Express the final equation in standard form. Contains the point (-8, 5) and is parallel to the line x − 3y = 6

Answer:

18

Step-by-step explanation:

The triangle on the left is a 30-60-90 triangle.

The ratio of the lengths of the sides is:

short leg  :   long leg   :    hypotenuse

    1           :     √3         :            2

The short leg of the left triangle is half the hypotenuse.

12√6 / 2 = 6√6

The long leg of the left triangle measures √3 times the short leg.

6√6 * √3

The triangle on the right is a 45-45-90 triangle.

The ratio of the lengths of the sides is:

short leg  :   long leg   :    hypotenuse

    1           :         1         :            √2

The length of the leg is the length of the hypotenuse divided by √2.

6√6 * √3 / √2 = 18

Answer:

B

Step-by-step explanation:

Hi!

3(5x+4)−20=13x−4                            

15x+12-20=13x-4                                         Distribute the 3 to the 5x and 4

15x-8=13x-4

2x-8=-4                                                        Subtract 13x from both sides

2x=4                                                             Add 8 to both sides

x=2                                                               Divide both sides by 2

So 2 is the answer :)

Step-by-step explanation:

let the point A( - 1 , -3 ) and B( 5 , -2 )

here, x1 = -1; x2 = 5

y1 = -3; y2 = - 2

Now, the distance between A and B

[tex]AB = \sqrt{(x _{1} - {x}_{2} ) {}^{2} + (y _{1} - y _{2}) {}^{2} } [/tex]

[tex]AB = \sqrt{( - 1 - 5) {}^{2} + ( - 3 ( - 2) {}^{2} }[/tex]

[tex]AB = \sqrt{36 + 1} = \sqrt{37} [/tex]

Thus, The Distance between AB is

[tex] \sqrt{37} [/tex]

Answer:

Yes, 50 square root plus 2 square root irrational

[tex] 6\sqrt{2}[/tex]

Step-by-step explanation:

[tex] \sqrt{50} + \sqrt 2[/tex]

[tex]= \sqrt{25\times 2} + \sqrt 2[/tex]

[tex]= 5\sqrt{2} + \sqrt 2[/tex]

[tex]= 6\sqrt{2}[/tex]

Since, [tex]\sqrt{2}[/tex] is irrational.

Therefore, [tex] \sqrt{50} + \sqrt 2[/tex] is also irrational and

[tex] \sqrt{50} + \sqrt 2=6\sqrt{2}[/tex]

When Lisa flips 2 fair coins, the probability of obtaining two tails is 1/4.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

Number of coins flips by Lisa = 2,

To find the probability of obtaining two tales,

The sample pace of flipping two coins = {(H, H), (H, T), (T, H), (T, T)}

The tale on both coins can come one time.

So the probability = number of favorable outcome / total observation

                              = 1 / 4

The required probability of obtaining two tails is 1 /4.

To know more about Probability on:

https://brainly.com/question/12478394

#SPJ3

Step-by-step explanation:

-5x - 5y + 4x - (2y + 3)

= - 5x + 4x - 5y - (2y + 3)

= - x - 5y - 2y - 3

= - x - 7y - 3 ( Answer )

Answer:

-x-7y-3

Step-by-step explanation:

distribute parentheses:

-(2y)-(3)= -2y-3

= -5x-5y+4x-2y-3

simplify

group like terms= -5x+4x-5y-2y-3

add similar elements= -x-5y-2y-3

add similar elements= -x-7y-3

Therefore, simplest expression is -x-7y-3

I hope this helps!!!

Essentially any like term is a variable with the same letter at the end or the same letter and power.

In this equation, we are given:

They are all different, so there are 3 different terms in the equation

Best of Luck!

[tex]\bold{\text{Answer:}\quad f(x)=\bigg\{\begin{array}{ll} -x-2&;x<0\\ -\frac{1}{2}x&;x\geq0 \end{array}}[/tex]

Step-by-step explanation:

Find the equation of each line in Slope-Intercept form: y = mx + b

Line 1 passes through (-5, 3) and (0, -2)   -->   m = -1,  b = -2

                                                                   -->  y = -x - 2

Line 2 passes through (0, 0) and (4, -2)   -->   m = -1/2,  b = 0

                                                                   -->   y = -(1/2)x + 0

Now that you have the equations, evaluate which x-values are included.

