find an antiderivative of f(x) = tan−1x satisfying f(0) = 1.

The slope of the line perpendicular to the given line is equal to -4/1.

The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

To find the slope perpendicular to the line you must find the negative reciprocal of 1/4. (Which just means change the sign then flip the fraction)

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Thus, the slope of the line perpendicular to the given line is equal to -4/1.

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The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

The larger the base of a log function, the closer the graph approaches the asymptote of x = 0.

We know that for a exponential function b^x = y, b is the base, y is the exponent to which the base b is raised and x is the result obtained.

We can write this in logarithmic form as:

log_b(x) = y

A logarithm base is the subscript of the logarithm that carries or raises the exponent.

For example in case of log_(3) 9 = 2, the base here is 3.

The change of base formula is:

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

Also as we know the bigger the logarithm base, the smaller the curve on the graph. This means, the larger the base of a log function, the closer the graph approaches the asymptote of x = 0.

The log function may increase at a slower rate if the base increases.

Therefore, if the base of a log function is large, the graph approaches the asymptote of x = 0.

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One of the factor of the given polynomial 6x^4 - 21x^3 - 4x^2 + 24x - 35 is (2x-7).

According to Rational Root Theorem,

Leading coefficient = 6

Trailing constant = 35

Factors of leading coefficient = 1, 2, 3, 6

Factors of trailing constant = 1, 5, 7, 35

Check for the rational roots

Let P = 7, Q = 2, then

P/Q = 3.5

F(P/Q) = 0

Apply Factor theorem which means the given polynomial must be divisible by P/Q, that is (2x-7)

Divide the polynomial into two groups

Group 1  6x^4 - 21x^3

Take 3x^3 common, we get

3x^3(2x - 7)

Group 2  - 4x^2 + 24x - 35

When we divide it by (2x - 7) we get (-2x + 5)

⇒ - 4x^2 + 24x - 35 = (-2x + 5)(2x - 7)

⇒ 6x^4 - 21x^3 - 4x^2 + 24x - 35 = (2x - 7)(3x^3 - 2x + 5)

Hence the correct option is A.

-- The given question is incomplete, the complete question is

"Which is a factor of the polynomial f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35? A) 2x - 7 B) 2x + 7 C) 3x - 7 D) 3x + 7" --

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The asymptotes in a given function is a line that the graph of a function approaches as either x or y go to positive or negative infinity.

An asymptote in a function is defined as the a line that the graph of a function approaches as either x or y go to positive or negative infinity.

There are various types of asymptote which include the following:

To determine the asymptote of a function in a graph is a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve.

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Answer:

x = -10

Step-by-step explanation:

Solve means to get the x all by itself on one side of the equation.

40 = -3x + 10

Subtract 10 from both sides.

30 = -3x

Divide both sides by -3.

30/-3 = x

-10 = x

x = -10

You can check your answer by putting it back into the equation and seeing if you get a true statement.

40 = -3x + 10

x = -10

Substitute.

40 = -3(-10) + 10

Multiply.

40 = 30 + 10

Add.

40 = 40

True! This means

x = -10 is correct.

Answer:

x>=-11/4

Step-by-step explanation:

f(x)=[tex]\sqrt{4x+9+2}[/tex]

The number which has a square root has to be greater than or equal to 0.

Hence, 4x+9+2>=0

Solve the inequality:

4x+9+2>=0

4x+11>=0

4x>=-11  ==> subtract 11 on both sides to isolate x

x>=-11/4 ==> divide both sides by 4

Answer:

8.8 mins

Step-by-step explanation:

to find how long in mins it would take to fill the tank

at 180 degrees the speed of water is 15 liters/min at 123 degrees

so [tex]\frac{15}{180} *123[/tex] = 10.25 liters/min

the capacity of the tank is 90.2 liters

[tex]\frac{90.2}{10.25} \\[/tex] = 8.8 mins

The probability that the upward face shows a number that is a multiple of 3 is p = 1/3 .

Given :

When a dodecahedral die is rolled the possible outcomes are:

s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

The total numbers of possible outcomes is 12.

The numbers of outcomes whose upward face is multiple of 3 .

= { 3 , 6 , 9 , 12 }

so Number of favorable outcomes = 4

What is probability ?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Probability = number of favorable outcomes / number of possible outcomes

= 4 / 12

= 1 / 3

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The distance traveled by the arrow cannot be determined from the given information. The distance traveled by the arrow depends on the speed at which it is fired, which is determined by the amount of energy released when the bowstring is released.

