If given an equation of a line such as y = -1/2x + 6, demonstrate on the whiteboard how to create an equation of a line parallel and perpendicular to this line that goes through another point such as (4, 10).

Answer:

-0.5 or -1/2

Step-by-step explanation:

The equation for slope is y₂-y₁ / x₂-x₁.

It should work with all of the points given. Any of the 2 points you choose will give you the slope -0.5 or -1/2.

The slope the straight line going through (-2,1) , (0,0) and (2,-1) is -1/2.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

The average slope of a straight line ;

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

So slope  associated with two points (-2,1) , (0,0)

⇒ (0 - 1) / (0 + 2)

⇒ -1/2

Since all three points are in a straight line so slope must be the same.

Hence "The slope the straight line going through (-2,1) , (0,0) and (2,-1) is -1/2".

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Answer:

a. square root is y = [tex]\sqrt{x}[/tex]

b. linear is y = x

c. cubic is [tex]y = x^3[/tex]

d. quadratic is [tex]y = x^2[/tex]

e. reciprocal squared is [tex]y = \frac{1}{x^2}[/tex]

f. absolute value is y = |x|

g. reciprocal is [tex]y = \frac{1}{x}[/tex]

h. cube root is [tex]y = \sqrt[3]{x}[/tex]

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

eleven less than (x)=x-11

x-11=12

  x=23

Answer:

G.

hope this explanation helps

Step-by-step explanation:

Answer:

Here mate!

Step-by-step explanation:

Enter numbers, scientific notation or E notation.

Scientific Notation: 3.45 x 10^5

E Notation: 3.45e5

HOPE IT HELPS AND IS CORRECT!

You need to work out the current UK percentage first.

Answer:

= 40

Step-by-step explanation:

2 ( 3 (5 + 2) -1)

= 2 * 20

= 40

Answer:

Step-by-step explanation:

[tex]2\left(3\left(5+2\right)-1\right)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3\left(5+2\right)-1\right)\:\\\\:\quad 20\\\\=2\times \:20\\\\= 40[/tex]

Answer:

30,370 feet

Step-by-step explanation:

The difference in elevations between two points will be 30370 feet.

It is given that Mt. Everest is 29000 feet above sea level and the shore of dead sea is 1370 feet below the sea level.

We have to find out the difference in elevation between the two points.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

As per the question ;

Height of Mt. Everest from sea level = 29000 ft. above

Height of shore of dead sea from sea level = 1370 feet below

As these both are in opposite directions , i.e., one above sea level and other below sea level , we should add both of these to find the difference in elevations between these two points.

i.e.,

The difference in elevations between two points will be ;

= 29000 + 1370

= 30370 feet

Thus , the difference in elevations between two points will be 30370 feet.

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Answer:

Hey there!

3(a+b)-2(2a-b)+4a-7a

3a+3b-4a+2b-3a

3b-4a+2b

5b-4a

-4a+5b

Let me know if this helps :)

Answer

[tex] \boxed{ \boxed{ \bold{ \red{ - 4a + 5b}}}}[/tex]

Step by step explanation

[tex] \sf3(a + b) - 2(2a - b) + 4a - 7a[/tex]

Distribute 3 through the parentheses

⇒[tex] \sf3a + 3b - 2(2a - b) + 4a - 7a[/tex]

Distribute 2 through the parentheses

⇒[tex] \sf3a + 3b - 4a + 2b + 4a - 7a[/tex]

Collect like terms

⇒[tex] \sf3a +4a - 4a - 7a + 3b + 2b[/tex]

Since , two opposites add up to zero, remove them from the expression

⇒[tex] \sf3a - 7a + 3b + 2b[/tex]

⇒[tex] \sf - 4a + 5b[/tex]

Hope I helped!

Best regards!!

Answer:

a) 2600

b) 1820

Step-by-step explanation:

let the number be 'x'

a)

[tex]x = 2000 + \frac{30}{100} (2000)[/tex]

[tex]x = 2000 + 600 = 2600[/tex]

b)

[tex]x = 2600 - \frac{30}{100} (2600)[/tex]

[tex]x = 2600 - 780 = 1820[/tex]

A=45

A=kx/y

where k is constant

substituting the values for k

k= 20×9/6=30

when x=9, y=6

A= 30×9/6=45

Answer:

D

Step-by-step explanation:

Area is found by LxWxH

Answer:

Step-by-step explanation:

[tex]Base = 10yd\\Height = 6yd\\\\Area = \frac{1}{2} \times base \times height\\\\A= \frac{1}{2} \times 10 \times 6\\\\A = \frac{60}{2} = \\\\30yd^2[/tex]

Answer:

yes

Step-by-step explanation:

Calculate the circumference (C) using

C = πd ( d is the diameter )

    = 180π cm

Each guest needs 70 cm, thus

180π ÷ 70 ≈ 8.078 ← number of guests at 1 table

18 × 8.078 = 145.404 ← number of guests at 18 tables.

There is enough tables to seat 145 guests

Answer:

5

Step-by-step explanation:

7c³d²

This term has tow variables, c and d

Power of c is 3

Power of d is 2

Degree of this monomial is = 3+2 = 5

Answer:

The answer is 12

Answer:

In the Northern Hemisphere, soil on south-facing slopes dries out faster and is warmer than soil on north-facing slopes due to longer exposure to sunlight – the opposite applies in the Southern Hemisphere.

Step-by-step explanation:

Answer:

16.12 units

Step-by-step explanation:

distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(8 - 10)² + (7 + 9)²]

d = √[(-2)² + (16)²]

d = √[4 + 256]

d = √260

d = 16.12

Answer:

205 litres

Step-by-step explanation:

Given:

Volume of water is given as:

[tex]V=100+20m[/tex] (in litres)

m is the time in minutes spent filling water in Eduardo's pool.

