write an algebraic expression to represent the following verbal expression
the cube of the difference of a number and 43.
A. x cubed - 43 cubed
B. (x-43) cubed
C. (43-x) cubed
D. (x+43) cubed
i already know C is incorrect

Answer:

see the picture 8.1 is answer

Answer:

36

Step-by-step explanation:

Number of boys = 30

also, Number of boys = 10(number of girls/2)

∴ 30 = 10(number of girls/2)

30×2 = 10(number of girls)

⇒ number of girls = [tex]\frac{60}{10}[/tex]

⇒ number of girls = 6

Total number of girls and boys = 30 + 6 = 36

The missing digit in this numbers are 11

Answer:

Variable

Step-by-step explanation:

A Variable is a letter or symbol used to represent a quantity that can change.

The symbol used to represent a quantity that can change is called a variable.

We have,

The symbol that is commonly used to represent a quantity that can change is called a variable.

In mathematics and algebraic equations, variables are often represented by letters such as x, y, or z.

Variables are placeholders for unknown or changing values that can be assigned different numerical or algebraic values during calculations or problem-solving.

They allow for the generalization and manipulation of mathematical expressions and equations.

Thus,

The symbol used to represent a quantity that can change is called a variable.

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Answer: 10 : t = 16   11 : x = -8   13 : x = 0

Step-by-step explanation: Im sure about 10 and 11 but not too sure about 13 and explanations are too hard for me to explain

Margaret needs 2 1/2 cups of sugar and chocolate chips to make the fudge.

To make the fudge, Margaret needs 1 1/4 cups of sugar and 1 1/4 cups of chocolate chips.

To find the total number of cups needed, add the amounts of sugar and chocolate chips: 1 1/4 + 1 1/4 = 2 1/2 cups.

Therefore, Margaret needs 2 1/2 cups of sugar and chocolate chips to make the fudge.

Answer:

75

Step-by-step explanation:

1200+9X=25X

1200=25X-9X

1200=16X

X=1200/16

X=75

To find the number of tote bags a company needs to sell in order to cover its costs, we need to set its daily costs equal to its daily revenue and solve for the number of bags. In this case, the solution to the equation indicates that the company needs to sell 80 tote bags each day to break even.

The subject of this question is business mathematics, specifically the mathematical concept of break-even point. The break-even point is the point at which total revenue equals total expenses, and the business is neither losing nor making money. In this case, the fixed costs, or overhead expenses, total $1200 per day, while the variable costs are $9 per tote bag. We can express daily costs, C, as C = $1200 + $9x, where x represents the number of tote bags. The daily revenue, R, is R = $25x. To find the number of tote bags needed to break even, you set C equal to R and solve the resulting equation $1200 + $9x = $25x. Solving this equation yields x = 80. Therefore, the company needs to sell 80 tote bags each day in order to break even.

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Here's my step-by-step explanation:

Let's get two facts straight: f(x) is a linear function. It's a line. g(x) is an exponential function. It's a curve.

Method 1: Elimination using f(x)

For f(x), the y-intercept (where on the y-axis it coincides with) in {f(x) = 7/3x - 3} is -3. And the only graph that has that is Graph 2.

Alright, so the first obvious solution, according to that graph, is (0, -3). And since we're speaking in terms of x (thus f(x) and g(x)), we pick the x-value from that coordinate and get 0.

The second solution is not as obvious; it's supposed to be (3,4) but the graph is kinda off. I attached a Desmos graph so you can see what I'm talking about a little more clearly.

Anyway, since we're speaking in terms of x we pick the x-value from that coordinate and get 3. Nice, we've got the solutions 0 and 3.

Hope this helps, let me know if I made a mistake.

