Solve the following system of equations and show all work. y = −x2 +4y = 2x + 1

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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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.

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:

55percent

Step-by-step explanation:

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

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?

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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-6.48 > -6.5

5.983 < 5.99

3.09 > 3.01

Hope it helps

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​

Answer:

The answer for the problem on the left is 70

The answer to the problem on the right is 120

Step-by-step explanation:

Left Problem:

The sum of the interior angles is 360

(n -2)180 is one formula to find the sum of the interior angles of a polygon.  n stands for the number of sides

(4-2)180

2(180

360

We know three of the angles we subtract them from 360 to find the missing angle

360-60-110-120 = 70

Right Problem:

We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180.  A straight line has an angle measurement of 180.

180-60 = 120

180 - 50 = 130

Now we just need to find x.  

The sum of the interior angles is

(n-2) 180

(5-2)180

3(180) = 540    Subtract what we know

540 -50 - 130 - 120 = 240

The x's have the same value so 2402 is 120 .

Each x is 120

The answer to the problem on the left is 70 and the answer to the problem on the right is 120.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, angles and relative position.

Left Problem:

The sum of the interior angles is 360.

(n -2)180 is one formula to find the sum of the interior angles of a polygon.  n stands for the number of sides

(4-2)180

2(180

360

We know three of the angles we subtract them from 360 to find the missing angle

360-60-110-120 = 70

Right Problem:

We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180.  A straight line has an angle measurement of 180.

180-60 = 120

180 - 50 = 130

The sum of the interior angles is

(n-2) 180

(5-2)180

3(180) = 540    Subtract what we know

2x =  540 -50 - 130 - 120 = 240

x = 240 / 2 = 120

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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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The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.

To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.

In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.

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The question is -

Which congruence criterion do you use in the following? Given: EB = BD, AE = CB, ∠ A = ∠ C = 90°.

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:0.625

Step-by-step explanation:

The factors are (x + 1)(x + 2)(x + 10)

The process of breaking down an entity—for instance, a number, a matrix, or a polynomial—into a product of another entity—or factors—that, when multiplied together, yield the original number, matrix, or other entity is referred to as factorization or factoring.

Given Equation x³ + 13x² + 32x + 20

so The value of x³ + 13x² + 32x + 20 is

x³ + x² + 12x² + 12x + 20x + 20

=x² (x+1) + 12x (x+1) + 20(x+1)

=(x + 1)(x² + 12x + 20)

=(x + 1)(x² + 10x + 2x + 20)

=(x + 1)[x(x + 10) + 2(x + 10)]

=(x + 1)(x + 2)(x + 10)

Hence the factors are (x + 1)(x + 2)(x + 10).

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The correct question is

Factorize x³ + 13x² + 32x + 20

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality.

The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

Here show an example for better understanding:

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

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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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y = -(5/3)x + 4 is slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

rewrite the equation of the given line in to slope-intercept form by solving for y

 3y + 5x = 6    

    3y = -5x + 6               (subtract 5x from both sides)

       y = -(5/3)x + 2           (divide both sides by 3)

Our line is parallel to this line, so it has the same slope, and a

y-intercept of 4, so we have...

 y = -(5/3)x + 4  

the equation ofa line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 1 and c = 3, hence

y = x + 3 ← is the equation of the line  

*slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

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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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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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Yes, △ ABC appears to be the same size and shape as △ XYZ by SAS similarity, and △ ABC can be mapped by translation and rotation, so option A is correct

What is triangle?

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Right triangles ABC and XYZ. ABC has a shorter leg equal to 5 and a hypotenuse equal to 13,

The triangles ABC and XYZ are similar by SAS similarity, as,

AC = XZ = 5,

AB = YZ = 13

∠ ACB = ∠ XZY

When you translate and then rotate triangle ABC, you will get triangle XYZ.

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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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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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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

Answer:

The length of the line segment is

d = √(x₂ - x₁)² + (y₂ - y₁)²

Answer:

145

Step-by-step explanation:

y = 5(25) + 20

y = 125 + 20

y = 145

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)=........

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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Answer:

Just use Desmos

Step-by-step explanation:

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:

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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