Stephanie is six years old. She is one year older than one-sixth the age of her mother. How old is Stephanie's mother?

The value of the expression log ₁₂20 is 4.33.

Given that the expression is log ₁₂20.

We are required to find the value of the expression by using the change of base formula.

The change of base theorem is used by a person when we have been given logarithm values with different bases.

(We know that [tex]log _{a} b[/tex]=log b/ log a)

The expression is log ₁₂20.

log ₁₂20=log 20/log 12          

Now we have to use values of log in the above expression to find its value.

=1.30/0.30

=4.33

Hence the value of the expression log ₁₂20 is 4.33.

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f(2) is -8

According to the question,

Given that,

f(x)=2x-3x^2

Substitute x = 2 into f(x) = 2x-3x^2

f(2)=2x-3x^2

f(2)=2x2 - 3x [tex]2^{2}[/tex]

f(2)= 4 - 3 x 4

f(2)= 4 - 12

f(2)= - 8

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Example of an Equation:

4y + 2 = 18

4×2 + 3x − 28 = 0

9m = 49.5

Equation Types

Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:

Linear equations

Quadratic equations

Cubic equations

Quartic equations

Differential equations

Parametric equations

Equation of a line

The standard form of the equation of a line is A x + By + C = 0. The slope-intercept form of an equation is y = mx + b, where m is the slope of the line and b is the y-intercept. However, there are various types of equations to represent lines.

Equation of x-axis

Generally, we say that the equation of the x-axis equation is of the form y = 0. However, we can also write the x-axis equation as x = c where c is constant.

The x-axis comprises all the real values of x, although the value of y is equal to 0 on the complete x-axis.

Thus, x can be recognised as constant and y as 0.

In the coordinate system representation, we can represent any point on the x-axis as (c, 0), where c is any real number.

Therefore, the x-axis formula will be x= c + y

Here,

c = constant

y = 0

The x-axis formula is x = c, where c is constant.

Equation in One Variable

The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.

17 – 9 = 8

x + 4 = 4y + 22z

4x2 + 3x – 7 = 0

The three examples above represent equations that propose equality (could be true or not) between two expressions.

The first equation does not contain any variable.

The second equation has three different variables, such as x, y and z. Thus, it is a multivariate equation.

The third equation contains only one variable, i.e. x.

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We need to know about logarithm to solve this problem. The answer of the given algorithm is -4.

Logarithm is the exponent that a base needs to be raised to get a certain number. There are a few rules of algorithm, log a + log b can be written as log ab, log a- log b can be written as log a/log b. When a number whose logarithm is being calculated is raised to a power, the power can be multiplied to the log itself. In this question we have to find the logarithm of 625 with base 1/5. To find the logarithm of this number we need to first write 625 in terms of 1/5, the log of number same as base is equal to 1.

[tex]log_{\frac{1}{5} } 625=-log_{\frac{1}{5} } (\frac{1}{5} )^{4} =-4log_{\frac{1}{5} } \frac{1}{5} =-4[/tex]

Therefore we found out the logarithm of 625 with base 1/5 to be -4.

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The product of ∛3 and 5√3 is 15√3⁸ (Option C).

This question can be easily solved by using the concept of roots. The two terms mentioned in the question are ∛3 ( cubic root of 3 ) and  5√3 (5th root of 3 ). This question can be solved in 4 easy steps

Step 1 : Identify the power of the root and take LCM of those numbers.

In this case, the powers of root for ∛3 and 5√3 are 3 and 5, respectively. Take LCM of 3 and 5.

LCM = 3 x 5 = 15

=> We get the LCM of 3 and 5 as 15.

Step 2 : Write the given numbers in the form of fractional powers

∛3 = 3¹ˡ³  => The power of 3 = 1/3

5√3 = 3¹ˡ⁵  => The power of 5 = 1/5

Step 3 : Multiply and divide the powers of the base number ( in this case 3 ) with a number such that you get the denominator as the LCM ( in this case 15 )

1/3  can be multiplied and divided by 5 to get the denominator as 15

=> 1 * 5 / 3 * 5 = 5 /15

1/5  can be multiplied and divided by 3 to get the denominator as 15

=> 1 * 3 / 5 * 3 = 3 /15

Step 4 : Find the product of the two terms

15√3⁵ x 15√3³ = 15√3³⁺⁵ = 15√3⁸

Therefore, using the concept of roots and fractions, we get the product of ∛3 and 5√3 as 15√3⁸.

