b. Write an expression equivalent to m+m+m+m that is a sum of two terms.

Type your answer in the box below.

logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x

What is logarithmic equation?

The given logarithmic equation is;

[tex]log x = 4[/tex]

Since, log with base 10 is written as [tex]log x[/tex]  simply, therefore, we have:

[tex]log_{10} x[/tex] = 4

Using the definition of logarithm, we get;

[tex]x = 10^{4}[/tex]

Equivalently, [tex]10^{4} = x[/tex]

Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x

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The complete question is -

Which exponential equation is equivalent to this logarithmic equation?

log x = 4

The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

In this question,

The power function is f(x) =-2x^3

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.

Then the end behavior is

As x -> ∞,

[tex]\lim_{x \to \infty} f(x)[/tex]

⇒ [tex]\lim_{x \to \infty} -2x^{3}[/tex]

⇒ [tex]-2(\infty)^3[/tex]

⇒ - ∞

Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

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This polynomial has only 3 terms, so it is a trinomial. Hope it helps!

Answer:

0.4

Step-by-step explanation:

4/10 is 4÷10 = 0.4

The "given series" should be for [tex]\cos(x)[/tex], not [tex]x[/tex], so that

[tex]\cos(x) = 1 - \dfrac{x^2}2 + \dfrac{x^4}{24} - \dfrac{x^6}{720} + \cdots[/tex]

In the limit (which should say [tex]x\to\infty[/tex], not [tex]n[/tex]), we have

[tex]\displaystyle \lim_{x\to\infty} \frac{\frac{x^2}{1+\cos(x)}}{x^4} = \lim_{x\to\infty} \frac{1}{x^2\left(2 - \frac{x^2}2 + \frac{x^4}{24} - \cdots\right)} = \boxed{0}[/tex]

Answer:

68

Step-by-step explanation:

We know the sum of interior angles for a quadrilateral must equal 360, so we can create the following equation

[tex]55+117+120+x=360[/tex]

Simplify

[tex]292+x=360[/tex]

Subtract 292 from both sides

[tex]x=68[/tex]

Answer:

68

Step-by-step explanation:

The sum of the interior angles of a quadrilateral is 360.  The sum of the interior angles or a triangle is 180.  If you think about a rectangle, you can cut that up into two triangles, so 180 + 180 = 360.

Now subtract out the 3 angles that you know

360-55-117-120 = 68

Answer:

30°

30 is the value of x that’s makes AB//CD.

Step-by-step explanation:

the angles of measures 2x + 40 and 3x + 10 are two Alternate interior angles

If these two angle were congruent then the lines AB and CD

would be parallel .

2x + 40 = 3x + 10

⇔ 40 - 10 = 3x - 2x

⇔ 30 = x

⇔ x = 30

Answer:

Solution Given:

let pitcher which is small be S medium be M and large be L and barrel be B.

By question

6S+3M+1L= 1B...... eq. 1

2S+1M+3L=1B.......eq. 2

The difference in 2L from the first to the second is 4S and 2M

Therefore, each L=2S+M

In equation 2

2S+1M+3L=1B

replacing 2S +1M by L,we get

L+3L=1B

4L=1B

Therefore, 4 large pitcher is required

Answer:

4 large pitchers

Step-by-step explanation:

Define the variables:

Create two equations with the given information and the defined variables.

Equation 1

If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:

⇒ 6x + 3y + z = b

Equation 2

If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:

⇒ 2x + y + 3z = b

Substitute Equation 2 into Equation 1

⇒ 6x + 3y + z = 2x + y + 3z

Subtract 6x from both sides:

⇒ 3y + z = -4x + y + 3z

Subtract y from both sides:

⇒ 2y + z = -4x + 3z

Subtract z from both sides:

⇒ 2y = -4x + 2z

Divide both sides by 2:

⇒ y = -2x + z

Substitute the found expression for y into Equation 1:

⇒ 6x + 3(-2x + z) + z = b

⇒ 6x - 6x + 3z + z = b

⇒ 4z = b

Therefore, 4 large pitchers are needed to fill the barrel.

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Answer:

There are 17 natural numbers divisible.

There are 17 natural numbers between 150 and 300 that are divisible by 9.

To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.

The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).

Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):

Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1

Number of multiples of 9 = (297 - 153) / 9 + 1

Number of multiples of 9 = 144 / 9 + 1

Number of multiples of 9 = 16 + 1

Number of multiples of 9 = 17

So, there are 17 natural numbers between 150 and 300 that are divisible by 9.

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Answer:

  (2, 2) ⇒ (-2, 2)

  (-5, 6) ⇒ (-6, -5)

  (2, 6) ⇒ (-6, 2)

  (-5, 2) ⇒ (-2, -5)

Step-by-step explanation:

The new coordinates can be found using the transformation function for figures rotated 90° about the origin.