To find:

Volume of water in the pool after the water is filled for [tex]5\frac{1}{4}[/tex] minutes.

Solution:

Here, volume of water in the Pool (in litres) is given by the equation:

[tex]V=100+20m[/tex] ....... (1)

Where m is the time for which Eduardo fills the pool.

Here, we are also given that

m = [tex]5\frac{1}{4}[/tex] minutes = [tex]\frac{5\times4+1 }{4}=\frac{20+1}{4}=\frac{21}{4}[/tex] minutes

And we have to find the value of V after [tex]\frac{21}{4}[/tex] minutes.

Let us put the value of m as [tex]\frac{21}{4}[/tex] minutes in the equation (1) to find the value of V.

[tex]V=100+20m\\\Rightarrow V = 100 + 20 \times \frac{21}{4}\\\Rightarrow V = 100+105\\\Rightarrow \bold{V = 205\ litres}[/tex]

So, the volume of water in the pool after [tex]\frac{21}{4}[/tex] minutes is 205 litres.

Answer: see below

Step-by-step explanation:

coefficient: the numerical before a variable (3x)

constant: a number that is represented as an individual (5)

variable: any nonnumerical symbols (x)

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

4x-7+15z-y+20

coefficient: 4 (4x), 15 (15z), -1 (-y)

constant: -7, 20

variable: x, y, z

Hope this helps!! :)

Please let me know if you have any question

Answer:

HCF of 96 and 404 by prime factorisation method:-

Since, 96 = 2 × 2 × 2 × 2 × 2 × 3

and, 404 = 2 × 2 × 101

So, HCF of 96 and 404 = Product of common prime factors

                                 = 2 × 2 = 4

LCM = 2 × 2 × 2 × 2 × 2 × 101 × 3

       = 9696

Step-by-step explanation:

i think i

don't no

Answer:

she can make 4 batches of brownies

Step-by-step explanation:

since she already made a batch of brownie with 1/2 cup and she has 3/2 cups left, that means she can make 3 more

3+1=4

hope this helps

The batches of brownies can Luisa make is 4 batches.

It is required to find the the batches of brownies can Luisa make.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

3 batches of brownies from 3/2 cups of chocolate left.

Step-by-step explanation:

From the question, we know that:

1/2 cups of chocolate = 1 batch of brownies

3/2 cups of chocolate = x

Cross Multiply

1/2 × x = 3/2

x = 3/2/1/2

x = 3/2 × 2/1

x = 3 batches.

That means she can make 3 more

3+1=4

Therefore, the batches of brownies can Luisa make is 4 batches.

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Answer:

The table represents a proportional relationship

Step-by-step explanation:

Given

x ------ y

1 ------- 15

2 --------30

4 ---------60

5 -------- 75

Required

Determine if the table shows a proportional relationship

To check this, we make use of the following formula;

[tex]k = \frac{y}{x}[/tex]

Where k is the proportionality constant

When x = 1, y = 15

[tex]k = \frac{15}{1} = 15[/tex]

When x = 2, y = 30

[tex]k = \frac{30}{2} = 15[/tex]

When x = 4, y = 60

[tex]k = \frac{60}{4} = 15[/tex]

When x = 5, y = 75

[tex]k = \frac{75}{5} = 15[/tex]

Since the value of k for all values of x and y is the same; i.e. 15

Then, the table represents a proportional relationship

Quick Answer: $5.86

Step-by-step explanation:

Hope it helps!! :)

Answer:

f(-2) = 2

Step-by-step explanation:

The question is asking for the y-value of the point located at x = -2 on the graph. The point is at (-2, 2), so f(-2) = 2.

Answer:

Step-by-step explanation:

Regular hexagon has six equal sides

Perimeter = 5 + 5 + 5 + 5 + 5 +5   or 6*5

                = 30 cm

Answer:

Step-by-step explanation:

Given,

Initial velocity ( u ) = 6 m/s

Final velocity ( v ) = 70 m/s

Time ( t ) = 4 seconds

Acceleration ( a ) = ?

Finding the acceleration

We know that,

[tex] \boxed{\sf{acceleration = \frac{v - u}{t} }}[/tex]

⇒[tex] \sf{ \frac{70 - 6}{4} }[/tex]

⇒[tex] \sf{ \frac{64}{4} }[/tex]

⇒[tex] \sf{16 \: m/ {s}^{2} }[/tex]

Hope I helped!

Best regards!

Answer:

15

Step-by-step explanation:

A third of 45 is 1/3 multiplied by 45 or 45 divided by 3, which is equal to 15.

Answer:

15

Step-by-step explanation:

45 divided by 3 = 15

Answer:

[tex](x-9)^{2}[/tex]

Step-by-step explanation:

By factorization, we get ----

[tex]x^{2} -18x+81\\=x^{2} -9x-9x+81\\=x(x-9)-9(x-9)\\=(x-9)(x-9)\\=(x-9)^{2}[/tex]

Answer:

d = 43

Step-by-step explanation:

Answer:

5,418.2 feet

Step-by-step explanation:

Nadia is carrying out mountain climbing.

She started climbing the mountain at an altitude of 19.26 feet below the sea level.

Nadia changed her altitude by climbing a total of 5,437.8 feet from her starting position.

Therefore, Nadia's altitude at the end of her climb can be calculated as follows

= 5,437.8-19.6

= 5,418.2

Hence Maria's altitude at the end of her climb is 5,418.2 feet

Answer:

5,418.2 feet

Step-by-step explanation: