What are the 3 different types of solutions a 2 variable system can have?

**Disclaimer** Hi there! I assumed the question to be finding the "y-intercept", "x-intercept", and "slope/gradient" of the equation "y = 3x - 9". The following answering will be according to this understanding. If it is incorrect, please tell me and I will modify my answer.

Answer:

y-intercept = (0, -9)

x-intercept = (3, 0)

slope (m) = 3

Step-by-step explanation:

What is being asked: to find the corresponding values

Given equation

y = 3x - 9

Concept

The y-intercept of a line is on the coordinate of (0, a), where [ a ] is a constant.

Substitute values into the equation

y = 3x - 9

y = 3 (0) - 9

y = 0 - 9

y = -9

Therefore, the y-intercept is [tex]\Large\boxed{(0, -9)}[/tex]

Concept

The x-intercept of a line is on the coordinate of (a, 0), where [ a ] is a constant.

Substitute values into the equation

y = 3x - 9

0 = 3x - 9

Add 9 on both sides

0 + 9 = 3x - 9 + 9

9 = 3x

Divide 3 on both sides

9 / 3 = 3x / 3

x = 3

Therefore, the x-intercept is [tex]\Large\boxed{(3,0)}[/tex]

Concept

In the linear formula, y = mx + b, [ m ] is the slope and [ b ] corresponds to the y-intercept.

Determine the slope

Given the equation, y = 3x - 9, when corresponds to the general linear equation formula:

                                                  y = mx + b

                                                  y = 3x - 9

Therefore, the slope is [tex]\Large\boxed{m=3}[/tex]

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Answer:

force = work/distance

force = 900/5

force = 180 N

Using the probability concept, the correct statement is:

B. P(hibiscus|red) = P(hibiscus).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, the probabilities are:

Same probabilities, hence the statement that they are different is false.

For item b, the probabilities are:

Equal, hence this is the correct statement.

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Answer:

(f - g)(x) = [tex]3^{x}[/tex] + 8x + 4

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= [tex]3^{x}[/tex] + 10x - (2x - 4) ← distribute parenthesis by - 1

= [tex]3^{x}[/tex] + 10x - 2x + 4 ← collect like terms

= [tex]3^{x}[/tex] + 8x + 4

Answer:

27

Step-by-step explanation:

volume = side³

v = 3³

v = 27

i dont know how to convert to whatever h is so this is the best answer i can give

We have lcm(2, 3, 5) = 30, but none of 30/2 = 15, 30/3 = 10, nor 30/5 = 6 are divisible by 2, 3, and 5, respectively.

To account for this, take the square of 30, 30² = 900. Then 900/2 = 450, 900/3 = 300, and 900/5 = 180 are respectively divisible by 2, 3, and 5.

Multiply this by 2 to get a 4-digit number. It follows that [tex]\boxed{a=1800}[/tex].

When you are bisecting AB using a string and you have secured the strong at point A to be more than half of AB, the next step is to C. Make an arc on AB from point A and another arc from point B .

If you are using a string, the first step is the secure that string at point A because the string will be used for the bisecting.

After the string is secured, take the length to just a little more than half of line AB.

Once that is done, use the string to make an arc on line AB from the top to bottom.

Unsecure the string and take it to point B. Once secured in point B, repeat the process done with point A.

This would bisect the line using a string.

In conclusion, option C - Make an arc on  AB from point A and another arc from point B is correct.

Options for this question include:

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The median of the list of numbers is 7

The number is given as:

9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5

Rearrange the numbers in ascending order

2.5, 2.9, 3.2, 4.4, 7, 8.1, 9.2, 9.4, 9.5

The median is the middle number.

The middle number here is 7

Hence, the median of the list of numbers is 7

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Answer: 37.92

Step-by-step explanation: We know that 3202 / 5 = 640.4.

We subtract that by 830 to get (830 - 640.4  =) 189.6. Then we do / by five again to get 37.92. That is the answer.

The centre angle of circular sector is n = 90 degrees (approximately).

A sector is referred to as a component of a circular made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radius of the circle at its ends.

A piece of pizzas can be used as an analogy for the form of a circle's sector.

The formula for finding the angle formed at the circular sector in radian is;

Let 'n' be the centre angle.

