A carpenter cuts a piece of lumber into two pieces. One piece is twice the size of the other.
If the smaller piece is 16 inches. How long was the whole piece of lumber before it was cut

Answer:

-11

Step-by-step explanation:

2x - 3y - z

2(-2) - 3(3) - (-2)

-4 -9 +2

-13+2

-11

Answer:

-11

Step-by-step explanation:

What we are solving for: 2x - 3y - z

x = -2

y = 3

z = -2

We can just plug in the variables.

[tex](2*-2) - (3*3) - (-2)[/tex]

[tex]-4-9+2[/tex]

Therefore, the answer is -11.

Hope this helped!!

Therefore √17 will lie between 4 and 4.5 on the number line .

In basic mathematics, real numbers are shown as a graphic of a graduated straight line called a number line. Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.

According to one standard, positive numbers always fall on the right side of zero, whereas negative numbers always fall on the left. The line also contains arrowheads at both ends, signifying that it continues in both the positive and negative directions indefinitely.

Let us find the decimal values of the given numbers.

13 lies between 9 and 16 , therefore √13 lies between 3 and 4 on the number line .

17 lies between 16 and 25 , therefore √17 lies between 4 and 5 on the number line .

22 lies between 16 and 25 , therefore √22 lies between 4 and 5 on the number line .

28 lies between 25 and 36 , therefore √28 lies between 5 and 6 on the number line.

Therefore √17 will lie between 4 and 4.5 on the number line as 4.5² = 20.25.

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The solution for the variable y according to the one-variable equation given in the task content is; y = -7.5.

It follows from the task content that the equation which is given in the task content and from which the variable y is to be determined is;

−140 = 18 + 20y − 8.

Hence, the equation can be solved as follows;

−140=18+20y−8

Evaluate each side of the equation;

-140 = 10 + 20y

Subtract 10 from both sides;

-150 = 20y

Divide through by 20; we have;

-7.5 = y.

Ultimately, the solution for the variable y as required in the task content is; y = -7.5.

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Answer:

2

Step-by-step explanation:

The value of the expression [tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex] after rationalizing the denominator is [tex]\frac{\sqrt{3}(x^{3})}{8}[/tex]..

A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Rationalizing the denominator is the process of shifting a root, such as a cube root or a square root, from the fraction's denominator to its numerator (numerator).

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

The numerator is the part of a fraction that comes before the vinculum.

The denominator of a fraction is the phrase that comes before the vinculum.

Consider the expression,

[tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex]

Now, let [tex]y=\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex]

[tex]y=\frac{\sqrt{3} x^{2}(x^{3})}{8x^{2}}[/tex]

Using the exponent rule [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]y=\frac{\sqrt{3}(x^{3})}{8}[/tex]

The value of the expression when rationalized [tex]\frac{\sqrt{3} x^{5}}{8x^{2}}[/tex] is [tex]\frac{\sqrt{3}(x^{3})}{8}[/tex].

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V 26

1

 <  

24

5

Step-by-step explanation:

Using the factored form of a polynomial for the given zeros, we can see that option A is the correct one, the function is:

F(x) = x*(x + 1)*(x - 2)

For a polynomial with the zeros:

x₁, x₂, x₃, ..., xₙ

The polynomial can be written as:

y = (x - x₁)*(x - x₂)*...*(x - xₙ)

In this case, the zeros are:

0, -1, and 2

Then we can write the polynomial as:

y = (x - 0)*(x + 1)*(x - 2)

If we simplify this, we get:y = x*(x + 1)*(x - 2)Which is the one we can see in option A, so we conclude that option A is the correct one.F(x) = x*(x + 1)*(x - 2)

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The number 8 is a solution to the equation 3m + 7 = 31

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

3m + 7 = 31

Subtracting 7 from both sides of the equation:

3m + 7 - 7 = 31 - 7

3m = 24

Dividing both sides of the equation by 3:

3m/3 = 24/3

m = 8

The number 8 is a solution to the equation 3m + 7 = 31

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4x you had  0.5x are the y -intercept.

How can you tell whether an exponential function is growing or deteriorating?

You can obviously plot it but if you can also conside that in your function you have 4x

; this tells you that as

x increases (gets bigger) certainly

4x will increase as well (you can consider

4²= 16 and 4³ = 64

). It is true that you have to multiply by

0.5

but nevertheless the entire function will grow anyway!

