How many solutions can 2 linear equations have?

On solving the provided question we can say that, - the factors of the given equations [tex]x^2 +6x - 16\\[/tex] are - x= -4 and x = 2

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

[tex]x^2 +6x - 16\\[/tex]

(x+4)(x-2)

x= -4 and x = 2

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(3,2) is not a solution because it does not satisfy the equation and the line on the graph does not pass through it.

How to find the solution to an equation?

We perform the same operations on both sides to ensure that the equality of both expressions is maintained.

Solving equations generally entails determining the values of the variables used in the equation for which the equation under consideration is true.

Given that:

The graph of the equation is  y = -3/4x + 3.

To find if the point (3, 2) a solution to the equation.

substitute the point to to satisfy the equation;

y = -3/4x + 3

y = -3/4(3) + 3

y = -9 / 4 + 3

y = 3/3 = 1

Hence, (3,2) isn’t a solution because it doesn't satisfy the equation  and also the line on the graph doesn’t go through it .

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The ordered pairs of the data that should be used to plot the points on the scatter plot are (18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), and (34, 3).

The appropriate set of axes to make a scatter plot of the data is a horizontal x-axis and a vertical y-axis. The horizontal x-axis would represent the age of the people while the vertical y-axis would represent the number of CDs bought. The ordered pairs of the data that should be used to plot the points on the scatter plot are (18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), and (34, 3).

A scatter plot is a graph that is used to represent the relationship between two variables. It is a graphical representation of data that shows the relationship between two variables by plotting a set of ordered pairs on a coordinate plane. The ordered pairs of the data are represented by a mark, usually a dot, on the graph. The horizontal x-axis is usually used to represent the independent variable and the vertical y-axis is used to represent the dependent variable. In this case, the x-axis is the age of the people and the y-axis is the number of CDs purchased.

A scatter plot can be used to find patterns in data and to identify relationships between two variables. By plotting the ordered pairs of the data on the coordinate plane, the scatter plot will show any correlations or trends that are present in the data. For example, if there is a positive correlation between age and the number of CDs purchased, the scatter plot will show a line of points that goes up and to the right. On the other hand, if there is a negative correlation between the two variables, the scatter plot will show a line of points that goes down and to the right. By plotting the data points on a scatter plot, it is possible to identify any patterns or trends that are present in the data.

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The sum of the roots of 3x² 10x 8 0 is -2.

The given equation, 3x² 10x 8 0, is a quadratic equation with two roots. To find the sum of the roots of this equation, we must first solve the equation. To do this, we use the quadratic formula, which states that the roots of the equation are x = [-b ± √(b² - 4ac)]/2a. Here, a = 3, b = 10 and c = 8.

Therefore, the roots of the equation are x = [-10 ± √(10² - 4(3)(8))]/2(3). This simplifies to x = [-10 ± √(-4)]/6. Since the square root of a negative number is not a real number, the roots of the equation are not real numbers, and the sum of the roots is undefined. Therefore, the sum of the roots of 3x² 10x 8 0 is -2.

x = [-10 ± √(10² - 4(3)(8))]/2(3)

x = [-10 ± √(-4)]/6

x = [-10 ± √(-4)]/6

Since the square root of a negative number is not a real number, the roots of the equation are not real numbers, and the sum of the roots is undefined.

Therefore, the sum of the roots of 3x² 10x 8 0 is -2.

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A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. So , x + 4x 11 cannot be solved as a quadratic equation.

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The expression x + 4x 11 does not fit this form, and therefore is not a quadratic equation. In the equation, x is an unknown variable, and 4x 11 is a linear expression. Since this expression does not contain the variable squared, it is not a quadratic equation.

x + 4x 11 cannot be solved as a quadratic equation.

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The fifth root of unity is given by  Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).

As given in the question,

Using the Euler Identity ,

e^(πi) = -1

Calculate the nth root of Unity so that it can be used to calculate for any value of n:

Zⁿ = 1

⇒Z = (1)^(1/n)

Apply Euler's Formula we get,

Z = cos (2kπ + 0)/n + i sin(2kπ + 0 )/n

⇒Z = cos ( 2kπ / n) + isin( 2kπ / n)

Using Euler' identity  we can write this as :

Z = e^(2kπ/n)

For k = 0 , 1 , 2 , 3..... (n-1)

Now substitute n = 5 to get the value of 5th root of unity we have

Z = e^(2kπ/5)

When k = 0 , 1, 2, 3, 4

k = 0 ⇒ Z = 1

k= 1 ⇒ Z = e^(2πi/5)

k = 2 ⇒ Z = e^(4πi/5)

k= 3 ⇒ Z = e^(-2πi/5)

k = 4 ⇒ Z = e^(-4πi/5)

Therefore, the value of 5th root of unity is equal to Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).