Let 'l' be the slant height of the cone which is equal to radius of circular sector.

Let 'r' be the radius of the cone.

First, calculate the total length of the circular sector say 'L' which is equal to the circumference of the circular base of the cone.

circumference = 2[tex]\pi[/tex]r

                        = 2×3.14×1

                        = 6.28

Now,

centre angle = length of circular sector/radius of circle

n = L/l

n = 6.28/4

n = 1.57 radian

Convert radian in degree as;

n = (1.57×180)/[tex]\pi[/tex]

n = 89.95

n = 90 degrees (approximately)

Therefore, the angle made by the circular sector is 90 dergees.

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The correct question is-

The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle n degrees. Find n.

Answer:

[tex]AC = \bf 4.13 \space\ cm[/tex]

Step-by-step explanation:

Using Pythagoras's theorem:

[tex]\boxed {a^2 = b^2 + c^2}[/tex],

where:

a ⇒ hypotenuse (AC, ? cm)

b, c ⇒ the two other sides of the triangle (AB = 2.2 cm, BC = 3.5 cm),

we can find the length of AC.

[tex]AC^2 = AB^2 + BC^2[/tex]

⇒ [tex]AC^2 = (2.2)^2 + (3.5)^2[/tex]

⇒ [tex]AC = \sqrt{(2.2)^2 + ((3.5)^2}[/tex]

⇒ [tex]AC = \sqrt{17.9}[/tex]

⇒ [tex]AC = \bf 4.13 \space\ cm[/tex]

Answer:

1.320000

2. 0.057

Step-by-step explanation:

Answer:

x=62

Step-by-step explanation:

This is a straight angle so they have to add up to 180.

124+x-6=180

118+x=180

x=180-118

x=62

Answer:

62

Step-by-step explanation:

124 + (x - 6) = 180

118 + x = 180

x = 62

Answer:

x>-2

Step-by-step explanation:

x>-2 is the answer since we are looking for x values that the graph takes.

The line x=-2 looks like an asymptote so x>-2 must be the answer

Answer: x>-2

Step-by-step explanation:

Answer: 1. an = n + 4,   2. ( 3 1/2, 3.5, 5),   3. 6 1/12,   4. 97,   5. 0.2 meters,    6. 4.52,   7. 3 1/18

Step-by-step explanation:

The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction

Emanuel did a mistake in her first step by taking negative sign twice.

Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.

Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.

For instance:

According to question,

= [tex]\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)[/tex]

Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.

Correct steps are:

Step 1:

[tex]\frac{(3)(4)(-1)}{(5)(9)(2)}[/tex]

Step 2:

[tex]\frac{-12}{90}[/tex]

Step 3:

[tex]-\frac{2}{15}[/tex]

Therefore, the step 1 was miscalculated by Emanuel.

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The complete question is -

Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)

Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction

Step 3 StartFraction 12 over 90 EndFraction

Step 4 StartFraction 2 over 15 EndFraction

In which step did his first error occur?

Answer:

[tex]\sf t_{20}= 0[/tex]

Step-by-step explanation:

      [tex]\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }[/tex]

6th term is 14 ⇒ [tex]\sf t_6 = 14[/tex]

                a + (6 - 1)d = 14

                    a  +  5d = 14  --------------(I)

14th term is 6 ⇒[tex]\sf t_{14} = 6[/tex]

             a + (14-1)d = 6

                  a + 13d = 6 ----------------(II)

Subtract equation (II) from equation(I)

        (I)          a + 5d = 14

        (II)         a + 13d = 6

                    -    -          -

                            -8d = 8

                               d  = 8 ÷(-8)      

                              [tex]\sf \boxed{\bf d= (-1)}[/tex]

Plugin d = -1 in equation (I)

a + 5(-1) = 14

      a -5  = 14

             a = 14 + 5

             [tex]\sf \boxed{\bf a = 19}[/tex]  

20th term:

 [tex]\sf t_{20}= 19 + 19*(-1)[/tex]

       = 19 - 19

   [tex]\sf \boxed{\bf t_{20} = 0}[/tex]

Answer:

0

Step-by-step explanation:

The number of terms of an Arithmetic progressions has the formular.

Tn = a + ( n - 1 ) d

From the question,

6th term = 14

14th term = 6

Therefore,

a + 5d = 14 -----------(1)

a + 13d = 6 ----------(2)

subtracting

-8d = 8

dividing bothsides by -8

[tex] \frac{ - 8d}{ - 8} = \frac{8}{ - 8} \\ d = - 1[/tex]

Therefore,

common difference= -1

substituting the value of d into equation (1)

a + 5 ( -1) = 14

a - 5 = 14

a = 14 + 5 = 19

First term = 19

For the 20th term

T 20 = a + 19d

19 + 19 ( -1 )

19-19 = 0

Therefore,

20th term = 0

Answer:

  (c)  (28/3)√6

Step-by-step explanation:

Side ratios of "special triangles" are used to solve this problem.

  30-60-90° triangle — 1 : √3 : 2

  45-45-90° triangle — 1 : 1 : √2

We need to apply these ratios a few times:

  CD : CE = √3 : 2   ⇒   CE = (7√3)(2/√3) = 14

  CE : BE = 1 : √2   ⇒   BE = 14(√2) = 14√2

  BE : AE = √3 : 2   ⇒   AE = (14√2)(2/√3) = (28√2)/√3

The fraction can be simplified by multiplying by (√3)/(√3):

  ((28√2)/√3)×(√3)/(√3) = (28√6)/3

  AE = (28/3)√6

Answer:

[tex]the \: answer \: is \: choice \: b \: \frac{ - 2 \sin(x) }{1 + \cos(x) } [/tex]

will give you an explanation if you want tag me on comment.

Answer:

x=5

h = 5 sqrt 2

Step-by-step explanation:

isosceles right triangles are always 45-45-90, ratio of those triangles are always x:x:x*sqrt 2

Answer:

300 gallons

Step-by-step explanation:

A saline solution is a solution of salt in water.

The percent is the percent of salt in the total amount of solution.

A 40% saline solution has 40% of salt out of the total volume.

Let the amount of pure water needed = x.

The amount of existing 40% solution is 500 gal.

Let the total amount of 25% saline solution made = y.

Equation of volumes of solutions:

500 + x = y

y = x + 500          Eq. 1

Equation of volume of salt:

500 gal of 40% saline solution has 0.4 × 500 gal = 200 gal of salt

Pure water has 0% salt.

The final product is a solution that is 25% saline. Its volume is y.

The volume of salt in the y gallons of 25% saline solution is 25% of y = 0.25y

The equation of salt content is:

200 + 0 = 0.25y

y = 800       Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

y = x + 500

y = 800

Substitute 800 for y in Eq. 1.

y = x + 500

800 = x + 500

x = 300

Answer: 300 gallons of pure water

Answer:

Step-by-step explanation:

Answer:

35.7 megabytes

Step-by-step explanation:

Let's first find 10% of the percent needed. If it is 234 megabytes and 10% has downloaded so far, we conclude that 10% of the download is 23.4 megabytes (since we move the decimal point one spot to the left to find ten percent).

To get to 15% of the percent needed, let's split 10% in half to get the amount of megabytes per every 5%.

23.4/2 = 11.7

We can now conclude that 5% = 11.7. Therefore, 15% will equal (23.4 + 11.7) 35.1 megabytes.

To find the remaining 3.5% left of the percent needed, we use a calculator.

3.5% x 18 = 0.63.

We will add that to the 35.1 megabytes, but we need to round to the nearest tenth, as the question stated. Therefore, we round to 0.6, add it to 35.1, to get a total of 35.7 megabytes.

For 18.5% of the download, it will be 35.7 megabytes.

The Set C is the subset of A and D.

According to the statement

we have given that the three sets which are A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}.

And we have to find that the subsets of these sets.

So,

For a set S to be a subset of a set T, all of the elements of the set S need to be contained in the set T. Firstly, all of the sets are their own subsets, that is, A⊆A,B⊆B,C⊆C,D⊆D.

It follows that B⊂A because of 2∈A and 6∈A. Since 2 is not belongs to C and D. that's why B is not a subset of C and B is not a subset of D.

Taking into account that 4∈A and 6∈A, we conclude that C⊂A. By analogy, since 4∈D and 6∈D, we conclude that C⊂D.

Since |A|>|B|∣A∣>∣B∣ and |A|>|C|,∣A∣>∣C∣, we conclude that A is not a subset of B and A is not a subset of C.

