What is the solution to the equation
2/3x+1/6=1​

Answer:

4 1/4

Step-by-step explanation:

f(x) = 2/3(6) + 1/4

f(x) = 4 + 1/4

f(x) = 4 1/4(4.25)

Mrs Martini age is 42 years and Tony age is 12 years

Step-by-step explanation:

The given is:

Assume that Tony is x years old now

∵ Mrs. Martini is 6 years more than 3 times as old as Tony

∵ Tony is x years old

- Multiply the age of Tony by 3 and add 6 to the product

∴ The age of Mrs Martini = 3 x + 6

8 years ago

- Subtract 8 from the age of each one

Tony age = (x - 8)

Mrs Martini age = (3 x + 6) - 8 = 3 x + 6 - 8 = 3 x - 2

∵ Eight years ago, Mrs Martini was 2 years less than 9 times as old

  as Tony was then

- Multiply Tony age by 9 and subtract 2 from the product

∵ Tony age from 8 years ago = x - 8

∵ Mrs Martini age from 8 years ago = 3 x - 2

∴ 9(x - 8) - 2 = 3 x - 2

- Simplify the left hand side

∴ 9 x - 72 - 2 = 3 x - 2

- Add like terms

∴ 9 x - 74 = 3 x - 2

- Subtract 3 x from both sides

∴ 6 x - 74 = -2

- Add 74 to both sides

∴ 6 x = 72

- Divide both sides by 6

∴ x = 12

∵ x represents the age of Tony

∴ Tony is 12 years old

∴ 3 x + 6 is the age of Mrs Martini

- Substitute x by 12

∵ 3(12) + 6 = 36 + 6 = 42

∴ Mrs Martini is 42 years old

Mrs Martini age is 42 years and Tony age is 12 years

Learn more:

You can learn more about word problems in brainly.com/question/10557938

#LearnwithBrainly

Answer:

The carpenter can make 9 pieces.

Step-by-step explanation:

6/(2/3)=(6/1)(3/2)=18/2=9

The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.

Step-by-step explanation:

Let,

Longer leg = a = x

Shorter leg = b = x - 6

Hypotenuse = c = x + 6

As the triangle is right angles, therefore, using pythagoras theorem;

[tex]a^2+b^2=c^2\\(x)^2+(x-6)^2=(x+6)^2\\x^2+(x^2-12x+36)=x^2+12x+36\\x^2+x^2-12x+36=x^2+12x+36\\ 2x^2-12x+36=x^2+12x+36[/tex]

Adding (-x² - 12x-36) on both sides

[tex]2x^2-12x+36-x^2-12x-36=x^2+12x+36-x^2-12x-36\\x^2-24x=0[/tex]

Taking x common;

[tex]x(x-24)=0\\[/tex]

Either,

x=0

or,

x-24 = 0     => x=24

As length cannot be 0 therefore,

Longer leg = x = 24 feet

Shorter leg = x-6 = 24-6 = 18 feet

Hypotenuse = x+6 = 24+6 = 30 feet.

The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.

Keywords: triangle, addition

Learn more about triangles at:

#LearnwithBrainly

Answer:

A), B) & D).

Step-by-step explanation:

Answer:

A) y = 7.25 when x = –7

C) y = 8.5 when x = –4

D) y = 10.25 when x = 5

Answer:

[tex]19 - \frac{6}{5}j[/tex]

written out on a computer keyboard, you would type: 19 - (6/5)j

Step-by-step explanation:

The terms that dont have a 'j' attached to them all group up and combine to this: 18 + (-5) + 6 = 18-5+6 = 13+6 = 19

The rest of the terms have a 'j', and they combine to: [tex]-\frac{2}{5}j - \frac{4}{5}j = \left(-\frac{2}{5} - \frac{4}{5}\right)j = \frac{-2-4}{5}j = -\frac{6}{5}j[/tex]

After combining both sets of like terms, we have 19 as the first result and [tex]-\frac{6}{5}j[/tex] as the second result. They are then added to get [tex]19 + \left(-\frac{6}{5}j\right) = 19 - \frac{6}{5}j[/tex]

We cant simplify any further because there are no like terms left.