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Answer:

The square root of 400 is represented by √400, where ‘√’ represents a radical and a radicand represents its value. It is rational to multiply 400 by 20, which is 20. Simple prime factorization or long division can be used to find the square root. Taking the square root of 400, we get √400 = ±20

Step-by-step explanation:

Answer:

b = a² - 6

Step-by-step explanation:

a = [tex]\sqrt{b+6}[/tex] ← square both sides to clear the radical

a² = b + 6 ( subtract 6 from both sides )

a² - 6 = b

The inequality describing the number of tickets that allows the theater to meet their minimum will be 5x + 10y ≥ 2000. Then the correct option is D.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A movie theater hopes to make at least $2,000 from a certain showing. Adult tickets are $10 each, while child tickets are $5 each.

Let x be the number of children's tickets sold and y be the number of adult tickets sold. Then the inequality is given as,

5x + 10y ≥ 2000

The inequality describing the number of tickets that allows the theater to meet their minimum will be 5x + 10y ≥ 2000. Then the correct option is D.

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Answer:

30,000

Step-by-step explanation:

Add 6,000 to 48,000, which equals 54,000

You then divide 54,000 by three = 18,000

Multiply 18,000 by 2 = 36,000

Subtract 6,000 frome 36,000 = 30,000

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The inequality expression 6 <= x < 15 to represent the statement "a number is at least 6 and less than 15"

Expressions are mathematical statements that are represented by variables, coefficients and operators

The mathematical statement is given as

a number is at least 6 and less than 15.

Represent the number with x

So, we have

x is at least 6 and less than 15.

At least 6 means greater than or equal 6

So, we have

x >= 6

Less than 15

So, we have

x < 15

When the above expressions are combined, we have

6 <= x < 15

Next, we plot the inequality expression 6 <= x < 15 to represent the statement "a number is at least 6 and less than 15"

See attachment for the inequality expression

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After rounding off the whole number it becomes 12,346.

According to the statement

We have to find that the value of the whole number.

So, For this purpose, we know that the

The whole numbers are the numbers without fractions and it is a collection of positive integers and zero.

From the given information:

The given number is a 12,345.6789

Then

We know that the

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers etc.

The number

12,345.6789

Its round off to the

12,346

Because when the number greater than 5 comes after the point then while rounding off we increased the number by 1.

So, After rounding off the whole number it becomes 12,346.

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Answer:

Choice 3 (2/3)

Step-by-step explanation:

Slope is equal to the change in y over the change in x.

If we look at the two coordinates, we'll see that to get from (1, 5) to (7, 9), you need to move up 4 and to the right 6.

4/6 = 2/3, which matches the 3rd choice

Hope this helps

Step-by-step explanation:

2x-4 > 8 or 3x-1 < -10

Grouping the like terms

2x > 8 +4 or 3x < -10 +1

2x > 12 or 3x < -9

2x > 12 3x < -9

2 2 3 3

x > 6 or x < -3

Answer:

0.14*10⁻¹ seconds

Step-by-step explanation:

3 × 10⁸ = 30*10⁷

Then:

4.2*10⁷ / 30*10⁷ = 4.2/30 = 0.14

0.14 = 1.4*10⁻¹ seconds

The equation has just two solutions, which are 11 and 7.

While the inequality will have a range of solutions, which is:

7 ≤ w ≤11

That is the difference.

Here we have an inequality:

|w - 9| ≤ 2

And an equation:

|w - 9| = 2

To solve these we can start by solving the equation, it gives two equations:

w - 9 = 2

w - 9 = -2

With these we can get two solutions for w,:

w = 2 + 9 = 11

2 = -2 + 9 = 7

Then the equation has just two solutions, which are 11 and 7.

While the inequality will have a range of solutions, which is:

7 ≤ w ≤11

That is the difference between the two.

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After converting the mathematical statement - xv plus 6x negative 5 equals 0 into mathematical equation, we get -

x = 5/(v + 6).

An equation of the form ax + b = 0 such that a ≠ 0 is called linear equation in one variable. The graph of this equation represents a straight line.

Given is a linear equation in the form of a mathematical statement -

xv plus 6x negative 5 equals 0.

In order to solve for x, we will first convert this mathematical statement into a linear mathematical equation. The mathematical equation can be written as -

xv + 6x - 5 = 0

We will solve this question using transpose method.

xv + 6x = 5

x(v + 6) = 5

x = 5/(v + 6)

Therefore, after converting the mathematical statement - xv plus 6x negative 5 equals 0 into mathematical equation, we get -

x = 5/(v + 6)

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The statement "15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245" is false

The statement is given as

15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245

When comparing greater and lesser values, we do not make use of the number of digits in them

Instead, we compare the values

Though, 15.7 is less than 15.245 but the reason is that 15.27 has lesser value than 15.245

Hence, the statement "15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245" is false

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Answer:  9v=162

Step-by-step explanation:

If you need the answer, Victors height is 18.

