Use your answer from Part I to find the slope of a line going through each set of points. Then
describe the line as positive, negative, zero, or undefined. Show your work and explain your
answer.

A. (5, 7) and (-4,-2)

B. (1, 3) and (1, -10)

The quadratic solution of the linear system of equations y = x2 + 5x - 3 is y = (x+3)(x-1).

1. Rewrite the equation as y = x2 + 5x - 3

2. Factor the equation by grouping the terms: y = (x+3)(x-1).

3. Set each factor equal to 0 and solve for x: x+3 = 0 and x-1 = 0

4. Solve each equation: x = -3 and x = 1

5. Substitute the values of x into the original equation to find the corresponding values of y:

y = (-3+3)(-3-1) = (-3)(-4) = 12

y = (1+3)(1-1) = (4)(0) = 0

Therefore, the solution of the linear quadratic system of equations y = x2 + 5x - 3 is y = (x+3)(x-1).

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The slope ratio for a line that makes an angle of 30 with the positive direction of the x-axis is 1:√3

The slope of a line is nothing but the change of the line in the y-coordinate concerning the change in the x-axis. So the slope is simply nothing but a ratio of change in the y-axis to change in the x-axis which is also called slope ratio.

m = change in y / change in x

tan 30= 1/√3 = change in y / change in x

tan 30= 1: √3

So the ratio of an angle of 30-degree slope will be 1:√3

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The x-intercept is 19.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate; y₁ - y coordinate

m - slope

Given the equation as;

Y=10x/3+19

Then;

the slope m = 10/3

The intercept is 19.

Hence, the x  intercept is 19.

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The number of small candles (x) and large candles (y) that were

sold 16 large candles and 12 small candles were sold.

number of small candles (x)

large candles (y)

4x+6y=144  ....equation 1.

x+y=28  ....equation 2.

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A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered.

A number line is a pictorial representation of numbers on a straight line. It's a reference for comparing and ordering numbers.

Steps to add/subtract on a number line:

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Answer:

3,5,7,9

Step-by-step explanation:

Let x be an odd integer

given that, consider four consecutive odd integers, which are

x , (x +2), (x+4), (x+6)

Now we have to determine these odd integers such that five times the second is equal to one more than eight times the smaller

5(x+2) = 1 + 8x

5x + 10 = 1 + 8x

10 - 1 = 8x - 5x

9 = 3x

x = 3

1 you are offered a gamble on the toss of a coin. if the coin shows tails, you lose $100. if the coin shows heads, you win $150. Yes one can  accept it.

As per the given data:

If you toss the coin.

Coin shows tails [tex]$\rightarrow$[/tex] lose $ 100

Coin shows heads [tex]$\rightarrow$[/tex] win $ 150

We would consider expected gain for us in each scenario.

Since, the probability of head is,

[tex]P(H) = \frac{1}{2}[/tex]

The probability of Tail is,

[tex]P(T)=\frac{1}{2}[/tex]

Therefore, expected gain [tex]$=150 \times \frac{1}{2}+(-100) \times \frac{1}{2}$$$[/tex]

= 75 - 50

= $ 25

Since, gain is positive number of 25 .

We can say on an average we can gain some Profit.

Hence one would accept the offer.

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Trigonometry Examples Popular Issue Trigonometry Solve the Triangle tri {} {30} {} {60} {} {90} Side Angle is given as b = c = a = A = 30 B = 60 C = 90 Side Angle b = c = a = A = 30 B = 60 C = 90

30 60 90 triangle sides If we know the shorter leg length a, we can find out that: b = a√3 c = 2a If the lasting leg length b is the one parameter given, then:

a = b√3/3 c = 2b√3/3 For hypotenuse c known, the legs formulas Now as follows: a = c/2 b = c√3/2 Or simply type your given values and the 30 60 90 triangle calculator will do the rest!

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Knowing merely angle-angle-angle (AAA) does not work, because it can result in triangles that are similar but not congruent.

