what is the solution of the linear-quadratic system of equations y=x^2+2x-3 y=2x+1

Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

Given,

In the question;

The equation is:

g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]

To find the is this the graph of g(x) or h(x).

Graph is given in the figure.

Now, According to the question;

g(x) = [tex]-x^{2} (x -2)[/tex]        and      h(x) = [tex]x^{2} (x -2)[/tex]

g(x) = 0                                    h(x) = 0

[tex]-x^{2} (x -2) = 0[/tex]                         [tex]x^{2} (x -2)[/tex] = 0

x = 0, 2                                    x = 0, 2

If we put x = 1 then,

g(1) = [tex]-(-1)^2(1-2)[/tex]     and   h(1) = [tex](1)^2(1-2)[/tex]

g(1)  =  -1 (-1)                          h(1) = 1(-1)

g(1)   = 1                                 h(1) = -1

But as shown in graph, graph take positive value at x = 1

∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]

Hence, Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

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The slope of the side connecting (0,−2) and (-2, 3) is: -5/2.

The slope of the side connecting (6, 0) and (4, 5) is: -5/2.

The slope (m) of a side connecting two points with given coordinates can be calculated using the slope formula shown below:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Slope of the side connecting (0,−2) and (-2, 3):

Slope (m) = change in y / change in x = (3 - (-2)) / (-2 - 0)

m = 5/-2

Slope (m) = -5/2.

Slope of the side connecting (6, 0) and (4, 5):

Slope (m) = change in y / change in x = (5 - 0) / (4 - 6)

m = 5/-2

Slope (m) = -5/2.

Therefore, the slope of both sides are the same, which is: -5/2.

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Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.

In order for us to find out the total possible combinations, we will use the formula as:

Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons

We are given that;

Number of possible chairpersons = 16

Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)

Thus, we can say that;

Total possible combinations = 16 * 15

Total possible combinations = 240 combinations

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From the graph of the given function , the value of f(1) = -1.

As given in the question,

From the graph of the given function,

Two coordinates from the graph are as follow:

( x₁ , y₁) = (1, -1)

( x₂ , y₂ ) = ( 0, -3 )

Equation of the line representing the function is given by:

(y - y₁) /(x-x₁) = ( y₂ -y₁)/ (x₂ -x₁)

⇒(y +1)/ (x-1) = (-3 +1)/ (0-1)

⇒ (y +1)/ (x-1) = 2

⇒y +1 = 2x -2

⇒ y = 2x -3

To get the value of x we have,

  y = f(x)

⇒f(x) = 2x -3

⇒f(1) = 2(1) -3

⇒f(1) = -1

Therefore, from the graph of the given function , the value of f(1) = -1.

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The graph of the linear equation for question 12 can be seen in the image at the end of the answer.

If we have a linear equation with a slope m and a point (h, k=, the point-slope form of that linear equation is:

y = m*(x - h) + k

Here the slope is m = -7/4 and the point is (2, -6)

Then the linear equation is:

y = (-7/4)*(x - 2) - 6

To graph the linear equation we need two points on it, and we already know one, so we need to find the other.

To do so we can evaluate in some value of x.

If we use x = -2 we will get:

y = (-7/4)*(-2 - 2) - 6

y = (-7/4)*(-4) - 6

y = 7 - 6 = 1

So we also have the point (-2, 1)

Now we just need to graph the two given points and connect them with a line.

Below you can see the graph.

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The required percentage of height of 34 and 54 inches are 85% and 135%.

Given that,
The percentage of the height of 34 inches and 54 inches against the height of 40 inches is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

a,
percentage = 34/40 × 100%
Percentage = 85%

b,
percentage = 54/40 × 100%
Percentage = 135%

Thus, the required percentages of height of 34 and 54 inches are 85% and 135%.

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The slope intercept form equation of the straight line is y = -1/2x + 6

Slope intercept form

Slope intercept form of the equation used to calculate the equation of a straight line by using the slope and intercept value.

