A line has a slope of –3 and a y-intercept of 3.

Answer:

Hi there!

The answer to this question is: x=6

Step-by-step explanation:

All the points are being mirrored across the line x=6.

Answer:

The answer is x=6

Step-by-step explanation:

The two shapes are mirror images of each other around x=6

Step-by-step explanation:

Hi there!

The best way to approach this problem is Soh Cah Toa.

In this case you can use sine. sine is opposite over hypotenuse.

so sin(17)= b/15

then to solve for b you multiply 15 on both sides to get 4.4

Answer:

Step-by-step explanation:

This question is an application of the sine law

Equation

b/sin(B) = c / Sin(C)

Givens

b = ????

B = 17

c = 15

C = 140

Solution

Keep in mind that this may not work.

b/sin(17) =   15 / sin(140)                          Multiply both sides by sin(17)

b = 15*sin(17)/sin(140)

b = 15*0.2924/0.6428

b = 6.8233

Answer:

The roots are rational

Step-by-step explanation:

Given

x² = 144 ( take the square root of both sides )

x = ± [tex]\sqrt{144}[/tex] = ± 12 ← both rational

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers.

12 = [tex]\frac{12}{1}[/tex] ← thus rational

- 12 = [tex]\frac{-12}{1}[/tex] ← thus rational

Answer:

The answer is that x^2=144 is rational

Answer:

-4x^2-6x+6

(third choice)

Step-by-step explanation:

To do f(x)-g(x) we must insert the expression for f(x) and g(x) into this:

This will give us:

(8x^2-2x+3)

-(12x^2+4x-3)

--------------------

-4x^2-6x+6

Horizontally if you prefer:

(8x^2-2x+3)-(12x^2+4x-3)

Distribute and get rid of paranthesis:

8x^2-2x+3-12x^2-4x+3

Pair up like terms:

8x^2-12x^2-2x-4x+3+3

Combine the like terms:

-4x^2-6x+6

Answer:

h(x) =  -4x^2 - 6x + 6

Step-by-step explanation:

f(x) - g(x)

=  8x^2 - 2x + 3 - (12x^2 + 4x - 3)    (Note the parentheses around g(x))

Distributing the negative over the parentheses:

= 8x^2 - 2x + 3 - 12x^2 - 4x + 3

= -4x^2 - 6x + 6 = h(x).

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x-12&(1)\\y=-4x-31&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\\dfrac{3}{4}x-12=-4x-31\qquad\text{multiply both sides by 4}\\\\3x-48=-16x-124\qquad\text{add 48 to both sides}\\\\3x=-16x-76\qquad\text{add}\ 16x\ \text{to both sides}\\\\19x=-76\qquad\text{divide both sides by 19}\\\\x=-4\\\\\text{Put it to (2):}\\\\y=-4(-4)-31\\y=16-31\\y=-15[/tex]

Answer:

445 dollars

Step-by-step explanation:

You are given he charges 47.5 per hour so 47.5x is how much you will pay for x hours and he charges a 65 dollar service fee.

So together he is charge you 47.5x+65 for x hours.

If it spends 8 hours, the cost will be 47.5(8)+65=445.

The total charges if it takes the plumber 8hours to complete the task is $445.00

According to the question,

For 1 hour the charge is $47.50

∴ For 8 hours, the charge is $(47.50 x 8) = $ 380

The service charge is to be added now.

∴ The final amount of money = $(380.00 + 65.00) = $445.00

The total charge is $ 445.00

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Answer:

The correct answer is A. Aimee's graph is correct because the ratio [tex]\frac{2}{3} :1[/tex] is equal to 2:3, which her graph shows in each point.

Step-by-step explanation:

We are given that Aimee noticed her plant grew 2/3 of an inch every week since it sprouted and a graph is drawn to show the plant growth.

We are to determine whether which of the given statements is correct.

The ratio [tex]\frac{2}{3} :1[/tex] is basically equal to 2:3. Therefore, the graph is correct as it shows the same ratio at each point.

For the points (6, 4) and (3, 2) = [tex]\frac{4-2}{6-3} =\frac{2}{3}[/tex]

Answer:it’s A great got it right on edge

Step-by-step explanation:

To solve the system of equations, we can use the method of substitution. However, when we substitute the expression for x in the second equation, we get an equation that is not true, indicating that the system has no solution.

To solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6, we can use the method of substitution. First, we can solve one of the equations for either variable, then substitute that expression into the other equation to solve for the other variable. Let's solve the first equation for x:

5x - 2y = -6

5x = 2y - 6

x = (2y - 6)/5

Now, substitute this expression for x in the second equation:

15((2y - 6)/5) - 6y = 6

6y - 18 - 6y = 6

-18 = 6

This leads to the equation -18 = 6, which is not true. Therefore, the system of equations has no solution. So, the correct answer is C. No solution.

recall your d = rt, distance = rate * time.

p = speed of the plane

w = speed of the wind

let's keep in mind that, when the plane is going with the wind, is not really going "p" fast is actually going "p + w" since the wind is adding speed to it, likewise, when the plane is going against the wind, the plane is going "p - w" fast, since the wind is subtracting speed from it.

[tex]\bf \begin{array}{lcccl} &\stackrel{km s}{distance}&\stackrel{kph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&3605&p-w&5\\ \textit{with the wind}&4605&p+w&5 \end{array}~\hfill \begin{cases} 3605=(p-w)5\\ \frac{3605}{5}=p-w\\ 721=p-w\\ 721+w=\boxed{p}\\ \cline{1-1} 4605=(p+w)5 \end{cases} \\\\\\ 4605=(p+w)5\implies \cfrac{4605}{5}=p+w\implies \stackrel{\textit{substituting in the 2nd equation}}{921=\left( \boxed{721+w} \right)+w}[/tex]

[tex]\bf 921=721+2w\implies 200=2w\implies \cfrac{200}{2}=w\implies \blacktriangleright 100=w \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{p=721+w\implies }p=721+100\implies \blacktriangleright p=821 \blacktriangleleft[/tex]

Answer:

Option 1: {x | x > 12 or x < 6}

Step-by-step explanation:

Given inequalities will be solved one by one:

[tex]\frac{2}{3}x >8\\2x > 8*3\\2x>24\\x > \frac{24}{12} \\x>12[/tex]

Or

[tex]\frac{2}{3}x<4\\2x<4*3\\2x<12\\x < \frac{12}{2}\\ x<6[/tex]

Hence we can see that the solution of both inequalities combined is:

x>12 or x<6

Hence, option 1 is correct ..

Answer:

center ( -5 , 7).

Step-by-step explanation:

Given  : If the equation of a circle is (x + 5)² + (y - 7)² = 36.

To find : Find its center .

Solution : We have given (x + 5)² + (y - 7)² = 36.

Standard equation of circle : (x – h)² + (y – k)² = r².

Where, (h ,k) = center , r =  radius .

On comparing (x + 5)² + (y - 7)² = 36.

h = -5 , k = 7

So, the center ( -5 , 7).

Therefore, center ( -5 , 7).

Answer:

$390.

Step-by-step explanation:

first you need to find out hour much the secretary gets paid an hour.  So you will divide $262.50 by 35 hours

262.50 / 35 = 7.50

so we know that she worked over time of 6 hours and that will be time and half

to figure out how much for time and a half.  We are going to divide her hourly rate by 2.  

7.50 / 2 = 3.75

then to find out how much she made for that 6 hours we will add

7.50 + 3.75 = 11.25

to get the amount for over time on Saturday we will multiply

11.25 x 6 = 67.50

Now for the double time we will double her pay so will add

7.50 + 7.50 = 15

so then we are going to multiply to get your pay for the 4 hours overtime

15(4) = $60

Now to find the total amount we are going to add all of our totals together.  

262.50 + 67.50 + 60 = 390.

Her total gross wage for the week is $390.

Answer:

$390.

Step-by-step explanation:first you need to find out hour much the secretary gets paid an hour.  So you will divide $262.50 by 35 hours

262.50 / 35 = 7.50

so we know that she worked over time of 6 hours and that will be time and half

to figure out how much for time and a half.  We are going to divide her hourly rate by 2.  

7.50 / 2 = 3.75

then to find out how much she made for that 6 hours we will add

7.50 + 3.75 = 11.25

to get the amount for over time on Saturday we will multiply

11.25 x 6 = 67.50

Now for the double time we will double her pay so will add

7.50 + 7.50 = 15

so then we are going to multiply to get your pay for the 4 hours overtime

15(4) = $60

Now to find the total amount we are going to add all of our totals together.  

262.50 + 67.50 + 60 = 390.

Her total gross wage for the week is $390

Answer:

95

Step-by-step explanation:

(9.5)(-2)(-5)

First multiply the first two terms:

9.5* -2(-5)

9.5* -2 = -19

= -19(-5)

now multiply the product of solved terms by -5

-19(-5)

Negative signs will change into positive because - * - = +

95....

Thus the answer is 95....

Answer:

your answer is 95

Step-by-step explanation:

you multiply (9.5) (-2)(5) and you get 95

Step-by-step answer:

If x and y both go by equal steps, not necessarily equal steps between x and y, the relation is linear

Here, x goes by steps of 6 (1,7,13,19) and y goes by steps of 3 (4,7,10,13), therefore the relation is linear.

To find the equation passing through all the points, we find first the slope, which is steps in y divided by steps in x, or

slope, m = 3/6 = 1/2

Next, we take any point from the data, say, P0=(x0,y0)=(1,4), and substitute in the point-slope form of the equation

y-y0 = m(x-x0)...........................(1)

since x0=1, y0=4, and m=1/2, we get the equation

y-4 = (1/2)*(x-1) .........................(2)

Simplify (2) to get the slope-intercept form of the linear relation:

y = (1/2)x + 7/2 ........................(3)

Finally, we check the results of the y-values for given values of x, using the relation given in equation (3):

y(1) = 4

y(2)=7

y(3)=10

y(4)=13

all of which correspond exactly to original data, so the equation of the linear relation is correct.

Answer:

y/2

Step-by-step explanation:

x+3=y+2

------  --------

3          2

Using cross products

2(x+3) = 3(y+2)

Distribute

2x+6 = 3y+6

Subtract 6 from each side

2x+6-6 = 3y+6-6

2x= 3y

Divide each side by 2

2x/2 = 3y/2

x = 3/2 y

We want to find x/3

Divide each side by 3

x/3 = 3/2 y * 1/3

x/3 = 1/2 y

Answer:Answer:

the figure is parallelogram

Explanation:

enter image source here

As The mutually edges are parallel each other and equal,

the name of figure is parallelogram .

Step-by-step explanation:

Answer with explanation:

The vertices of Quadrilateral ABCD are ,A(−5,7), B(6,−3), C(10,2), and D(−1,12).

Distance formula between two points (a,b) and (c,d), is given by

          [tex]=\sqrt{(a-c)^2+(b-d)^2[/tex]

[tex]AB=\sqrt{[-5-6]^2+[7-(-3)]^2}\\\\AB=\sqrt{121+100}\\\\AB=\sqrt{221}\\\\BC=\sqrt{[10-6]^2+(2+3)^2}\\\\BC=\sqrt{16+25}\\\\BC=\sqrt{41}\\\\CD=\sqrt{[10+1]^2+[2-12]^2}\\\\CD=\sqrt{121+100}\\\\CD=\sqrt{221}\\\\DA=\sqrt{[-1+5]^2+[12-7]^2}\\\\DA=\sqrt{16+25}\\\\DA=\sqrt{41}\\\\AC=\sqrt{[10+5]^2+[2-7]^2}\\\\AC=\sqrt{225+25}\\\\AC=\sqrt{250}\\\\BD=\sqrt{[6+1]^2+[-3-12]^2]}\\\\BD=\sqrt{49+225}\\\\BD=\sqrt{274}[/tex]

Opposite side of Quadrilateral[AB=CD, AD=BC] is equal, but Diagonals are not equal.

So, it is a Parallelogram.

Answer:

Step-by-step explanation:

It's a right triangle.