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Answer:

To solve this problem, we can first use the area of the flower border to calculate the perimeter of the flower border. Since the flower border is 4 meters wide and has an area of 264 square meters, we know that it has a perimeter of 264 / 4 = 66 meters.

Next, we can use the perimeter of the flower border to calculate the dimensions of the lawn. Since the total perimeter of the lawn and flower border is 66 meters and the width of the flower border is 4 meters, we know that the length and width of the lawn must be 31 meters and 5 meters, respectively.

Finally, we can use the dimensions of the lawn to calculate the radius of the sprinkler. Since the lawn is a rectangle with a length of 31 meters and a width of 5 meters, we know that the center of the lawn is located 15.5 meters from each of the longer sides and 2.5 meters from each of the shorter sides. Therefore, the minimum radius of the sprinkler must be 15.5 meters in order to reach the entire flower border.

Rounded to the nearest tenth of a meter, the minimum spraying radius necessary is 15.5 meters.

There are 35% sixth-graders at Kendrick's school who picked the museum.

Percentage is a part of the whole number.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.

1 %= 1/100.

Given that,

Total number of sixth-graders at Kendrick's school = 56,

Also,

The number of s sixth-graders that picked the museum = 14.

The percentage of the sixth-graders that picked the museum

= (14/56) x 100

= (1/4) x 100

= 25 %

25 percent of the sixth-graders picked the museum.

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The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal. Only if two triangles with the same respective angles are identical would the congruence stay true.

Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you're trying to determine if two triangles are congruent,

there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them. If the three angles (AAA) between two triangles are congruent, that does not imply that the triangles must be congruent. They have the same shape (and can be considered comparable), but we don't know how big they are.

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Answer:

sin2theta

= (4root2)/9

cos2theta = -7/9

tan2theta

= (4root2)/-7

Step-by-step explanation:

see image.

Draw a picture to help see your angles and the triangle trigonometry. Use Pythagorean theorem and triangle trig to find sintheta and tantheta. Use Double Angle Formulas to find the answers to the question. See image.

The value of the sin 2θ, cos 2θ, and tan 2θ will be - 0.628, -0.778, and 0.808, respectively.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The trigonometric equation is given below.

cos θ = 1/3

cos θ = 0.3333

θ = 289.47°

The value of the sine of angle 2θ will be given as,

sin 2θ = sin (2 × 289.47°)

sin 2θ = sin 578.94°

sin 2θ = -0.628

The value of the cosine of angle 2θ will be given as,

cos 2θ = cos (2 × 289.47°)

cos 2θ = cos 578.94°

cos 2θ = -0.778

The value of the tangent of angle 2θ will be given as,

tan 2θ = tan (2 × 289.47°)

tan 2θ = tan 578.94°

tan 2θ = 0.808

The value of the sin 2θ, cos 2θ, and tan 2θ will be - 0.628, -0.778, and 0.808, respectively.

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Answer:

Step-by-step explanation:

X = ?

y = ?

The big triangle ABC is a right triangle,  we can use Pythagoras theorem to find side y,  then use SOH CAH TOA to find angles   :)

also, there is a special rule for a triangle set up like this one

2CD = BD

for this triangle then,

2CD = 9

CD = 4.5

X = 13.5

now use Pythagoras to find y

[tex]13.5^{2}[/tex] = [tex]6^{2}[/tex] + [tex]y^{2}[/tex]

182.25 -36 = [tex]y^{2}[/tex]

[tex]\sqrt{146.25}[/tex] = y

12.093386 = y

now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find  angle B or C, i'll find C

CAH  =  Cos(C) = Adj / Hyp

Cos(C) = 6 / 13.5

arcCos(Cos(C)) = arcCos(6/13.5)

C = 63.6122°

now find B

180 = 90 + 63.6122 + B

26.3877° = B

got it?

Answer:

Step-by-step explanation:

Hi

Answer:

The mean price for this sample is $1,385.00

Step-by-step explanation:

⭐What is the "mean" of a sample?

To find the mean for this data, we need to divide the sum of the prices for the computers bought by the total number of computers bought.

Sum of the prices for the computers:

[tex]14(1400)+12(1050)+5(2150)[/tex]

[tex]= 19,600 + 12,600 + 10,750[/tex]

[tex]= 42,950[/tex]

Total number of computers bought:

[tex]14+12+5[/tex]

[tex]= 31[/tex]

Mean price:

[tex]\frac{42,950}{31}[/tex]

[tex]= 1,385.00[/tex]

Therefore , the solution of the problem of equation is you can calculate maximum value  of a equation by max = c - (b2 / 4a).

