a. Using variables, write out the formula for the point-slope form of the equation.

b. Determine the slope of the line.

c. Identify the point (-2, 2) as (x1, y1).

d. Write the equation of the line in point-slope form.

Show all work on how you found the slope or determined the slope from the graph. Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.

Answer: People attended the two performances are 683

What makes something common?

A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10. A factor that everyone whole numbers share is 1, or 1.

What is a greatest common factor?
It is the biggest number that two numbers are divisible by.

For example, if you did 12 and 24

The factors of 12 are:

1, 2, 3, 4, 6, 12

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, and 24

Their greatest common factor would be 12 since, it is the greatest number that each number can be divisible by.

Step-by-step explanation:

Number of people attend Friday event = 728
Number of people attend Saturday event = 728 - 45 = 683
Hence the answer is 683

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Answer:

6(y-2) would be 6y-12

Step-by-step explanation:

In the scientific notation, the total population of Brazil and Lithuania is 2.02255 x 10⁸

Scientific notation

A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 is known as Scientific notation.

Given,

In 2010, the population of Brazil was about 1.987 x 10⁸ people. The population of Lithuania was about 3.555 x 10⁶ people.

Here we need to find the total population of Brazil and Lithuania and expression the value in scientific terms.

Here we know that,

Population of Brazil = 1.987 x 10⁸

Population of Lithuania = 3.555 x 10⁶

In order to find the total population, first we have to make the exponent of the two value as equal,

For that we have to rewrite the population of Brazil as,

Population of Brazil = 198.7 x 10⁶

Now, we have to add the two population count in order to find the total population,

=> (198.7 x 10⁶) + (3.555 x 10⁶)

Take the exponent term as common,

=> (198.7 + 3.555) x 10⁶

=> 202.255 x 10⁶

Now, we have to move the two decimal point to simplify this one, then we get,

=> 2.02255 x 10⁸

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24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.

Let x ounces of 15% alcohol must be mixed with the 16 ounces of 20% alcohol.

The amount of alcohol in 16 ounces solution is = (20/100) * 16 ounces

                                                                              = 3.2 ounces

The amount of alcohol in x ounces  solution is = (15/100) * x

                                                                              = 0.15x ounces

Total amount of alcohol is = (16 + x) ounces

According to the problem we get an equation,

(3.2 + 0.15x)/(16 + x) = 17/100

100(3.2 + 0.15x) = 17(16 + x)

320 + 15x = 272 + 17x

320 - 272 = 17x - 15x

48 = 2x

x = 48/2

x = 24

Therefore, 24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.

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Using the proportion rule, the ratios 1/3 and 2/5 does not form a proportion.

In the given equation,

We have to check the ratios 1/3 and 2/5 form a proportion or not.

As we know that proportion is a ratio in which both ratios are equal to each other.

So to check whether the given statement is proportion or not we put both equation equal to each other.

So the ratios are 1/3 and 2/5.

Now checking the proportion.

1/3=2/5

Multiply by 15 on both side.

1/3 ×15=2/5 ×15

Simplifying

1×5=2×3

5=6

As we can see that both side is not equal so the given ratio is not proportion.

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Answer: true

Step-by-step explanation:

Co-interior angles are the two angles that occur between two parallel lines intersected by a transversal.

The sum of the co-interior angles is 180 degrees.

The value of x is 15.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Co-interior angles are the two angles that occur between two parallel lines intersected by a transversal.

The sum of the co-interior angles is 180 degrees.

(8x + 9)° and 51° are co-interior angles.

So,

8x + 9 + 51 = 180

8x = 180 - 60

8x = 120

x = 120/8

x = 15

Thus,

The value of x is 15.