Graphically:

graph{0.5*(4^x) [-14.24, 14.24, -7.12, 7.12]}

If you want, try to think at the case where instead of having

4x you had  0.5x .

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Answer:

  7

Step-by-step explanation:

You want the value of the expression ||-2|-|3-12||.

Inner groups are evaluated first:

  ||-2|-|3-12|| = |2 -|-9||

  = |2 -9|

  = |-7| = 7

The value of the expression is 7.

__

Additional comment

The absolute value function changes negative signs to positive:

  |-2| = 2

It has no effect on positive signs.

  |2| = 2

Answer:

46

Step-by-step explanation:

A right angle is always equal to 90.

You are given the angle 44 so all you need to do is 90-44 which gives you 46

Hope this helps! Have a great day :)

Answer:

<2 = 46 degrees

Step-by-step explanation:

The angle measuring 44 degrees and <2 are complementary, therefore, they add up to 90 degrees.

Let [tex]x[/tex] be <2

[tex]44 + x = 90 \text{ // Subtract 44 on both sides}\\44 + x - 44 = 90 - 44\\\to x = 46[/tex]

This is a translation of one unit up of f(x), and we will get:

f(x) + 1 = 3x + 3

Here we need to learn to rewrite functions:

Here we know that:

f(x) = 3x + 2

And

g(x) = x^2 - x

(we will not use g(x) in this problem)

So, f(x) +1 can be rewritten by just replacing f(x) by the equation above, so we can redefine:

h(x) = f(x) + 1

Now we replace the function f of x to get:

h(x) = 3x + 2 + 1 = 3x + 3

In this way, we conclude that:

f(x) + 1 = 3x + 3

This is a translation of one unit up of f(x).

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The value of x for a given logarithmic expression is 2 or -4.

What is a logarithmic function?

Logarithmic function is the inverse of an exponential function. It is denoted by using the word, log. For example log 10 = 1.

Solving the given equation: log ₂ ( x² + 2x ) = 3

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

Now, the equation becomes,

log ( x² + 2x ) / log 2 = 3

log ( x² + 2x ) = 3 × log 2

log ( x² + 2x ) = log 2³

log ( x² + 2x ) = log 8

Applying exponent both the sides, we get,

e^[log ( x² + 2x )] = e^[log 8]

x² + 2x = 8

x² + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2 or -4

Hence, the value of x for a given logarithmic expression is 2 or -4.

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The ratio of time inside to time eating lunch Ratio: 3:2

The ratio of time eating lunch to time watching television Ratio: 10:3

The ratio of time reading to time drawing Ratio: 3:2

What is the ratio?

A ratio is a mathematical comparison between two numbers that indicates how many times one value is contained within the other.

Description: The ratio of time inside to time eating lunch

Ratio: 3:2

Description: The ratio of time eating lunch to time watching television

Ratio: 10:3

Description: The ratio of time reading to time drawing

Ratio: 3:2

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Answer:

the ratio of time inside to time eating lunch 10: 3

the ratio of time eating lunch to time watching television 3:2

the ratio of time reading to time drawing 2:1

Step-by-step explanation:

I got it wrong following the other person this is what Khan academy says is correct.

The volume of the cube is determined as 27 unit³.

The volume is calculated using the formula V = s³, in which "s" is the length of a square box's side.

The cube's side length is 3 units.

The volume of a cube = 3³ unit³.

= 3×3×3

= 27

Thus, the volume of the cube is estimated as 27  unit³.

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Answer:

log3(sqrt(81)) = 2

Step-by-step explanation:

When a distribution is skewed, the median is used to measure the center and the interquartile range  is used to measure variation.

The fundamental characteristics of mean for skewed data distribution:

Therefore, a skewed data set's center cannot be found using the mean.

In a skewed data collection, the median always stays quite near to the center. The best way to measure the center is hence to use the median.

Additionally, the mean and median of a normal distribution are equal, and both are used to locate the middle of the data set.

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Answer:

x/5 - 4

Step-by-step explanation:

The mean or the average height of all the corn plants is 43.8 inches.

There are various mean types in mathematics, especially in statistics.

The average of the frequency distribution is given by the mean of the data set .

