3n^2+4m+5
A. 2
B. 3
C. 4
D. 5

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:

$47.70

Step-by-step explanation:

To find what a number is in percent form, divide it by 100

9% ÷ 100 = 0.09

Multiply this by $530 to find the commission

530 × .09 = 47.7

$47.70

The equation of f(x) from the graph if, G(x) = x², is F(x) = 2x² + 3, so option A is correct.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given:

G(x) = x²,

As you can see from the graph, the vertex of the parabola is (0, 3),

Write the equation of a parabola as shown below,

y = a(x - 0)² + 3

y = ax² + 3

Here a is the slope of the parabola,

slope = 4 / 2  (from the graph),

slope = 2

Thus, the equation will be,

y = 2x² + 3 or  F(x) = 2x² + 3

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Using coordinates O(0,0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0) has the advantage of allowing the graph to be stretched or shrunk uniformly in both the x- and y-directions by a factor of 2. This can be useful if the scale of the graph needs to be adjusted, or if the graph needs to be compared to another graph with a different scale. It can also make the graph easier to read if the values of the variables being plotted are very large or very small.

By using coordinates that are multiples of the original coordinates, the shape of the graph is preserved, but the scale is changed. This can be useful if the purpose of the graph is to compare the relationships between different variables, rather than to provide an accurate representation of the actual values of the variables.

Answer:

the snail was going 0.005m/second

Step-by-step explanation:

15m/3000

Answer:

Step-by-step explanation:

ormula for finding the asymptote of hyperbola is

y-k =+/- b/a( x-h).

Answer:

0.2

Step-by-step explanation:

[tex]P(A \cap C)=P(A)P(C)=(0.5)(0.4)=0.2[/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:

Equilateral Triangle

A triangle with all the sides equal is called an equilateral triangle.

Isosceles Triangle

A triangle with at least two sides equal is called an isosceles triangle.

Scalene Triangle

If all the sides of a triangle are unequal, i.e., if the sides are of different lengths, the triangle is called a scalene triangle.

Acute Triangle

An acute triangle is a triangle whose all the three interior angles are acute. In other words, if all interior angles are less than 90 degrees, then it is an acute-angled triangle.

Obtuse Triangle

Obtuse triangles are those in which one of the three interior angles has a measure greater than 90 degrees. In other words, if one of the angles in a triangle is an obtuse angle, then the triangle is called an obtuse-angled triangle.

Right Triangle

A right triangle is a triangle in which one of the angles is 90 degrees. In a right-angled triangle, the side opposite to the right angle (90-degree angle) will be the longest side and is called the hypotenuse. You may come across triangle types with combined names like right isosceles triangle and such, but this only implies that the triangle has two equal sides with one of the interior angles being 90 degrees.

Answer:

5. ∠HTS

6. DI

7. UF

8. ∠E

Step-by-step explanation:

5. We are given that ΔTSR ≅ ΔTSH, and according to CPCTC (corresponding parts of congruent triangles are congruent), ∠RTS corresponds with ∠HTS. Therefore, ∠RTS ≅ ∠HTS.

6. We are given that ΔECD ≅ ΔDJI, and according to  CPCTC (corresponding parts of congruent triangles are congruent), segment DE corresponds with segment DI. Therefore, DE ≅ DI.

7. We are given that ΔVUT ≅ ΔVUF, and according to  CPCTC (corresponding parts of congruent triangles are congruent), segment UT corresponds with UF. Therefore, UT ≅ UF.

8. We are given that ΔPQR ≅ ΔEFG, and according to  CPCTC (corresponding parts of congruent triangles are congruent), ∠P corresponds with ∠E. Therefore, ∠P ≅ ∠E.

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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Answer:

Sienna

Step-by-step explanation:

Sienna achieved higher scores of 15-17 much more consistently than Willem, who often scored just 12 or 13.

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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Answer:

24.6 cm^2

Step-by-step explanation:

3.28m = 328 cm

75mm = 0.075 cm

Area of rectangle: L x W

328 times 0.075 = 24.6 cm^2

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:

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

Simplify the given expression:

Refer to the photo taken.

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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Answer:

Refer to the attached photo.

Step-by-step explanation:

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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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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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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Integration services are precise design and implementation tasks that connect the functionality and/or data of two or more applications with existing or future Information systems architecture.

Integrate to combine, mould, or mix into a working or cohesive whole.

information is a stimulus that, to its recipient, has significance in a particular setting. Info that is entered into and stored in a computer is referred to as data in a wide sense. It is possible to read data that has undergone processing, such as formatting and printing, once again as info.

You may include sources into your writing in three different ways:

Quoting: This refers to using another author's identical words in your writing without modifying them.

Giving a summary entails outlining the main ideas of a source.

Putting another author's thoughts into your own words is known as paraphrasing.

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Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I'm guessing you misspelled 410 as 419, but the equation is y=mx+b

Kim wants the money amount she puts in to pay off her $410 phone, or in other words, add up to $410.

The constant, or b, is 50. The m is 35, and the x is the months.

35m + 50 = 410

Answer: C. 35m + 50 = 410

Step-by-step explanation:

We know the cost is 410, so it will be = 410

We know that she pays 35 each month, which mean it is 35m

She put down 50 at the beginning, so it is + 50

So our equation is

35m + 50 = 410

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!

Multiplicity value is a measure of the number of times a given entity appears in a relationship.

It is expressed as either a single value (1:1, 1:N, or M:N) or as a range of values (e.g. 1..4). This value is used to define the type of relationship between two entities.Multiplicity value is a measure of the number of times a given entity appears in a relationship. It is expressed as either a single value, such as 1:1, 1:N, or M:N, or as a range of values, such as 1..4. These values are used to define the type of relationship between two entities. For example, a 1:1 relationship means that one entity is related to one other entity, such as one customer to one order. A 1:N relationship means that one entity is related to multiple other entities, such as one customer to multiple orders. An M:N relationship means that multiple entities are related to multiple other entities, such as multiple customers to multiple orders.

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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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