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

a, b - legs

Find x-intercept and y-intercept of a line 4x + 5y = 20.

x-intercept (y = 0):

4x + 5(0) = 20

4x + 0 = 20

4x = 20     divide both sides by 4

x = 5

y-intercept (x = 0):

4(0) + 5y = 20

0 + 5y = 20

5y = 20      divide both sides by 5

y = 4

Therefore the legs are a = 5, b = 4.

Substitute:

[tex]A=\dfrac{(5)(4)}{2}=\dfrac{20}{2}=10[/tex]

Look at the picture.

Answer:

p(z<0.42) = 0.6628

Step-by-step explanation:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. That is to say:

μ = 0

σ² = 1

Using a calculator, we find that:

p(z<0.42) = 0.6628 (See picture attached)

Answer:

0.66276.

Step-by-step explanation:

We are asked to find the approximate value of p(z<0.42) for a standard normal distribution.

Our given expression means the probability of getting a z-score less than 0.42.

We need to find the probability of getting the area corresponding to a z-score less than 0.42 under normal distribution curve.

We will normal distribution table to solve our given problem.

[tex]p(z<0.42)=0.66276[/tex]

Therefore, the approximate value of our given expression would be 0.66276.

Answer:

2)A plane has length and width.

3)A plane extends infinitely in all directions

5)A plane is a flat surface.

Step-by-step explanation:

We can think of a plane as a line in space with no height, only length and width.

Yes, a plane is a two-dimensional surface, hence it has length and width.

2)A plane has length and width (TRUE)

The plane surface extends infinitely far, therefore it extends infinitely in all direction.

3)A plane extends infinitely in all directions (TRUE)

5)A plane is a flat surface(TRUE)

The correct options are 2,3 and 5.

See attachment

Answer:

B,C,E

Step-by-step explanation:

Step-by-step explanation:

Average=total numbers of songs /registered users

Average= 4*10^9/5*10^7

Average=40*10^8/5*10^7

Average=8*10^(8-7)

Average=8*10^(1)

Average=80 songs downloaded per user

The Average number is 80 songs downloads per user.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers.

Given:

Total Registered user = 5 x [tex]10^7[/tex]

Downloaded songs = 4 x [tex]10^9[/tex]

So, Average=total numbers of songs /registered users

Average = 4 x [tex]10^9[/tex]/ 5 x [tex]10^7[/tex]

Average= 40 x [tex]10^8[/tex]/ 5 x [tex]10^7[/tex]

Average = 8 x [tex]10^{(8-7)[/tex]

Average= 8 x 10

Average= 80 songs.

Hence, 80 songs downloaded per user.

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Answer:

Step-by-step explanation:

f(x) + n - shift a graph of f(x) n units up

f(x) - n - shift a graph of f(x) n units down

f(x + n) - shift a graph of f(x) n units to the left

f(x - n) - shift a graph of f(x) n units to the right

=============================================

We have

[tex]f(x)=x^2,\ g(x)=x^2+(-8x)+7[/tex]

Convert the equation of g(x) to the vertex formula:

[tex]y=a(x-h)^2+k[/tex]

[tex]g(x)=x^2+(-8x)+7\\\\g(x0=x^2-2(x)(4)+7\\\\g(x)=\underbrace{x^2-2(x)(4)+4^2}-4^2+7\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\g(x)=(x-4)^2+7=f(x-4)+7\\\\\text{shift the graph of f(x) 4 units to the right and 7 units up}[/tex]

[tex]\bf \begin{array}{ll} \stackrel{year}{term}&value\\ \cline{1-2} a_1&3\\ a_2&3r\\ a_3&3rr\\ a_4&3rrr\\ a_5&3rrrr\\ &3r^4 \end{array}\qquad \qquad \stackrel{\textit{5th year}}{108}=3r^4\implies \cfrac{108}{3}=r^4\implies 36=r^4 \\\\\\ \sqrt[4]{36}=r\implies \sqrt[4]{6^2}=r\implies 6^{\frac{2}{4}}=r\implies 6^{\frac{1}{2}}=r\implies \sqrt{6}=r[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} r=\sqrt{6}\\ a_1=3\\ n=11 \end{cases}\implies a_{11}=3(\sqrt{6})^{11-1} \\\\\\ a_{11}=3(\sqrt{6})^{10}\implies a_{11}=3\left(6^{\frac{1}{2}} \right)^{10}\implies a_{11}=3\cdot 6^{\frac{10}{2}} \\\\\\ a_{11}=3\cdot 6^5\implies a_{11}=3\cdot 7776\implies a_{11}=23328[/tex]

Answer:

The investment be worth $23328 after 11 years.