Hence the statement here indicates that the average height of all the plants combined is 43.8 inches

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permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

The factorial function (symbol: !) just means to multiply a series of descending natural numbers.

a) The number of four people committees that can be selected from a group of 16 people is:

no. of committees are possible = 16!/ 4!

(16x15x14x13)/(1x2x3x4)=1820

b)Given that

One person is the chair, and the rest are general members

n! / (n − r)!

where n is the number of things to choose from,

Pick a chairman:: 16 ways

Pick 3 others:: 15C3 = 455 ways

Ans: 16×455 = 7200

c)

Each committee has a chair, a secretary, a refreshment person and a cleanup person.

The number of combinations of assignments within each committee is: 4x3x2x1=24.

The total number of committees with each committee member’s responsibility is: 1820x24=43680.

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In order for the parallelogram to be a rhombus, Then the value of x is equal to 3°.

Rhombus : A rhombus is a diamond-shaped quadrilateral that has all four sides equal. We can see rhombus-shaped figures in our day-to-day lives. Some of the real-life examples of a rhombus are shown in the below-given figure: a diamond, a kite, an earring, etc.

Since Diagonals bisect at 90°

(9x +31)°​ = 180° - 90° - 32°

To solve the product or quotient,

9x = 180° - 90° - 32° - 31°

We can add or subtract the values,

9x = 58° - 31°

We can divide the products,

x = (58° - 31°)/9

x = 27°/9

x = 3°

Therefore,

The value of x must be 3° in order for the parallelogram to be a rhombus.

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The percentage error of the candidate is 38.1%.

So, the percentage error:

Now,

He ought to have received x-15 = 120-15 = 105.

Therefore, the percentage error of the candidate is 38.1%.

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The values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C

Complementary angles are defined as angles that sum up to 90 degrees.

Example:

If x and y are complementary angles, then;

x + y = 90°

From the information given, we have the angles;

since they are complementary, then;

2x - 7 + 3x + 2 = 90

collect like terms

2x + 3x = 90 + 5

Add like terms

5x = 95

Make 'x' the subject of formula

x = 95/5

x = 19

But;

m∠WYX = (2x − 7) = ( 2(19) - 7) = 38 - 7 = 31°

m∠WYZ = (3x + 2)° = (3(19) + 2) = 57 + 2 = 59°

Thus, the values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C

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In mathematics, an inverse function is one that "reverses" another function. The inverse function of F(x) = x² - 1 is ±√(x + 1).

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Let the function be f(x) = x² - 1

y = x² − 1

x = y² − 1

simplifying the above equation, we get

y² = x + 1

y = ± √(x + 1)

Because there are two possible values of y for each value of x, there is no inverse function.

The inverse function of F(x) = x² - 1 is ±√(x + 1).

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The total amount subtracted from her account after 8 months of having the membership is given by −8|30| = −$240

What is the number operation symbol of the amount subtracted from her account?

The amount subtracted from Marsha's account per month would be negative since it reduces the account balance after the car wash membership fee has been paid, in other words, the total amount subtracted for 8 months is determined as the negative $30 per month multiplied by 8 months

total amount subtracted for 8 months=-30*8

total amount subtracted for 8 months=-$240

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Answer:

I think it is b

Step-by-step explanation:

The logarithmic form of the exponential equation 2³=8 is (D) log₂ 8=3 .

In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.

The general properties of logarithm for a fixed base are:

The given exponential equation is  2³=8.

To convert the above equation to logarithmic form we have to take logarithm to the base 2 on both sides of the equation.

Taking log₂ on both sides of the equation we get:

log₂(2³)=log₂(8)

Now we know from the properties of logarithms

logₐxⁿ=n logₐx

therefore:

3×log₂(2)=log₂8

Now logₐa=1, so

3×1=log₂8

or, log₂ 8 = 3

Therefore the required logarithmic equation is log₂ 8 = 3.

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Answer:Isolate the g

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides

w (-7) = -√g + 7 (-7)

w - 7 = -√g

multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

to get rid of the square root, you must square both sides

Note: -1w is the same as -w

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

simplify (combine all like terms)

g =w² - 7w - 7w + 49

g = w² - 14w + 49

g = w² - 14w + 49 is your answer

hope this helps

Step-by-step explanation: