1. a) Solve the following linear-quadratic system of equations graphically.
y + 2x²– 8x – 1= 0
y+ 2x – 9= 0

b.) GRAPH

c.) Verify your solution (s) algebraically.

Answer:

(2x,2y)

Step-by-step explanation:

Hope this helps!!!

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

[tex](0,7),(-13,-97)[/tex]

Equation Form:

[tex]x=0,y=7\\x=-13,y=-97[/tex]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(8*x+7)=0

Equation of a Straight Line

Solve   y-8x-7  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.'

n this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-8x-7  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000

 y-intercept = 7/1  =  7.00000

Calculate the X-Intercept :

When y = 0 the value of x is 7/-8 Our line therefore "cuts" the x axis at x=-0.87500

 x-intercept = 7/-8  = -0.87500

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 23.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 23.000 - 7.000 = 16.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = 16.000/2.000 =  8.000

Geometric figure: Straight Line

 Slope = 16.000/2.000 = 8.000

 x-intercept = 7/-8 = -0.87500

 y-intercept = 7/1 = 7.00000

Pull out like factors :

  -x2 - 5x - 7  =   -1 • (x2 + 5x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  x2 + 5x + 7

The first term is,  x2  its coefficient is  1 .

The middle term is,  +5x  its coefficient is  5 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   1 • 7 = 7

Step-2 : Find two factors of  7  whose sum equals the coefficient of the middle term, which is   5 .

     -7    +    -1    =    -8

     -1    +    -7    =    -8

     1    +    7    =    8

     7    +    1    =    8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Find the Vertex of   y = -x2-5x-7

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens down and accordingly has a highest point (AKA absolute maximum) .    We know this even before plotting  "y"  because the coefficient of the first term, -1 , is negative (smaller than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -2.5000  

Plugging into the parabola formula  -2.5000  for  x  we can calculate the  y -coordinate :

 y = -1.0 * -2.50 * -2.50 - 5.0 * -2.50 - 7.0

or   y = -0.750

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -x2-5x-7

Axis of Symmetry (dashed)  {x}={-2.50}

Vertex at  {x,y} = {-2.50,-0.75}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   -x2-5x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

x2+5x+7 = 0  Subtract  7  from both side of the equation :

  x2+5x = -7

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  -7  +  25/4    or,  (-7/1)+(25/4)

 The common denominator of the two fractions is  4   Adding  (-28/4)+(25/4)  gives  -3/4

 So adding to both sides we finally get :

  x2+5x+(25/4) = -3/4

Adding  25/4  has completed the left hand side into a perfect square :

  x2+5x+(25/4)  =

  (x+(5/2)) • (x+(5/2))  =

 (x+(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2+5x+(25/4) = -3/4 and

  x2+5x+(25/4) = (x+(5/2))2

then, according to the law of transitivity,

  (x+(5/2))2 = -3/4

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(5/2))2   is

  (x+(5/2))2/2 =

 (x+(5/2))1 =

  x+(5/2)

Answer:

for x=5, x=4 , x=2

Step-by-step explanation:

zero points, the x values that make this formula to be zero.

5-5=0

4-4=0

2-2=0

these values satisfied

Answer: x=18/5  y=127/5

Step-by-step explanation:

For both equations

1. subtract from both sides

2. divide to find what the variable equals

Answer:

i dont know use the internet

Step-by-step explanation:

this is the right way

Answer:

32.97 inches

Step-by-step explanation:

Given

Solving

Answer:

x-b=-3

Step-by-step explanation:

1. Simplify

|x-b|=c

x-b=c

If c=-3 then,

Answer= x-b=-3

Check the picture below.

Answer:

There are 24 bicycles and 11 tricycles in the shop

Step-by-step explanation:

We can make a system of equations to find the answer:

x for bicycles and y for tricycles:

x + y = 35

2x + 3y = 81

2x because bicycles have 2 wheels, 3y because tricycles have 3 wheels, and have set the total to 81 because 81 wheels in total.

Solving, we will find that there are 24 bicycles and 11 tricycles in the shop.

9-R= C

hope this helps :)

He has 100 + 120 = 220 coins in his purse.

He has n + p coins if he has n nickels and p pennies.

Answer:

assuming they only have to pay for parking once, 8 friends can go, if each person has to pay for parking and ticket only 5 people can go, Im assuming it'll be 8 for the answer tho I hope I'm right

There are 8 people can go to the amusement park.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total amount = $285.75

Parking = $13.75

Price of ticket per person = $34.