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Answer:

1

Step-by-step explanation:

1) substitute z with 4 in the equation

(m^3)^4

2) multiply the index

m^3*4

=m^12

3) m^12≠ m^7

therefore, 1 is a lie

The statements above which is a lie is number 1

Statement 1 :

(m^3)^z = m^7

m^3z = m^7

3z = 7

z = 7/3 (False)

Statement 3 :

(4^5)^z = 4^20

4^5z = 4^20

5z = 20

z = 4 (True)

Statement 2 :

(12^3)^2 = 12^6

(12^y)^x = 12^6

12^6 = 12^6

(True)

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Answer: 2 < x < 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a line is written as [tex]y=mx+c[/tex].

What is the equation of a line?

The equation [tex]y = mx + c[/tex] is the general equation of any straight line where [tex]m[/tex] is the gradient of the line and [tex]c[/tex] is the [tex]y -intercept[/tex] .

Here the given equation is

[tex]y=1.5x+20[/tex]       ........[tex](1)[/tex]

when [tex]x=0[/tex]

[tex]y=1.5(0)+20\\y=20[/tex]

when [tex]x=1[/tex]

[tex]y=1.5(1)+20\\y=1.5+20\\y=21.5[/tex]

when [tex]x=-1[/tex]

[tex]y=1.5(-1)+20\\y=-1.5+20\\y=18.5[/tex]

Draw the graph

Hence, by using the values of [tex]x[/tex] and [tex]y[/tex] we formed a straight-line graph.

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Answer:

[tex]r \geqslant - 16[/tex]

Step-by-step explanation:

[tex] \frac{ - 10 + r}{2} \geqslant - 13[/tex]

multiply both sides by 2:

[tex] - 10 + r \geqslant - 26[/tex]

add 10 on both sides:

[tex]r \geqslant - 16[/tex]

Answer:

[tex]r \ge -16[/tex]

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

[tex]\frac{-10+r}{2} \ge -13[/tex]

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

[tex]\frac{-10+r}{2} *2 \ge -13 *2[/tex]

[tex]-10+r \ge -26[/tex]

Add 10 to both sides, and simplify

[tex](-10+r)+10 \ge (-26)+10[/tex]

[tex]r \ge -16[/tex]

The Algebraic expression that cannot be factorized is [tex]x^{2}[/tex] + 1

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

[tex]x^{2}[/tex] + -3x -18  can be expressed as  [tex]x^{2}[/tex] -6x +3x -18 which can be factored as (x -6)(x +3)

Also  [tex]x^{2}[/tex] + 7x + 6, (x+6)(x+1)

[tex]x^{2}[/tex] + 5x + 6 , (x+3)(x+1)

But  [tex]x^{2}[/tex] + 1 cannot be factored because since it does not have a variable of x.

In conclusion,  [tex]x^{2}[/tex] + 1 cannot be factored.

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The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3

Linear sequence is a sequence of number in order with same difference .or same ratio.

when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.

The sequence in the given question

-5 , -2 , 1 , 4 , 7, . . . .

The first term of sequence : a₁ = -5

The second term : a₂ = -2

Common difference : d = a₂ - a₁

=> d = -2 - (-5)

=> d = -2 + 5

=> d = 3

The nth rule of linear sequence is aₙ = aₙ₋₁ + d

replacing the value of d

aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.

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Answer:

15.62 is the length of the side of the rhombus.

Step-by-step explanation:

Formula:

A = (e x f)/2

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

Don't be a secret agent. You never know what's going to happen.

Step-by-step explanation:

Until he slipped on a puddle of goose poop. His hat flew off, revealing a shiny, bald head, which he immediately grabbed his scarf to cover. In his rush, he failed to notice a goose prodding at the secret package in his pocket. With a flurry of wingbeats, the goose flew off with the secret package in its beak. The secret agent suddenly realized that the goose was a spy in disguise from a rival organization.

Answer:

Step-by-step explanation:

Fraction=2/100

Decimal=0.02

Percent=2%

Answer: 0.02 as a decimal and 2%

Step-by-step explanation:

its correct!

Answer:

[tex]\huge\boxed{\sf 1 \frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\displaystyle =\frac{2}{3} + \frac{4}{6} \\\\Equalize \ the \ denominator \\\\= \frac{2 \times 2}{3 \times 2} + \frac{4}{6} \\\\= \frac{4}{6} + \frac{4}{6} \\\\Add \\\\=\frac{4+4}{6} \\\\= \frac{8}{6} \\\\Simplify\\\\= \frac{4}{3} \\\\Convert \ into \ mixed \ fraction\\\\= 1 \frac{1}{3} \\\\\rule[225]{225}{2}[/tex]

The volume of the sphere can be calculated using the formula V = 4/3πr³

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. It is a perfectly-round 3D shape with one continuous curved surface

We have a sphere.

Since the dimensions of a sphere are not given, we will assume it. Assume the radius of sphere be [r]. Then the approximate value of the volume of the sphere can be calculated using the formula -

V = 4/3πr³

Where -

[r] is the radius of sphere

Therefore, the volume of the sphere can be calculated using the formula V = 4/3πr³

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Answer:

50m/s = (50 ÷ 1000 × 60 × 60)km/h

           = 180km/h

Answer:

4

Step-by-step explanation:

Since YP is an angle bisector, Angle 1 and 2 are equal.

We know WYX is 17x+4 so

2 times Angle 1 is 17x+4

[tex]2(8x + 4) =17x + 4[/tex]

[tex]16x + 8 = 17x + 4[/tex]

[tex]4 = x[/tex]

Answer:

A ................................

The answer is : p = -4

the following are the steps to solve it::

13 - 3p = -5 (3 + 2p)

calculate the area of the right hand first by multiplying the number 5 by the number in brackets

13 - 3p = -15 - 10p

move everything that contains p to the left side

13 - 3p + 10p = - 15

count all containing p

13 + 7p = -15

move the ones that don't contain p to the right

7p = -15 - 13

count on the right side

7p = - 28

p = -4

The equation of the line q that is perpendicular to line p is  y = - 3 / 5 x - 9.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, p has an equation of y = 5 / 3 x - 4 Line q includes the point (-10,-3) and is perpendicular to line p.  The equation of line q can be found as follows:

The product of the slope of perpendicular lines is equals to negative one.

Therefore, let's find the slope of line q.

m₁m₂ = -1

5 / 3m₂ = - 1

m₂ = - 3 / 5

Hence, the equation of line q is y = - 3 / 5x + b.

Let's find the y-intercept using (-10, -3)

-3 = - 3 / 5(-10) + b

-3 = 6 + b

-3  - 6 = b

b = -9

Therefore, the equation of line q is y = - 3 / 5 x - 9

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Step-by-step explanation:

[tex]1 - (\frac{1}{4} + \frac{2}{3}) \\ = 1 - ( \frac{3 + 8}{12}) \\ = 1 - ( \frac{11}{12} ) \\ = \frac{1}{12} [/tex]

Answer:

[tex]1 \frac{7}{12}\; \sf pounds[/tex]

Step-by-step explanation:

To find the amount of flour Grandma has left over, subtract the amount she used to make rolls from the original amount.

Given calculation:

[tex]3 \frac{1}{4}-1 \frac{2}{3}[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

[tex]\implies \dfrac{3 \times 4+1}{4}-\dfrac{1 \times 3+2}{3}[/tex]

[tex]\implies \dfrac{13}{4}-\dfrac{5}{3}[/tex]

Change both fractions into equivalent fractions so both fractions have the same denominator:

[tex]\implies \dfrac{13 \times 3}{4\times 3}-\dfrac{5 \times 4}{3 \times 4}[/tex]

[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\implies \dfrac{39}{12}-\dfrac{20}{12}=\dfrac{39-20}{12}=\dfrac{19}{12}[/tex]

Divide the numerator by the denominator:

[tex]\implies 19 \div 12 = 1 \; \sf remainder \; 7[/tex]

The solution as a mixed number is the whole number and the remainder divided by the denominator:

[tex]\implies 1 \frac{7}{12}[/tex]

Step-by-step explanation:

We know rhat

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 - \cos(x) }{2} } [/tex]

whenever x lies from 90 to 180.

If

[tex] \csc(x) = 9[/tex]

Using Reciprocal Identities

[tex] \sin(x) = \frac{1}{9} [/tex]

Using Pythagorean Identity,

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

[tex]( \frac{1}{9} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]

[tex] \cos {}^{2} (x) = \frac{80}{81} [/tex]

[tex] \cos(x) = \frac{4 \sqrt{5} }{9} [/tex]

Cosine is negative in when x lies between 90 and 180 so

[tex] \cos(x) = - \frac{4 \sqrt{5} }{9} [/tex]

So

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{2} } [/tex]

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{9 + 4 \sqrt{5} }{18} } [/tex]

For cosine remember

[tex] \cos( \frac{x}{2} ) = \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]

Cosine is negative in second quadrant so

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 - \frac{4 \sqrt{5} }{9} }{2} } [/tex]

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{9 - 4 \sqrt{5} }{18} } [/tex]

For tangent,

[tex] \tan( \frac{x}{2} ) = \frac{ \sin( \frac{x}{2} ) }{ \cos( \frac{x}{2} ) } [/tex]

[tex] \frac{ \sqrt{ \frac{1 - \cos(x) }{2} } }{ \sqrt{ \frac{1 + \cos(x) }{2} } } [/tex]

[tex] = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]

Tangent is negative over 90<x<180 so

[tex] - \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]

[tex] - \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{1 - \frac{4 \sqrt{5} }{9} } } [/tex]

[tex] - \sqrt{ \frac{ \frac{9 + 4 \sqrt{5} }{9} }{ \frac{9 - 4 \sqrt{5} }{9} } } [/tex]

[tex] - \sqrt{ \frac{9 + 4 \sqrt{5} }{9 - 4 \sqrt{5} } } [/tex]

[tex] - \sqrt{ \frac{1}{(9 - 4 \sqrt{5) {}^{2} } } } [/tex]

[tex] - \frac{1}{9 - 4 \sqrt{5} } [/tex]

so

[tex] \tan( \frac{x}{2} ) = - \frac{1}{ 9 + 4 \sqrt{5} } [/tex]

or

[tex] \tan( \frac{x}{2} ) = - 9 + 4 \sqrt{5} [/tex]

Answer:

75%

Step-by-step explanation:

5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.

Let x be the number of pints of the first fruit juice (i.e., 30%) and y be the number of pints of the second fruit juice (i.e., 80%).

Since the total number of pints to make the 75% pure fruit juice is 50, it can be represented using the equation:

x + y = 50 -----(1)

Also, x pints of the first juice = 0.30x, y pints of the second juice = 0.80y and 50 pints of the mixture to be produced = 50(0.75)= 37.5. Therefore:

This is represented as ;

30% × x + 80% × y = 50 of 75%

Make x in the subject x + y = 50

Substitute:

x = 50 - y in 30% × x + 80% × y = 50 of 75%

0.30 (50 - y) + 0.8 × y = 50 of 0.75

15 - 0.3y + 0.8y = 37.5

Collect like terms :

-0.3y + 0.8y = 37.5 - 15

0.5y = 22.5

y = 45

Recall that :

x = 50 - y

x = 50 - 45

x = 5

Hence, 5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.

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Answer:

D. 4 5/13

Step-by-step explanation:

For every time we divide by 13, we consider that a whole number. The whole number is the number on the outside of the fraction. It is equal to 13/13 in this case. So, we can divide 57 by 13, 4 times and have 5/13 left over. Therefore, the answer is D. 4 5/13! :)

Answer:

$25940

Step-by-step explanation:

Future value of an Investment at r% for n years is given by:

Future Value = Initial Investment (1 + r/100)n

If r = 10% and n = 10 years

Future Value = 10000(1 + 10/100)10

= 10000(1.1)10

= 10000(2.594)

= $ 25940

Hence the required value is $ 25940.