Step-by-step explanation:

It is given that the annual growth reflects a geometric sequence.

An initial investment of $3 is worth $108 after 5 years.

It means the initial value of first term of the gp, a₁ = 3

The 5th term of the gp, a₅ = 108

The nth term of a gp is

[tex]a_n=ar^{n-1}[/tex]              .... (1)

where, a is first term and r is common ratio.

The 5th term of the gp is

[tex]a_5=ar^{5-1}[/tex]

From the given information it is clear that the 5th term of the gp is 108. Substitute a₅ = 108 and a=3.

[tex]108=(3)r^{4}[/tex]

Divide both sides by 3.

[tex]\frac{108}{3}=r^{4}[/tex]

[tex]36=r^{4}[/tex]

Taking fourth root on both the sides.

[tex]\sqrt{6}=r[/tex]

Substitute r=√6, a=3 and n=11 to find the investment worth after 11 years.

[tex]a_{11}=(3)(\sqrt{6})^{11-1}[/tex]

[tex]a_{11}=3(\sqrt{6})^{10}[/tex]

[tex]a_{11}=23328[/tex]

Therefore the investment worth $23328 after 11 years.

Answer:

Step-by-step explanation:

SAS - Side Angle Side

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

the opposite sides have the same lengths.

the angles formed by these sides are right angles

Answer: [tex]80\ ft^2[/tex]

Step-by-step explanation:

You know that the model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 and the new area will be 160 square feet.

Since you know that the area of the new enlarged patio will be 160 square feet, you need to divide the area  of the new enlarged patio  in order to find the area of the landscaper’s model.

This is:

[tex]Area_(model)=\frac{160\ ft^2}{2}\\\\Area_(model)=80\ ft^2[/tex]

Answer:

I think its 40

Step-by-step explanation:

i come back and see:)

I got it right. good luck

Answer:

No solution.

Step-by-step explanation:

If the linear equations in a system are parallel, that means there is no solution.

39

52 divided by 4 is 13. 52 pickles divided into 4 pickles for each meal is 13. 39 patties divided by 3 patties is 13 aswell so. the answer: 39

The number of meat patties that are needed if 52 pickles are used is:

                                     39 meat patties.

It is given that:

The Big Burger recipe calls for 3 meat patties, 2 slices of cheese, and four pickles.

This means that for every 4 pickles there are 3 meat patties.

This means that for every 1 pickles there are: 3/4 meat patties.

Hence, for every 52 pickles there are: 3/4×52 meat patties

                                                            = 39 meat patties.

Answer:

v=26.41 m/s

Step-by-step explanation:

From the Newtons laws of motions, we sew that x= (2v₁²sin∅os∅)/g where x is the horizontal distance v is the initial speed and ∅ is the launch angle.

From trigonometry we see that 2 sin∅cos∅=sin 2∅

Therefore,  x=(v²sin2∅)/g

x=22m

∅=9°

g=9.8m/s²

22m=v²×sin(2×9)/(9.8m/s²)

v²=(22×9.8)/(sin 18)

v²=697.696

v=√697.696

v=26.41 m/s

Answer:

A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)

Step-by-step explanation:

* Lets revise the rotation and translation

- If point (x , y) rotated about the origin by angle 90° counterclockwise

 ∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° counterclockwise

 ∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° counterclockwise

 ∴ Its image is (y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Now lets solve the problem

- The vertices of the polygon are:

  A = (-7 , 8) , (B = (-4 , 6) , C = (-4 , 3) , D = (-8 , 3) , E = (-9 , 6)

