q20 ANSWER FOR 20 POINTS

Answer:B 1 real zero

Step-by-step explanation:

The correct option to make the triangle prism by net will be;

⇒ First option.

A triangular prism is also known as a pentahedron which comprises of two triangle bases and three rectangular sides.

Since, The net of the triangular prism is formed as a result of unfolding that occurs along the edges and faces as they are laid out in a pattern of two dimensions.

Hence, From the given question ;

We would see that the first option matches and correlates with triangular prism in question.

Thus, The ''first option'' from the diagram given represents the triangular prism in the question.

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The figure of the question is shown in image.

Answer:

6 -19i

Step-by-step explanation:

5 - 8i + 1 - 11i

Collect like terms

5 + 1 -11i -8i

6 - 19i

Answer:

u = -42

Step-by-step explanation:

Now we have to,

→ find the required value of u.

The equation is,

→ -23u = 966

Then the value of u will be,

→ -23u = 966

→ u = 966/-23

→ u = -(966/23)

→ [ u = -42 ]

Hence, the value of u is -42.

The rate of change of this linear function is -2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁)

From the given table, (-2, 15), (-4, 23) and (-5, 27).

Substitute, (x₁, y₁)=(-2, 15) and (x₂, y₂)=(-4, 23) in (y₂-y₁)/(x₂-x₁), we get

Rate of change =(23-15)/(-4+2)

= 8/(-2)

= -4

Therefore, the rate of change of this linear function is -2.

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The relation given by the set of ordered pairs {(5,2),(4,2),(3,2),(2,2),(1,2)} is not a function. This is because there are multiple y-values (2) for the same x-value (5, 4, 3, 2, 1).

A function is a relation where each input (x-value) has one and only one output (y-value).

To further illustrate this, let's look at a more concrete example. Consider the following set of ordered pairs:

{(1,2), (2,4), (3,6), (4,8), (5,2)}

Here, we can see that the x-value 5 is paired with the y-value 2, but the x-value 1 is paired with the y-value 2 as well. This means that there is more than one y-value associated with a single x-value, which means this relation is not a function.

To better understand why this relation is not a function, let's look at the mathematical definition of a function. A function is defined as a relation between two sets of values (x and y) such that each x-value has one and only one y-value associated with it. Mathematically, this can be expressed as:

f: X → Y,

where X is the set of all x-values and Y is the set of all y-values.

In our example, the relation between the x-values and y-values does not satisfy this definition, as there is more than one y-value associated with a single x-value. Therefore, this relation is not a function.

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The solution is Option C.

The L'Hopital's rule is applied to the equation lim x approaches 0 (1-cosx)/x

L'Hopital's rule then states that the slope of the curve when t = c is the limit of the slope of the tangent to the curve as the curve approaches the origin, provided that this is defined. The limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.The tangent to the curve at the point [g(t), f(t)] is given by [g′(t), f′(t)]

And , lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

The equation is A = lim x approaches 0 (1/x)

On simplifying the equation , we get

The limit diverges as the function diverges and limit does not exist

And ,  lim x approaches 0₊ (1/x) ≠ lim x approaches 0₋ (1/x) = ∞

b)

The equation is A = lim x approaches 0 ( 2x² - 1 ) / ( 3x - 1 )

On simplifying the equation , we get

when x = 0 ,

Substitute the value of x = 0 in the limit , we get

A = ( 2 ( 0 )² - 1 ) / ( 3 ( 0 ) - 1 )

A = ( 0 - 1 ) / ( 0 - 1 )

A = 1

c)

The equation is A = lim x approaches 0 ( 1 - cosx ) / x

On simplifying the equation , we get

Applying L'Hopital's rule , we get

lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

f ( x ) = ( 1 - cos x )

g ( x ) = x

f' ( x ) = sin x

g' ( x ) = 1

So ,

lim x approches 0 [ f' ( x ) / g' ( x ) ] = lim x approches 0 ( sin x / 1 )

when x = 0

sin ( 0 ) = 0

Therefore , the value of lim x approaches 0 (1-cosx)/x = 0

d)