And the general form of slope intercept equation is

y = mx + c

where

m refers the slope

c refers the y - intercept

Given,

Here we have the graph of straight line.

Through the given graph we have to identify the equation of slope intercept form.

In order to find the slope intercept form equation we need two values they are slope and the y intercept.

So, to find these two values, we need two points,

So we have selected the points from the given graph. They are (2,5) and (4,4).

Now we have to use the slope formula to find the value of the slope,

m = (4 - 5) / (4 - 2)

m = -1/2

Now, we have to use the slope and one of the point (4,4), to find the value of y intercept,

4 = -1/2 (4) + c

4 = -2 + c

c = 6

Now, we have identified the values of slope and the intercept.

Then the slope intercept form equation of these straight line is written as,

y = -1/2x + 6

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The graph of the linear equation can be seen in the image at the end.

We start by defining the variables we will use:

x = number of weeks.

y = money that Anika has.

We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:

y = $5*x

To graph this linear equation we need to find two points on the line, if x = 0 we get:

y = $5*0 = $0

So we have the point (0, 0)

if x = 1

y = $5*1 = $5

So we have the point (1, 5)

Now we can graph these two points and connect them with a line, the graph can be seen below.

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The 95% confidence interval for the proportion of respondents who say yes is of:

(0.5562, 0.6176)

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters, which are the sample size and the estimate, are given as follows:

[tex]n = 990, \pi = \frac{581}{990} = 0.5869[/tex]

The lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 - 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.5562[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 + 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.6176[/tex]

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Answer:

20 slices

Step-by-step explanation:

If there were 11 large pizzas with 8 slices per pizza, that would mean that there are a total of 88 slices of pizza.

If there are four classrooms, that means that if each classroom had 20 slices, there would be enough for everyone with 8 pieces leftover.

20 x 4 = 80

The number of touchdowns is 4.

The number of extra-point kicks is 4.

and the number of field goals is 2.

What are linear equations in three variables?

If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.

How to solve the system of linear equations in three variables?

Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.

Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".

Total points scored in game = 20+14 =34

Now,

According to the given question,

                                6x + y + 3z = 34 -----------(I)

                                x = y ----------(II)

                                x = 2z

                                z = [tex]\frac{x}{2}[/tex] -----------(III)

Putting the values of "y" and "z" in equation (I), we get

                              6x + x + 3×[tex]\frac{x}{2}[/tex] = 34

                               [tex]\frac{17x}{2}[/tex] = 34

                               x = 4

Now, putting the value of "x" in equations (II) and (III), we get

                               y = 4.

                               z = 2.

Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.

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Marissa will have $720 in 7 years when she has $48 in her saving account that earns 2% simple interest per year.

where

Calculation

From, A = P(1 + RT)

where, p = $48

R = 2%

T= 7 years

A = 48(1 + 2*7)

A = $720

Hence, Marissa will have $720 in her bank account after 7 years.

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The completion of the trend analysis for sales with 2010 as the base year is as follows:

                             2013           2012           2011           2010

Sales            $ 620,000   $ 580,000   $ 450,000   $ 600,000

Trend Analysis      103%             97%              75%             100%

Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.

To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.

The other years' results are compared to the base year's by dividing each year's result by the base year's.

Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.

2013 (D) = 103% ($620,000/$600,000 x 100)

2012 (C) 97% ($580,000/$600,000 x 100)

2011 (B) 75% ($450,000/$600,000 x 100)

2010 (A) = 100% ($600,000/$600,000 x 100)

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Answer:

Step-by-step explanation:

Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)

where, (h,k) is the center and r is the radius.

therefore, from the question by rearranging the equation,

x² + y² + 4x − 6y + 12=0

viz, (x² +4x+4) + (y²-6y+9)-1=0  

(x+2)^2 + (y-3)^2=1

therefore from eqn1, (-2,3) is the center and radius is 1

Answer:

y = 2(x - 1)^2 - 9

Step-by-step explanation:

The vertex form of a parabola is y = a(x - h)^2 + k

(h, k) is the vertex, aka (1, -9)

(x, y) is the point that is passed through aka (2, -7)

Using this, we can substitute these values into the equation.