The name of radicals are cation and anion

A radical is an atom, molecule, or ion that has an unpaired valence electron. A notable example of a radical is the calcium ion

A radical can be electrically stable, positively charged and negatively charged.

Positively charged radicals are called cations and the negatively charged radicals are called anions.

If a balanced atom loses one or more electrons, it will become a positively charged cation.And if a balanced atom gains one or more electrons, it will become negatively charged anions.

Therefore the names of radicals are cations and anions i.e positively charged radicals and negatively charged radicals respectively.

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Answer:

Divide both sides by -3.

Step-by-step explanation:

This question is asking you how to get from step 1: [tex]-3(p-7) = -15[/tex] to step 2: [tex]p - 7 = 5[/tex].

We can see that the expression inside of the parentheses (p - 7) didn't go away from step 1 to step 2, and the term that was being multiplied by (p-7) had gone away. The only way you can "get rid" of a multiplied term is by doing the inverse of multiplication, which is division. Thus, you have to divide both sides by -3 to get to step 2.

Answer:

61

Step-by-step explanation:

Using the exterior angle theorem,

[tex]c-15+c-18=c+28 \\ \\ 2c-33=c+28 \\ \\ c-33=28 \\ \\ c=61[/tex]

Distance of 125 feet covered in 5 seconds, so the speed is 25 feet/second.

Any object's distance traveled in a unit of time is referred to as speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

The distance = 125 feet.

The time taken to cover the distance = 5 seconds.

To find the unit rate.

Apply formula,

speed = distance / time

          = 125 / 5

          = 25 feet / second

The required speed is 25 feet / second.

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By taking the modulus value of both of their balances we obtain that the difference Maria and Charles allowable balance is $10.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, The table shows the allowable balance of several children.

From the given table we can conclude that Maria's allowable balance is

- 15.25 and Charles's allowable balance is - 5.25.

So, The difference of their allowable balance is |- 15.25| - |- 5.25|.

= 15.25 - 5.25.

= 10.

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Answer:

2+3=5

Step-by-step explanation:

2+

3=

5

answer 2+3=5

Answer:

$0.55/ounce

Step-by-step explanation:

The problem gives us the ratio of cost to ounce. We need to create a proportion (when you set two ratios equal to each other) to solve for one variable of the second ratio.

⭐ The first ratio is [tex]$4.95/9 ounces[/tex], which means that it costs $4.95 for 9 ounces.

⭐ The second ratio is [tex]x/1 ounce[/tex], where x is the cost for 1 ounce of frozen yogurt.

. . . . . . . "per ounce" means "for every 1 ounce"

⭐ We need to set these two ratios equal to each other and solve for x.

. . . . . . . In proportions, keep the units of the numerators and denominators the same. In this case, we'll keep the cost as the numerators and the ounces as the denominators.

. . . . . . . [tex]\frac{4.95}{9} = \frac{x}{1}[/tex]

. . . . . . . [tex]\frac{4.95}{9}(1) = x[/tex]

. . . . . . . ∴ x = $0.55/ounce

The 5 types of expression include:

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. They include monomial, polynomial, binomial, trinomial, multinomial.

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Answer:

linear inequation with 1 variable

Answer:

The boats cross paths at the points (1,8) and (4,11)

Step-by-step explanation:

First, we want to find the points of intersection between the two paths. We are given two equations, both in the form y=(equation). Since we want to find the intersection points, we set the two equations equal to each other (since both equal y we can plug one of the equations in for y into the other equation) to get

-x^2+6x+3=x+7

From here, we solve this like a normal quadratic equation, move all variables to one side first

-x^2+5x-4=0

This factors to -(x-1)(x-4)=0, giving us x=1 and x=4

Now we plug these back into one of the original equations (in this case the linear equation is much more simple) to give us the points (1,8) and (4,11)

Answer:

x = 2

Step-by-step explanation:

5 / 2-2

5 / 0 = 0

0 is undefined

The sum of two or more numbers that results in a third number is called a factor.

The factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] exists 2x + 1.

The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them.

What can split a number exactly are factors. So there is no residual after division. Factors are the sums of two or more numbers that produce a third number. Consequently, a factor is a number that divides another.

The use of more variable factors—those whose values do fluctuate with output—occurs as production rises and falls. Workforce, energy, and directly used raw materials are examples of typical variable components.

Let the given equation be [tex]$& x^2+\frac{x}{6}-\frac{1}{6} \\[/tex]

[tex]$& =\frac{6 x^2+x-1}{6} \\[/tex]

simplifying the above equation, we get

[tex]$& =\frac{1}{6}\left(6 x^2+x-1\right)[/tex]

We will factorize the polynomial by splitting its middle term.