The equation is A = lim x approaches 0 ( cos 2x ) / 2

On simplifying the equation , we get

when x = 0 ,

A = cos ( 2 ( 0 ) / 2

A = cos ( 0 ) / 2

A = 1/2

Hence , the L'Hopital's rule is applied to lim x approaches 0 ( 1 - cosx ) / x

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Answer:

Step-by-step explanation:

= 8^3+7+8+(9*2/3)*2= 8^3+7+8+(18/3)*2= 8^3+7+8+(6)*2= 8^3+7+8+6*2= 512+7+8+6*2= 512+7+8+12= 519+8+12= 527+12= 539

A similarity transformation is a rigid movement followed by scaling, so this type of transformation can change the position and size, but not the shape.

In geometry, a similarity transformation is a rigid movement followed by scaling, so this type of transformation can change the position and size, but preserve the shape and angles.

Thus, two or more shapes are similar if they have the same shape and corresponding angles, but their corresponding sides are proportional in length.

This type of transformation is often also referred to as dilation.

The rule of dilatation:

[tex]D_{k}[/tex] (x,y) = (kx, ky)

with [tex]D_{k}[/tex] is the coordinate point of the new image and k is the scale factor.

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The numbers that are written in scientific notation are:

The concept here is  scientific notation, which can be expresed as a*10^b. where a is the digits and a is the power.

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It is also known as standard form in the UK and scientific form, standard index form, and standard form.

Therefore, option A , C and F are correct.

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The numbers that are written in scientific notation are:

From the question, we have the following parameters that can be used in our computation:

The list of options

As a general rule of scientific notation, the numbers can be repesented as

a * 10^b

Where the variable a is any number between 1 and 10

And b is a real number

Using the above as a guide, we have the following:

Other numbers are not in scientific notation

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The utilization of machinery, originally propelled by water or steam and later by electricity, is the primary feature of the factory system.

The cube root of a number x equals a number y, hence in mathematics, y3 = x. Each non-zero real number has exactly one real cube root, three separate complex cube roots, and one set of conjugate complex cube roots. The cube root of a number is produced when it is multiplied three times. The last cube root is denoted by the symbol, which is three cube roots. Finding an integer's cube root is the opposite of cubing it. The cube root of a number can be found using the relatively simple method of prime factorization. A cube root is represented by the symbol.

given

The utilization of machinery, originally propelled by water or steam and later by electricity, is the primary feature of the factory system.

The employment of machinery or economies of scale, the centralization of industries, and the standardization of interchangeable parts are the main sources of the system's additional characteristics.

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The size of XYZ in the triangle based on the application of trigonometry ratio is 66.4°.

Based on the information given, it should be noted that we can apply trigonometry to solve the triangle.

In this case, the hypothenuse is 15cm and the adjacent is 6cm. The trigonometry ratio will be:

cos = adjacent / hypothenuse.

cos x = 6 / 15

cos x = 0.4

x will be the inverse cos to find the value. This will be 66.4°.

Therefore, the angle is 66.4°.

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To make the ratio of red to blue counters 3:1, you will need 3 times as many red counters as blue counters.

If the current ratio is 1:3, then for every 1 red counter, there are 3 blue counters. To make the ratio 3:1, you will need 3 red counters for every 1 blue counter.

So, if you have x red counters and y blue counters, where the ratio of red to blue is 1:3, then you will need 3x red counters and y blue counters to make the ratio 3:1. This means you will need 3x - x = 2x more red counters.

For example, if you have 6 red counters and 18 blue counters, the ratio of red to blue is 1:3. To make the ratio 3:1, you will need 3×  6 = 18 red counters and 18 blue counters. This means you will need 18 - 6 = 12 more red counters.

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Answer: 10

Step-by-step explanation: 1/2 + 3/4= 5/4 or 1 1/4

1 1/4 / 1/8= 10

Based on the information provided, to prepare a total of 220 pancakes Kai needs 30 cups of pancake mix.

