Please someone helpp

The change of base formula states that for any logarithm base b and any positive number x: log_b(x) = (log_c(x)) / (log_c(b)), where c is any base.

The change of base formula is a mathematical formula that allows you to convert a logarithm with one base to a logarithm with another base. The formula states that for any logarithm base b and any positive number x: log_b(x) = (log_c(x)) / (log_c(b)), where c is any base.

One way to prove this is to use the properties of logarithms:

Using these properties, we can write log_b(x) as:

log_b(x) = log_b([tex]c^{(log_c(x))}[/tex])

log_b(x) = log_b([tex]c^{(log_c(x))}[/tex]) / log_b(c¹)

log_b(x) = log_c(x) / log_c(b)

Therefore, the change of base formula is proven.

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Answer:

do 3*4 then divide by 12

Step-by-step explanation:

Answer:

no it is not proportion

Step-by-step explanation:

you would have to divied 56/20 which will be 56/2 that is 28

and then 20/2 which is 10 so then it will be

28/10 and 24/10

So on solving the provided question we cans ay that the coefficient of y² in the expression 2x²y -10xy²+ 5y is 10

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

Here,

the coefficient of y² in the expression 2x²y -10xy²+ 5y is 10

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If we want to be able to represent every hexadecimal value from 016 to ff16, the number of bits we need would be 8 bits.

The term hexadecimal refers to a numbering system in base 16. It can be used to represent large numbers with fewer digits. Most number systems are in decimal or base ten, however, hexadecimal is a type of number system which is in base 16. Hexadecimal has the base ten numbers from 0 to 9 and followed by six alphabetic characters A, B, C, D, E, and F. To represent every hexadecimal value from 016 to ff16, 8 bits will be needed.

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Answer: 18

Step-by-step explanation: For every 16 minutes in those 48 minutes, she tried on 6 dresses. 16 goes into 48 three times. That means there are three pairs of 16 minutes. 3 (pairs of 16 minutes) x 6 (the number of dresses each time) is 18.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given steps are :

[tex]\qquad \sf  \dashrightarrow \: 144 {x}^{2} - 100[/tex]

[tex]\qquad \sf  \dashrightarrow \: (12x + 10)(12x - 10)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2(6x + 5)(6x - 5)[/tex]

The error is in third step ~

Correct method :

[tex]\qquad \sf  \dashrightarrow \: (12x + 10)(12x - 10)[/tex]

[ take 2 common out of both ]

[tex]\qquad \sf  \dashrightarrow \:2 (6x + 5) \sdot2(6x - 5)[/tex]

[ 2 times 2 will be 4 ]

[tex]\qquad \sf  \dashrightarrow \: 4(6x +5 )(6x - 5)[/tex]

The range of pixel values in digital images is typically 0-255 because it corresponds to the number of bits used to represent each pixel. Most image file formats use 8 bits per color channel (red, green, and blue) to represent each pixel, and 8 bits can store a maximum of [tex]2^8[/tex] = 256 different values, with one of the values being reserved for transparency.

When working with 8-bit images, each color channel can take on one of 256 different values, from 0 to 255. This is known as an 8-bit color depth. Each pixel in the image is represented by a combination of red, green, and blue values, so the total number of possible colors is 256 x 256 x 256 = 16,777,216.

The use of 8-bit color depth allows for a wide range of colors to be represented in an image, while also being small enough to be easily stored and transmitted.

Also, it's worth mentioning that with the development of technology, the use of high-bit color-depth images has become more common in the field of photography, digital art, and video, where 16-bit and 32-bit color depths are frequently used.

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The set of inequalities represented by x + y ≥ 3 is the Michael wants to buy enough cupcakes and fudge with his $15 to feed at least three siblings.

A interaction between two expressions like values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a link among two values that do not equal. Egality and inequality are different. The not equal symbol is typically used to indicate that two values are also not equal (). Different inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities.  Negative values are split or added on either side. Switch between the left and right.

given

Michael wants to spend his $15 on enough cupcakes and fudge to feed at least three siblings.

A cupcake costs $2 but a slice of fudge costs $3.

With this inequality approach, the following scenario is simulated:

2x + 3y ≤ 15

x + y ≥ 3

The set of inequalities represented by x + y ≥ 3 is the Michael wants to buy enough cupcakes and fudge with his $15 to feed at least three siblings.

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Answer:

[tex]f\left(x\right)=\begin{cases}-9x&x\: < \:0\\ \:\:\:9x&x > \:0\end{cases}[/tex]

Step-by-step explanation:

The first thing to note is that absolute value functions are piecewise functions.

A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain or inputs(in this case the x-values).

In this case, the absolute value function is
[tex]f(x) = 9|x|[/tex]

To write this function as a piecewise function you have to use the definition of  [tex]f(x) = |x|[/tex] :

[tex]f\left(x\right)=\begin{cases}-x&x\: < \:0\\ \:\:\:x&x > \:0\end{cases}[/tex]

Applying this to [tex]9|x|[/tex] we multiply each of the parts by 9 to get

[tex]f\left(x\right)=\begin{cases}-9x&x\: < \:0\\ \:\:\:9x&x > \:0\end{cases}[/tex]

At [tex]|x| = 0, f(x) = 9|x| = 0\\[/tex]

The graph of the function is attached for easier understanding

For polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) after dilation the vertices will be

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem, for r = 1/4 we have

preimage                                     image

A (-4, 6)   → (1/4 * -4, 1/4 * 6) →   A' (-1, 3/2)

B (−2, 2)   → (1/4 * -2, 1/4 * 2) →  B' (-1/2, 1/2)

C (4, −2)  → (1/4 * 4, 1/4 * -2) →   C' (1, -1/2)

D (4, 4)   → (1/4 * 4, 1/4 * 4)   →  D' (1, 1)

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Answer:

Third Answer Choice....A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

Step-by-step explanation:

1/4 = 0.25

Multiply by every number

A' = ( -1, 1.5 )
B' = ( -0.5, 0.5 )
C' = ( 1, -0.5)
D' = (1, 1)

If it says its wrong i dont even know whys that, because this is the only way i know that everyone can solve easily

Answer: 16

Step-by-step explanation:

2 x 2 = 4        2 x 4 = 8           2 x 8 = 16

Answer:

2*2*2*2 in exponential form is 2^4

Step-by-step explanation:

2*2*2*2= 16

2^4=16

Hope this helps :D

The equation for the parabola given is y=(x-2)^2+1.

What is parabola?

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

In general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as:

y^2 = 4ax

If the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes,

x^2 = 4ay

Apart from these two, the equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.

Now, To find the correct equation from the graph

we can check the equation by putting values

when x then  y

         2          1

          3         2

         4          5

As only equation in option C follows given values

Hence,

           The equation for the parabola given is y=(x-2)^2+1

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Before tax, a new video game costs $10.00 in the store London visited

The calculations will be involving 100 because the question is a percentage problem and percent is a fraction of a hundred.

A 20% discount was being offered in the shop London visited. This is equal to 20%, and expressed as

= 20/100

= 0.20.

Discount factor: (1 - 0.2) = 0.8

The price of the video game will be multiplied by the discount factor to determine a new price.

The new video game's selling price before taxes is $50 * 0.2, which equals $10.

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(1) There are 2b+1 integer solutions to the equation x-a=b. (2) and (2) There are 2b-1 integer solutions to the equation x-a = b.

Integers include 0 as well as positive and negative numbers that are indicated by minus signs. An equivalent positive number's additive reciprocal is a negative number. In mathematical notation, a group of integers is typically denoted by a bold Z or a bold "mathbb Z." An integer is a number that can be positive, negative, or zero and is not a fraction (pronounced IN-tuh-jer). An example of an integer is the number -5, 1, 5, 8, 97, and 3,043 Non-integer examples are 1.43, 1. 3/4, 3.14, and other numbers. A group of integers and their antipodes are known as integers. The set of integers excludes decimals and fractions.

given

This type of absolute value difficulty can be resolved by interpreting the expression x-a = b as indicating that the difference between x and an is at most b. Therefore, x is only 9 away from 68 if x-68 = 9. 68-9 = 59; 68+9 = 77. (77-59)+1 = 19 is the total number of integers from 59 to 77, inclusive.

A) Using the same meaning, x must be closer to -4 by no more than 8 than usual. -4-8 = -12; -4+8 = 4. The integer solutions range from -11 to 3 inclusive, or 15 numbers, because this is a rigorous inequality.

B) This one indicates that x is only three values away from five, ranging from three to seven.

(1) There are 2b+1 integer solutions to the equation x-a=b. (2) and (2) There are 2b-1 integer solutions to the equation x-a = b.

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Answer:20

Step-by-step explanation:

80 times .25 or 1/4 is 20

Answer:20

Step-by-step explanation:

So, 25% is 1/4 of 100, so if you divide 80 by 4 you get 20, which is 25% of 80.

Another way to do this is on a calculator, do 80 x 25 / 100, this works with finding the percentage of anything!

The coordinate of a point is its location on a grid. The point will be located halfway between -2 and -3 on the x-axis, on -4 on the y-axis

Coordinate points:

A set of values that show an exact position on graphs is usually a pair of numbers. The first number shows the distance along, and the second number shows the distance up or down.

One number line is horizontal and is called the x-axis, and the other number line is the vertical number line and is called the y-axis. The two axes meet at a point called the origin.

The coordinate is given as:

[tex]Point=(2\frac{1}{2} ,-4)[/tex]

Express as decimals

Point=(-2.5,-4)

The above point means that:

X=-2.5

y=-4

Therefore, The point will be located halfway between -2 and -3 on the x-axis, on -4 on the y-axis

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Answer: 2.16 x 10^2

Step-by-step explanation:

6^3 = 216
2.16 x 10^2

The system of inequalities that shows the possible number of tables that the senior class can rent is x + y ≥ 65 and 12x + 9y ≤ 2000

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

Inequalities are used to show the nonequal comparison of numbers and variables.

Let x represent the number of round tables and y represent the number of square tables.

Each round table weighs 12 pounds, and each square table weighs 9 pounds. They need a minimum of 65 tables altogether, hence:

x + y ≥ 65      (1)

Also, The maximum weight that a delivery truck can carry is 2000 pounds, hence:

12x + 9y ≤ 2000     (2)

The system of inequalities is x + y ≥ 65 and 12x + 9y ≤ 2000

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The values of x are [tex]\frac{\sqrt{31} + 2 }{3} , \frac{-\sqrt{31} + 2 }{3}[/tex] and y are [tex]\frac{19\sqrt{31} + 146 }{9} , \frac{-19\sqrt{31} + 146 }{9}[/tex].

Given Equations,

4x² + x - y = 0 ...(1)

-x² - 5x + y - 9 = 0

The above equation can be written as:

-x² - 5x + y = 9 ...(2)

Using the elimination method, the second term of both equations can be eliminated by adding the equations.

Therefore,

4x² +  x  - y = 0

-x² - 5x + y = 9

_____________

3x² - 4x = 9

Using the Completing the square method,

3x² - 4x = 9

Divide the equation by 3 on both sides,

[tex]x^{2} - \frac{4}{3}x = 3[/tex]

[tex]x^{2} - \frac{4}{3}x + (\frac{2}{3}) ^{2} = 3 + (\frac{2}{3}) ^{2[/tex]

[tex]( x - \frac{2}{3})^{2} = 3 + \frac{4}{9}[/tex]

[tex]( x - \frac{2}{3})^{2} = \frac{31}{9}[/tex]

[tex]( x - \frac{2}{3}) = \sqrt{\frac{31}{9}}[/tex]

[tex]x = \frac{\sqrt{31} }{3} + \frac{2}{3} , - \frac{\sqrt{31} }{3} + \frac{2}{3}[/tex]

[tex]x = \frac{\sqrt{31} + 2 }{3} , \frac{-\sqrt{31} + 2 }{3}[/tex]

Now, Put the value of x  in equation (1), we get the value of y.

