a. Describe the type of indeterminate form (if any) that is obtained by direct substitution. (b) Evaluate the limit, using L’Hôpital’s Rule if necessary. (c) Use a graphing utility to graph the function and verify the result in part (b). lim┬(x→[infinity]) x ln x

The radical form of the given expression 15x^(1/4) is equal to ( 15 ) × [tex]\sqrt[4]{x}[/tex].

As given in the question ,

Given expression is written as :

15x^(1/4)

Using th formula to conversion of the exponential form into the radical form in general form is given by:

( z )^ ( m / n ) = [tex]\sqrt[n]{z^{m} }[/tex]

in the given expression the value of :

z is equal to x

m is equal to 1

n is equal to 4

Now, Substitute the values  of the given variables in the formula of radical form we get,

15 x^(1/4)

= ( 15 ) ×  [x^(1/4) ]

= ( 15 ) × [tex]\sqrt[4]{x^{1} }[/tex]

Raising any variable or the number to the power one is always equal to same variable or the number itself.

=  ( 15 ) × [tex]\sqrt[4]{x}[/tex]

Therefore, the radical form of the given exponential form of the expression 11x^(1/4) is written as :  ( 15 ) × [tex]\sqrt[4]{x}[/tex].

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Answer:

Step-by-step explanation:

The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.

1111 is not a prime number. It is a composite number, which means it can be factored into smaller integers. The factors of 1111 are 11 * 101. Prime numbers are numbers that are divisible by only 1 and itself. Only numbers that are greater than 1 and are not divisible by any other number except 1 and itself are prime numbers.

1, 11, 101, and 1111 are all divisors of the number 1111. A number must have exactly two elements in order to be deemed a prime number. 1111 is not a prime number since it has more than two components, namely 1, 11, 101, and 1111.

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Therefore , the solution of the given problem of quadratic equation comes out to be (x−1)(x+6).

The quadratic equation x ax2+bx+c=0 is an equations regression model in a single variable. a 0. According to the First Theorem of Algebra, this polynomial has at exactly one solutions because it is of second order. There could be simple or complex solutions. A four-variable equation is referred to as a quadratic equation. This implies that it must have at least one squared word. A typical formula for resolving math problems is "ax2 + bx + c = 0," where the numerical factors or constant a, b, and c stand in for the undefined variable "X."

Here,

Given : x²+5x+6

=> x²+bx+c.

Find two integers with the product c and the sum b.

Whose product in this instance is 6 and Whose summation is 5.

Put these integers to use in factoring the expression.

(x−1)(x+6)

Therefore , the solution of the given problem of quadratic equation comes out to be (x−1)(x+6).

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Answer:

ok whats the question

Step-by-step explanation:

Your friend's 80% average now represents 85% of the overall grade. This is because we are aware that the final, which is worth 15%, is the only thing left.

If your friend receives a 100 on the final, they will receive the highest possible course grade:

The following equation must be solved for "f," the result of the final test, in order to obtain a score of 75:

The term exponential 1 is represented as e¹ and the value of exponential 1 is 2.71828...  .

The term Exponent can be defined as the method of expressing the large numbers in terms of powers.

For Example : if 2 is multiplied 4 times then , its exponent form is [tex]2^{4}[/tex]

According to the rule of exponent ; any number that is raised to the power of (1)one is equal to the number itself.

Thus , e to power of 1 can be written as e¹ .

and we know that value of e is 2.7182818284.....  .

So , exponent to the power 1 is [tex]e^{1} = 2.7182818284...[/tex] .

Therefore , the value of exponent 1 is 2.7182818284...  .

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Answer:

Pwede po b may pic

Step-by-step explanation:

para lang po maka answer kami

The statement 7+5(x-3) = 22 is true for x = 6.

Finding the equation's solution is the concept of solving an equation. The value of the variable that may be used to verify the equation is known as a solution.

The same number added on both sides

Taking away the same amount from both sides

using the same integer on both sides when multiplying

using the same integer to divide into both sides

Here we have

7 + 5(x-3) = 22    

The above expression can be solved as follows

7 + 5(x-3) = 22      

Multiply 5 and (x - 3) terms

=> 7 + 5x - 15 = 22

=> 5x - 8 = 22        [ ∵ -15 + 7 = -8 ]    

Add 8 on both sides

=> 5x - 8 + 8 = 22 + 8

=> 5x = 30

Divided by 5 into both sides  

=> 5x/5 = 30/5

=> x = 6

Therefore,

The statement 7+5(x-3) = 22 is true for x = 6.