[tex]$& \frac{1}{6}\left(6 x^2+x-1\right) \\[/tex]

[tex]$& =\frac{1}{6}\left(6 x^2+3 x-2 x-1\right) \\[/tex]

simplifying the above equation, we get

[tex]$& =\frac{1}{6}(3 x(2 x+1)-1(2 x+1)) \\[/tex]

[tex]$& =\frac{1}{6}(3 x-1)(2 x+1)[/tex]

[tex]$\frac{1}{6^{}}(3 x-1)$[/tex] and (2x + 1) are factors of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex]

Therefore, the correct answer is option B. 2x + 1

The complete question is:

Which among the following is a factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] ?

A. 3x + 1

B. 2x + 1

C. [tex]$x-\frac{1}{5}$[/tex]

D. [tex]$x-\frac{1}{2}$[/tex]

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Refer to the photos taken.

Answer:

A gain of 3 points

Step-by-step explanation:

I'm not sure the options are correct. But normally, you add up the lost points on the both days. Then you compare it to the gained point on Wednesday.

Answer:

The digit 5 in the number 357 is in the tens so it represents 50 whereas the digit in the number 465 is in the ones/units so it represents 5.

Answer:

the inverse of f(x)=2x−7 f ( x ) = 2 x - 7 .

Step-by-step explanation:

check if f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) )

Answer:

f(x) = 1/4 x² - 7

Step-by-step explanation:

x + 7 ≥ 0

x ≥ -7

y/2 = 2 /2 √(x+7)

y/2 = √(x+7)

y ≥ 0

(y/2)² = √(x+7)²

y²/4 = x +7

x = y²/4 - 7

f(x) = x²/4 - 7

Answer:

m∠DFE = 69°

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Therefore, as ABC is the tangent to the circle, and OB is the radius of the circle:

⇒ m∠CBO = 90°

Interior angles of a triangle sum to 180°.  Therefore:

⇒ m∠COB + m∠CBO + m∠BCO = 180°

⇒ m∠COB = 180° - m∠CBO - m∠BCO

⇒ m∠COB = 180° - 90° - 48°

⇒ m∠COB = 42°

Angles on a straight line sum to 180°.  Therefore:

⇒ m∠DOE + m∠COB = 180°

⇒ m∠DOE = 180° - m∠COB

⇒ m∠DOE = 180° - 42°

⇒ m∠DOE = 138°

The angle at the center is twice the angle at the circumference.

Therefore:

⇒ m∠DOE = 2 × m∠DFE

⇒ m∠DFE = m∠DOE ÷ 2

⇒ m∠DFE = 138° ÷ 2

⇒ m∠DFE = 69°

Answer: The answer is 100 :)

Step-by-step explanation:

you multiply L x W and that would be 10 x 10 and if you do the math right you should get an answer of 100

The equation of line passing through the points (3,-2) and (-2,3) in

(a) point slope form is  y + 2 = -(x - 3) ;

(b) slope intercept form is y = -x + 1   ;

(c) standard form is  x + y = 1 .

The Standard Form of equation of line is written as ⇒ " Ax + By = C " .

it is given that the line is passing through the points (3,-2) and (-2,3) ;

So , the slope(m) is = (3+2)/(-2-3) = 5/(-5) = -1 .

(a) the point slope form is (y - y₁) = m(x - x₁) ;

substituting x₁ = 3 and y₁ = -2 ;

we get ;

(y + 2) = (-1)(x - 3)

y + 2 = -(x - 3) .

(b) the slope intercept form is ⇒ y = mx + c ,

-2 = (-1)3 + c ;

-2 = -3 + c ,

c = -2 + 3 ;

c = 1 ; the equation is ⇒  y = -x + 1 .

(c) the standard form is :

arranging the equation y = -x + 1  ,

we get ;

x + y = 1 .

Therefore , the required equations of line are mentioned above .

The given question is incomplete , the complete question is  

How do you write the equation of the line in point slope form , slope intercept form and standard form given that it passes through (3, -2) , (-2, 3) ?

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Answer:

-9z + 72

Step-by-step explanation:

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

Volume of A /Volume of B =  ( a / b )^3

a is the radius of solid A and b is the radius of solid B.

solid figures

In Geometry, the shape or the figure that has three dimensions (length, breadth and height), are known as solids or three-dimensional shapes. Example:-Cube, Cuboid and Sphere. The major types of solid shapes are: cubes, cuboids, prisms, pyramids, platonic solids, torus, cone, cylinder, and sphere.

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