First, let's work with the vertex

We know that h = 1 and k = -9:  y = a(x - 1)^2 - 9

Now, let's substitute in the point that was given: -7 = a(2 - 1)^2 - 9

Now, we can find the a-value by simplifying: -7 = a - 9   -->  a = 2

Finally, we can make the equation by taking our equation that we made with the vertex but just putting the a-value in since we know it.

y = 2(x - 1)^2 - 9 is the equation of the parabola in vertex form

I hope this helps! Let me know if it is wrong

Perimeter meaning: the continuous line forming the boundary of a closed geometric figure.

side length: 15

perimeter: 368

The only equation given that represents the Exponent Property of Logs is; Option A: log(A^r) = r*log(A)

The  exponent property of logarithm says that the log of a power is the exponent times the logarithm of the base of the power. For example;

logₐ(MN) = logₐM + logₐN

logₐ(M/N) = logₐM - logₐN

logₐ(3²) = 2logₐ3

The first example above shows the product rule of logarithms

The second example shows the quotient rule of logarithms

The third rule shows the power rule

Now, looking at the options, the only one that shows the correct pattern of exponent property of logarithm is;

Option A: log(A^r) = r*log(A)

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The dimensions of the playground are;

Width = 60 feet

Length = 160 feet

The formula for calculating perimeter of a rectangle is expressed as;

Perimeter = 2( l + w)

Where;

We have the values as;

Perimeter = 440 feet

Length = 3w - 20

Width = w

Now, substitute the values into the formula, we have;

440 = 2( 3w - 20 + w)

expand the bracket

440 = 2( 4w - 20)

440 = 8w - 40

collect like terms

8w = 480

Make 'w' the subject of formula

w = 60 feet

Length = 3(60) - 20

Length = 180 - 20

Length = 160 feet

Hence, the values are 60feet and 160 feet

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Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

To simplify this, we would use Order of Operations (BEDMAS)

So, to simplify 3 + (3-8)^2 -7 we will follow the order of Operations

[tex]3 + (3-8)^{2} - 7\\3 + (-5)^{2} - 7\\3 + 25 - 7 \\28 - 7\\21[/tex]

So the answer is 21

Answer:

2

Step-by-step explanation:

y    4-2=2

x     2-1=1    

2/1=1

hope it helps.

If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.

Formulate an equation

1.30x + 1.60y = 3400

Hence,

x =4y Equation 1

1.30x + 1.60y = 3400 Equation 2

Substitute eq1 into eq2

1.30(4y) + 1.60y = 3400

5.2y +1.60y =3400

6.8y =3400

Divide both side by 6.8y

y =3400/6.8

y = 500

Number of euro

4y where y = 500

4(500)

=2000

Therefore  the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.

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Answer:

x = 20 degrees ; y = 70 degrees

Step-by-step explanation:

angle supplementary to 40 = 180 - 40 = 140 degrees

in isosceles triangle has the angles of the base with the same measure

140 + (2x) = 180

2x = 180 - 140

2x = 40

2/2 x = 40/2

x = 20 degrees

90 - 20 = 70 degrees

70 + y + 40 = 180

110 + y = 180

y = 180 - 110

y = 70 degrees

Answer:

Step-by-step explanation:

The pattern is that two larger numbers differ by 2 and the smaller is the root of twice the sum of the larger two.

The given formula gives rise to the above observations. it tells you

a = 2x

b = x^2 -1

c = x^2 +1

This is a special case of Euclid's formula ...

a = 2mn

b = m^2 -n^2

c = m^2 +n^2

for n=1.