So, money left after paying for parking

=285.75 - 13.75

= 272

Now, number of people in amusement park

= 272/34

=8

Hence, 8 people can go to the amusement park.

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Answer:

A & B

Step-by-step explanation:

15/20 is not equal

6/8 is not equal

30/50 is equal

12/20 is equal

Hey there!

3/5

= 3 ÷ 5

= 0.60

= 60%

• So, we’re looking for something that’s equivalent to 0.60 or 60%

Option A.
15/20

= 15 ÷ 20

= 15 ÷ 5 / 20 ÷ 5

= 3 / 5

= 3 ÷ 5

= 0.60

= 60%
So, Option A. could possibly be your equivalent to your fraction

Option B.
6/8

= 6 ÷ 8

= 6 ÷ 2 / 8 ÷ 2

= 3 / 4

= 3 ÷ 4

= 0.75

= 75%
So, Option B. isn’t equivalent because it’s too big and not what we’re looking for!

Option C.
30/50

= 30 ÷ 50

= 30 ÷ 5 / 50 ÷ 5

= 6 / 10

= 6 ÷ 2 / 10 ÷ 2

= 3 / 5

= 3 ÷ 5

= 0.60

= 60%
So, Option C. could possibly be your equivalent to your fraction.

Option D.

12/20

= 12 ÷ 20

= 12 ÷ 2 / 20 ÷ 2

= 6 / 10

= 6 ÷ 2 / 10 ÷ 2

= 3 / 5

= 3 ÷ 5

= 0.60

= 60%

So, Option D. could possibly be your equivalent to your fraction.

To sum it all up, your answer is:

Option B. 6/8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Here is the completed two-way frequency table:

                         Comedy     Action     Total

Boys                    37              57              94

Girls                    68               38             106  

Total                   105              95             200

Number of boys that prefer comedy = number of students that prefer comedy - Number of girls that prefer comedy

105 - 68 = 37

Number of boys that prefer action = total numer of boys - Number of boys that prefer comedy

94 - 37 = 57

Total number of students the prefer action = Total number of students - total number of students that prefer comedy

200 - 105 = 95

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Answer:

1/10

Step-by-step explanation:

There are ten options and Salad is one of them; therefore, the answer would be 1/10.

The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:

6= πd and then divide both sides of the equation by π you get that d = 1.90

To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:

1 = 0.9549θ

Answer:

60

Step-by-step explanation:

1/6 x 360

Central angle is equal to measure of intercepted arc.

60 degrees

Answer:

Step-by-step explanation:

i think this is the answer

Answer: Neither

Step-by-step explanation:

Answer:

There are 6 congruent triangles in a regular hexagon.

The triangles are equilateral (all sides are equal in length).

Using side length of equilateral triangle formula:

[tex]\sf x=\sqrt{\dfrac{4}{3}h^2}[/tex]

where x is the side length and h is the height

[tex]\sf \implies x=\sqrt{\dfrac{4}{3}\cdot 6^2}[/tex]

[tex]\sf \implies x=\sqrt{48}[/tex]

[tex]\sf \implies x=4\sqrt{3} \ units[/tex]

Therefore, perimeter = 6 × 4√3 = 24√3 units

Radius = side length of triangle = 4√3 units

Side Be a

[tex]\\ \rm\rightarrowtail h=\dfrac{\sqrt{3}}{2}a[/tex]

[tex]\\ \rm\rightarrowtail 6=\dfrac{\sqrt{3}}{2}a[/tex]

[tex]\\ \rm\rightarrowtail 12=\sqrt{3}a[/tex]

[tex]\\ \rm\rightarrowtail a=12/\sqrt{3}[/tex]

[tex]\\ \rm\rightarrowtail a=4\sqrt{3}[/tex]

Perimeter:-

Answer:

Step-by-step explanation:

Break up the shape into a trapezoid and rectangle:

Trapezoid area = (Top + Bottom) * Height / 2

= (9 + 20) * (21-16) / 2

= 29 * 5 / 2

= 72.5

Rectangle area = Length * Width

= 20 * 16

= 320

Combining, the total area = 72.5 + 320

= 392.5 in^2

Answer:

A = 392.5 in²

Step-by-step explanation:

The composite figure is made up of a rectangle and a trapezoid.

