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Write an equation for the translation of x2 + y2 = 49 by 3 units left and 4 units
O(x + 3)2 + (y + 4)2 = 49
O(x + 3)2 + (y – 4)2 = 49
O(x – 3)2 + (y – 4)2 = 49
O(x – 3)2 + (y + 4)2 = 49

In geometry, there are several ways to prove that two triangles are congruent, which means that they have the same size and shape. Here are three common methods for proving triangle congruence SSS congruence, ASA congruence, and SAS congruence.

Side-Side-Side Congruence: If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent. This can be written as:

If AB = DE, AC = DF, and BC = EF, then ∆ABC ≅ ∆DEF

Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. This can be written as:

If ∠A = ∠E, ∠B = ∠F, and AC = EF, then ∆ABC ≅ ∆DEF

Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. This can be written as:

If AB = DE, ∠A = ∠E, and BC = EF, then ∆ABC ≅ ∆DEF

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Answer:

145

Step-by-step explanation:

y = 5(25) + 20

y = 125 + 20

y = 145

A transformation that leaves a geometric figure's size or shape unaltered is known as a rigid transformation (also known as isometry). is a unique type of metamorphosis in which a figure's size or shape are left unaltered.

During a rigorous alteration of the geometric object, the distance between each pair of its points is maintained. In other words, an object's size and shape are maintained through a hard transformation. For example, the rigid transformation of a triangle preserves the triangle's angles and lengths. Consider a rigid form distortion that resembles a cardboard shape.

There are translations, reflections, and isometric rotations. As a result, none of these changes have an impact on the figure's size. If neither the size nor the shape of the figures are changed, the figures are constant.

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First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.

By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

Answer: Z=[tex]\frac{3}{2}[/tex]x-y

Step-by-step explanation: first multiply both by the reciprocal of 2/3 to cancel it. the reciprocal of 2/3 is 3/2

x(3/2)=y+z

then to solve for x, move the to the left side by -y on both sides

you're then left with z=x(3/2)-y

The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.

What is mean of rational zero ?

A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

Have given ,

f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex]

This is a fourth degree polynomial.

Using the rational root theorem, the possible zeros of the polynomial are the factors of 15.

We know that

Factors of 15 = ± 1, ±3, ±5, ±15

Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.

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Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.

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An example of a complex equation is the Navier–Stokes equations, which are used to describe the motion of fluids and are one of the most important equations in fluid mechanics.

A complex equation is a mathematical expression that contains multiple variables, operations, and powers. This can include exponents, logarithms, trigonometric functions, and other variables. Complex equations can be used to solve problems or to make predictions, and can be used in a wide range of fields, including economics, engineering, and physics.

These equations consist of a set of partial differential equations that describe the motion of a fluid, such as air or water, and the forces acting on it. The Navier–Stokes equations are used to predict the behavior of liquids and gases in a wide range of applications, from aeronautics, to weather prediction, to oceanography.
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According to the properties of geometry the correct option is C.

What is geometry?

The study of measurements, sizes, shapes, locations, angles, and proportions of objects is known as geometry.

Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.

If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.

Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.

It is given that LMN is dilated by a scale factor of 0.5.

Since scale factor is lies between 0 to 1, therefore it shows the compression.

Therefore sides of L'M'N' is smaller than LMN.

Since corresponding angles of similar figure are congruent.

So, options A, B and D represent the correct statements. Only option C represents a false statement because the sides of similar figure are proportional not congruent.

Therefore option C  is correct.

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Copying of line segment involves 6 steps.

Steps to copy line segment are:

1) Draw a point that will serve as the new line segment's endpoint.

2) Open the compass width from the original line segment's beginning with the compass pin in that position.

3)Place the compass pin at the new line segment's plotted point using the above-mentioned step's adjusted compass width, and then draw an arc in the area where the new line segment is to be situated.

4) Decide where the other end of the new line will be on the arc.

5) Draw a line from the location chosen in the previous step to the point designated as the start of the new line segment.

6) The original line segment's length and the length of the line depicted above are equal.

Copying of line segment involves 6 steps.

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Q Which of the following is the first step when copying a line segment to construct a new line segment?

a. draw a line segment

b. use a straight edge to connect the point not on the line segment to a point in the arc

c. plot a point not on the original line segment

d. draw an arc​

One had all three,  had exactly two and 21 had life skill book according to given situation.

A mathematical problem is one that can be represented, examined, and potentially resolved using mathematical techniques.

Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?

Let X people have all three books then

three books=X

Math and Eng=7-X

Math and Life= 6-X

Eng and Life= 9-X

Then:

X+(7-X)+(6-X)+(9-X)+[22-(7-X)-(6-X)]+[21-(7-X)-(9-X)]+[25-(16-X)-(9-X)]=50

After simplification

X=1

(i). One had all three books

(ii) 6 had two

(iii). 21 had life skill book.

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Answer: x=-1    x=1/3

Step-by-step explanation:

f(x)=3x²+2x-1

[tex]3x^2+2x-1=0\\\\3x^2+(3x-x)-1=0\\\\(3x^2+3x)-x-1=0\\\\3x(x+1)-(x+1)=0\\\\(x+1)(3x-1)=0\\\\x+1=0\\\\x=-1\\\\3x-1=0\\\\3x=1[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=\frac{1}{3}[/tex]

Answer:0.625

Step-by-step explanation:

In lambda expressions and lambda (λ) phrases, the Greek letter lambda () is used to signify binding a variable in a function. You can have typed or untyped lambda calculus.

Functions can only be used in typed lambda calculus if they are able to accept the "type" of data that the input is. The Greek symbol lambda () is commonly used to represent wavelength, which is equal to the speed (v) of a wave train in a medium divided by its frequency (f): wavelength = v/f. The majority of the time, students struggle to understand calculus because they don't practice after class, can't concentrate in class, have gaps in their math knowledge, and believe it's a waste of time.

The actions you can do to make calculus simple are listed below. Calculus is the most difficult math topic, and very few students, whether in high school or elsewhere, succeed in it. In vector space, linear algebra is a subset of abstract algebra. Matrix technology makes things less abstract and easier to understand because it is more concrete. The mean number of events within a particular period of time or space is denoted by the Greek letter lambda () in the Poisson distribution formula. For instance, = 0.748 floods annually.

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Correct Question:

What does λ mean in calculus?

Answer:

1d=25m

30d=?

cross mutiply

30×25=750messages

Answer:

The equation is m = 25d

Ashley would send 750 text messages after 30 days.

Step-by-step explanation:

The equation is y = mx + b

We see that each day the number of text increase by 25, so our equation is

m = 25d

Now we ask how many text messages Ashley would send in 30 days. We need to put 30 in for d and solve it.

m = 25(30)

m = 750 text messages

So, Ashley would send 750 text messages in 30 days.

The solution to the system of equations is x = 3/2 and y = 7/4.

The given system of equations can be written as:

y = -x^2 + 4

y = 2x + 1

To solve this system of equations, we can use the substitution method. First, we'll substitute the expression for y in the second equation into the first equation. We can then solve the resulting equation for x.

In the first equation, [tex]y = -x^2 + 4[/tex] . Substituting this expression into the second equation, we get:

[tex]-x^2 + 4 = 2x + 1[/tex]

We can rearrange the terms on the left side of the equation to solve for x. To do this, we'll subtract 4 from both sides, then add x^2 to both sides:

-4 = 2x + 1 - 4

-4 + 4 = 2x + 1 - 4 + 4

0 = 2x - 3

Now, we'll divide both sides of the equation by 2 to solve for x:

0/2 = (2x - 3)/2

0 = x - 3/2

We can rearrange the terms on the right side of the equation to solve for x. To do this, we'll add 3/2 to both sides:

0 + 3/2 = x - 3/2 + 3/2

3/2 = x

Now that we have the value of x, we can substitute it into either equation to solve for y:

[tex]y = -x^2 + 4y = -(3/2)^2 + 4y = -(9/4) + 4[/tex]

y = 7/4

Therefore, the solution to the system of equations is x = 3/2 and y = 7/4.

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Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.

In the given question, we have to verify the linear approximation at (0, 0).

f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y

Let f(x, y) = √(y+cos^{2}x)

f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)

f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]

f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]

f(x, y) ≈ 1+0(x-0)(1/2)(y-0)

f(x, y) ≈ 1+1/2y

Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.

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The complete question is:

Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y

Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........

The quadratic equation [tex]2x^{2}+3x-5=0[/tex] has a discriminant of 49.

In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its classification or solution. If the discriminant is positive, the roots of a quadratic or cubic equation with real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots include a conjugate pair of complex roots.

For an equation, [tex]ax^{2}+bx+c=0[/tex]

Discriminant, D = [tex]b^{2}-4ac[/tex]

Given in question,

[tex]2x^{2}+3x-5=0[/tex]

a = 2

b = 3

c = -5

D = [tex]3^{2}[/tex] - 4(2)(-5)

  = 9 + 40

  = 49

Hence, the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] is 49.

Correct Question :

What is the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] ?

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The expanded form of a 3-term binomial is typically written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial is given by ax^2 + bx + c = a(x^2 + bx/a + c/a).

1. Take the coefficients of the binomial (which are the constants a, b and c)

2. Multiply the coefficient a with the remaining terms in the binomial (x^2 + bx + c).

3. Simplify the expression by multiplying the coefficient a with the terms (x^2 + bx/a + c/a).

4. The result is the expanded form of the 3-term binomial ax^2 + bx + c.

The expanded form of a 3-term binomial can be written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial can be obtained by multiplying the coefficient a with the remaining terms in the binomial (x^2 + bx + c) and simplifying the expression.

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Answer:

Just use Desmos

Step-by-step explanation:

The cost per kilometer for Emanuel's taxi ride is given as follows:

$9/4.

To obtain the cost per kilometer of the tax ride, we apply the proportion, dividing the total cost by the distance of the taxi ride.

From the text given in this problem, the parameters are given as follows:

Then the cost per kilometer for Emanuel's taxi ride is found applying the proportion as follows:

Cost per kilometer = 32/14.22 = 2.25.

We have that the fraction equivalent of .25 is given as follows:

1/4.

Thus the proper fraction that represents the cost is given as follows:

2 + 1/4 = 8/4 + 1/4 = $9/4.

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Answer:

The length of the line segment is

d = √(x₂ - x₁)² + (y₂ - y₁)²

Answer:

[tex]x=2+2\sqrt{ 26}[/tex]

[tex]x=2-2\sqrt{ 26}[/tex]

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_{10}(x^{2}-4x)=2[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 10^2=x^2-4x[/tex]

[tex]\implies 100=x^2-4x[/tex]

[tex]\implies x^2-4x=100[/tex]

Add the square of half the coefficient of the term in x to both sides of the equation:

[tex]\implies x^2-4x+\left(\dfrac{-4}{2}\right)^2=100+\left(\dfrac{-4}{2}\right)^2[/tex]

[tex]\implies x^2-4x+\left(-2\right)^2=100+\left(-2}\right)^2[/tex]

[tex]\implies x^2-4x+4=100+4[/tex]

[tex]\implies x^2-4x+4=104[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex]\implies (x-2)^2=104[/tex]

Square root both sides:

[tex]\implies x-2=\pm \sqrt{104}[/tex]

[tex]\implies x-2=\pm \sqrt{4 \cdot 26}[/tex]

[tex]\implies x-2=\pm \sqrt{4} \sqrt{ 26}[/tex]

[tex]\implies x-2=\pm 2\sqrt{ 26}[/tex]

Add 2 to both sides:

[tex]\implies x=2\pm 2\sqrt{ 26}[/tex]

Therefore, the solutions are:

By using a² + b² = c² this formula we can find the missing length of a triangle.

A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.

If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:

a² + b² = c²

a = √(c² - b²)

b = √(c² - a²)

c = √(a² + b²)

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Using the concept of limit, As the x tends to -infinity value, In the expression f/x, The answer is f/x tends to large(infinity) value with negative magnitude.

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals. A limit describes the value that a function approaches as its inputs approach a certain value. All calculus is based on the concept of a limit.

According to product law for limits, the limit of a product of functions is equal to the sum of the limits of each individual function. The limit of a quotient of functions is equal to the quotient of the limit of each function, according to the quotient law for limits.

as [tex]\lim_{x \to \infty} \frac{f}{x}[/tex]

=f/ -infinity

=- [infinitely large value]

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8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection.

It is a statistical summary of statistical variability or dispersion.

So, the sum of all the values:

8 + 9 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 34 = 200

A number of observations:

= 10

Formula: Mean = (sum of all observations)/(Total number of observations)

Now, calculate using the formula as follows:

Mean = (sum of all observations)/(Total number of observations)

Mean = (200 / 10)

Mean = 20

Now, we must determine how far the provided values are from the mean.

20 - 8 = 12

20 - 9 = 11

20 - 12 = 8

20 - 15 = 5

20 - 16 = 4

20 - 20 = 0

24 - 20 = 4

30 - 20 = 10

32 - 20 = 12

34 - 20 = 14

Formula:

Mean deviation = (sum of the distance of each value from mean) / (Total number of observations.)

Sum of each value's deviation from the mean = 12 + 11 + 8 + 5 + 4 + 0 + 4 + 10 + 12 + 14 = 80

Mean deviation = 80 / 10 = 8

Therefore, 8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.

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Complete question:
What is the mean deviation of the data:8,9,12,15,16,20,24,30,32,34?​

Answer:

55percent

Step-by-step explanation:

[tex]\frac{44}{80} =0.55\\0.55x100\\55[/tex]

To be a relation of a function for every value of x there must be a single value of y thus the given relation is not a function.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given table,

At x = 9

y = 9 and y = 3

Since at a single value of x there exist two values of y thus it will not be a function.

Hence "The provided relation is not a function since there must only be one value of y for a relationship to be considered a function.".

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Answer: 0

Step-by-step explanation:

The slope of a line that contains the points (13, -2) and (3, -2) would be 0, since the y-coordinate of both points is the same. The slope of a line is determined by the difference in the y-coordinates of the two points, divided by the difference in their x-coordinates. In this case, the difference in the y-coordinates is 0, so the slope is 0.