4x² + x - y = 0

y = 4x² + x

[tex]y = 4( \frac{\sqrt{31} + 2 }{3})^{2} + \frac{\sqrt{31} + 2 }{3} , 4( \frac{-\sqrt{31} + 2 }{3})^{2} + \frac{-\sqrt{31} + 2 }{3}[/tex]

[tex]y = \frac{19\sqrt{31} + 146 }{9} , \frac{-19\sqrt{31} + 146 }{9}[/tex]

Therefore,

the values of x are [tex]\frac{\sqrt{31} + 2 }{3} , \frac{-\sqrt{31} + 2 }{3}[/tex] and y are [tex]\frac{19\sqrt{31} + 146 }{9} , \frac{-19\sqrt{31} + 146 }{9}[/tex].

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Answer:

You have to add them all you will get 2,455 then you divide by how many numbers are there so there's 7 numbers so 2,455 divided by 7 equals=350 is the answer rounded to the nearest tenth

So on solving the provided question, we can say that by equation, 122 sodas and 80 hot dogs

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

let x be  of sodas sold

and let x - 42 be of hot dogs sold

so, the equation formed is

[tex]x+x-42=202\\2x = 244\\x=122\\[/tex]

122 sodas and 80 hot dogs

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The value of m from the exponent is 35.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

[tex](x^m)[/tex]³ = [tex](x^{13) ^5[/tex] x [tex](x^{-8}) ^{-5}[/tex]

Now, solving the exponents

[tex](x^m)[/tex]³ = [tex](x^{65})[/tex] x [tex](x^{40}) }[/tex]

Now, using the property

[tex]x^m . x^n = x^{m+n}[/tex]

So, [tex](x^m)[/tex]³ = [tex](x^{65+ 40})[/tex]

[tex](x^{3m})[/tex] = [tex](x^{105})[/tex]

Now, comparing the base

3m = 105

m= 105/3

m= 35

Hence, the value of m is 35.

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The product of (−21)(19)(−5) is 1995.

What is product?

In mathematics, the product is the result of multiplying two or more numbers or expressions together. The product is an important concept in mathematics and is used in many areas, including arithmetic, algebra, calculus, and geometry.

The problem asks us to find the product of (−21)(19)(−5). To solve this problem, we can multiply the three numbers together in any order because multiplication is associative.

So, let's multiply the numbers from left to right:

(−21)(19)(−5) = (−399)(−5)

We then simplify this expression by multiplying -399 and -5 together:

(−399)(−5) = 1995

Therefore, the product of (−21)(19)(−5) is -1995.

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Answer:

Let x be the amount of currency deposited

The checks deposited were 2x

The total deposit is x+2x = 3*x = 793

x = 793/3 = $264

So, Alicia deposited $264 in currency.

From the sequence 2 [tex]\frac{1}{2}[/tex], 2 [tex]\frac{1}{3}[/tex], 2 [tex]\frac{1}{4}[/tex], ..., f(n) can be expressed as 2 + [tex]\frac{1}{(n+1)}[/tex] where n is the term number in the sequence. Hence, the correct answer is A.

Each term in the sequence is 2 plus a fraction where the denominator is one more than the term number. For example:

In general, the n-th term in the sequence will have the fraction [tex]\frac{1}{(n+1)}[/tex].

Therefore, the function f(n) that generates this sequence is 2 + [tex]\frac{1}{(n+1)}[/tex]. This function takes an input of n and outputs the corresponding term in the sequence.

This question should be written as:

Given the sequence 2 [tex]\frac{1}{2}[/tex], 2 [tex]\frac{1}{3}[/tex], 2 [tex]\frac{1}{4}[/tex], ....,  what is f (n)?

The correct answer is A.

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Answer:

No Solution

Step-by-step explanation:

4(x+3)=3x+2+x

4x+12=3x+2+x

4x+12=4x+2

0=-10

The equation has no solutions.

Hope this helped! :)

The length of the hypotenuse of the right-angle triangle ΔCDE will be 9 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The triangle ΔCDE is a right-angle triangle. The angle ∠D is a right-angle triangle.

The length of the hypotenuse is given as,

sin 50° = 6.9 / x

0.766 = 6.9 / x

x = 6.9 / 0.766

x = 9.0073 ≈ 9 units

The length of the hypotenuse of the right-angle triangle ΔCDE will be 9 units.

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