9v = 162

/9       /9

V = 18

Step-by-step explanation:

we are given a variable of victors height as v

according the expression

9 × v = 162

9v = 162

divide both sides by 9

v = 18

Answer: 1/3-5(n)

Step-by-step explanation:

Answer: i think that it is 2/-6

Step-by-step explanation:

Answer:

[tex]y10 = - 5[/tex]

Answer:

10

Step-by-step explanation:

it us a right triangle so we can use the equation

a^2 + b^2 = c^2

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

10 = c

The Lateral Surface Area of a Right triangular prism is given by:

= (a + b + c) × h

= (ah + bh +ch)

where a, b and c are the dimensions of base and h is the height of the Right triangular prism.

The given dimensions of base are:

a = 5 cm

b = 2.5 cm

c = 5.6 cm

The height of the Right triangular prism is 8 cm.

Now, the Lateral Surface Area of a Right triangular prism will be

= (5 + 2.5 + 5.6) × 8

= (40 + 20 + 44.8)

= 104.8 [tex]cm^{2}[/tex]

Therefore, the Lateral Surface Area of the Right triangular prism is 104.8 [tex]cm^{2}[/tex].

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The solution for the equation ln 5 x=4 is 10.92.

ln 5 x=4

5 x = [tex]e^{4}[/tex]

x = 10.92

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} ~\hfill \stackrel{mixed}{3\frac{1}{6}}\implies \cfrac{3\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{19}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{35}{6}\div \cfrac{19}{6}\implies \cfrac{35}{6}\cdot \cfrac{6}{19}\implies \cfrac{35}{19}\cdot \cfrac{6}{6}\implies \cfrac{35}{19}\cdot 1\implies 1\frac{16}{19}[/tex]

Answer:

Step-by-step explanation:

Recursive formula is used to represent the terms using the previous term of the sequence.

Using the explicit equation find the first two terms and their difference:

The recursive formula for this sequence is:

Answer:

160π

Step-by-step explanation:

The surface area of a right circular cylinder can be calculated using the following equation:

[tex]\boxed{\mathrm{Surface \ area = }2 \pi rh + 2 \pi r^2}[/tex] ,

where h is the height and r is the radius of the base of the cylinder.

We are told that the rod is 16 inches tall, therefore h = 16. We are also told that the radius of the base is 4 inches, therefore r = 4. Using this information along with the formula above, we can calculate the surface area of the metallic rod:

Surface area = [tex](2 \times \pi \times 4 \times 16) + (2 \times \pi \times (4)^2)[/tex]

                     = [tex]128\pi + 32\pi[/tex]

                     = [tex]\bf 160\pi[/tex]

Therefore the surface area of the metallic rod is 160π.

Answer:

[tex]144\pi \: or \: 145\pi[/tex]

SA to cylinder is

[tex]2\pi \: rh + \pi \: r {}^{2} [/tex]

=2

[tex] 2 \times \pi \times r \\ \times h + \pi \times r {}^{2} [/tex]

2

[tex]2\pi \times 4 \times 16 + \pi \times 4 \times 4[/tex]

answer =

[tex]144\pi \: to \: 145\pi[/tex]

Answer:

[tex]\frac5{12}[/tex]

Step-by-step explanation:

[tex]\frac34 - \frac13\\\\\to \frac34 \times \frac33 - \frac13 \times \frac44\\\\\to \frac9{12} - \frac4{12}\\\\\to \frac{9 - 4}{12} \to \frac5{12}[/tex]

If PQR is similar to WXY and PQ=12 cm and WX=9 cm and the area of WXY is 72cm², then the area of PQR is equal to 128 cm².

The area of PQR can be determined by first finding the scale factor. The scale factor in mathematics can be defined as the ratio of the length of a side of one figure (which in this case is a triangle) to the length of the side of a similar figure.

Therefore, the scale factor = 9 / 12

Now by using theorem 61,

area ΔWXY / area ΔPQR = (9/12)²

As the area of WXY = 72cm², therefore;

72 / area ΔPQR = 81 / 144

81 (area ΔPQR) = 144 × 72

81 (area ΔPQR) = 10,368

area ΔPQR = 10,368 / 81

area ΔPQR = 128 cm²

Hence, the area of PQR is calculated to be 128 cm².

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$6208.86 amount should be put into an account that pays 5.2% annual interest compounded.

It is given that a student wants to save $ 8000 for college in five years having interest 5.2% annual interest compounded .

Putting [tex]A=\$8000 , \ r= 5.2\% , \ t=5 \ years[/tex] in equation (1) , we get

  [tex]8000=P(1+\frac{5.2}{100} )^5\\\\8000=P(1+0.052)^5\\\\8000=P(1.052)^5\\\\8000=1.28848P\\\\P=\$6208.86[/tex]

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Answer: I don't know if this is scientific notation, but I got 900 gallons.

Step-by-step explanation:

1.5 x 10 = 15

15 x 60 = 900

(I used 60 because there's 60 seconds in one minute)