Answer:

see explanation

Step-by-step explanation:

64x + 27 ← is not a sum of cubes. We would require

64x³ + 27 ← sum of cubes and factors as

64x³ + 27 = (4x + 3)(16x² - 12x + 9)

Answer: 12 inches cubed

Step-by-step explanation:

volume=length x width x height

volume=1.5 in x 2 in x 4 in

volume=12 in^3

Answer:

1. False

2. c. (1, -7)

3. Input= 1 and 4; Output=6, 12 and 18. The rule is the input×3

Step-by-step explanation:

1. 8+4=±5+7

8+4= 12 & ±5+7= 2

The left side  12  does not equal to the right side  2 , which means that the given statement is false.  

2. I'm not sure how to show my work.

3.

Input: 0, 1, 2, 3, 4, 5, 6

Output: 0, 3, 6, 9, 12, 15, 18

0×3=0; 1×3=3; 2×3=6; 3×3=9; 4×3=12; 5×3=15; 6×3=18

1. The equation is false.

2. The ordered pair that is a solution of the equation y = -11x + 4 is (-1, -7).

3. The rule for the table is to square the input and add 3.

1. Given

8 + 4 = -5 + 7

12 = 2

The left side of the equation is 12, and the right side of the equation is 2. 12 is not equal to 2, so the equation is false.

2. The ordered pair that is a solution of the equation y = -11x + 4 is (-1, -7).

To see this, we can substitute the x-value of -1 into the equation and solve for y:

y = -11(-1) + 4

y = 11 + 4

y = 15

We can also substitute the y-value of -7 into the equation and solve for x:

-7 = -11x + 4

-11x = -11

x = 1

Therefore, the ordered pair (-1, -7) satisfies both sides of the equation, so it is a solution.

The other ordered pairs do not satisfy both sides of the equation. For example, if we substitute the x-value of 0 into the equation, we get y = 4, which does not equal -7.

3. The rule for the table is square the input and add 3.

To see this, we can look at the first few rows of the table:

Input | Output

-------|--------

0      | 3

3      | 12

9      | 28

We can see that squaring the input and adding 3 gives us the output for each row. For example, squaring the input of 0 gives us 0, and adding 3 gives us 3, which is the output for the first row.

We can also see that this rule works for all of the rows in the table. Therefore, the rule for the table is to square the input and add 3.

Here is the completed table:

Input | Output

-------|--------

0      |    3

3      |    12

9      |    28

16     |    45

25    |    64

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Final answer:

The slope of the line represented by the equation 2x + 5y = 10, passing through points (5, 0) and (0, 2), is calculated as -2/5, meaning the slope is negative two-fifths.

Explanation:

The slope of the line represented by the equation 2x + 5y = 10 can be calculated by using the coordinates of two points through which the line passes. In this case, the points are (5, 0) and (0, 2). According to the slope formula, slope (m) is defined as the change in y (the rise) over the change in x (the run). Therefore, the slope is:

The slope of the line is negative two-fifths (-2/5). Since the slope is negative, this indicates that as the x-value increases, the line moves down the y-axis.

Answer:

Jamie has 14 dimes and 26 nickels

Step-by-step explanation:

nickels : x

dimes : y

[tex]x + y = 40 \\ x = y + 12 \\ \\ replace \: x \:in \: the \: first \: equation \\ y + 12 + y = 40 \\ 2y = 28 \\ y = 14[/tex]

Jamie has a total of 40 coins out of which there are 14 dimes and 26 nickels.

Let x represent the number of dimes. Since Jamie has 12 more nickels, the number of nickels is x + 12.

The total number of coins is 40, so x + x + 12 = 40.

Solve for x:

2x + 12 = 40, 2x = 28

x = 14.

Answer:

(p×2)+3

Step-by-step explanation:

I'm not too sure, I've only just started practicing this stuff?

Answer:

w=6

Step-by-step explanation:

3w+5=23

3w=23-5

3w=18

w=6

The solution to the equation 3w + 5 = 23 is w = 6.

The given equation is 3w + 5 = 23.

We need to solve for w.

Subtract 5 from both sides of the equation to isolate the term with 3w:

3w + 5 - 5 = 23 - 5

3w = 18

Divide both sides of the equation by 3 to solve for w:

(3w) / 3 = 18 / 3

This simplifies to:

w = 6

Therefore, the solution to the equation 3w + 5 = 23 is w = 6.

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Answer: x = 4

Step-by-step explanation:

5x + 34 = -2 + 14x

5x - 5x + 34 = -2 + 14x -5x       Remove 5x from both sides

34 = -2 +9x

34 + 2 = -2 + 2 + 9x               Add 2 to both sides (remove constant)

36 = 9x

36/9 = 9x/9       Divide both sides by 9 to isolate the variable

4 = x

or

x = 4

Answer:

x = 31

Step-by-step explanation:

Let x: total amount of questions in the Chemistry test.

Then 52% represents the ratio of questions properly answered vs total questions:

[tex]\frac{Correct}{Total} = 52%[/tex]

The number of correct questions is the number of total questions take the number of missed questions.

[tex]Correct questions = Total questions - missed questions[/tex]

Since, missed questions = 15

[tex]\frac{x-15}{x} = 52%[/tex]

Also, 52% can be expressed as 0.52. Then, the expression can be rewritten as:

[tex]\frac{x-15}{x} = 0.52[/tex]

Then, rearranging:

[tex] x - 15 = 0.52x [/tex]

[tex] x - 0.52x = 15 [/tex]

[tex] 0.48x = 15 [/tex]

[tex] x = 15/0.48 [/tex]

[tex] x = 31.25 [/tex]

Rounding to the nearest unit: x = 31

Answer:

5/6

Step-by-step explanation:

Let x = 0.8333.....

Then 10x = 8.333...

Now we subtract x from 10x.

               10x = 8.333...

       -           x = 0.833...

    -----------------------------

                  9x = 7.5

9x = 7.5

9x/9 = 7.5/9

x = 7.5/9 = 15/18 = 5/6

Answer: 5/6

The repeating decimal .83 repeating is equal to the fraction 83/99 in simplest form. A repeating decimal can be expressed as a fraction using the method of setting up equations, exploiting the fact we know which digits are repeating.

To express the repeating decimal .83 repeating as a fraction in simplest form, we first need to understand what a repeating decimal is. A repeating decimal is a decimal fraction in which a digit or group of digits repeats infinitely. In the case of .83 repeating, the group of digits that is repeating is '83'. This means that the decimal can be written out as .838383..., and so on, infinitely.

To represent this as a fraction, we can use the method of setting up a pair of equations. Let's define the repeating decimal like this: x = .8383... . Now, multiply x by 100 since there are two repeating digits, yielding the equation: 100x = 83.8383... . Subtract the first equation from this to give 99x = 83, or x = 83/99 when simplified. So, the decimal .83 repeating is equal to the fraction 83/99 in simplest form.

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Answer:

[3⅖, -⅘], [5, -2]

Step-by-step explanation:

I could not do any more, but I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

Step-by-step explanation:

To find the equation of a parallel line, we first need to find the slope of 3y + 7 = 2x.

We need to find it because, if two lines are parallel, then that means they have the same slope.

The best way to do this is solve for y:

[tex]3y+7=2x\\3y=2x-7\\y=\frac{2}{3}-\frac{7}{3}[/tex]

Due to the rule that in y = mx + b, m = the slope, we find that the slope is 2/3.

Now we use that slope in the same formula to find b of the line we're trying to find the equation for, and then we'll have our answer. We find b by plugging in (2, 6) for x and y:

[tex]y = mx+b\\y=\frac{2}{3}x+b\\6=\frac{2}{3}(2)+b\\18=4+3b\\ 14=3b\\\frac{14}{3} = b[/tex]

So our line is:

[tex]y=\frac{2}{3}x+\frac{14}{3}[/tex]

To find the equation of a line parallel to a given line and passing through a given point, first find the slope of the original line. Then, using the slope-intercept form of a line, substitute the given point's coordinates and the slope to find the equation of the parallel line.