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 5, -1)\\(x_ {2}, y_ {2}) :( 4, -5)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5 - (- 1)} {4-5} = \frac {-5+ 1} {- 1} = \frac {-4} {- 1} = 4[/tex]

Thus, the equation is of the form:

[tex]y = 4x + b[/tex]

We substitute one of the points and find b:

[tex](x,y):(5,-1)\\-1=4(5)+b\\-1=20+b\\-1-20=b\\b=-21[/tex]

Finally, the equation is:

[tex]y = 4x-21[/tex]

Answer:

[tex]y = 4x-21[/tex]

Answer:

c = 56

Step-by-step explanation:

The two angles 'c' and '124' form a straight angle. They add to 180

c+124 = 180

c+124-124 = 180-124 ... subtract 124 from both sides

c+0 = 56

c = 56

Answer:

56 <3

Step-by-step explanation:

The never intersecting and the coplanar lines describe the parallel lines. The correct option is C and E.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

Therefore, the never intersecting and the coplanar lines describe the parallel lines. The correct option is C and E.

To know more about parallel lines follow

https://brainly.com/question/16742265

#SPJ2

The solution to a system of linear inequalities is the set of values that satisfy all the inequalities at once, graphically represented as the overlapping shaded region on a coordinate plane.

The solution to a system of linear inequalities is defined as the set of values that satisfy all inequalities in the system simultaneously. To find this solution set, each inequality is graphed on the same coordinate plane to determine the region where all inequalities overlap. Within this region, any point represents a solution to the system. If an inequality is non-strict (less than or equal to or greater than or equal to), the boundary line is included in the solution set and is usually drawn as a solid line. If the inequality is strict (less than or greater than), the boundary line is not included in the solution set and is depicted as a dashed line. The solutions are typically represented graphically by shading the area of the plane that satisfies all conditions.

Answer:

Step-by-step explanation:

Here we have to multiply to find the total...

30 volumes, then each individual book with 700 pages, therefore, the answer would be 21,000 pages

To calculate the total number of pages in the series, multiply the number of volumes (30) by the pages per volume (700) to get a total of 21,000 pages.

The question asks for the total number of pages in a series of books, assuming each of the 30 volumes has 700 pages. Therefore, the calculation we need to perform is: 30 volumes × 700 pages per volume.

The formula to calculate the total number of pages is:

Total Pages = Number of Volumes × Pages per Volume

By inserting the given values into the formula:

Total Pages = 30 × 700 = 21,000 pages.

Hence, the total number of pages in the series is 21,000.

Answer:

A) B) E)

Step-by-step explanation:

I had this question on one of my tests and I got it right :)

Answer:

Part 16) [tex]y\leq -x+2[/tex]

Part 17) [tex]y>\frac{1}{3}x-1[/tex]

Step-by-step explanation:

Part 16) we know that

The solution of the inequality is the shaded area below the solid line

The slope of the solid line is negative

The y-intercept of the solid line is the point (0,2)

The x-intercept of the solid line is the point (2,0)

The slope of the solid line is

[tex]m=(0-2)/(2-0)=-1[/tex]

The linear equation of the solid line in slope intercept form is

[tex]y=-x+2[/tex]

therefore

The inequality that represent the graph is

[tex]y\leq -x+2[/tex]

Part 17) we know that

The solution of the inequality is the shaded area above the dashed line

The slope of the dashed line is positive

The y-intercept of the dashed line is the point (0,-1)

The x-intercept of the dashed line is the point (3,0)

The slope of the dashed line is

[tex]m=(0+1)/(3-0)=\frac{1}{3}[/tex]

The linear equation of the dashed line in slope intercept form is

[tex]y=\frac{1}{3}x-1[/tex]

therefore

The inequality that represent the graph is

[tex]y>\frac{1}{3}x-1[/tex]

Answer:

It's Either B Or D

Step-by-step explanation:

only because They Only number that are closer so you can reverse it is 18 or 96

Answer:

The numbers increase by 3

Step-by-step explanation:

The difference between all the numbers in the sequence have a gap of 3

9 and 12 --gap of 3

12 and 15--gap of 3

18 and 21--gap of 3

21 and 24--gap of 3

Answer

y=3+ before

Step-by-step explanation:

you add 3 to every number

Answer:

3n + 1

Step-by-step explanation:

Note the sequence has a common difference between consecutive terms, that is

7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3

This indicates that the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 4 and d = 3, thus

[tex]a_{n}[/tex] = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1

Answer:

[tex]\large\boxed{a(n)=3n+1}[/tex]

Step-by-step explanation:

It's an arithmetic sequence:

[tex]a(1)=4\\\\a(2)=a(1)+3=4+3=7\\\\a(3)=a(2)+3=7+3=10\\\\a(4)=a(3)+3=10+3=13\\\\a(5)=a(4)+3=13+3=16\\\vdots[/tex]

An explicit formula of an arithmetic sequence:

[tex]a(n)=a(1)+(n-1)d[/tex]

d - common difference

We have

[tex]a(1)=4,\ d=3[/tex]

Substitute:

[tex]a(n)=4+(n-1)(3)[/tex]            use the distributive property

[tex]a(n)=4+3n-3[/tex]

[tex]a(n)=3n+1[/tex]

Answer:

Value of I is $4290

Step-by-step explanation:

We have been given that,

Formula for simple interest is given by

Plugging the known values

On simplifying, we get

Hence, value of I is $4290

Answer:

Table A represents a function, but Table B does not represent a function.

Step-by-step explanation:

We have to select the correct option among the given 4 options after judging the given two tables attached to this question.

The first table shows that for each x values there is only one y value. Therefore, this is a function.

But in the second table shows that for each x value there are multiple y values since we are getting y = 1 and 2 for x = 5.

Hence, table B is not a function. it is just a relation. (Answer)

Answer:

d.

Step-by-step explanation:

Answer:

The value 3 represents the vertical translation upwards of [tex]f(x)[/tex] to [tex]g(x)[/tex]

Step-by-step explanation:

The question is incomplete or missing data.

The correct question

What value represents the vertical translation from the graph of the parent function [tex]f(x) = x^2[/tex] to the graph of the function

[tex]g(x) = (x + 5)^2 + 3[/tex]?

Given functions:

Parent function

[tex]f(x) = x^2[/tex]

Translated function

[tex]g(x) = (x + 5)^2 + 3[/tex]

Translation rules

For horizontal shift

[tex]f(x)\rightarrow f(x+c)[/tex]

If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.

If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.

For vertical shift

[tex]f(x)\rightarrow f(x)+c[/tex]

If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.

If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.

From the functions given the translation rule can be given as:

[tex]f(x)\rightarrow f(x+5)+3[/tex]

[tex]g(x)=f(x+5)+3[/tex]

This shows the graph is shifted left by 5 units and upwards by 3 units.

Thus the value 3 represents the vertical translation of [tex]f(x)[/tex] to [tex]g(x)[/tex]

Answer: 2,000,000,000

Step-by-step explanation:

Question 1:

No, \(x^3 \cdot x^3 \cdot x^3\) equals \(x^9\), while \(x^3 \cdot 3 \cdot 3\) equals \(9x^3\), representing different operations and values.

Question 2:

Incomplete. The expression \(1/x^3\) can be rewritten as \(x^{-3}\) using negative exponents.

Question 3:

Incorrect. The product of \(\sqrt{x}\) and \(4\sqrt{x}\) equals \(4x\), not \(5x\). Use exponents to simplify.

Question 4:

The expression \(x^{5/6} \cdot x^{1/6}\) simplifies to \(x\). Show the steps of exponent addition.

Question 5:

Unjustified. Determine equivalent expressions by simplifying each and comparing results. Justify based on mathematical properties.

Here's a review of your work:

Question 1:

Your reasoning is incorrect. The expressions are not equivalent because they represent different operations. \( x^3 \cdot x^3 \cdot x^3 \) means \( x \) multiplied by itself 3 times, which is \( x^9 \). \( x^3 \cdot 3 \cdot 3 \) is a multiplication of constants, which equals \( 9x^3 \). So, the expressions are not equivalent because they result in different values.

Question 2:

Your answer is incomplete. It seems like you've provided a template for simplifying radicals, but you haven't actually applied it to the given expression. To simplify \( \frac{1}{x^3} \), you can rewrite it as \( x^{-3} \).

Question 3:

Your answer is incorrect. The product of \( \sqrt{x} \) and \( 4\sqrt{x} \) is not simply \( 5x \). To rewrite it in simplest rational exponent form, you should use the property of exponents which states that \( \sqrt{a} = a^{1/2} \). So, \( \sqrt{x} \) is equivalent to \( x^{1/2} \), and \( 4\sqrt{x} \) is equivalent to \( 4x^{1/2} \). Multiplying these expressions together, you get \( 4x^{1/2} \cdot x^{1/2} = 4x^{1/2 + 1/2} = 4x^1 = 4x \).

Question 4:

You haven't shown your process for simplifying \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} \). To simplify, use the property of exponents which states that when you multiply two terms with the same base, you add their exponents. So, \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} = x^{\frac{5}{6} + \frac{1}{6}} = x^{\frac{6}{6}} = x^1 = x \).