What is the equation?

Equations are created by connecting two expressions with the same sign to form a mathematical statement. An example is the equation

3x - 5 = 17. We may ascertain that the variable x has a value of 4 by resolving this equation.

According to the given question:

You can use the formula max = c - (b2 / 4a) to determine the maximum value if you are given the formula y = ax2 + bx + c.

The greatest value is k in the equation y = a(x-h)2 + k when the a component is negative.

Therefore , the solution of the problem is you can calculate maximum value is by max = c - (b2 / 4a).

Complete question:

How do you calculate maximum value of a equation?

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Answer:

To solve the equation 5x - 4y = -12, we can first get all of the terms containing x on one side of the equation and all of the terms containing y on the other side. To do this, we need to add 4y to both sides of the equation. This gives us 5x = -12 + 4y. Then, we can divide both sides of the equation by 5 to get x = (-12 + 4y)/5. This is the value of x that makes the equation true.

Step-by-step explanation:

Answer: I= 3÷y-5x÷12

solve for y

​ Step-by-step explanation: 5x−4y=−12I

Swap sides so that all variable terms are on the left-hand side.

−12I=5x−4y

Divide both sides by −12.

-12I/-12= 5x−4y/-12

Dividing by −12 undoes the multiplication by −12.

I=-12I/-12= 5x−4y/-12

Divide 5x−4y by −12

I=3÷y-5x÷12

​

The probability of 2 people insists on sitting side by side is 2/7. In the next, the probability of 2 people insists on sitting side by side is 2/5

The possibility of occurring a particular events is called probability.

it is expressed in ratio of two data. The probability has no unit to measure.

Number of students =7, among them 2 are insists on sitting side by side

now probability to sit in such a way = 2/7

again, 2 students will never sit side by side so the number became 5.

probability to sit side by side = 2/5

hence, the result is 2/7 and 2/5

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The arrow diagram is

2 3 5

| | |

v v v

2 3 5

To prove that R is a function, we must show that "a R b" exists for each element an in X. R is a function since the only element b in X that fulfills the relation is a.

The range of R is X = {2, 3, 5}.

Generally, The relation R on X is defined as "a R b" if and only if "a = b" for all a,b in X. This means that for any element a in X, the only element b in X that satisfies the relation is a itself. We can represent this relation using an arrow diagram as follows:

2 3 5

| | |

v v v

2 3 5

To show that R is a function, we need to demonstrate that for each element a in X, there is exactly one element b in X such that "a R b". In this case, we have already shown that the only element b in X that satisfies the relation is a itself, so R is a function.

The range of the function R is the set of all possible values of b for which "a R b" is true. In this case, the range of R is the set X itself, because for any element a in X, the only element b in X that satisfies the relation is a itself. Therefore, the range of R is X = {2, 3, 5}.

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There is a 4.5% (or 0.045) probability that the maximum safe weight will be surpassed.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.

Probability and odds are two distinct ideas.

Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

So, we know that;
Average u = 1.8 tons

r = 0.5 for the standard deviation

n = 35 data points

68 tons or more would be the combined weight of the 35 automobiles. Each car's average weight should be greater than:
X = 68/35 = 1.943

After that, we can utilize that to calculate the z value.

Z = (X - u)/(r/√n)

Z = (1.943 - 1.8)/(0.5/√35)

Z = 1.692

We must determine the p-value at Z > 1.692 in order to evaluate the likelihood:

P(Z > 1.692) = 0.0453

Therefore, there is a 4.5% (or 0.045) probability that the maximum safe weight will be surpassed.

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Answer:

a=b=0

Step-by-step explanation:

y=(ax)/b so now plug in the points

first 0=6a/b

next 2=3a/b

0=6a

2b=3a

a,b =0

You probably put the wrong problem but this is what I got.

The coefficient of the variable x  in the expression 2-5x-4+8 is -5

Given that,

The expression is 2-5x-4+8 which can be simplified as -5x+6

To find : The coefficient of the variable x in the expression

The coefficient of x in 2-5x-4+8  is -5

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

Coefficient is the number that is beside the variable in the equation.

As we can see that the term that is in multiplication with x is -5.

Hence, the coefficient of x in the equation  is -5.

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Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.

Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

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A word expression example is "as busy as a bee." This phrase is used to describe someone who is very busy and active.

The phrase “as busy as a bee” is often used to describe someone who is very active and busy. This phrase is a testament to the hard work that bees have to do every day in order to ensure the survival of their hive. Similarly, people who live an active lifestyle can reap the same benefits of a hard-working bee. From physical health benefits to improved mental health, living an active lifestyle can have a profound impact on one’s overall well-being.

When it comes to physical health, engaging in regular physical activity can reduce the risk of chronic diseases, such as heart disease, stroke, and diabetes. Additionally, regular physical activity can help to improve physical fitness and boost energy levels. Not only does this make it easier for individuals to perform everyday tasks, but it can also help to improve one’s mood and reduce feelings of stress and anxiety. In addition to physical health benefits, an active lifestyle can also promote improved mental health. Exercise can help to reduce symptoms of depression, as well as improve one’s self-esteem and overall sense of well-being.

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Answer:

90 degrees

Step-by-step explanation:

the centre angle of the triangle is 180°.
ABC is its circumference angle, that is half the centre one

The resource-constrained schedule has a duration of 24 and a duration of 17 with 2 critical schedules.

Resource-constrained project scheduling entails the planning of project operations that are subject to priority and resource limitations in order to best achieve the objective(s). The range of problems kinds is extensive in this field.

Given,  reinterpreting the resource demands over time for a left-justified schedule assuming you have five people available. For  Map, the earliest start times for each activity to the resource demands over time

ACT         activity ES EF LS LF Slack

1->2  a 0 3 0 3 0

1->4         b 0 3 10 13 10

2->3 c 3 5 3 5 0

2->5 d 3 8 3 8 0

5->8 e 8 15 8 15 0

3->6 f 5 9 5 9 0

6->9 g 9 11 9 11 0

4->10 h 3 5 13 15 10

10->12 I 5 7 15 17 10

8->12 j 15 17 15 17 0

9->12 k 11 17 15 17 0

The resource-constrained schedule has a duration of 24  

day    1 2 3 4 5 6 7      8          9   10 11 12 13

activity a,b a,b a,b c,d c,d (d,f,h)(d,f,h) d,f f, I e, I e e e

resources 5 5 5 4 4 5 5 3 4 4 3 3 3 3    

day    14   15     16 17 18 19 20 21 22 23 24

activity e e     e j,g j,g k k k k k k

resources 3 3 3 5 5 3 3 3 3 3 3

There are 2 critical schedules

first - (1-2)-->(2-5)-->(5-8)-->(8-12)

second - (1-3)-->(3-6)-->(6-9)-->(9-12) with duration 17.

Therefore, The two important schedules in the resource-constrained schedule each have a duration of 24 and 17, respectively.

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Since the leading coefficient can be any real number, The characteristic of the leading coefficient are the characteristic of a real number.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

The characteristics of the leading coefficient are:

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Answer: 10 hours

Step-by-step explanation:

If you are using 1 gallon of gas per hour and have 10 gallons of gas you subtract 1 gallon for every hour you use the car.

Here, the value of x = 20, x² = 400 and x³ = 8000.

What is Factorization ?

The breaking or breakdown of one entity into a product of another entity, or factors, which when multiplied together yield the original number, is known as factorization or factoring in mathematics.

We've   x³ = 8000           ...............equation 1

we can factor it as follows :

8000 = 2×2×2×10×10×10

8000 = 2³ × 10³

8000 = 20³  .............................equation 2

Now, By comparing equation 1 and 2,

We get, x = 20.

So, x² = 20 × 20 = 400.

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The end behavior of the graph is that it tends towards negative infinity as x approaches negative infinity, and tends towards positive infinity as x approaches positive infinity.

The end behavior of the graph of f(x) = x5 - 8x4 + 16x3 can be determined by looking at the leading term of the polynomial. The leading term of the polynomial is x5, which is positive for positive values of x and negative for negative values of x. Therefore, as x approaches negative infinity, the graph of f(x) will tend towards negative infinity, and as x approaches positive infinity, the graph of f(x) will tend towards positive infinity. To understand this further, consider what happens when x is very large, either positive or negative. As the absolute value of x increases, the leading term of the polynomial, x5, will have an increasingly large influence on the value of the polynomial, and any other terms will become insignificant. Therefore, for very large values of x, the graph of f(x) will almost entirely reflect the behavior of the leading term, which is to approach negative infinity for negative values of x and positive infinity for positive values of x.

f(x) = x5 - 8x4 + 16x3

When x is very large, either positive or negative:

When x is very large and positive:

f(x) ≈ x5

f(x) → ∞

When x is very large and negative:

f(x) ≈ -x5

f(x) → -∞

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