How do you solve 1/6+(-1/2)

The required solution to the given equation is a = 2.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

abc - 3ac - 4ab + 12a - 2bc + 6c + 8b - 24 = 0

Subtract 2bc + 6c + 8b from both sides,

abc - 3ac - 4ab + 12a - 2bc + 6c + 8b - 24 - (2bc + 6c + 8b) = - (2bc + 6c + 8b)

Rearrange the likewise terms and apply the arithmetics operation,

abc - 3ac - 4ab + 12a - 24 = -8b + 2bc - 6c

abc - 3ac-4ab+12a=-8b+2bc-6c+24

[tex]a\left(-3+b\right)\left(c-4\right)=-8b+2bc-6c+24[/tex]

[tex]\dfrac{a\left(-3+b\right)\left(c-4\right)}{\left(-3+b\right)\left(c-4\right)}=-\dfrac{8b}{\left(-3+b\right)\left(c-4\right)}+\dfrac{2bc}{\left(-3+b\right)\left(c-4\right)}-\dfrac{6c}{\left(-3+b\right)\left(c-4\right)}+\dfrac{24}{\left(-3+b\right)\left(c-4\right)};\quad \:b\ne \:3[/tex]

After solving, we get as:

a = 2

Thus, the required solution is a = 2.

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The length and width of the rectangle are 50 metres and 10 metres respectively.

A rectangle is a quadrilateral with opposite sides parallel to each other and opposite side equal to each other.

The length of a rectangle is five times its width.

Therefore,

l = 5w

The perimeter of the rectangle is 120metres.

Hence,

perimeter of the rectangle = 2(l + w)

where

Therefore,

120 = 2(5w + w)

120 = 2(6w)

120 = 12w

divide both sides by 12

w = 120 / 12

w = 10 metres

l = 5(10)

l = 50 metres

Therefore,

width = 10 metres

length = 50 metres

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Answer:

DE = 7

Step-by-step explanation:

work is in the

Hello!  Hope this is helpful.  I'll give you an example so you can figure this out on your own.

If a line segment is AD + DE, and AD is (x + 4) and DE is (x + 8), then AE is (x + 4) + (x + 8).

Combine like terms, terms with the same variable (x) or none.

x + 8 + x + 4 = 2x + 12.  
The whole line is the length 2x + 12.

With this, try solving it!

Answer:

Step-by-step explanation:

The angles are supplementary, so they add to 180.

x + (6x -2 ) = 180

7x = 182

x = 182/7 = 26 = m∠2

6(26) - 2 = 154 = m∠1

Step-by-step explanation:

what is the question ?

how much water does the full bucket contain ?

if so, then I understand that

11 2/3 gallons = 5/6 bucket

(11×3 + 2)/3 gallons = 5/6 bucket

35/3 gallons = 5/6 bucket

what do we need to do to get 1 bucket (5/5 or 6/6 or 3/3 or ...) on the right side ?

we multiply everything by 6/5 :

35/3 × 6/5 gallons = 5/6 × 6/5 bucket

(6×35)/(5×3) gallons = 1 bucket

(2×7)/(1×1) gallons = 1 bucket

14 gallons = 1 bucket

the bucket can contain 14 gallons of water.

Eric borrowed $3300 from the first loan and $3000 - $3300 = $-300 from the second loan (which is not possible). This means that the solution is not valid and Eric may have made a mistake in calculating the interest.

Interest is a fee charged by a lender to a borrower for the use of money. It represents the cost of borrowing money and is typically expressed as a percentage of the loan amount. Interest is paid over a period of time and is calculated based on the principal amount of the loan, the interest rate, and the length of the loan term.

There are two main types of interest: simple interest and compound interest. Simple interest is calculated only on the principal amount of the loan, while compound interest is calculated on both the principal and the accumulated interest over time. Compound interest results in a faster growth of the loan balance compared to simple interest.

Let's call the amount Eric borrowed from the first loan "A" and the amount he borrowed from the second loan "B". We can set up two equations to represent the simple interest he owed on each loan after 2 years:

A * 0.03 * 2 = interest owed on loan 1

B * 0.025 * 2 = interest owed on loan 2

The total interest owed on both loans after 2 years is $165:

A * 0.03 * 2 + B * 0.025 * 2 = 165

We also know that Eric borrowed a total of $3000:

A + B = 3000

We can substitute the second equation into the first to get an equation in terms of one variable:

A * 0.03 * 2 + (3000 - A) * 0.025 * 2 = 165

Expanding and simplifying the right side:

A * 0.03 * 2 + 3000 * 0.025 * 2 - A * 0.025 * 2 = 165

A * 0.03 * 2 - A * 0.025 * 2 = 165 - 3000 * 0.025 * 2

A * (0.03 - 0.025) = 165 - 3000 * 0.025 * 2

A * 0.005 = 165 - 3000 * 0.025 * 2

A = 165 / 0.005 + 3000 * 0.025 * 2 / 0.005

Solving for A:

A = 3300

So, Eric borrowed $3300 from the first loan and $3000 - $3300 = $-300 from the second loan (which is not possible). This means that the solution is not valid and Eric may have made a mistake in calculating the interest or the amounts borrowed.

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Answer:

Step-by-step explanation:

easy all you neec to do is add all the sides and you got it f u

Answer:

[tex](x,y)=(3,-7)[/tex]

Step-by-step explanation:

[tex]x-y=10 \implies 2x-2y=20 \\ \\ (3x+2y)+(2x-2y)=-5+20 \implies 5x=15 \implies x=3 \\ \\ \therefore 3-y=10 \implies y=-7 \\ \\ \therefore (x,y)=(3,-7)[/tex].

Answer: y=-25

Step-by-step explanation:

3(y+10)-2y=5

3y+30-2y=5

y+30=5

y=5-30

The system of equations has a solution y=x+2 y=3x. The slopes then are m = 1 and m = 2, respectively. There is only one way to solve it.

Interception locations on the x+2 axis are as follows: X Intercepts (-2,0), Y Intercepts (-0,0). (0,2) . x+2 : A line equation with the form y=m x+b has a slope of m m=1. Points of three-axis interception Intercepts for X and Y are (0,0). (0,0) . 3 x :A line equation with the form y=m x+b has a slope of m m=3.

A set of values for the variables x, y, z, etc. that simultaneously satisfy every equation in a system of equations is known as the solution. The collection of all solutions is known as the solution set for a system of equations. Finding every answer using formulas containing a certain number of parameters is the definition of system solving. The solution(s) to the problem is/are the point(s) where all the lines intersect.

Therefore the correct answer is option b) One Solution .

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One of the most basic ideas within the number system is that there is a 10-to-1 relationship between the values of any two adjacent places

A decimal number is a number that consists a whole and a fraction part separated by a decimal point.

When multiplying decimals, we must follow these steps:

By understanding place value, we can interpret the meaning of each digit in a decimal number

For example, if we multiply 73.24 ✕ 5.1, we will first multiply 7324 by 51. Then, counting all the decimal of the factors, there are 3 decimal places altogether. From the rightmost digit of the product to the left, count the same decimal places and put the decimal point

Hence, the number of the decimal places in the factors, when added up, is equal to the number of the decimal places in the product.

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Since we are aware that the back wheel's radius is 9 inches, we can enter this information into the formula C=2[tex]\pi[/tex]r. C=2(9), which is 56.52 when simplified, is the new formula.

By dividing the circle's diameter by, you may determine a circle's circumference (pi). By dividing 2radius by pi, or 3.14, you may also determine the circumference.Using the equations C=2[tex]\pi[/tex]r or C=[tex]\pi[/tex]d, one can determine a circle's circumference. The formula C=2[tex]\pi[/tex]r can be applied as we know the back wheel's radius to be 9 inches.

C=2(9) is the new formula, which is reduced to 56.52. C=[tex]\pi[/tex]d or C=2[tex]\pi[/tex]r are two formulas that can be used to get the circumference of a circle. We can enter these numbers into the formula C=[tex]\pi[/tex]d because we are aware that the circle's diameter is 8 cm, and a rough value for pi is 3.14. C=(3.14)(8), a more straightforward version of the formula, yields 25.12.

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it is between D.) 8400 and 8500.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

8.42×10³

=8420

Hence, it is between D.) 8400 and 8500.

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On solving the provided question, we can say that in the given graph the function will be so, g(x) = -1/2 |x|

Mathematicians use graphs logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

in the given graph

we have two lines that are straight from the origin, so the function must be in modulus

so, g(x) = -1/2 |x|

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The maximum exposure incorporating all types of ad is equal to 54000 viewers.

simplex method, standard technique in linear programming for solving an optimization problem, typically one involving a function and several constraints expressed as inequalities. The inequalities define a polygonal region, and the solution is typically at one of the vertices. The simplex method is a systematic procedure for testing the vertices as possible solutions.

Given here: A store with $9000 monthly advertising budget.

n = the number of newspaper ads

r = the number of radio ads

t = the number of TV ads

This is a linear programming problem with the following constrains:

0 ≤ n ≤ 30

0 ≤r ≤60

0 ≤ t ≤ 20

600b + 30r + 3000t≤9000 divide both sides by 30

20n + r + 100t ≤ 300

The objective function is:

F(n, r, t) = 4000n + 3000r + 12000t

Use simplex method or any other method to find the maximum that Max  F (n,r,t)=54000

Hence, The maximum exposure incorporating all types of ad is equal to 54000 viewers.

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Answer:

3.

12a + 21(12) = 21a

252 = 21a - 12a

252 = 9a

a = 252/9

a = 28 mins

Sam takes 28 minutes

Step-by-step explanation:

im not sure about 4

The equation of the line that has a slope of -4 and goes through -1,6 is  4x-y+2 = 0

In general, a straight line has the equation y = mx + c, where m denotes the gradient and y = c denotes the point at which the line intersects the y-axis. The y-axis intercept is denoted by the value c. A straight line with a gradient of m and an intercept of c on the y-axis has the equation y = mx + c. Finding the slope and y-intercept will allow you to write the equation of a graphed line in y-intercept (y=mx+b) form. Slope is defined as the ratio of y-to-x changes. Choose two points on the line, and then create a sloping triangle joining them.

The equation of a straight line that passes through a point [x1 , y1} and having a slope ‘m’ is given by (y - y1) = m (x - x1)

Given m = 4 and point ( 1,6), then the equation of the line is

(y-6) = 4 (x-1) i.e, y - 6 = 4x - 4

i.e, 4x -y -4+6 =0 i.e, 4x - y = - 2 or 4x-y+2 = 0

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A correlation coefficient of r = 0.15 indicates that r2 = 0.152 = 0.0225 represents the quality of fit for the data obtained through linear regression analysis.

Making predictions from the data using the line of best fit is not reasonable. A correlation coefficient of r = 0.15 indicates that r2 = 0.152 = 0.0225 represents the quality of fit for the data obtained through linear regression analysis.

When the dependent and independent variables have a perfect correlation (r2=1), the dependent variable can be accurately predicted.

When r2 is zero, there is no connection at all between the dependent and independent variables.

A reasonable correlation between the dependent and independent variables is present when r2 > 0.9.It is not feasible to use the line of best fit to generate predictions because the value of r2=0.0225 is so low.

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You would know that the dilation is going to produce a similar figure because the image and the pre image are going to have congruent and corresponding sides.

Due to the congruent matching angles between the image and pre-image, dilations result in identical figures. Based on the scale factor, the corresponding side lengths of the figures will be proportionate. The scale factor causes the sides to be either extended or contracted while maintaining the form.

Each preimage point has a line leading to its corresponding image point that is congruent. Dilations are a particular kind of transformation that are not isometries.