To prepare 22 pancakes Kai needs a total of 3 cups of pancake mix, which means the ratio is 22 to 3 or 22:3.

To find the total of pancake mix Kai need for this new number of pancakes different methods can be applied:

First method: Rule of three

3 cups of pancake mix = 22 pancakes

            x                        = 220 pancakes

x (number of cups) = 220 pancakes / 22 panckes x 3

x = 10 x 3

x= 30

This means Kai needs 30 cups

Second method: Find the number of cups for 1 pancake

3 cups  / 22 pancakes=  0.13636

220 x 0.13 = 29.9 which can be rounded as 30 cups

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The required value of x can be obtained as per the similarity of triangles as 18.84 units.

A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.

For two similar triangles the ratio of corresponding sides are always equal.

The given diagram shows two similar triangles.

As the ratio of corresponding sides are equal,

The following equation can be written as,

⇒ 26/35 = 14/x

⇒ 26x = 14 × 35

⇒ x = 18.84

Hence, the value of x can be obtained as 18.84 units.

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The two functions of f(x)= -6x2 + 5 and g(x)= 5 result in the y-intercept of function g(x) being 2 as a result (1. 5)

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

y-intercept for f(x) is f(0)

so f(0) =

=> 0+5

=>5

so the y-intercept of f(x) is 5

now y-intercept of g(x) is g(0)

so g(0) = 7*0 +2

=>0 +2

=>2

The two functions of f(x)= -6x2 + 5 and g(x)= 5 result in the y-intercept of function g(x) being 2 as a result (1. 5) .

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Answer:

Step-by-step explanation:

Sorry, but Ummm the question doesn't make sense

The sum of the vertical opposite angle m∠q and the angle m∠r us equal to 85.5°.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

The line MN and PQ intersect each other, so m∠q and the angle m∠MOP are equal

m∠q = 54°

m∠p = 180° - 54° {sum of angles on a straight line}

m∠p = 126°

m∠p = 4 × m∠r {cross multiply}

m∠r = 126°/4

m∠r = 31.5°

Therefore, the sum of the vertically opposite angle m∠q and the angle m∠r is 54° + 31.5° = 85.5°.

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Answer:

A line segment joining any two points on the circle is called a chord.

Step-by-step explanation:

A chord is a line segment with both endpoints on the same circle.

Answer:

The meaning of segment joining is ⇔ A line segment joining any two points on the circle is called a chord.

Line segment joining midpoints of opposite sides of quadrilateral.

Step-by-step explanation:

I hope this helps and have a wonderful day!

Answer:

  (d)  4/9

Step-by-step explanation:

You want the probability of drawing D, D from a set of cards {A, D, D} if two are drawn with replacement.

The probability of drawing a D is 2/3. The probability of doing it again is the same. Thus, the probability of doing it twice, assuming the draws are independent, is ...

  P(D, D) = P(D)·P(D) = (2/3)(2/3) = 4/9

P(D, D) = 4/9

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Answer:

268.2 cm²

Step-by-step explanation:

Create the following ratio for both pentagons:

side : area

9      : 603.45 cm²

4      :  A

We can see that multiplying 603.45 cm² by 4/9 will solve for A, as multiplying 9 by 4/9 will solve for 4.

4 = 9 × (4/9)

A = 603.45 cm² × (4/9)

A = 268.2 cm²

So, the area of the smaller pentagon is 268.2 cm².

The value of x give the sides in the rectangle is 4cm.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has. Based on the information, it's important to note that the perimeter of a rectangle is given as:

= 2(length + width)

Since rectangle a has sides 6cm long and x+2cm long. rectangle b has sides 3cm long and 2x+1 cm long and the perimeter is the same. This will be calculated by equating the perimeter for both rectangle A and B.

