Which expression is equivalent to
x2 - 8x + 13 = 0

Answer:

Line a and Line b are parallel. The slopes are equal

Line b is perpendicular to line c. The slopes are different

Step-by-step explanation:

The standard form of an equation is y =- mx+C

m is the slope

Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1

For Line a: 4x-3y = 2

Rewrite

-3y = -4x+2

y = 4/3 x - 2/3

Slope of line a is 4/3

Line b: y = 4/3x + 2

mx = 4/3x

m = 4/3

slope of line b is 4/3

Line c = 4y+3x = 4

4y = -3x + 4

y = -3/4 x + 1

Slope of line c is -4/3

Since line a and b have the same slope, they arer parallel

mb * mc = 4/3 * -3/4

mb*mc = -1

Since the product of slope of line b and c is -1, they are perpendiclar

Answer:

12^2 = 144 and 13^2 = 169

So, the answer is 12 and 13

Step-by-step explanation:

Answer:

68.9°

Step-by-step explanation:

Using Sine rule

x/sin X = y/sin Y

4.5/sin X = 4/sin 56

sin X × 4 = 4.5 × sin 56

sin X = 4.5 × sin 56/4

X = arc sin (4.5 × sin 56/4)

X = 68.85449°

Approximately = 68.9°

Answer:

Step-by-step explanation:

use the number then do ÷

Answer:

1/7

Step-by-step explanation:

Answer:

80,66

Step-by-step explanation:

70 + 82 + 90 = 242

for average: you have 3 tests, so 242÷3 = 80,66667

Answer:

90 inches

Step-by-step explanation: 7 feet*12 inches= 84 and .5 feet*12 inches= 6.

84 inches+ 6inches=90inches

Answer: 1.2ft × 12

= 14.4"

Step-by-step explanation:

GIVE ME DA BRAINS

Answer:

160

Step-by-step explanation:

vertical angles

Answer:

its 80

Step-by-step explanation:

because of vertical angles the 160 is the same for the other side so you subtract the 80

Answer: Function A; 14 meters per seond

Step-by-step explanation:

do Distance/time for Function A: so you can show 140/10, or 280/20, it doesnt matter as they are all constant/consistent.

A has a rate of 14 m/s

B's  rate is given, 13 m/s

So A has a faster rate of 14 meters per second

Answer:

3 and 8

Step-by-step explanation:

3 and 8 are the only numbers that have a variable, or the letter beside it

Answer:

-3.5x - 31.5

Step-by-step explanation:

-3.5(x+9)

= -3.5x + -3.5(9)

= -3.5x - 31.5

Answer:

65

Step-by-step explanation:

Answer:

1 and 6 (alternate exterior angle)

2 and 5(corresponding angle)

4 and 5(co interior angle)

3 and 5(alternate interior angle)

Answer:

X axis is on the left of the Coordinates (x,y) and Y axis is on te right

X goes sideways

Y goes Vertical

Step-by-step explanation:

Given:

The equation of a circle is

[tex]x^2+y^2=169[/tex]

A tangent line l to the circle touches the circle at point P(12,5).

To find:

The gradient of the line l.

Solution:

Slope formula: If a line passes through two points, then the slope of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is

[tex]m_1=\dfrac{5-0}{12-0}[/tex]

[tex]m_1=\dfrac{5}{12}[/tex]

We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.

Product of slopes of two perpendicular lines is always -1.

Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.

[tex]m\times m_1=-1[/tex]

[tex]m\times \dfrac{5}{12}=-1[/tex]

[tex]m=-\dfrac{12}{5}[/tex]

Therefore, the gradient or slope of the tangent line l is [tex]-\dfrac{12}{5}[/tex] .

Answer:

x = - 2, y = 1

Step-by-step explanation:

Comparing both the equations,

→ y = y → x + 3 = - 2x - 3

=> x + 3 = - 2x - 3

=> x + 2x = - 3 - 3

=> 3x = - 6

=> x = - 6/3 = - 2

Substitute the value of x in any of these:

=> y = x + 3 = - 2 + 3 = 1

Answer:

Step-by-step explanation:

If a solution exists for the system of equations y=y so we can say

x+3=-2x-3 Add 2x to each side

3x+3=-3 Subtract 3 from each side

3x=-6. Divide each side by 3

x=-2, since y=x+3

y=-2+3

y=1

So the solution to the system of equations is the point (x,y)=(-2,1)

Answer:

10 students didnt turn in work

Step-by-step explanation:

10. its like saying 100 divided by 25

Answer:

24.16

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

If we have 84 feet of streamers. You cut 24 pieces that are each 1/2 yard long then 48 feet of streamers we left.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that we have a 84 feet of streamers.

You cut 24 pieces that are each 1/2 yard long.

Need to find the feet of streamers we left.

We know that 1 yard is equal to 3 feet.

Therefore, 1/2 yard is equal to 1.5 feet.

The total length of the streamers that were cut is:

24 pieces x 1.5 feet/piece = 36 feet

To find out how much streamer is left, we can subtract the length of the cut streamers from the total length we started with:

84 feet - 36 feet = 48 feet

Therefore, you have 48 feet of streamers left.

To learn more on Unit of Measurement click:

https://brainly.com/question/14026238

#SPJ2

Answer:

Number of [tex]\frac{1}{3}[/tex] liters required to fill the tank = 27

Step-by-step explanation:

Amount of water needed to fill the tank = 9 liters

Measure of water to fill a vessel = [tex]\frac{1}{3}[/tex] liters

Number of [tex]\frac{1}{3}[/tex] liters vessels required to fill the tank = [tex]\frac{9}{\frac{1}{3}}[/tex]

                                                                                  = 9 × [tex]\frac{3}{1}[/tex]

                                                                                  = 27

Therefore, number of [tex]\frac{1}{3}[/tex] liters required to fill the tank = 27

20:50 or if you have to add it 70

Answer:

(b³+11b²+24)ft³

Step-by-step explanation:

Volume of the rectangular prism = Length * Width * Height

Given the dimension

Length = b+8 ft

Width = b ft

Height = (b+3)ft

Volume of the rectangular prism = b(b+8)(b+3)

Volume of the rectangular prism = b(b^2+3b+8b+24)

Volume of the rectangular prism = b(b^2+11b+24)

Volume of the rectangular prism = b(b^2)+b(11b)+1(24)

Volume of the rectangular prism = b^3+11b^2+24

Hence the Volume of the rectangular prism is (b³+11b²+24)ft³

Step-by-step explanation:

ES6 has a new Set data structure for storing sets of unique objects. However it is based on object references as opposed to value comparisons. As far as I can tell this makes it impossible to have a set of pairs of numbers without stringifying.

For example, typing in Chrome's console (needs Chrome 38+):

> var s = new Set(); < undefined > s.add([2, 3]); < Set {[2, 3]} > s.has([2, 3]) < false <--- was hoping for 'true'

This appears to be by design: since I passed a different array of [2, 3] to has(), it returns false, because although the contents is the same it only looks at object references, and I allocated a new and different array to pass to has(). I would need to store a reference to the original array I passed to add() to check with has(), but this is not always possible. For example if the number pairs represent co-ordinates, I might need to check if the set has [obj.x, obj.y], but this will always return false since it allocates a new array.

The workaround is to stringify the arrays and key on strings like "2, 3" instead. However in something performance-sensitive like a game engine, it is unfortunate if every set access needs to make a string allocation and convert and concatenate number strings.

Does ES6 provide any feature to solve this problem without stringifying, or is there any feature on the horizon with ES7 that could help as well?

javascriptperformancedata-structuressetecmascript-6

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asked Sep 21 '14 at 13:06



AshleysBrain

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3 Answers

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As you've noted [2, 3] === [2, 3] is false, meaning you can't use Set like this; however, is Set really the best option for you?

You may find that using a two-level data structure like this will be better for you

var o = {}; function add(o, x, y) { if (!o[x]) o[x] = {}; o[x][y] = true; } function has(o, x, y) { return !!(o[x] && o[x][y]); } function del(o, x, y) { if (!o[x]) return; delete o[x][y]; // maybe delete `o[x]` if keys.length === 0

Answer:

First one is 2. The second one is 5.

Step-by-step explanation: