Evaluate the expression: 5 + 3 × (5 - 2)²

The standard form of the complex number is respectively 2√3 i - 15 + √300 i,4 - 7 i, and -14 + 9 i.

Complex numbers are helpful in finding the square root of negative numbers.

A complex number is the sum of a real number and an imaginary number.

(a)

As per the given, 2√-3 - 15 + √-300

Since, √-1 = i thus,

2√3 i - 15 + √300 i

(b)

As per the given, (15 - 10i)/(2 + i)

By rationalization,

(15 - 10i)/(2 + i) x (2 - i)/(2 - i)

⇒ (30 - 15 i - 20 i + 10 i²)/(2² - i²)

⇒ (30 - 10 - 35 i)/(4 + 1)

⇒ 4 - 7 i

(c)

As per the given, 3(2 + i) - 4(5 - 2i)

⇒ 6 + 3i - 20 + 8i

⇒ -14 + 9 i

Hence "The complex number has the following conventional forms: 2√3 i - 15 + √300 i,4 - 7 i, and -14 + 9 i".

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Refer to the photo taken.

The triangle JKL is similar to triangle MNL by AA similarity and all three sides of the triangle are equal, so JKL = MNL.

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

JK || MN and  L is the midpoint of JM,

As the line JK || MN  then,

∠ MNL = ∠ JKL (The alternate angle of the parallel line are equal)

∠ LMN = ∠ LJK (The alternate angle of the parallel line are equal)

∠ JLK = ∠ NLM (The corresponding  angle of the parallel line are equal)

Thus, all the sides will also be equal as the angles are equal.

Hence, the area will also be equal.

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The image is the final appearance of a figure after a transformation operation. The pre-image is the original appearance of a figure in a transformation operation.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

Preimages are the original, unaltered shapes, and images are the new (transformed) shapes. To put it another way, a transformation is a process that maps a preimage onto an image.

Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

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The mode for a particular set of observations is 5 since it occurs the majority of the time.

The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.

Here,

given set of observation:

5, 7, 8, 5, 7, 6, 9, 5, 10, 6

Mode is the number which occurs the highest time.

So here 5 occurs the highest times(3 times).

So,5 is the mode.

The mode for given set of observation is 5 as it occurs most time.

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The average speed of Chen when skating is 5 miles per hour

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

Time = 3/4 of an hour

Distance covered = 3 3/4 miles

The average speed can be calculated using the following equation

Average speed = Distance covered/Time

Substitute the known values in the above equation, so, we have the following representation

Average speed = (3 3/4)/(3/4)

Evaluate the quotient

Average speed = 5

Hence, the average speed is 5 miles per hour

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The slope of the given straight line equation 3x+y=-12 is m=-3.

Finding the change in values divided by the change in values will reveal the slope between two places. As long as the line is linear, you can really use any two locations along the line to get the slope (straight line). An easy approach to do it is to use the end points since they are provided.

Negative, positive, zero and undefined are four types of slope.

The equation is given as:

3x+y= -12

Separate y we get:

y= -3x-12

This is a straight line equation and we can compare it with y=mx+c where m is the slope.

Upon comparison with general equation slope m=-3.

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The equation x^2 - 5x + 7 = 0 has no real roots.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

x^2 - 5x + 7 = 0

On comparing the given equation with the general form of a quadratic equation, we get that:

a = 1, b= -5, and c = 7

If D = b^2 - 4ac < 0, then the roots of the quadratic equation are imaginary or there are no real roots.

Therefore, b^2 - 4ac = (-5)^2 - 4x1x7 = -3<0.

Hence, we conclude that the nature of the roots of the give equationis imaginary, thus it has no real roots.

The question is incomplete, the complete question is x^2 - 5x + 7 = 0

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Answer:

----------------------

Simplify the given expression:

Answer:

550 kWh

Step-by-step explanation:

To find the number of kilowatt hours of electricity the Abubakar family will be using 12 months after they've started decreasing their usage, we can substitute 12 for x in the equation y = –25x + 850. This gives us y = –25 * 12 + 850 = –300 + 850 = 550.

Therefore, the Abubakar family will be using 550 kilowatt hours of electricity 12 months after they've started decreasing their usage.

The vertex form of line f(x) = ax² + bx + c  is y = a(x - h)² + k where the vertex is (h, k).

The vertex form of a line is one of the representations of the line in an equation format. Here the line focused on the coordinates of the vertex.

For a line, f(x) = ax² + bx + c, the vertex form is y = a(x - h)² + k; vertex at (h, k).

To convert the general form to the vertex form, the general equation is simplified as below:

y = ax² + bx + c

  = ax² + bx + c + b²/4a - b²/4a

  = a(x² + b²/4a² + b/a) + (c - b²/4a)

  = a(x² + (b/2a)² + 2b/2a) + (c - b²/4a)

  = a(x + b/2a)² + (c - b²/4a)

⇒ y = a(x - (-b/2a))² + (c - b²/4a)

Consider -b/2a = h and (c - b²/4a) = k, then we get

y = a(x -h)² + k; vertex form of the given line.

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Answer:

Refer to the attached photo.

Step-by-step explanation:

 By the property of alternate interior angles, Option (1) is the correct statement.    

  ∠XWY ≅ ∠ZYW

   Property of the alternate angles states, if two parallel lines are cut by a transversal, then the alternate angles are congruent.

By this property,

Lines XW and YZ are the parallel lines intersected by a transversal WY.

Here, ∠XWY and ∠ZYW represent the interior angles between the parallel lines and the transversal.

Therefore, interior alternate angles ∠XWY and ∠ZYW will be congruent.

Hence, Option (1) will be the correct option.

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The average rate of change of the inductor's energy between t = 0.0 to t = 1 .0 is 6

The term circuit in defined as an inductor and a resistor is called an RL-circuit here the inductor resists any current change in the circuit and the resistor dissipates energy, then the resulting in the exponential decay of current if no current or voltage source is present.

Here we need to calculate the average rate of change for the inductor's energy,

Here we know that the values of t1 = 0, and t2 = 1

Similarly, here we know the value of flow of current as f(t1) = 12 and f(t2) = 18.

Now, the average rate of change is calculated as

=> [18 - 12]/1 - 0

When we simplify the expression, then we get,

=> 6/1

=> 6

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As per the given function, the line of the functions has the same intersecting point (-0.2, 0).

The term function in math refers  a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we have the consider the functions f(x) = 23x + 5 and g(x) = 32x + 7.

And we need to find  the slopes indicate about the lines.

While we looking into the given functions,

f(x) = 23x + 5

g(x) = 32x + 7

Now, we have to identified that the slope of the function f(x) is 23 and the slope of the function g(x) is 32.

And now we have to apply some sample values on the function, then we get the following table of values.

And by using the table we have to plot the graph then we get the graph like the following.

Through graph we have identified that both functions has the same intersecting point (-0.2, 0).

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Answer:

Step-by-step explanation:

put it into the y=mx+c equation

y=-2x+8

therefore th y intercept is at (0,8)

and the gradient in -2

Answer:

16x^8y^3

Step-by-step explanation:

Simplify the expression.

Answer:

[tex]-8x^7(-2xy^3) = 16x^8y^3[/tex]

Step-by-step explanation:

⭐Multiplication rules

⭐ Exponent multiplication rule

⭐ Multiplying two terms with variables

We need to utilize these 3 key points (⭐) when multiplying to terms with variables.

First, let's multiply the coefficients:

-8 * -2 = 16

Next, let's multiply the variables:

[tex]x^7 * xy^3[/tex]

These two variables have the same base (x), so we will add their exponents up.

* remember: if you see a variable without an exponent, it has an exponent of 1 *

[tex]x^7 * x = x^8[/tex]

The variable [tex]y^3[/tex] will stay the same because there is no other y variable.

= [tex]x^8y^3[/tex]

Now, "attach" the variables to the product of the coefficients:

= [tex]16x^8y^3[/tex]

The height of pyramid if the length and slant height is known is . h² = S² - (x/2)².

We can employ the Pythagoras theorem to accomplish this as the triangle is right-angled and is created by the slant height (s), its altitude (h), and 1⁄2 of side length of a base (x/2).

As a result, (x/2)² + h² = s².

We can utilize this while figuring out how to find the pyramid's volume given the slant height.

h² = S² - (x/2)²

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There probability two ways to pick two representatives with one majoring in mathematics and the other majoring in computer science.

In order to pick two representatives with one majoring in mathematics and the other majoring in computer science, there are two approaches that can be taken. The first approach is to pick one representative who majors in mathematics first, then the second representative who majors in computer science. The second approach is to pick one representative who majors in computer science first, then the second representative who majors in mathematics. Both of these approaches would yield two representatives, one with a mathematics major and the other with a computer science major. It is important to note that whichever approach is taken, both representatives must be chosen from the same pool of potential representatives. Thus, the pool of potential representatives should be large enough to encompass both mathematics and computer science majors in order to successfully pick two representatives with one majoring in mathematics and the other majoring in computer science.

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Probability that at least one of them is a universal donar is 0.5263.

What is probability ?

What is probability explain?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given,

Probability of getting a universal donor is 0.072.

X be the “random variable” which “describes the number of universal donors” in the “sample of 10 people”.

X follows a “binomial distribution” with n=10 and p=0.072

P(X=x) = ([tex]{n}C^{x}[/tex])*([tex]p^{x}[/tex])*([tex]q^{n-x}[/tex]) ; x=1(1)10 ; q=1-p

Required probability,

P(X≥1)= 1 - P(X=0)

= 1 - (10C0)*([tex]0.072^{0}[/tex])*([tex]0.928^{10}[/tex])

= 1 - 0.4737 = 0.5263

Probability that at least one of them is a universal donar is 0.5263.

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Sanjay needs 90 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w.

What is an equation in maths?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Given that we have all the equations set up, we need to solve for W.

1.) w+3w=90

4w=90

w=22.5

2.) w+3w+w+3w=90

8w=90

w=11.25

3.) 2*w+2*3w=90

2w+6w=90

8w=90

w=11.25

4.) 2*(3w+w)=90

6w+2w=90

8w=90

w=11.25

Now, out of all those which one was different?

A. (w+3w=90)

This equation did not match with all the others is (w+3w = 90)

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Answer:

16 inches

Step-by-step explanation:

Using the Pythagorean theorem, the distance is [tex]\sqrt{65^2-63^2}=16[/tex].

Answer:0

Step-by-step explanation:

So this is an exponential equation. And the dy/dx is impossible because anything time 0 is 0. So there is no Rise over run, most commonly known as your slope.

Option. A ) 0 is correct

It is given that,y = 3x⁰ = 3

we have asked to differentiate the function y with respect to x.

for constants, the slope is always zero and the graph looks like a line parallel to the x-axis

[tex]dy/dx[/tex] = 0

therefore, the differentiation of y=3 is 0.

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Answer:

the snail was going 0.005m/second

Step-by-step explanation:

15m/3000

A geometric sequence is an exponential function. Instead of y=ax, we write an=crn where r is the common ratio and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by multiplying the previous term by the common ratio, ak+1=ak * r.

Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem.

There are many shapes in geometry based on their dimensions. Circle, Triangle, Square, Rectangle, Kite, Trapezium, Parallelogram, Rhombus and different types of polygons are the 2-d shapes. Cube, Cuboid, Sphere, Cone and Cylinder are the basic three-dimensional shapes.

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Put the polynomial in conventional form. Count the number of terms in the polynomial. The degree of the polynomial is one more than the number of terms.

Begin by writing the polynomial in standard form. This means that the terms should be written in descending order of degree, with the coefficient of the leading term being positive. Make sure that each term is separated by a plus or minus sign.Count the number of terms in the polynomial. Include the constant term, even if it is equal to zero.The degree of the polynomial is one more than the number of terms. For example, if the polynomial has two terms, its degree is three. If the polynomial has three terms, its degree is four.If the polynomial has an exponent that is not a whole number, it is called a rational polynomial. The degree of a rational polynomial is equal to the degree of the numerator of the rational expression. If the polynomial has a negative exponent, it is called an inverse polynomial. The degree of an inverse polynomial is equal to the negative of the exponent. If the polynomial is a combination of rational and inverse polynomials, the degree is equal to the highest

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Answer:

3x3 is a cubic polynomial

Step-by-step explanation:

Since the highest degree of exponent in 3x3 is 3, the polynomial is a cubic polynomial.

... Hope this helped! Have a wonderful New Year!

The factors of x³ 4x² x 6 are (1) x³, (2) 4x², (3) x and (4) 6. These factors are the numbers that can be multiplied together to give x³ 4x² x 6 as the product.

To find the factors of x³ 4x² x 6, we must first expand the expression. x³ 4x² x 6 can be expanded to x³ x x 4x² x 6, which can be further simplified to x³ + 4x² + 6. The factors of this expression are the numbers that can be multiplied together to give x³ 4x² x 6 as the product. In this case, the factors are (1) x³, (2) 4x², (3) x, and (4) 6. In other words, x³ 4x² x 6 can be written as (x³)(4x²)(x)(6). Understanding the factors of an expression is an important skill in algebra, as it can help you simplify and solve equations.

The factors of x³ 4x² x 6 can be calculated by factoring the expression:

x³ 4x² x 6 = (x³)(4x²)(x)(6)

This can be further simplified to:

x³ 4x² x 6 = x⁴ (4x²)(6)

Therefore, the factors of

x³ 4x² x 6 are (1) x³, (2) 4x², (3) x, and (4) 6.

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The solution of three consecutive numbers is the addition of one more value to a base number.

For example, the solution of three consecutive numbers of 5 is 6, 7, 8.

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.

When we want to find the consecutive numbers of a base number we only have to do a sum, which we can express in the following way:

Cn = N + n

Example:

N = 5

Three consecutive numbers are:

n= 1, 2, 3

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