2(6 + x + 2) = 2(3 + 2x + 1)

12 + 2x + 4 = 6 + 4x + 2

Collect the like terms

-2x = 8 - 16

-2x = -8

Divide

x = 8/2

x = 4

Therefore, the value of x based on the calculation is 4cm.

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It takes 10 hours to reach a population of 200,000 at the growth rate of 7% per hour.

We can use the formula for compound interest to calculate the time it takes for the population of bacteria to reach 200,000.

The formula is:
A = P(1+r)^t

Where:
A = final amount (200,000)
P = initial amount (50,000)
r = growth rate (7% per hour expressed as decimal)
t = time (in hours)

We can rearrange the formula to solve for t:
t = log(A/P) / log(1+r)

By plugging in the given values:
t = log(200000/50000) / log(1+ 0.07)

The answer will be in hours, so we need to use a calculator or a log function in a programming language to get the answer.

Alternatively, you can use the rule of 70, which says that the number of years required to double a population at a given growth rate is approximately 70/growth rate. So in this case it is 70/7 = 10 hrs.

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The total number of possible four-digit PINs that cannot begin or end with a 0 and must be an even number is 10,000 - 900 - 4,500 = 4,500. Thus, the correct answer is c. 4,500.

To determine this:

There are 10 options for the first digit (1-9) and 10 options for the last digit (2, 4, 6, 8). For the middle two digits, there are 10 options for each digit (1-9). Therefore, the total number of possible four-digit PINs is 10 x 10 x 10 x 10 = 10,000.

However, we must subtract the number of PINs that begin or end with a 0, which is 9 x 10 x 10 x 1 = 900. We must also subtract the number of PINs that are odd numbers, which is 9 x 10 x 10 x 5 = 4,500.

Therefore, the total number of possible four-digit PINs that cannot begin or end with a 0 and must be an even number is 10,000 - 900 - 4,500 = 4,500. Thus, the correct answer is c. 4,500.

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Triangle properties include triangle inequality, angle sum, congruence, exterior angle theorem, and isosceles triangle theorem.

1. Triangle Inequality: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. Angle Sum of a Triangle: The sum of the angles of a triangle is always equal to 180°.

3. Congruence of Triangles: If two triangles have all three sides equal, then they are congruent (the same size and shape).

4. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

5. Isosceles Triangle Theorem: If two sides of a triangle are equal in length, then the angles opposite those sides are also equal in measure.

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The five properties of triangle is listed below.

The term triangle is defined as the polygon with three angle, sides and vertices.

Here we have to list down the properties of triangle.

The basic five properties of triangle are as follows:

1) in geometry, total amount of space inside the triangle is called the area of a triangle. And it is measured by square units.

2) The property of perimeter of a triangle is equal to the sum of all three sides of the triangle.

3) And the another property states that sum of the length of the two sides of a triangle is greater than the length of the third side.

4) according to the angle, the property states that sum of the angles of a triangle is always 180 degrees.

5) If angles of an equilateral triangle are equal and has a measure of 60⁰ each.

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Answer:

The difference in temperature is 16 degrees. To find the difference, you subtract the initial temperature from the final temperature: 5 - (-11) = 16.

Step-by-step explanation:

Answer:

The difference in temperature is 16 degrees. You can find the difference by subtracting the initial temperature from the final temperature: 5 degrees - (-11 degrees) = 5 + 11 = 16 degrees

Answer:

Step-by-step explanation:

Let the length of the smaller piece be l inches. Then the larger piece is 3*l = 3l inches. But l + 3l = 72. Hence, 4l =72. l= 72/4 = 18. Therefore, the smaller piece has a length of 18 inches.

Answer:

s= -3

Step-by-step explanation:

Given 18=-6s

We need to figure out what the variable "s" is

18=-6s  Divide both sides by -6

18/-6=-3 Simplify

Answer: s=-3

Hope this helps :)

Answer:

s=-3

Step-by-step explanation:

Im not completely sure what the quotation marks mean but ill try my best :)

18=-6s

18/-6=-3

-3=s