A set of triangles must have equal sides and angles in order for them to be congruent. The sides of the triangles may or may not be equal in the case of a triangle with all of the corresponding angles equal, or the AAA condition.

Only if the two triangles are similar would the congruence be true for two triangles with identical respective angles. Thus, we are unable to utilize AAA to establish the congruence of two triangles.

A set of triangles must have equal sides and angles in order for them to be congruent. The sides of the triangles may or may not be equal in the case of a triangle with all of the corresponding angles equal, or the AAA condition. Only if the two triangles are similar would the congruence be true for two triangles with identical respective angles.

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The AAA (angle-angle-angle) similarity theorem can be used to express it as follows: two triangles have equal corresponding angles if and only if their corresponding sides are proportionate.

The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.

Proof:

Consider two triangles ABC and DEF, such that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F as shown in the figure.

Now, cut DP= AB and DQ= AC and join PQ. Hence, we can say that a triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ, which gives ∠B = ∠P = ∠E and also, the line PQ is parallel to EF.

Therefore, by using the basic proportionality theorem, we can write

DP/PE = DQ/QF.

(i.e) AB/DE = AC/DF. …(1)

Similarly,

AB/DE = BC/EF …(2)

From (1) and (2), we can write:

AB/DE = BC/EF = AC/DF.

Therefore, the two triangles ABC and DEF are similar.

Hence, AAA(Angle-angle-angle) is proved.

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Your instrument's pads, finish, springs, and other metal components can all be damaged if you let dirt, moisture, and other debris build up inside of it. It can also corrode strings and other metal components. These faults might cause expensive long-term consequences and are not easily fixed.

Clean the body, head stock, tuners, and fret board using a damp cloth dipped in vinegar, making careful to follow up with a dry towel. Keep in mind that too much moisture ruins wooden instruments. To keep your case odor-free, wait 30 minutes before storing it.

Due to the fact that these solutions often offer the best material compatibility profile and effective filth removal, neutral or detergent solutions with a pH close to neutral are frequently employed for instrument cleaning. Sometimes neutral pH solutions with proteases added to them help remove organic debris.

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Answer: (16 + -4)

Step-by-step explanation:

You have to swap the negative numbers with positives and positive numbers for negative.

The ideal way to find the intercepts of an equation with the "x" and "y" axes is to evaluate both values when the image is 0, as described below:

First let's define equation

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

Now that we know what an equation is and its structure, let's explain it with an example.

Let the equation

2y = 4x + 2, determine its intersections with the axes "x" and "y".

First, we clear:

y = (4x + 2)/2

y = 2x + 1

0 = 2x + 1

2x = -1

x = -1/2

y = 2(0) + 1

y = 1

As we can see, to find the intercepts, we only have to evaluate the equation when y = 0 and when x = 0.

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Answer:

Below

Step-by-step explanation:

3 * 2/4  =

3/1   * 1/2

(3*1) / (2*1) =  3/2 = 1  1/2

The SSS postulate states that "if all the three sides of a triangle are equal to the sides of another triangle then the given triangles are congruent" is proved.

Assume that the lengths of all three sides of the triangles ABC and DEF are known.

The diagram is attached at the end of the solution.

Pick a side from triangle ABC. Find the side with the same length as triangle DEF. For example, we pick [tex]\overline{AB}[/tex] and find that [tex]\overline{D E}[/tex] is equivalent in length to [tex]\overline{AB}[/tex].

Next, write a proof statement about our conclusion and the reason for it. For the reason clause, we state that the two sides are given, since no other work was involved besides reading the lengths of the sides of the diagram. The three dots in the upside-down triangle means "because".

[tex]$$\overline{AB} \cong \overline{DE}$$[/tex]

Choose the other side from triangle ABC. Find the side with the same length as triangle DEF.

We choose the second side [tex]\overline {BC}[/tex] and find from the diagram that [tex]\overline{EF}[/tex] has the same length. The proof statement for this step is:

[tex]$$\overline{BC} \cong \overline{EF}$$[/tex].