Line 1: open dot at x = 0 and line goes to the left        -->  x < 0

Line 2: closed dot at x = 0 and line goes to the right   --> x ≥ 0

Now you have all the information you need to write the piecewise function:

                                [tex]\large\boxed{f(x)=\bigg\{\begin{array}{ll} -x-2&;x<0\\ -\frac{1}{2}x&;x\geq0 \end{array}}[/tex]

The piece wise function can be written as

[tex]f(x) = -x-2 \; for\; x < 0[/tex]

[tex]f(x) = \dfrac{-1}{2}x \; for\; x \geq 0[/tex]

The Equation of line passing through  [tex](x_1,y_1)\; and \; (x_2,y_2)[/tex] can be given  by equation (1)

[tex]y -y_1 = \dfrac{y_2 -y_1 }{x_2 - x_1} (x-x_1) ........(1)[/tex]

The equation of line passing through (0,-2) and (-5,3) =

[tex]y-(-2) = \dfrac{3-(-2)}{-5-0}\times (x-0)[/tex]

[tex]y +2 = -x\\y = -x -2 ......(2)[/tex]

Similarly the line passing through (0,0) and (4,-2) =

[tex]y- 0 = \dfrac{-2 -0}{4-0} (x-0)\\y = \frac{-1}{2} x......(3)\\2y =-x \\x +2y =0[/tex]

The first line has an open circle at (0,  -2) and continues up through (-5, 3) with an arrow instead of an endpoint.

The second line has a closed circle at (0, 0) and continues down with a negative slope through (4, -2) with an arrow instead of an endpoint. [tex]f(x) = \dfrac{-1}{2}x \; for\; x < 0[/tex]

Hence the piece wise function can be defined by equations (2) and (3)

[tex]f(x) = -x-2 \; for\; x < 0[/tex]

[tex]f(x) = \dfrac{-1}{2}x \; for\; x \geq 0[/tex]

For more Information please refer to the link below

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Answer:

600 feet

Step-by-step explanation:

60 feet per minute

m = minute

60m

60(10)

600 feet

Answer:

Step-by-step explanation:

(4x - 2)° + [180° - (7x - 3)°] + 41° = 180°

(4x)° - 2° + 180° - (7x)° + 3° + 41° = 180°

          +2°-180°-3°-41°                           +2°-180°-3°-41°

- (3x)° = - 42°    

  ÷(-3)       ÷(-3)

   x° = 14°

   x = 14

Answer:

$3.58

Step-by-step explanation:

Since the cost is increasing, you need to add the two values together.

$3.49 + $0.09 = $3.58

The price of gasoline after the increase is $3.58.

Answer:

Amount of dirt needed to fill the cone = 28.28 in³ (Approx)

Step-by-step explanation:

Given:

Diameter = 6 in

Radius (r) = 6 / 2 = 3 in

Height (h) = 3 in

Find:

Amount of dirt needed to fill the cone

Computation:

Volume of cone = (1/3)πr²h

Volume of cone = (1/3)(22/7)(3)(3)(3)

Volume of cone = 28.28 in³

Amount of dirt needed to fill the cone = 28.28 in³ (Approx)

Answer: Distributive Property

Step-by-step explanation:

[tex]-2\bigg(\dfrac{3}{4}x+7\bigg)\\\\\\\text{DISTRIBUTE -2 to both terms:}\\-2\bigg(\dfrac{3}{4}x\bigg)+(-2)7\\\\\\\text{Simplify:}\\-\dfrac{3}{2}x-14[/tex]

Answer:

64

Step-by-step explanation:

56/7 = 8

8*8 = 64

64 tests

Answer: x^2+4x+3

Step-by-step explanation:

f(g(x)) >>> replace the g(x) with the given information

f(x+2) >>> replace every (x) in the given f(x) with (x+2)

(x+2)^2-1 >>> foil it out

x^2+4x+4-1 >>> simplify

x^2+4x+3 >>> ANSWER!! :)

Answer:

[tex]\large \boxed{\mathrm{see \ below}}[/tex]

Step-by-step explanation:

13 upon 5 is 13/5

13/5 in decimal form is 2.6

11 upon 6 is 11/6

11/6 in decimal form is 1.833333...

17 upon 8 is 17/8

17/8 in decimal form is 2.125

Answer:

For domain,

9-x2>=0

or,(x+3)(x-3)<=0

using wavy curve method,we get

Domain=[-3,3]

As domain matches only in first option,so the correct option is option first

Answer:

2 and -9

Step-by-step explanation:

Answer:

B. -1

Step-by-step explanation:

examples:

1 and -1

1/2 and -2

Answer:

B=-1

Step-by-step explanation:

diagonals are perpendicular line, the slope of perpendicular line are opposite reciprocal.

example if the slope line AC =3

the slope of BD=-1/3

-1/3*3=-1

Answer:

y=2

because 4x2 =8 then 8-4 equals to 4 which is what your trying to get

Answer:

parallelogram, rectangle, rhombus

Step-by-step explanation:

Answer:

heyooo i am here to clarify the answer is {parallelogram, rectangle and rhombus}

Step-by-step explanation:

in short, the answer is

A.

C.

D.

i hope you do good on your test !!

-cookie <3

Answer: 12464 feet

Step-by-step explanation:

Given: The deepest point of Lake Titicaca in South America is -922 feet relative to its surface.

We use absolute function, then the deepest point of Lake Titicaca in South America is |-922|=922 feet.

The deepest point is 11,542 feet above sea level.

That means, the elevation of the surface of the lake is the sum of 922 feet and  11,542 feet which is given by (922+ 11,542) feet =12464 feet

Hence, the elevation of the surface of the lake = 12464 feet

Answer:

95

Step-by-step explanation:

Answer:

X = 5

Step-by-step explanation:

x in (-oo:+oo)

x/8 = 0.625 // - 0.625

x/8-0.625 = 0

1/8*x-0.625 = 0 // + 0.625

1/8*x = 0.625 // : 1/8

x = 0.625/1/8

x = 5

x = 5

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

:)

Answer:

x = 5

Step-by-step explanation:

First convert the decimal to an improper fraction

That's

So we have

Multiply through by 8

That's

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Using the formula for calculating the length of an arc to get the angle of Maple Street to Elm Street;

Length of an arc = θ/360 * 2Πr  where r is the radius of the circle.

Given r = 10m and length of the arc = 15m

On substituting;

15 =  θ/360 * 2π(10)

15 = θ/360 * 20π

θ/360 = 15/20π

θ/360  = 0.2387

θ = 360* 0.2387

θ = 85.9°

Hence Maple street is at 85.9° to Elm street.

Answer:

[tex]\approx \bold{85.98^\circ}[/tex]

Step-by-step explanation:

Given that

Radius of circle = 10 metres

Bryan drives 15 metres around the circle.

To find:

The angle of Maple street to Elm street = ?

Solution:

Kindly refer to the image attached.

The Elm street meets the circle at A.

Maple street at B.

Given that arc length AB = 15m

Radius of circle = 10 m

We have to find the angle of arc.

Let us use the formula:

[tex]\theta = \dfrac{l}{r}\\\Rightarrow \theta = \dfrac{15}{10} \\\Rightarrow \bold{\theta = 1.5\ radians}[/tex]

Converting to degrees:

[tex]\pi\ rad = 180^\circ\\1.5\ rad = \dfrac{180}{\pi} \times 1.5^\circ\\\theta \approx \bold{85.98^\circ}[/tex]

Step-by-step explanation:

Taking LHS of the identity:

(a + b +c)2

This can also be written as:

= (a + b + c) (a + b + c)

Multiply as we do multiplication of trinomials and we get:

= a(a + b + c) + b(a + b + c) + c(a + b + c)

= a2 + ab + ac + ab + b2 + bc + ac + bc + c2

Rearrange the terms and we get:

= a2 + b2 + c2 + ab + ab + bc + bc + ac + ac

Add like terms and we get:

= a2 + b2+ c2 + 2ab + 2bc + 2ca

Hence, in this way we obtain the identity i.e. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

1st set = 4 letters

2nd set = 4x 4 = 16 letters

3rd set = 16 x 4 = 64 letters

4th set = 64 x 4 = 256 letters

5th set = 256 x 4 = 1,024 letters

6th set =1024 x 4 = 4,096 letters

7th set = 4096 x 4 = 16,384 letters

8th set = 16,384 x 4 = 65,536 letters

Each letter cost 2

Total cost = 65,536 x 2 = 131,072

[tex]A=a\cdot b\cdot \sin\angle AB\\\\A=5\cdot8\cdot\sin63^\circ\\\\A=40\cdot0.891\\\\\boxed{A=35.64}[/tex]

Answer:

[tex]\huge \boxed{\mathrm{35.64 \ units^2 }}[/tex]

Step-by-step explanation:

The adjacent side lengths and an angle is given.

We need to find the height of the parallelogram.

A small right triangle is formed with an angle of 63 degrees and an hypotenuse of 5 units.

We can use trigonometric functions to solve for the height.

sin θ = opp/hyp

sin 63 = h/5

Multiplying both sides by 5.

h = 5 sin 63

h ≈ 4.45503262

Area of parallelogram = base × height

A = 8 × 4.45503262

A = 35.640261

Answer:

  D)  3.57%

Step-by-step explanation:

The percentage change is given by ...

  percent change = ((new value) -(old value))/(old value) × 100%

  = (3.19 -3.08)/3.08 × 100% = 0.11/3.08 × 100% = (11/3.08)% ≈ 3.57%

__

When dealing with percentages, you need to be clear about what number represents 100%, the reference value against which errors or changes are measured. Here, it is the π of the mug, 3.08.