 104

         4t = 104

         t = 26

Answer:

Step-by-step explanation:

One of the Answers is C

The measure of the diagonal brace of the rectangular painting is 69.5 inches.

A diagonal is a line segment that joins one corner (vertex) of a polygon to another but is not an edge (side). In other words, it joins any two non-adjacent vertices of a polygon. So, we form a diagonal in a polygon when we directly join any two vertices which are not joined by any side.

The diagonal of the brace and the length of one side and width of one side form a right-angled triangle and by Pythagoras we have

diagonal^2 = length(L)^2 + width(W)^2

diagonal^2 = 60^2 + 35^2

diagonal^2 = 3600 + 1225

diagonal^2 = 4825

diagonal = [tex]\sqrt{4825}[/tex]

diagonal = 69.5 inches

In conclusion the diagonal of the brace is 69.5 inches

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The answer will be 5/117.

Let us understand the process. First, we have to do -\

1/9x{-5/13).

Then we have to then calculate -1x-5 which is equal to 5.

Again, we have to calculate 9x13 which is equal to 117.

Therefore, the answer will be 5/117.

To know more about -1/9(-5/13) :

3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers.

Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

According to our question-

-3x3 + 2x2 + 11x - 20 + (10/(-x-7)) = 3x4 + 19x3 - 25x2 - 57x + 150

In order to perform synthetic division, we must first remove the minus sign from the divisor and write out

-7 | -3 -19 25 57 -150

| 21 -14 -77 140

-3 2 11 -20 -10

obtain that

3x4 + 19x3 - 25x2 - 57x + 150 / (-x-7) is equivalent to 3x4 - 19x3 - 25x2 - 57x + 150 / (x+7) is equivalent to 3x3 + 2x2 + 11x - 20 + (10/(-x-7)).

Hence, 3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.

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11.4 centimeters is the radius of the cylinder .

What does volume mean in plain terms?

The capacity of a solid shape is determined using volume, a three-dimensional quantity.

                     It implies that a closed figure's volume determines how much three-dimensional space it can fill.

The volume of a cylinder is given by

   v = πr²h

The total volume of the two hemispheres is given by

   v' = 2× 2/3 πr³

    v' = 4/3 πr³

Now, the total volume of the solid is given by:

  [tex]V_{T}[/tex] = πr²h + 4/3 πr³

  Now, substitute the value of the total volume in the above expression and then solve for h.

       12 = πr²h + 4/3 πr³

        h = 12/πr² - 4r/3

Now, the surface area of the curved surface is given by:

        A = πrh

Now, the surface area of the two hemispheres is given by

      A' = 2 × (2πr² )

      A' = 4πr²

Now, the total area is given by

    [tex]A_{T}[/tex] = 2πr ( 12/πr² - 4r/3) + 4πr²

 Simplify the above expression.

  [tex]A_{T} =[/tex]  24/r + 4πr²/3

Now, differentiate the total area with respect to 'r'.

      [tex]\frac{dA_{T} }{dr}[/tex] = -24/r² + 8πr/3

Now, equate the above expression to zero.

     0 = -24/r² + 8πr/3

Simplify the above expression in order to determine the value of 'r'.

        8πr³  =  60

         r =  11.4

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Answer:

8

Step-by-step explanation:

128/n * n = 16 * n

128 = 16n

128/16 = 16/16 n

n = 8

Answer:

Paulina is reading a book with 677pages total. If she has already read 345 and plans to read 23 pages a day, how many days, x, will she nees to read at that pace until she finishes the entire book?

Step-by-step explanation:

[tex]345 + 23x = 677[/tex]

23x=677-345

x=677-345/23

x=332/23

x= 14.43 days

Answer:

19

Step-by-step explanation:

replace x with 10

f(10)=9+10

f(10)=19

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Answer:

Step-by-step explanation:

You want to know the values of k that make the line 4y = k(x +4) either parallel or perpendicular to the line 12y = 9x +8.

The slopes of parallel lines are the same. When the equation of a line is written in "y =" form, the slope is the coefficient of x. Here, the two equations written in that form are ...

For parallel lines, we want to choose the value of k so that the slopes are equal:

  k/4 = 3/4

  k = 3 . . . . . . . . multiply by 4

The slopes of perpendicular lines have a product of -1. This means we want to choose k so that ...

  (k/4)(3/4) = -1 . . . . . the product of slopes k/r and 3/4 is -1

  k = -16/3 . . . . . . . . . multiply by 16/3

__

Additional comment

The attached graph shows the original line (dashed red) and the parallel and perpendicular lines with their respective values of k.

Answer:

×=3

......................

The cost of each desk is $42.

The initial cost to make these new school desks is $635.

What is a solution of linear function?

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Assume that the cost of each desk be m.

The initial cost to make these new school desks be c.

Then the total cost will represent by the equation:

y = mx + c .....(i)

Putting x =21 and y = 1517 in the equation (i)

1517 = 21m + c ...(ii)

Putting x = 47 and y = 2609 in the equation (i)

2609 = 47m + c ...(iii)

Subtract equation (ii) from (iii)

47m + c =2609

21m + c = 1517

(-)     (-)     (-)

___________

26m = 1092

Divide both sides by 26

m = 42

Putting m = 42 in equation (ii)

1517 = 21 × 42 + c

1517 = 882 + c

c = 1517 - 882

c = 635

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If zookeeper have to divide the 28 gallon of water equally among 13 animal then each animal will get 2.15 gallon of water.

8 pints, 4 quarts, or 16 cups make up a gallon. Depending on whether you use Imperial or Metric measurements, there are 128 fluid ounces in a gallon.

The volume of a gallon is about equal to 3.78541 liters. Consequently, a gallon is larger than three liters.

According to given to given condition

total amount of water:

=28 gallon

no. of animals:

=13 animal

then each animal get water:

=28/13

=2.15 gallon of water

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Answer: In 6 years the sum of Manas' age and his sister's age will be 48 years.

Step-by-step explanation:

We know that value of a dozen is 12 and the score is 20.

Hence,

Uncle Mike's age = 12+20 = 32 years

Since Manas' sister is 8 years younger than Mike,

Her age = 32 - 8 = 24 years

We know that Manas is half her age. Therefore,

Manas' age  = 24 ÷ 2 = 12 years

After x years the sum of Manas' age and his sister's age will be 48 years.

Manas' future age = (12 + x) years

His sister's future age = (24 + x) years

The Sum of their ages is 48 years. Hence,

(24 + x) + (12 + x) = 48

36 + 2x = 48

2x =  48 - 36

2x = 12

x = 12 ÷ 2

x = 6

Therefore, in 6 Years sum of their ages is 48 years.

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Answer: B

Step-by-step explanation:

For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].

For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].

Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.

Answer: $44.85

Step-by-step explanation:

Take 39 times 0.15% = $5.85

39 + 5.85 = $44.85

The total cost is $44.85

Answer: 44.85

Step-by-step explanation:

15% of 39 = 5.85

Answer:

1/2

Step-by-step explanation:

we can make this a fraction

29/59

if we look at our answer choices it is not 0 and it is not a whole number yet and definitely not 2 but it is close to 1/2

29/59=0.49

1/2= 0.5

Which are very close to each other

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The height of the right triangle if the area of the triangle is 150 square units = 30 units

In this question, we have been given a right triangle's height is 3 times the length of its base.

We need to find the height of the right triangle if the area of the triangle is 150 square units.

Let h be the height and b is the base of the right triangle.

A right triangle's height is 3 times the length of its base.

So we get an equation,

h = 3b              ............(1)

Using the formula of area of right triangle,

A = 1/2 * b * h

150 = 1/2 * b * 3b                  .........(from equation (1))

300 = 3b^2

b^2 = 100

b = 10

Subatitute above value of b in equation (1),

h = 3 * 10

h = 30 units

Therefore, the height of right triangle is 30 units

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The length of the hypotenuse is 6.71

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:

[tex]{\displaystyle a^{2}+b^{2}=c^{2},}[/tex]

Given ,

Pythagorean therum

a^2 + b^2 = c^2....a and b are ur legs and c is the hypotenuse

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2...take the sqrt of both sides....this eliminates the ^2

sqrt 45 = c

6.708 rounded = 6.71 = c

Therefore the length of the hypotenuse is 6.71

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The odds of you contracting an sti by the time you are 25 years old is 50%.

Even if a person has only had one physical relationship, that partner could be infected. Of course, the risks of contracting STDs (also known as sexually transmitted illnesses, or STIs) increase if a person has unprotected intercourse with a variety of partners.

Many persons with STDs have no evident indications or symptoms. As a result, individuals may assume they are "clean" and inform partners they don't need to use a protection.

But that's not a good idea. For example, almost six out of ten young people infected with HIV are unaware of their status. As a result, they risk infecting others with the AIDS virus.

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Based on the information provided, the correct statement is: The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.

A residual is the difference between the actual value of the dependent variable (in this case, the number of customers) and the predicted value of the dependent variable based on the model (in this case, the line of fit). In other words, it is the error or deviation between the observed data and the model.

In this case, the smallest residual is 14, and the largest residual is 51. This means that the model is most accurate when predicting the number of customers on days with temperatures close to 82°F and least accurate when predicting the number of customers on days with temperatures close to 91°F. The large residual of 51 corresponds to an outlier in the data, which means that the model is not a good fit for this data point and may not accurately predict the number of customers on days with temperatures close to 91°F.

Option A is correct because it correctly describes the range and magnitude of the residuals and identifies the largest residual as corresponding to an outlier in the data. Options B, C, and D are all incorrect because they either do not correctly describe the range or magnitude of the residuals or do not correctly identify the largest residual as corresponding to an outlier in the data.

What do you mean by statistical?

statistics is defined as: the branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

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The value for df within in an experiment with two levels of factor a and three levels of factor b and five samples for each treatment condition is between 3.

Let n1 represent factor A's level of freedom.

Let n2 represent factor B's degree of freedom.

If factor A has five levels, then n1 = 2.

If Factor B has seven levels, then n2 = 3.

The formula is used to express how the degrees of freedom interact;

df = (n1 - 1)+(n2 - 1) (n2 - 1)

df = n1 -1 + n2- 1

df = n1 + n2 -2

Replace n1 and n2 to obtain df;

df = 2 + 3 - 2

df = 3

Thus, the value for df within in an experiment with two levels of factor a and three levels of factor b and five samples for each treatment condition is 3.

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