Question 5:

You haven't justified which expressions are equivalent. To determine equivalence, you need to simplify each expression and compare them to each other.

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Long division setup showing an incomplete calculation

We need to find this number

Lets write the steps above

∵ The dividend = 3302

∵ The divisor = 13

- 2 hundreds means 200 and 5 tens means 50

∵ The quotient = 200 + 50 + x

∵ Dividend = divisor × quotient

∴ (13 × 200) + (13 × 50) + (13 × x) = 3302

∵ 13 × 200 = 2600

- Subtract 2600 from the dividend

∴ 3302 - 2600 = 702

∵ 13 × 50 = 650

∴ 702 - 650 = 52 ⇒ 650 is the unknown value

∵ 13 × x = 13x

∵ 52 - 13x = 0

- Add 13 x to both sides

∴ 52 = 13x

- Divide both sides by 13

∴ x = 4

∴ 3302 ÷ 13 = 200 + 50 + 4

∴ 3302 ÷ 13 = 254

∴ From the steps above the missing number subtracted from

   702 is 650

The unknown value is being subtracted from 702 is 650

Learn more:

You can learn more about the division operation in brainly.com/question/1747117

#LearnwithBrainly

Answer:

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Long division setup showing an incomplete calculation

13 is in the divisor

3302 is in the dividend

2 hundreds and 5 tens is written in the quotient

2600 is subtracted from 3302 to give 702

An unknown value represented by a box is being subtracted from 702

We need to find this number

Lets write the steps above

∵ The dividend = 3302

∵ The divisor = 13

- 2 hundreds means 200 and 5 tens means 50

∵ The quotient = 200 + 50 + x

∵ Dividend = divisor × quotient

∴ (13 × 200) + (13 × 50) + (13 × x) = 3302

∵ 13 × 200 = 2600

- Subtract 2600 from the dividend

∴ 3302 - 2600 = 702

∵ 13 × 50 = 650

∴ 702 - 650 = 52 ⇒ 650 is the unknown value

∵ 13 × x = 13x

∵ 52 - 13x = 0

- Add 13 x to both sides

∴ 52 = 13x

- Divide both sides by 13

∴ x = 4

∴ 3302 ÷ 13 = 200 + 50 + 4

∴ 3302 ÷ 13 = 254

∴ From the steps above the missing number subtracted from

  702 is 650

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Answer:

(6, 28) or x=6, y=28 or The numbers are 6 and 28.

Step-by-step explanation:

4x+4=y

x+y+5=39

--------------

4x+4=y

x+y=39-5

----------------

4x+4=y

x+y=34

------------

x+(4x+4)=34

x+4x+4=34

5x+4=34

5x=34-4

5x=30

x=30/5=6

4(6)+4=y

24+4=y

y=28

x=6, y=28

Store B is offering the better deal on ground beef

Step-by-step explanation:

Dean is comparing prices on ground beef

We need to know which store is offering the better deal on ground beef

To find the better deal we must to find the unit price of each store

The unit price = total price ÷ number of pounds

∵ Store A is selling 5 pounds of ground beef for $23.49

∴ The unit price of Store A = 23.49 ÷ 5 = $4.698

∴ The unit price of Store A is $4.698 per pound

∵ Store B is selling 8 pounds of ground beef for $36.96

∴ The unit price of Store B = 36.96 ÷ 8 = $4.620

∴ The unit price of Store B is $4.620 per pound

∵ $4.620 < $4.698

∴ The unit price of Store B is less than the unit price of Store B

∴ Store B is cheaper than Store A, then it is offering the better deal

Store B is offering the better deal on ground beef

Learn more:

You can learn more about the word problems in brainly.com/question/317697

#LearnwithBrainly

Answer:

56

Step-by-step explanation:

4 x 2 = 8

8 x 7 = 56

Answer = 56

Answer:

The number of adults who went to the zoo was 21 and the number of children was 105.

Step-by-step explanation:

The complete question is

The Jurassic Zoo charges $5 for each adult admission and $3 for each child. The total bill for the 126 people from a school trip was $420. How many adults and how many children went to the zoo?

Let

x -----> number of adults

y ----> number of children

we know that

[tex]x+y=126[/tex] ------> equation A

[tex]5x+3y=428[/tex] ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

The solution is the point (21,105)

see the attached figure

therefore

The number of adults who went to the zoo was 21 and the number of children was 105.

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

You could add (-1.07 + 2.971) to get (1.901)

Then do (1.901 - 4.3) to get a negative number; (-2.399)

I would double check this all with a calculator