These two lines represent a system of equations.
What is the solution to that system?
Help ?

Answer:

[tex]x=\frac{1+\sqrt{41}}{5},\\x=\frac{1-\sqrt{41}}{5}[/tex]

Step-by-step explanation:

The quadratic formula states that the solutions for a quadratic is standard form [tex]ax^2+bx+c[/tex] are equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

In [tex]5x^2-2x-8=0[/tex], we can assign the values:

Thus, we have:

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(5)(-8)}}{2(5)},\\x=\frac{2\pm \sqrt{164}}{10},\\\begin{cases}x=\frac{2+ \sqrt{164}}{10}, x=\frac{1}{5}+\frac{\sqrt{41}}{5}=\frac{1+\sqrt{41}}{5}\\x=\frac{2- \sqrt{164}}{10}, x=\frac{1}{5}-\frac{\sqrt{41}}{5}=\frac{1-\sqrt{41}}{5}\end{cases}[/tex]

Answer:

(1+√41)/5, (1-√41)/5

Step-by-step explanation:

quadratic formula is (-b±√(b^2-4ac))/2a

in this equation,

a = 5

b = -2

c = -8

plug in the values

(2±√(4 - 4(5)(-8))/10

(2±√(4 + 160)/10

(2±√(164)/10

(2±2√(41))/10

1. (2+2√41)/10

(1+√41)/5

2. (2-2√41)/10

(1-√41)/5

Answer:

Domain { -13,12,20 }

Step-by-step explanation:

The domain is the input values

Domain { -13,12,20 }

We list them in order from smallest to largest and do not list repeats

Answer:

6x < - 39 3/4

Step-by-step explanation:

Answer:

angle x= 60

so it is in the ratio 1:2:√3

√3x=3

ie.x=√3/3

adjacent side=x=√3/4

Step-by-step explanation:

everything can be found in the picture

Answer:

y = 1/2x - 3/2

Step-by-step explanation:

y2 - y1 / x2 - x1

5 - (-4) / 13 - (-5)

9 / 18

1/2

y = 1/2x + b

-4 = 1/2(-5) + b

-4 = -5/2 + b

-3/2 = b

Answer:

three trillion four hundred and sixty eight million, seven hundred and twenty nine thousand and one hundred sixty five

Step-by-step explanation:

Answer:

y = [tex]\sqrt{x-5}[/tex]

This is the correct answer because I got it right.

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { C) \:7 + 4 \sqrt{3}}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {( - 2 - \sqrt{3} )}^{2} [/tex]

[tex] = ({ - 2})^{2} - 2.( - 2). \sqrt{3} + { (\sqrt{3}) }^{2} [/tex]

[tex] = 4 + 4 \sqrt{3} + 3[/tex]

[tex] = 7 + 4 \sqrt{3} [/tex]

[tex] ({a - b})^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]

[tex] \sqrt{a} \times \sqrt{a} = a[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

B. ) 36-48-60

Step-by-step explanation:

From Pythagoras theorem, we can determine the sides of the triangle by testing the options

a^2 + b^2 = c^2

Then test the options

B. ) 36-48-60

36^2 + 48^2 = 60^2

3600 + 2304 = 3600

3600= 3600

Since both sides have equal values, then OPTIONS B express a correct sides of the triangle

C.) 6-10-14

6^2 + 10^2 = 14^2

36+ 100= 196

136= 196( it doesn't make an equality then it's not the answer

Answer:

Step-by-step explanation:

Tangent from the point outside the circle are equal

WX  = XY

7x - 29 = 2x + 16 {Add 29 to both sides}

7x  = 2x + 16 +29

7x = 2x + 45 {Subtract 2x from both sides}

7x - 2x = 45

5x = 45     {Divide both sides by 5}

x = 45/5

x = 9

WX = 7x - 29

       = 7*9 - 29

        = 63 - 29

WX = 34

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

Rule:

if A+B = 90, then cos(A) = sin(B) and sin(A) = cos(B)

This can be rephrased into cos(A) = sin(90-A) and sin(A) = cos(90-A)

We'll focus on the second case sin(A) = cos(90-A)

Simply replace A with x and we have the same idea.

---------

So,

sin(x) = cos(90-x)

cos(90-x) = sin(x)

cos(90-x) = 4/5

You can prove this by drawing out a right triangle as shown below.

Answer:

4

Step-by-step explanation:

Answer:

There are several different means:

Arithmetic: 4 (This is most likely your answer.)

Geometric: 3.0862

Harmonic: 2.3736

Hope that this helps!

The base is 5 units and the height is 4 units.

Hope this helps! :)

Median is the middle value.

Writing the values from smallest to largest you have :

1/8, 1/8, 2/8, 2/8, 2/8, 3,8, 3/8, 4/8, 5/8

There are 9 values. The middle value ( median) would be the 5th number ( this would give you 4 numbers below it and 4 numbers above it.

The Median is 2/8

Answer:

2/8 is the median. In decimal, it is 0.25.

Happy learning!

--Applepi101

Don't forget the square brackets.

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

Work Shown:

[tex]|5x-3| \le 12\\\\-12 \le 5x-3 \le 12\\\\-12+3 \le 5x-3+3 \le 12+3 \ \text{ ... see note 1}\\\\-9 \le 5x \le 15\\\\-9\div 5 \le 5x\div 5 \le 15\div 5 \ \text{ ... see note 2}\\\\-1.8 \le x \le 3\\\\[/tex]

note 1: I added 3 to all sides to undo the "-3" in the middle.

note 2: I divided all sides by 5 to go from 5x to x (ie it undoes the multiplication on x).

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

From there, we convert from compound inequality notation to interval notation.

Something in the form [tex]a \le x \le b[/tex] converts to the interval notation [a,b]

The square brackets say to include the endpoint.

So [tex]-1.8 \le x \le 3[/tex] converts to the final answer of [-1.8, 3]

x is any real number between -1.8 and 3, including both endpoints.

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

It appears you had the right idea. You just needed to convert -9/5 to -1.8, and you also needed to surround everything with square brackets.

If your teacher wanted the answer in fraction form, then you would say [-9/5, 3]

Answer:

6.)

The answer is 63 inches because this value is closer to the mean and while the data is positively skewed (as in the mean is greater than the median) it's not by that much.

7.)

This would mean that the data is symmetric. By this, I mean that there would have to be an equal amount of data on either side of the mean. For example, for every entry 2 units below from the mean there must be one 2 units above the mean and so on. There would also have to be many entries on the mean/median (so that it would also be the mode)

8.)

We can observe that there are no real outliers that would heavily influence the data and so we can just take the mean

the mean of student A is: (68+72+73+67)/4= 70

The mean of student B is: (74+73+73+74)/4=73.5

We can see that student A, on average, is closer to 70 than student B and can therefore conclude that student A is more percise

Answer:

f(x)=−4(x+ 41 ) 2 − 4 11

Explanation:

The given function is

f(x) = - 4 {x}^{2} - 2x - 3f(x)=−4x 2 −2x−3

To write the function is vertex form, we need to complete the square.

We first factor -4 to get:

f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3f(x−4(x2 + 21 x)−3

Add and subtract the square of half the coefficient of x.

f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3f(x)=−4(x 2 + 21 x+ 16 1 )− 41 −3

We factor the perfect square trinomial and simplify to get:

f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4}f(x)=−4(x+ 41 ) 2 − 4 11

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

Work Shown:

Rise = -3

Run = 2

Slope = rise/run = -3/2 = -1.5

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

Notes:

Answer:

m = - 3 / 2

Rise : -3

Run : 2

Step-by-step explanation:

According to the picture,

first coordinate : ( 2 , 1 )

second coordinate : ( 4 , - 2 )

Formulae : m=(y2-y1)/(x2-x1)

Substituting,

m = ( - 2 - 1 ) / ( 4 - 2 )

m = - 3 / 2

If this helps you, please mark brainliest!

Answer:

The area of flower bed is 8.96 m^2.

Step-by-step explanation:

Length of lawn = 6 x

width of lawn = x

length of flower bed = x + 4

width of flower bed = x - 1

Area of shaded region = 40 m^2

Area of the shaded region

6 x (x) - (x +4)(x -1) = 40

[tex]5 x^2 - 3 x - 36 = 0 \\\\x = \frac{-3\pm\sqrt{9 + 720}}{10}\\\\x = \frac{-3\pm 27}{10}=2.4 m, - 3 m[/tex]

As length cannot have negative value, so x = 2.4 m.

Area of flower bed = (x + 4)(x - 1) = (2.4 + 4)(2.4 - 1) = 8.96 m^2

Answer:

If you were to use the sine formula you would have to use the cosine formula to get one of the opposite sides and then use the sine formula.

For the area why not use 1/2 * 20 to get the base.

Then the height would be 24 * sin 63 = 21.38

That would give an area of 213.8

Answer:

9r^6 - 3g^2 / 5

Step-by-step explanation:

I think this would be the answer. Sorry if I am incorrect :')

Answer:

d = 3h - 6

Step-by-step explanation:

Given

h = [tex]\frac{d}{3}[/tex] + 2 ( subtract 2 from both sides )

h - 2 = [tex]\frac{d}{3}[/tex] ( multiply both sides by 3 )

3(h - 2) = d , that is

d = 3h - 6

Answer:

D

Step-by-step explanation:     Time Stamp (6  9  10  32)

Easiest way is to graph both equation and look for the intersections  see attached sreen shot

or  solve by substitution

y = 2x

y = x²- 8

2x = x²- 8                  solve for x

0  = x² - 2x - 8          factor

0 = (x - 4)(x + 2)

0 = 0   when x = 4 and -2      

calculate the y values

y = 2x      x = 4

y = 8                              (4, 8)

y = 2x      x = -2

y = -4                            (-2, -4)

Answer:

B because when at B angels are the same qnd A and c are also same

Answer:

x = √3

Step-by-step explanation:

Find the diagram attached

Given

Opposite = √3

Adjacent = x

Acute angle theta = 45degrees

According to SOH CAH TOA;

tan theta = opp/adj

tan 45 = √3/x

x = √3/tan45

x = 1

x = √3

Hence the value of x in its simplest radical form is √3