- The polygon rotates 270° counterclockwise about the origin

∵ Point (x , y) rotated about the origin by angle 270° counterclockwise

∴ Its image is (y , -x)

∵ A = (-7 , 8)

∴ Its image = (8 , 7)

∵ B = (-4 , 6)

∴ Its image = (6 , 4)

∵ C = (-4 , 3)

∴ Its image = (3 , 4)

∵ D = (-8 , 3)

∴ Its image = (3 , 8)

∵ E = (-9 , 6)

∴ Its image = (6 , 9)

- After the rotation the image will translate 2 units to the left and

 3 units up

∴ We will subtract 2 units from each x-coordinates of the vertices and

  add 3 units to each y-coordinates of the vertices

∵ Point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

∵ Point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

∴ A' = (8 - 2 , 7 + 3)

∴ A' = (6 , 10)

∴ B' = (6 - 2 , 4 + 3)

∴ B' = (4 , 7)

∴ C' = (3 - 2 , 4 + 3)

∴ C' = (1 , 7)

∴ D' = (3 - 2 , 8 + 3)

∴ D' = (1 , 11)

∴ E' = (6 - 2 , 9 + 3)

∴ E' = (4 , 12)

* The coordinates of its image are:

  A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)

After a 270° counterclockwise rotation and 2 units left and 3 units up translations, the polygon's image has the new coordinates A''(-10,-4), B''(-8,-1), C''(-5,-1), D''(-5,-5), and E''(-8, -6).

In trigonometry and geometry, a 270° counterclockwise rotation of a point (x, y) about the origin gives a new point (-y, x). Now, let us consider the transformation of point A(-7, 8). After a 270° rotation, the new point is A'(-8, -7) and after translating 2 units left and 3 units up, the final transformed point A'' is (-8-2, -7+3) = (-10, -4).

Following the same process, B'(-6, -4), C'(-3, -4), D'(-3, -8), E'(-6, -9) and, after translation, B''(-8, -1), C''(-5, -1), D''(-5, -5), E''(-8, -6). Thus, the coordinates of the polygon A'B'C'D'E' after a 270° counterclockwise rotation and a 2 unit left and 3 units up translations are A''(-10,-4), B''(-8,-1), C''(-5,-1), D''(-5,-5), and E''(-8, -6).

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Final answer:

The value of the discriminant of the quadratic equation -2x² - 8x + 8 is 128. The positive discriminant suggests that the equation has two distinct real roots.

Explanation:

The discriminant of a quadratic equation can be calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.

In the given quadratic equation -2x² - 8x + 8, a = -2, b = -8, and c = 8. Substituting these values into the discriminant formula:

D = (-8)² - 4(-2)(8) = 64 - (-64) = 128.

The value of the discriminant is 128. The discriminant value can provide information about the nature of the roots of the quadratic equation. If the discriminant is positive (greater than 0), then the equation has two distinct real roots. If the discriminant is 0, then the equation has one real root (a repeated root). If the discriminant is negative, then the equation has no real roots.

Step-by-step explanation:

Let's say the two digit number is 10x + y, where x is the first digit and y is the second digit.

The sum of the digits is 8:

x + y = 8

If 8 is subtracted from the number, the digits switch place.

10x + y − 8 = 10y + x

Simplify the second equation:

9x − 8 = 9y

Substitute from the first equation.

y = 8 − x

9x − 8 = 9 (8 − x)

9x − 8 = 72 − 9x

18x = 80

x = 4.444

There's a problem.  x isn't an integer.  Are you sure you copied the problem correctly?  Perhaps you meant if 18 is subtracted from the number, the digits switch place.

9x − 18 = 9 (8 − x)

9x − 18 = 72 − 9x

18x = 90

x = 5

y = 8 − x

y = 3

So the number is 53.

[tex]x+y=8\\10x+y-8=10y+x\\\\x+y=8|\cdot9\\9x-9y=8\\\\9x+9y=72\\\underline{9x-9y=8}\\18x=80\\x=\dfrac{80}{18}=\dfrac{40}{9}[/tex]

x is not integer, so there must be a mistake in the problem.