Since m and n can be any integer values, there are certainly many other. Pythagorean triples that do not match the formula given in the problem. Using n=2, for example, the triples are:

a = 4x

b = x^2 -4

c = x^2 +4

Some triples from this set of formulas are (5, 12, 13), (20, 21, 29), (28, 45, 53), (36, 77, 85).

It should bm be noted that triples from this set of formulas will not match directly those from the formulas in the problem statement, but triples from both lists may reduce to the same primitive triple.

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Complete question

Examine this set of Pythagorean triples from part C. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.

Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings.

x-value Pythagorean Triple

3 (6,8,10)

4 (8,15,17)

5 (10,24,26)

6 (12,35,37)

The length and breadth expressions where one dimension is the GCF are; 7y and (2y²-5).

Area of a Rectangle

Given that a rectangle is a two-dimensional shape with one of the dimensions being the GCF, as specified in the question;

Consequently, the length and breadth expressions are 7y and (2y²-5) respectively.

Additionally, the rectangle's area when y=2 is; 14(2³) - 35(2) = 52.

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For 10m long ladder whose foot is leaning against a vertical wall and from the base of the wall it is 6m away then height of the wall at a point ladder reaches is equal to 8m.

As given in the question,

Wall , ladder and base forms a right angled triangle

Length of the ladder leaning against the wall is hypotenuse = 10m

Distance between the ladder and base of the wall is base= 6m

Let us consider 'h' be the height of the wall is altitude.

Wall , ladder and base forms a right angled triangle

Using Pythagoras theorem we have,

(Hypotenuse)² = (Base)² + (altitude)²

⇒10² = 6² + h²

⇒100 =36 +h²

⇒h² =100 -36

⇒h² =64

⇒h = 8m

Therefore, for 10m long ladder whose foot is leaning against a vertical wall and from the base of the wall it is 6m away then height of the wall at a point ladder reaches is equal to 8m.

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Answer:

[tex] \huge{ \boxed{r =100( \sqrt[n]{ \frac{A}{P} } - 1)}}[/tex]

Step-by-step explanation:

[tex]A = P(1 + \frac{r}{100} )^{n} \\ [/tex]

First of all in order to make r the subject we have to first divide both sides of the equation by P

That's

[tex] \frac{A}{P} = \frac{P( {1 + \frac{r}{100} })^{n} }{P} \\[/tex]

We'll finally get

[tex] \frac{A}{P} = ( {1 + \frac{r}{100}) }^{n} \\ [/tex]

Next we have to remove the power n and to do that we find the square root of 'n' of both sides as

We have

[tex] \sqrt[n]{ \frac{A}{P} } = \sqrt[n]{( {1 + \frac{r}{100} })^{n} } \\ \\ \\ \sqrt[n]{ \frac{A}{P} } = 1 + \frac{r}{100} [/tex]

Next we subtract 1 from both sides to isolate r/100

We have

[tex]\sqrt[n]{ \frac{A}{P} } - 1 = 1 - 1 + \frac{r}{100} \\ \sqrt[n]{ \frac{A}{P} } - 1 = \frac{r}{100} [/tex]

Finally to isolate r , we multiply both sides by 100

[tex] \frac{r}{100} \times 100 =100 \times (\sqrt[n]{ \frac{A}{P} } - 1)[/tex]

We have the final answer as

[tex]r =100( \sqrt[n]{ \frac{A}{P} } - 1) \\ [/tex]

Hope this helps you

The possible values for n and m are:

m = √5 and n = 7/5

In this question, we have been given the locations of numbers n and m.

From their locations in the diagram, we need to find the possible values for n and m.

From the location of n we can say that the value of n is a rational number but not an integer.

We know that rational numbers are of the form p/q where p, q are integers with q ≠ 0

And the value of m is an irrational number.

So, the possible value of n am m:

m = √5 and n = 7/5

Therefore, the possible values for n and m are:

m = √5 and n = 7/5

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