Step 3: Pick the last side from triangle ABC.  From triangle DEF, identify the side that is the same length. [tex]\overline{AC}[/tex] and [tex]\overline{DF}[/tex] have the same length. We add another proof statement.

[tex]$$\overline{AC} \cong \overline{DF}$$[/tex]

Step 4: We've discovered that the two triangles have three pairs of congruent sides. That means, by the SSS congruence theorem, triangles ABC and DEF are congruent.

Add a proof statement for this conclusion. The list of the proof statements looks like this.

[tex]$\overline{AB} \cong \overline{DE}[/tex] because [tex]\overline{AB}$[/tex] and [tex]$\overline{DE}$[/tex] are given.

[tex]$\overline{BC} \cong \overline{EF}[/tex] because [tex]$\overline{BC}$[/tex] and [tex]$\overline{EF}$[/tex] are given.

[tex]$\overline{AC} \cong \overline{DF}[/tex] because [tex]$\overline{AC}$[/tex] and [tex]$\overline{DF}$[/tex] are given.

[tex]$\triangle A B C \cong \triangle D E F$[/tex] by SSS congruence theorem.

We have proved that the SSS congruence theorem holds for triangles ABC and DEF.

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The product of a fraction and its reciprocal is 1

In mathematics, we know that the fraction that is obtained by swapping or interchanging the numerator and the denominator with each other is known as the Reciprocal of the given fraction.

For example, if we have the fraction 3/5, it is safe to say that the reciprocal of this fraction will be 5/3.

Now, this means that 3/5 * 5/3 = 1.

Thus, we can say that the product of a fraction and its' reciprocal is the same as 1.

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Complete question is;

The _____ of a fraction and its reciprocal is 1. (a) sum (b) difference (c) product (d) quotient​

Answer:

⭐Congruent is another word for "same"

The formula of r in term ∅ of is [tex]\frac{∅}{360} * 2\pi r[/tex]

What is circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

What is arc in circle?

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. 

The whole circle of 360 makes arc length of 2πr.

Thus angle of θ will make a length = [tex]\frac{∅}{360} * 2\pi r[/tex].

The formula of r in term ∅ of is [tex]\frac{∅}{360} * 2\pi r[/tex]

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In a grouped data,

it is not possible to find the median for the given observation by looking at the cumulative frequencies.

The middle value of the given data will be in some class interval. So, it is necessary to find the value inside the class interval that divides the whole distribution into two halves.

In this scenario, we have to find the median class.

To find the median class, we have to find the cumulative frequencies of all the classes and n/2.

After that, locate the class whose cumulative frequency is greater than (nearest to) n/2. The class is called the median class.

After finding the median class, use the below formula to find the median value.

[tex]Median = l +(\frac{\frac{n}{2}- cf}{f} )*h[/tex]

Where

l is the lower limit of the median class

n is the number of observations

f is the frequency of median class

h is the class size

cf is the cumulative frequency of class preceding the median class.

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The entire numbers, which consist of positive integer numbers and zero, are the number without any fractions. It is denoted by the letter "W," and the set of numbers is "0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...." So, the first five whole numbers are 0 through 4, respectively.

An integer is either zero, a positive natural number, or a negative integer denoted by a minus sign. The inverse additive of the matching positive integers is represented by the negative numbers. The blackboard bold  Z boldface Z is a common way to represent the set of integers in mathematical notation.

Whole numbers refer to the entire set of natural numbers, including "0." Here are some examples: 0, 11, 25, 36, 999, 1200, etc.

The entire numbers, which consist of positive integer numbers and zero, are the number without any fractions.

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The features of the sinusoidal function are given as follows:

The general definition of the sine function in this problem is given as follows:

y = asin(b(x+c))+d.

The parameters of the general function are explained as follows:

The equation in this problem is given as follows:

y=−1/2sin(3πx−5)−2​.

From the vertical shift, the midline is given as follows:

y = -2.