Rotation 90° (counterclockwise) about the origin can be described by ...

  (x, y) ⇒ (-y, x)

The end points of the diagonal that comes closest to the origin will be transformed to ...

  (2, 2) ⇒ (-2, 2)

  (-5, 6) ⇒ (-6, -5)

The other diagonal end points will be on the same horizontal and vertical lines as these.

  (2, 6) ⇒ (-6, 2)

  (-5, 2) ⇒ (-2, -5)

Answer:

Hope you like my answer

Answer:

radius = 10 feet

Step-by-step explanation:

C represents the circumference.

C = 2πr  ,where r is the radius.

We are given C = 62.8 ft

Equating the two expressions of C :

2πr = 62.8

Then

2 × 3.14 × r = 62.8

Then

6.28 × r = 62.8

Then

[tex]r = \frac{62.8}{6.28} = 10[/tex]

Answer:

Rotate 180 degrees with the center the origin (0,0)

Step-by-step explanation:

Try drawing a small square in the first quadrant, then reflect it like the direction. If you use tracing paper and and copy the figure, you will see that if you rotate the figure at the origin, it will land on the same spot as the translations.

The constant of proportionality is 25 and the distance at 10 seconds is 250 m.

To find the constant of proportionality, find the slope of the graph.

Now, input in slope intercept form of equation to find distance at 10 seconds.

The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get;

f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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The complement of the interval [2, 3) is  ( -∞, 2) ∪ (3, ∞).

According to the given question.

We have an interval [2, 3).

Let A = [2, 3)

Which is defined as

[2, 3) = {x ∈ r : 2 ≤ x < 3}

This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.

And, here it is also given that the universal set is r ( set of real numbers).

As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.

[tex]A^{c} = U - A[/tex]

Where,

[tex]A^{c}[/tex] is the complement of interval A

Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.

So, we can say that

[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]

Where, [tex]A^{c}[/tex] is the complement of the interval A.

Hence, the complement of the interval [2, 3) is  ( -∞, 2) ∪ (3, ∞).

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Answer:

[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]

Step-by-step explanation:

The quadratic equation is:

[tex]3x^2 - 10x + 5 = 0[/tex]

The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]

are

[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

in this case we have a = 3, b = -10, and c = 5

So, substituting for a, b and c we get

[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]

[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]

[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]

Simplifying we get

[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex]  (First root/solution)

[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex]  (Second root/solution)

Answer:

domain should be x=1

range is all real numbers

Step-by-step explanation:

Answer:domain should be x=1

range is all real numbers

Step-by-step explanation:

Orders of top-three finishers that are possible is given as follows:

[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]

In a broad sense, a permutation of a set is the rearrangement of its elements inside an already ordered set, or the arrangement of its members into a sequence or linear order. The act or process of altering an ordered set's linear order is referred to as "permutation."

The number of possible permutations of x elements from a set of n elements is given by:

[tex]n P_{r}=\frac{n !}{(n-r) !}[/tex]

The order in which the cars finish is important, hence the permutation formula is used instead of the combination formula.

In this problem, 3 cars are taken from a set of 14, hence the number of different orders is given as follows:

Using the permutation formula, it is found that the number of different orders of top-three finishers that are possible is given as follows:

[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]

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I understand that the question you are looking for is:

How many different orders of top-three finishers are possible? drag the tiles to the correct locations on the equation. not all tiles will be used.

The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

In this question,

A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .

The magnitude of the xy plane, hypotenuse = 25 units

The x component of the xy plane, base = 12 units

Let θ be an angle, then the angle it makes with the positive x axis is

[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]

⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]

⇒ [tex]\theta = cos^{-1}(0.48)[/tex]

⇒ [tex]\theta = 61.3145[/tex]

Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

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The complete fractional question given in the above picture is 55/3 = 1 + 52/3 = 2 + 49/3 = 5 + 40/3 = 8 + 31/3 = 10 + 25/3

Let

55/3 = 1 + x/3

55/3 = (3+x) / 3

55/3 × 3 = 3 + x

55 = 3 + x

55 - 3 = x

52 = x

55/3 = 2 + x/3

55/3 =(6+x) / 3

55/3 × 3 = 6+x

55 = 6 + x

55 - 6 = x

49 = x

55/3 = x + 40/3

55/3 = (3x+40) / 3

55/3 × 3 = 3x + 40

55 = 3x + 40

55 - 40 = 3x

15 = 3x

x = 15/3

x = 5

55/3 = x + 31/3

55/3 = (3x+31) / 3

55/3 × 3 = 3x + 31

55 = 3x + 31

55 - 31 = 3x

24 = 3x

x = 24/3

x = 8

55/3 = 10 + x/3

55/3 = (30+x) / 3

55/3 × 3 = 30 + x

55 = 30 + x

55 - 30 = x

25 = x

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Answer:

Step-by-step explanation:

1. $135

2. a. no

    b. $340

3. a. 33

   b. $135*33= $4455+340= $4795

4. a. $7630 = 135v + 340

     b. 135v + 340 = 7630

          135v = 7290

              v = 54 vacuums        

Answer:

1. Given.

2. Reflexive Property of Congruence.

3. Alternate Interior Angles Theorem.

4. SAS

5. <4 ~= <2

6. Converse of Alternate Interior Angles Theorem.

Answer:

D

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards.

this is angle D in the diagram

A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.

A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.

Given: [tex]$1.13^x = 2.97[/tex]

Taking log on both sides, we get

log [tex]$1.13^x[/tex] = log 2.97

x log 1.13 = log 2.97

x = log 2.97/log 1.13

Therefore, the value of logarithmic equation x = log 2.97/log 1.13.

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Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

The correct option is C.

One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.

Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.

Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:

x + y = 18

We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,

1x + 1.5y = 21

Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:

X+1.5Y = 21, and X+Y = 18

equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

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Answer:

[tex]x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}[/tex]

Step-by-step explanation:

So when it says simplify the right side, all it's doing is distributing the square root across division.

So when we distribute the square root we get the fraction

[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}[/tex]

And it's important to know that you cannot distribute the square root across addition/subtraction, but you can with multiplication.

There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex] and this works both ways, so we can use this to combine like radicals or separate them into multiple. In this case we can separate the square root of 4a^2 into two radicals

[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4} * \sqrt{a^2}}[/tex]

And from here it's pretty easy to see that the square root of 4 is 2, and the square root of a^2 is a, since the square exponent and square root just cancel out.

So we get the following expression on the right side

[tex]\frac{\sqrt{b^2-4ac}}{2a}[/tex]

Answer:

Power Bars are cheaper!

Step-by-step explanation:

FG: $18/12 Bars = $1.50 per bar

PB: $21.75/15 Bars = $1.45 per bar

Answer:

Super Power bars

Step-by-step explanation:

In order to find the best price, we want to calculate the unit rate, or the price for each bar. Let's start with the Fee Great energy bars. Since they are $18 for 12 bars, we divide 18 by 12 to figure out how much each bar costs. We get 1.5, or $1.50 per bar. Next lets claculate the unit rate for the Super Power bars. Since its $21.75 for 15 bars, we divide 21.75 by 15. We get 1.45, or $1.45 per bar. Since the price for one bar is cheaper for the Super Power bars as $1.45 is less than $1.50, the Super Power bars are the best price for each bar.

The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides

Inequalities are expressions that have unequal values, when compared

The inequality is given as

-4x > 120

When 4 is added to both sides, the inequality becomes

4 - 4x > 120 + 4

The above is not the solution to the inequality.

The solution is as follows:

We have:

-4x > 120

Divide both sides inequality by -4

x < -30

Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides

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Answer: (a−c)(b−c)>0

Step-by-step explanation:

ab>1 and ac<01. a>0 if c<0 and also b>02. a<0 if c>0 and also b<0

how i did it:

At the vert first, write the inequality as an equation.

Solve the provided equation for one or more values.

Now, display all the values obtained in the number line.

Use open circles to show the excluded values on the number line.

Find the interim.

At the moment, take any random value from the interval and substitute it in the inequality equation to check whether the values reassure the inequality equation.

Intervals that reassure the inequality equation are the solutions of the given inequality equation.

The limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.

According to the given question.

We have to find the limit of [tex]\lim_{x \to \infty} 5x - lnx[/tex]

As we know that L'hospital rule is a theorem which provides a technique to evaluate limits of indeterminate forms.

And the formual for L'hospital rule is

[tex]\lim_{x \to \ c} \frac{f_{x} }{g_{x} } = \lim_{x \to \ c} \frac{f^{'}( x)}{g^{'} (x)}[/tex]

[tex]\lim_{x \to \infty} 5x - lnx[/tex]  can be written as

[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]

If we put the value of limit in lnx/x we get an indeterminate form ∞/∞.

Therefore, [tex]\lim_{x \to \infty} \frac{lnx}{x} = \frac{\frac{1}{x} }{1}[/tex]

[tex]\implies \lim_{x \to \infty} \frac{1}{x} = 0[/tex]   (as x tends to infinity 1/x tends to 0)

So,

[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]

[tex]= \lim_{x \to \infty}x(5 -0)[/tex]

[tex]= \lim_{n \to \infty} 5x \\= \infty[/tex](as x tends to ∞ 5x also tends to infinity)

Therefore, the limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.

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