Taking into account that |D|>|B|∣D∣>∣B∣ and |D|>|C|,∣D∣>∣C∣, we conclude that D is not a subset of B and D is not a subset of C. Since,2 not belongs to D that's why A is not a subset of D.

Since 8 not belongs to A, D is not a subset of A.

Overall, The Set C is the subset of A and D.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}. Determine which of these sets are subsets of which other of these sets.

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5 students like hockey more than football.

To find out How many more students like hocket than football:

Refer to the given table -

Students who do not like football and like hockey = a = 30

Students who like football and do not like hockey = b = 25

Now,

[tex]=a-b\\=30-25\\=5[/tex]

Therefore, 5 students like hockey more than football.

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The question you are looking for is shown below:

The two-way table shows the number of students in a school who like hockey and/or football. like hockey does not like hockey total like football 50 25 75 do not like football 30 45 75 total 80 70 150.

How many more students like hocket than football?

The linear equation for the cost that the household spend in water is given by:

C(d) = 237d + 1200.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the free usage of 1200 liters is the y-intercept, while the daily usage of 237 liters is slope. Hence the function for the amount the household spends in water in d days is given as follows:

C(d) = 237d + 1200.

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The Time taken by Jacob to run the dash race is (80 - t) seconds

We are told that;

Total distance for the dash race = 500 yards

Time taken by Jacob to run the dash race = 80 seconds

Now, we are told that Juan ran the same dash race but used t less seconds than Jacob. Thus;

Time taken by Jacob to run the dash race = (80 - t) seconds

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The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.

According to the statement

we have given the statement and we have to show that the statement is a true or false after analyzing.

So, to analyse the statement

Context diagrams show the interactions between a system and other actors (external factors) with which the system is designed to interface. System context diagrams can be helpful in understanding the context .

But we know that the standardized names is not used within each set of symbols. so, this is used in a randomly sets.

that's why the given statement is not true in the case of the standardized names.

So, The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.

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Answer:

1/2=20/40 19/20=38/40

Step-by-step explanation:

so the first option

The curve passes through the point (3, 3), so [tex]y=3[/tex] when [tex]x=3[/tex]. Then

[tex]y = ax^2 + bx \implies 3 = 9a + 3b \implies 3a + b = 1[/tex]

The tangent line to the curve at (3, 3) has gradient [tex]\frac{dy}{dx}[/tex] at [tex]x=3[/tex]. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

Then when [tex]x=3[/tex], the gradient is 4, so

[tex]2ax + b = 4 \implies 6a+b=4[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we find

[tex](6a+b) - (3a+b) = 4-1 \implies 3a = 3 \implies \boxed{a=1}[/tex]

and it follows that

[tex]3 + b = 1 \implies \boxed{b = -2}[/tex]

Cost to put a 0. 5 ft layer of topsoil on the entire garden is $1000.

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. Measurements are made in square units, with square meters serving as the reference unit 

Area of a Square = Side × Side.

Therefore, the area of square = Side square units.

Side of a square garden= 10 ft.

Area of a square garden= Side × Side= 10 × 10 =100 square ft.

Cost of the whole garden = 100×$5 =$500

Cost to put a 0. 5 ft layer of topsoil on the entire garden =$500/0.5

=$1000

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The cost need to put a 0. 5 ft layer of topsoil on the entire garden is $1000

According to the given statement

we have given that the

side length of the square garden is 10ft.

topsoil cost per foot is $5

And we have to find the cost which required to put a 0. 5 ft layer of topsoil on the entire garden.

So,

The  side length of the square garden is 10ft.

Now, the volume of the cube is (a)^2

And

Total volume of cube = 10*10

Total volume of cube = 100 per square foot.

Now, we find the cost required for a topsoil.

Cost required to put a topsoil of 1 foot in the total volume of cube = volume*cost

So,

Cost required to put a topsoil of 1 foot in the total volume of cube = 1000*5

Cost required to put a topsoil of 1 foot in the total volume of cube = $5000

if we put a topsoil of 0.5 feet then

The cost required = $5000/0.5

The cost required = $1000.

So, The cost need to put a 0. 5 ft layer of topsoil on the entire garden is $1000

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