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Answer:106,34,40

Step-by-step explanation:

The fourth multiple of 6 is 24, and the third multiple of 8 is 24, the sum gives:

24 + 24 = 48

To take the multiples of a number A, we just need to multiply it by whole numbers, for example let's start with 6, the multiples are:

6*1 = 6

6*2 = 12

6*3 = 18

6*4 = 24

The fourth multiple of 6 is 24.

And with 8 the multiples are:

8*1 = 8

8*2 = 16

8*3 = 24

The third multiple of 8 is 24, then the sum of these two gives:

24 + 24  = 48

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Answer:

65%

Step-by-step explanation:

20 = 100%

7 = x%

7•100 ÷ 20 = 35%

so 35% is spent on rent so the other 65% that rest is the answer .

The length of AC is equivalent to 10.5 units.

Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically -

K = a/b

Rewriting, we get -

a = Kb

If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka]

Given are the two similar triangles as ΔABC and ΔDEF.

We can write the proportionality between the sides as -

{AB/DE} = {BC/EF} = {AC/DF} = {K} (constant)

{AB/DE} = {AC/DF}

6/4 = x/7

x = (6 x 7)/4

x = 42/4

x = 21/2

x = 10.5

Therefore, the length of AC is equivalent to 10.5 units.

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Answer:

infinite number of solutions

Step-by-step explanation:

If you just distribute the 2 on the right side of the equation,

6x + 12 = 2(3x + 6)

6x + 12 = 6x + 12

The two sides of the equation are identical. And if we were to proceed to solve (but they said don't) and subtracted 6x from both sides we would get 12 = 12 .

The variable falls out of the equation and a true statement is left behind, there are infinite solutions.

The figures below are similar figure A  the sides  are 20 and 17.5 so it is   scale factor.

Figures A and B are scaled at a ratio of 1:x.

Scale factor is defined as the difference between the dimensions of the new and old forms, according to the basic equation for calculating scale factors in figures.

A scale factor is the ratio between the scale of an original item and a new object that is a representation of it but is of a different size.

The distance between the two points in Figure A and Figure B is divided by the distance between the two points in Figure A to determine the scale factor.

14 / 16 = 20 /x = 17.5

x = 17.5

The figures below are similar figure A  the sides  are 20 and 17.5 so it is   scale factor.

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the function that models the inverse variation: y = 48/x. This can be solved using the formula of equation.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

It is given that, x and y vary inversely

x - 12 = 0

therefore, x = 12

y - 4 = 0

therefore, y = 4

Equation of inverse variation is: y = c/x

4 = c/12

c = 48

Thus, equation of inverse variation is: y = 48/x

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If each unit on the coordinate plane represents one mile, Michael does not live far enough from the school for bus service.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Based on the information provided about Michael, we know that he is living at the closest point to the school (the origin) on Maple Street,  which is represented by the line y = 4x + 6.

Therefore, slope (m) = 4

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

4 × m₂ = -1

m₂ = -1/4

Since line 2 passes through the origin (0, 0), it can be modeled by this equation;

y = mx + c

y = -1/4(x) + 0

y = -x/4

Now, we can determine the coordinates for the location of Michael's house;

4x + 6 = -x/4

16x + 24 = -x

16x + x = 24

17x = 24

x = 24/17

x = 1.41

y = -x/4

y = -1.41/4

y = -0.35

Therefore, the coordinates of Michael's house is (1.41, -0.35).

For the distance from Michael's house to school, we have:

Distance = √[x² + y²]

Distance = √[1.41² + (-0.35)²]

Distance = √(1.9881 + 0.1225)

Distance = 1.45 mile.

In conclusion, Michael does not live far enough from the school for bus service because a distance of 1.45 mile is less than 3 miles.

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Answer:

£26750

Step-by-step explanation:

x = salary before the increase

x  + x(1.052) = 28141

1.052x = 28141

x = 28141/1.052 = 26750

This means he got a £1391 raise