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Answer:

Below

Step-by-step explanation:

f(1)    -  2 = a(1) + b

        - 2 = a + b             (1)

f(5)     10 = a (5) + b

          10 = 5a + b            (2)

Multiply first underlined equation by -5  to get

      10 = -5a  - 5b       add this to the second equation (this will eliminate 'a')

      20 = - 4 b       so   b = -5

then the first equation becomes   - 2 = a +  (-5)

             which shows a = 3

so your function is just    f(x) = 3x  -5

Answer: I don't speak spanish

Step-by-step explanation:

D) if the value of its discriminant is positive and a perfect square the   The roots are rational and not equal.

b2 – 4ac > 0  Real and the value of roots are unequal

b2 – 4ac = 0  Real and value of roots are  equal

b2 – 4ac < 0 Distinct and Imaginary roots

b2 – 4ac > 0 (is a perfect square)  Real, rational and value of roots are Distinct

These are the four conditon for the nature of root and the condition which is driving force for the loop .

so form the above statement conditon 4 satisfies and hence the quadratic equation have real rational and distinct or not equal root.

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Therefore , the solution of the given problem of trigonometry comes out to be the reciprocal of both the cosine is the secant.

Trigonometry, a branch of mathematics, studies relationships between angles and sides of triangles. Trigonometric exists throughout all of geometry and can be reduced to a grouping of triangles from any horizontal form. Calculus, difficult or real trigonometry, algebra, and infinite series are only a few examples of the mathematics that are related to one another in a startlingly complex way.

Here,

The reciprocal of both the cosine is the secant. This is the fraction of a right triangle's hypotenuse towards the side closest to a particular angle.

The secant of slope in a right angled triangle is calculated by dividing the height of the y axis by the width of the neighboring side.

Thus, its fundamental formula is: sec X  =[tex]\frac{Hypotenuse}{Adjacent Side}[/tex]

Additionally, it is the cosine value's reciprocal.

Therefore , the solution of the given problem of trigonometry comes out to be the reciprocal of both the cosine is the secant.

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Equation represents the comet's orbit [tex]\frac{x^{2} }{100} -\frac{(y-6)^2}{64} =1[/tex], So correct option is C.

A coordinate plane, also known as a Cartesian plane, is a two-dimensional surface that is used to graph points, lines, and shapes. It is named after the mathematician René Descartes, who is credited with inventing the system in the 17th century.

The coordinate plane is divided into four quadrants by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin and is assigned the coordinates (0,0). The x-axis runs horizontally and is used to measure values along the horizontal (or "x") direction, while the y-axis runs vertically and is used to measure values along the vertical (or "y") direction.

Each point on the coordinate plane can be represented by an ordered pair of numbers, called coordinates, that indicate its position in relation to the x- and y-axes. The coordinates of a point are written as (x, y), where x is the point's distance from the y-axis and y is the point's distance from the x-axis.

The equation that represents the comet's orbit is:

[tex]\frac{x^{2} }{100} -\frac{(y-6)^2}{64} =1[/tex]

This is the standard equation for a hyperbola in the center form, where the center is at (0,6), the distance between the center and the vertex is 8 and the distance between the center and the focus is 2.

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The required equation of the line is y = -18x + 1673.  

One of the most common ways to represent a line's equation is in the slope-intercept form of a line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line.

Slope-intercept form of a line is y = mx + c

where m = slope and c - y-intercept of the line.

Here we have

Given points (86, 125) and

Slope of the line m = -18  

As we know

Slope intercept form of a line is y = mx + c  

Given m = - 18

=> y = (-18)x + c

=> y = -18x + c

Given points (86, 125) substitute in the above line

=> 125 = -18(86) + c

=> 125 = -1548 + c

=> c = 1673  

Therefore,

The required equation of the line is y = -18x + 1673.  

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Answer: To solve the equation 4x^2 + 5 = 6 by factoring, we need to start by isolating x^2 on one side of the equation.

We have:

4x^2 + 5 = 6

subtracting 5 from both sides:

4x^2 = 1

Dividing both sides by 4:

x^2 = 1/4

Taking the square root of both sides:

x = ± √(1/4)

x = ± 1/2

So the solutions are x = 1/2 or x = -1/2.

It's important to note that we can't factor any x^2 term as it's a squared term and it's not possible to factor it out with any integer or variable.

Answer: 52(4x+8) in simplified form is 208x + 416.

Step-by-step explanation:

To simplify 52(4x+8) we need to first use the distributive property, which states that:

a(b+c) = ab + ac

So, we can rewrite 52(4x+8) as:

52 * 4x + 52 * 8

Now we can just multiply the numbers:

52 * 4x = 208x

52 * 8 = 416

so the expression simplifies to:

208x + 416

So, 52(4x+8) in simplified form is 208x + 416.

The value of the expression will be:

9. 5(n + 5) = 5n + 25

10. -9(10 - 6r) = -90 + 54r

11. -6(m + 6) = -6m - 36

12. 3(4 - 6m) = 12 - 18m

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

The value of the expression will be:

9. 5(n + 5)

= (5 * n) + (5 × 5)

= 5n + 25

10. -9(10 - 6r)

= -90 -+ 54r

= -90 + 54r

11. -6(m + 6)

= -6m - 36

12. 3(4 - 6m)

= 12 - 18m

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When cosx is negative and cotx is negative, an angle x lies in Quadrant II. Hence, the correct answer is B.

The correct answer is Quadrant II because the cosine and cotangent of an angle are related to the x- and y-coordinates of a point on the unit circle, respectively.

In Quadrants I and IV, the cosine function is positive, while in Quadrants II and III, it is negative. In Quadrants I and III, the cotangent function is positive, while in Quadrants II and IV, it is negative. This means:

Therefore, an angle x that satisfies both conditions of cos x being negative and cot x being negative must be in Quadrant II.

This question should be provided with answer choices, which are:

The correct answer is B.

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28) The constant of proportionality is (k = 2)

29) x and y do not change in the same way

30) The constant of proportionality (k = 5/xy)

x = 2y shows direct variation because as x increases, y also increases and as x decreases, y also decreases. The constant of proportionality, also known as the "k" value, is 2, it represents the ratio of x to y. (k = 2)

y - x = 6 does not show direct variation because the relationship between x and y is not constant, x and y do not change in the same way.

xy = 5 shows direct variation because as x increases, y also increases and as x decreases, y also decreases. To find the constant of proportionality, we can divide both sides by xy.

k = 5/xy

In this case, the constant of proportionality is not a fixed value, it is a variable depending on the values of x and y. It represents the ratio of xy to the product of x and y.

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The expression that represents the perimeter of the triangle is P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters. This result is obtained by adding up the lengths of the three sides of the triangle.

A perimeter of a triangle is the sum of the side lengths of the triangle. It can be expressed as

P = a + b + c

Where

The side lengths of a triangle are

Find the perimeter!

P = a + b + c

P = (9f+g)(9f+g) cm + (5f+9h)(5f+9h) cm + (2h+7g)(2h+7g) cm

P = (81f² + 9fg + 9fg + g² + 25f² + 45fh + 45fh + 81h² + 4h² + 14gh + 14gh + 49g²) cm

P = (106f² + 18fg + 50g² + 90fh + 85h²+ 28gh) cm

P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters

Hence, the perimeter's expression is P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters.

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Answer:

8g+11h+14f

Step-by-step explanation:

Answer:

3.here,tan45°=10/n

or,1=10/n

:.n=10

Now from Pythagoras theorem,

m²=(10)²+n²

or,m=√100+100

:.m=10√2

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In coordinate geometry, the slope of a line, m, is defined as the ratio of the change in y to the change in x of any two distinct points on the line. It can also be written as the ratio of the rise to the run.

What is meant by coordinate geometry?

Coordinate geometry (or analytic geometry) is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.

To find the slope of a line, we can use the two-point form of the equation of a line, which is:

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, we can use any two distinct points (x1, y1) and (x2, y2) on the line. To find m1 and m2, we use the following formulas:

m1 = (y2-y1) / (x2-x1)

m2 = (x2-x1) / (y2-y1)

It is important to note that m1 and m2 are the same value, just in different forms. m1 is the slope and m2 is the reciprocal of the slope.

In cases when x2-x1=0 (parallel to y-axis) or y2-y1=0(parallel to x-axis) the slope would be undefined and undefined respectively.

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A sentence for the equation 4m=52 is,

B) Four times m is equal to fifty-two.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

4m=52

i.e. we have,

4×m = 52

Hence, A sentence for the equation 4m=52 is,

B) Four times m is equal to fifty-two.

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The evaluation of the algebra tiles are as follows;

A) The area of the algebra tiles is; 2·x² + 3·x

The perimeter of the tiles is; 6·x + 6

B) If the algebra tiles were rearranged, the area remains 2·x² + 3·x

Algebra tiles are figures that can be manipulated to help explore and understand concepts such as expanding algebraic expressions, factoring expressions, and equations.

Please find attached the possible shape in the question created with MS Word.

A) The area of the of the shape is the sum of the areas of the individual shapes, which are found as follows;

The perimeter is the sum of the width and lengths of the rectangles as follows;

The width of the rectangle with area x = 1 unit

The width of the boxes with area x² = x

The length of the sides of each rectangle = x unit

The perimeter, P, of the figure is therefore;

B) The area of the each of the algebra tiles remain the same when the tiles are rearranged, such that the area, of the new shape, which is the sum of the areas of the individual tiles remain the same.

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The angle which would be tangent  a 90 degree in the given diagram would be ∠JYQ, ∠JYW  , ∠FYG and ∠FHG

A circle's tangent is a single-pointed line that intersects the circle. The point of tangency is the location where the circle and the tangent cross. The circle's radius, where the tangent touches it, is perpendicular to it.

Therefore, JY is perpendicular to QW which means

∠JYQ=∠JYW=90 degrees

Since, J is the center of circle and GF is diameter, there is a theorem which says that angle substended by diameter at any point of circle is 90 degree.

Therefore, ∠FYG =∠FHG=90 degrees.

Hence, ∠JYQ, ∠JYW  , ∠FYG and ∠FHG are all the equal to 90 degree.

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Yes , the given statement is true. Number 152 is representing as multiple of 8.

As given in the question,

Given number is equal to 8:

Given multiple is equal to 152:

Multiple is the number which we get after multiplying the given number by any integer.

Multiple of 8 are given by :

8 , 16, 24, 32, 40, 48, 56, 64, ......., so on

Here 152 represents the multiple of 8.

When we multiply 8 by 19 we get a number equals to 152.

The given statement is true.

Therefore, the given statement is true as 152 is one of the multiple of 8.

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Answer:

36 square units

Step-by-step explanation:

The figure is made up of a rectangle above with length 6 and width 4.

The bottom part is a triangle with a base of 6 and a height of 4.

total area = area of rectangle + area of triangle

total area = LW + bh/2

total area = 6 × 4 + 6 × 4/2

total area = 24 + 12

total area = 36

Answer:

36 square units

Step-by-step explanation:

We can split the given figure into two familiar figure by drawing a line segment as shown in the attached figure

This splits the composite figure into a rectangle at the top and an inverted triangle at the bottom

The rectangle has a length(horizontal portion) of 6 units and a width(vertical portion) of 4 units

Area of rectangle = length x width = 6 x 4 = 24 square units

The triangle has a base of 6 units and a height of 4 units

Area of rectangle = 1/2 x base x height = 1/2 x 6 x 4 = 1/2 x 24 = 12 square units

Area of figure = 24 + 12 = 36 square units

Exponential 4 can be written as x^4. This is an exponential expression and is used to represent a repeated multiplication of the base, 4, by itself.

In this case, the base is 4, and the exponent, x, represents the number of times 4 is multiplied by itself. For example, 4^3 can be written as 4x3, which is equal to 4*4*4. This is the same as saying “4 multiplied by itself 3 times.”

Exponential notation is a useful way to express large numbers. For example, 4^10 can be written as 4x10, which is equal to 4,096. The exponential form of this expression allows us to quickly calculate the result without having to write out the entire equation.

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For the function:

f(x) = -24

The domain and range are:

Domain: all real number.

Range:  {-24}

For a function:

y = f(x)

The domain is the set of possible inputs, this is, possible values of x.

The range is the set of possible outputs, this is, possible values of y.

Here the function is:

f(x) = -24

Notice that the input can be any value, we don't have any restrictions, and the output can only be -24, then we have:

Domain: all real number.

Range:  {-24}

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