To find an equation of the line parallel to 3y+7=2x and passing through point (2,6), we need to find the slope of the original line and then use it to create the equation of the parallel line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

The given equation 3y+7=2x can be rearranged to y = (2/3)x + 7/3.

The slope of this line is 2/3. Since a line parallel to another line has the same slope, the slope of the parallel line is also 2/3.

Using the point (2,6) and the slope 2/3, we can use the slope-intercept form to find the equation of the parallel line: y = (2/3)x + b. Plugging in the coordinates of the given point, we get 6 = (2/3)(2) + b.

Solving for b, we find that b = 5/3. Therefore, the equation of the line parallel to 3y+7=2x and passing through (2,6) is y = (2/3)x + 5/3.

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Answer:

x=16

Step-by-step explanation:

The Distributive property says a(b+c) = ab+ac

1) You have 4(x-1)... This can be simplified to 4x-4

4x-4-5=3x+7

2) Combine alike terms:

4x-9=3x+7

3) add a 9 to both sides:

4x=3x+16

4) subtract a 3x from both sides:

x=16

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

3 divided by 1 is 0.33 repeating

The answer is choice A.

Answer:

the answer is A that stuff is real easy

Answer:

[tex]-\frac{5}{14}[/tex]

Step-by-step explanation:

When you add fractions, sometimes you have to raise a number to make it more easier for you.

As in this case, we have two fractions in which seem to not be the same, but note this.

7 is multiple of 14, meaning to make our life easier, we can do this method:

[tex]\frac{2 * 2}{7 * 2}  = \frac{4}{14}[/tex]

Whoa! Now we have the same denominator for both fractions, now we made this problem way more easier than it was before.

Do the math:

[tex]\frac{-9 }{14} + \frac{4}{14}[/tex]

==> [tex]-\frac{5}{14}[/tex]

The fraction in the simplest form is -5/4.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Operators who let do a basic mathematical calculation.

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

We have been given that expression of fraction as

⇒ -9/14 + 2/7

We have to determine the fraction in the simplest form.

⇒ -9/14 + 2/7

Take the LCM,

⇒ (-9 + 2×2)/7

⇒ (-9 + 4)/7

⇒ -5/4

Therefore, the fraction in the simplest form is -5/4.

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The equation of the line with a slope of 2/3 and y-intercept of 4 is y = 2/3x + 4.

The equation of a line in slope-intercept form (which is the most common form we deal with in algebra) is y = mx + b, where m is the slope and b is the y-intercept.

In this case, you're given that the slope (m) is 2/3 and the y-intercept (b) is 4. Substituting these values into the equation gives you the equation of the line: y = 2/3x + 4.

This is the equation that represents the given line

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Final answer:

The equation of the line with a slope of 2/3 and a y-intercept of 4 is y = 2/3x + 4.

Explanation:

To find the equation of a line with a slope of ⅓ and a y-intercept of 4, we can use the slope-intercept form of a line, which is y = mx + b where m is the slope and b is the y-intercept.

The given slope is ⅓, so m = ⅓. Given that the y-intercept is 4, b = 4.

Plugging these values into the slope-intercept equation, we get y = ⅓x + 4, which is the equation of the desired line.

The equation of a line is a mathematical expression that describes the relationship between the independent variable (x) and the dependent variable (y) for points on that line in a Cartesian coordinate system. It allows you to represent a straight line graphically on a two-dimensional plane.

Answer:

6

Step-by-step explanation:

6y - 2 = 34

6y = 36

y = 6

Answer:

y = 6

Step-by-step explanation:

6y - 2 = 34

    +2     +2

6y = 36

[tex]\frac{6y}{6} = \frac{36}{6}[/tex]

y = 6