The period is calculated as follows:

p = 2π/3π = 2/3.

The phase shift and the amplitude are given, respectively, by:

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Answer:

9. 33% Increase

10. 14 games

11. $3.6

12. $10.80

13. 630

14. 6.3

The limiting speed of particle can be obtained as 12 cm/sec.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

The mass of particle is given as 6 grams.

Suppose the limiting speed be x cm/s.

As per the given question, the following equation can be formed as below,

6 × 980 = 490x

⇒ x = (6 × 980)/490

⇒ x = 12

Hence, the value of the limiting speed is 12 cm/sec.

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Answer:

Soft drink: $3

Burger: $4

Step-by-step explanation:

We have equations

4x + 6y = 34

4x + 2y = 22

Multiply the second equation by -1

4x + 6y = 34

-4x + -2y = -22

4y = 12

y = $3

Now put 3 back in to solve for burger

4x + 6(3) = 34

4x +18 =34

4x = 16

x = $4

The real roots of the quadratic equations are

x = -6 and x = 1

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 5x - 6 = 0   be equation (1)

On simplifying the equation , we get

x² - 1x + 6x - 6 = 0

Taking the common factors in the equation , we get

x ( x - 1 ) + 6 ( x - 1 ) = 0

On factorizing the equation , we get

( x + 6 ) ( x - 1 ) = 0

So , we have two real solutions to the equation ,

( x + 6 ) = 0  and  ( x - 1 ) = 0

So ,

when ( x + 6 ) = 0

Subtracting 6 on both sides of the equation , we get

x = -6

And ,

when ( x - 1 ) = 0

Adding 1 on both sides of the equation , we get

x = 1

Therefore , the values of x are -6 and 1

Hence , the real roots of the quadratic equations are -6 and 1

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Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

[tex]\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\[/tex]

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The salary of an employee with 6 years of experience, based on the line of best fit, is B. $ 58,587

First, find the slope of the line of best fit as:

= ( Y2 - Y1) / ( X2 - X1 )

= ( 57, 126 - 52, 000 ) / ( 5 - 0 )

= 1, 025.2

The y - intercept can be found by substituting the values of y, x, and the slope into the linear function of y = mx + c. The point to be used is (5, 57, 126) :

57, 126 = 1, 025.2 ( 5 ) + c

c = 52, 000

The line of best fit is:

y = 1, 025.2x + 52, 000

If an employee with 6 years experience, their salary would be:

= 1, 025.2x + 52, 000

= 1, 025.2 (6 ) + 52, 000

= $ 58,587

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For the given expression 3x² + 5x = - 4, the value of the discriminant is equal to -23.

As given in the question,

Given expression is written as :

3x² + 5x = - 4

⇒ 3x² + 5x + 4 = 0

General formula of the discriminant for the given quadratic function

ax² + bx + c = 0 is written as :

Discriminant is written as  'D'

D = b² - 4ac

Here b = 5 , a = 3 and c = 4

Substitute the value in the discriminant formula we have,

D = 5² - 4(3)(4)

⇒D = 25 - 48

⇒ D = -23

Therefore , the value of the discriminant for the given quadratic expression 3x² + 5x + 4 = 0 is equal to -23.

The above question is incomplete ,the complete question is :

What is the value of discriminant 3x² + 5x = -4 ?

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Sometimes the triangle's circumcenter is outside of it. In actuality, it may lie outside the triangle, as in the case of an acute triangle, or it may land at the midway of the hypotenuse of a right triangle.

the location that is equally spaced from each of a triangle's three vertices and where the three perpendicular bisectors of its sides meet.

The circumcenter of a triangle is found at the junction of all sides' perpendicular bisectors, or lines that are at right angles to each side's midpoint. The triangle's perpendicular bisectors are shown to be contemporaneous by this (i.e. meeting at one point).

Sometimes the triangle's circumcenter is outside of it. In actuality, it may lie outside the triangle, as in the case of an acute triangle, or it may land at the midway of the hypotenuse of a right triangle.

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