Calculate the area of the rectangle:

[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=20 \times 16\\&=320\; \sf in^2\end{aligned}[/tex]

Calculate the area of the trapezoid:

[tex]\begin{aligned}\textsf{Area of a trapezoid}&=\dfrac{\text{base}\;a+\text{base}\;b}{2} \times \text{height}\\&=\dfrac{9+20}{2} \times (21-16)\\&=\dfrac{29}{2} \times 5\\&=72.5\; \sf in^2\\\end{aligned}[/tex]

Therefore, the area of the composite figure it the sum of the area of the rectangle and the area of the trapezoid:

[tex]\begin{aligned}\textsf{Total area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of trapezoid}\\&=320+72.5\\&=392.5 \; \sf in^2\end{aligned}[/tex]

Therefore, the area of the composite figure is 392.5 in².

Answer:

6/(x + 1) + 11/(x + 1)^2.

Step-by-step explanation:

6x + 17 / (x +1)^2 =  A / (x + 1) + B /(x + 1)^2

Multiply through by (x + 1)^2:

6x + 17 =  A(x + 1) + B

Let x = -1, then:

-6 + 17 = 0 + b

So B = 11.

Let  x = 1:

6 + 17 = A(1+1) + 11

23 = 2A + 11

A = (23-11)/ 2

A = 6.

Answer:

36

Step-by-step explanation:

triangular numbers are

1, 3, 6, 10, 15, 21, 28, 36, .....

square numbers are

1, 4, 9, 16, 25, 36, ..........

the smallest number that is triangular and square is 36

Answer:

the median is 3.5

Step-by-step explanation:

there are 27  dots                                                                                                      27/2=13.5                                                                                                                 therefore the answer is the 13th dot and a half                                                              3.5 :)                                                                                                                                      (i dont know for sure but i think the mean is 3)

The mean is 3 and the median is 3 for this list of numbers.

From the dot pot,

Arrange the number in order:

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5

Now,

Mean = Average of all the values.

Median = Midvalue of the number.

Now,

There are 30 numbers in the list, so the mean is:

Mean = 90/30 = 3

To find the median, we need to find the middle number.

Since there are an even number of numbers in the list, we take the average of the two middle numbers:

The middle two numbers are both 3, so the median is:

Median = (3 + 3)/2 = 3

Therefore,

The mean is 3 and the median is 3 for this list of numbers.

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Answer: D

Step-by-step explanation:

The quadrilateral will be a rhombus. Then the correct option is D.

The definition of a quadrilateral is a planar form with four sides, four vertices, and four angles. Concave and convex are the two primary kinds.

Type of quadrilateral are:

The length of the side CD is given as,

CD² = (0 + 5a)² + (a - a)²

CD = 5a units

The length of the side BC is given as,

BC² = (- 5a + 9a)² + (a + 2a)²

BC² = (4a)² + (3a)²

BC² = 25a²

BC = 5a units

The length of the adjacent sides is equal. Then the quadrilateral will be a rhombus.

Thus, the correct option is D.

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Answer:

8.49 and No

Step-by-step explanation:

C² - b² = a² (pythagorus rule rearranged for a²)

9² - 3² = a²

81 - 9 = a²

a² = 72

a = 8.49 and no they aren't a triple.

Answer:

2.

Step-by-step explanation:

This is called the ambibuous case where  2 sides are given and angle opposite one of these sides.

2 traingles are possible.

Answer:

second one down

4 860 000 000 000

Step-by-step explanation:

count out 12 zeros after the 4 and you will find the one in decimal notation

The decimal notation for the given scientific notation is 4860000000000. (option b)

The decimal notation is an alternate method to represent the fractional value. It means that it is the fractional representation using base 10. The fractions can be converted into decimals and vice versa.

Given is a scientific notation, 4.86 × 10¹², we need to convert it into a decimal notation,

4.86 × 10¹²

= 4.86 × 10,000,000,000,000

= 4.86 × 100 × 100000000000

= 486 × 100000000000

= 48600000000000

Hence, the decimal notation for the given scientific notation is 4860000000000. (option b)

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Answer:

3.4 tonnes

Step-by-step explanation:

Kg --> tonnes = / 1000

50 x 40 / 1000 = 2. 2 + 1.4 = 3.4.

After 23 years $125.32 will be matured to $46,683.28.

The formula for Recurring maturity is given by:

[tex]A=Pn +\frac{ P*n*(n+1)}{24} *\frac{r}{100}[/tex]

Where A=matured amount

P =Principal value

n=Number of months

r=Interest rate(annual)

We have P= $125.32

n=23*12 = 276 months

r=2.5*12 =30%

Put these values in the above formula

we get A= $46,683.28

Therefore, After 23 years $125.32 will be matured to $46,683.28.

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