describe system of linear equations using practical situation and mathematical expressions

pahelp pooo​

Answer:

Step-by-step explanation:

Sum of interior angles of any triangle is 180°:

Answer:

Top box: 15

Bottom box: 480

Answer:

[tex]\left[\begin{array}{ccc}5&15&20\\120&360&480\end{array}\right][/tex]

Explanation:

For every 5 gallons, there's 120 miles. If we know we have 360 miles, we can see how many times 120 goes into 360, which is 3.

5 * 3 = 15.

Then just reverse the process

Answer:

- 7x^2 + 3xy - 9y

Step-by-step explanation:

(2xy- 4x^2) - (9y + 3x^2 - xy)

Add the second polynomial:

Change all the signs in the second polynomial because it has a negative sign before the parentheses.

= 2xy - 4x^2 - 9y - 3x^2 + xy

Combine like terms:

(-4x^2 - 3x^2) + (2xy + xy) - 9y

= -7x^2 + 3xy - 9y

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider,

[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]

On taking LCM, we get

[tex]\rm \:  =  \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]

and

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]

So, using these Identities, we get

[tex]\rm \:  =  \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{2(7 - 3)}{7 + 3} [/tex]

[tex]\rm \:  =  \: \dfrac{2 \times 4}{10} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{5} [/tex]

Hence,

[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]

Answer:

-9/16 > -7/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.x +y = 1   Yes

2. Power of variable e is 3. So, it is not a linear equation

No.

3) Great than symbol is there. No, it is not a linear equation.

4. 2x -y = 2x + 5

2x - y - 2x = 5

      -y = 5 is not a linear equation with two variable.

No.

5. No.

1) (5,14)  ; (19,7)

[tex]Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{7-14}{19-5}\\\\=\dfrac{-7}{14}\\\\=\dfrac{-1}{2}[/tex]

2) (-10 , 1)  ; (-10 ,4)

x- coordinate is same for both the points. So, the line is parallel to y-axis

Slope = undefined

[tex]3) (-3,-3) ; (15,13)\\\\slope=\dfrac{13-[-3]}{15-[-3]}\\\\=\dfrac{13+3}{15+3}\\\\=\dfrac{16}{18}\\\\=\dfrac{8}{9}[/tex]

[tex]4)(\dfrac{-1}{2},\dfrac{1}{7}) ; (\dfrac{-3}{2},\dfrac{2}{7})\\\\Slope=\dfrac{\dfrac{2}{7}-\dfrac{1}{7}}{\dfrac{-3}{2}+\dfrac{1}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{\dfrac{-2}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{-1}\\\\\\=\dfrac{-1}{7}[/tex]

Compare with y = mx + b  ; here m is slope

1. y = -2x - 8

slope = -2

2. x = 3

Line is parallel to y-axis.

So, slope = undefined

3.2x - y = 4

        2x - 4 = y

y = 2x - 4

Slope = 2

4.) 2x + y - 5 = 0

       y = -2x + 5

Slope = -2

Answer:

y = 6x-13

Step-by-step explanation:

Given: y+1=6(x-2)

Distribute 6: y +1 = 6x -12

Isolate y: y = 6x -13 (subtracted 1 from both sides)

This is now in the form y = mx +b

Hope this helps!

[tex]\\ \sf\longmapsto 3x-4=y[/tex]

[tex]\\ \sf\longmapsto y=3x-4[/tex]

Done !

Here

Note:-

Standard form

[tex]\\ \sf\longmapsto y=mx+b[/tex]

Answer:

[tex]⟼3x−4=y \\ \\

isolate y

\begin{gathered}\\ \sf\longmapsto y=3x-4\end{gathered}⟼y=3x−4

Done !

Here

m=3

b=-4

Note:-

Standard form

\begin{gathered}\\ \sf\longmapsto y=mx+b\end{gathered}⟼y=mx+b

[/tex]

Answer:

v = 1

u = 2

Step-by-step explanation:

Given is a special right triangle with angle measures as follows:

90-60-30

The side lengths would be :

2x- x[tex]\sqrt{3}[/tex]-x

in the image it shows that the second side length (the one that sees angle measure 60) is [tex]\sqrt{3}[/tex] from this we can conclude x = 1 so:

v = 1 and

u = 2

Answer: 44.44 mph

(50 + 40) / 2 = X

88.88/2 = X

44.44= X

Step-by-step explanation:

Answer:

Hi there!

Here is your answer...

The Area of the Parallelogram is:

The Perimeter of the Parallelogram is:

[tex]64ft[/tex]

Step-by-step explanation:

To find the Area of a Parallelogram you must first identify the Base and Height. In this instance the Base would be the top and bottom which we know are 17ft in length. The Height would be the dotted line that we know it 12ft tall. The next step would be to Multiply the Base by the Height. That would give us 204. After we add the correct units we have [tex]204ft^{2}[/tex].

To find the Perimeter we would simply add together all side lengths. We know that the top and bottom are equal to 17ft and the left and right are equal to 15 feet. This gives us 17+17+15+15. Which would equal 64, add the units and it becomes [tex]64ft[/tex].

Area=base x height

Perimeter = base + base + angle +angle

(angle is the side length.)

Answer:

0, 1, and 2

This is the answer

Answer:

The fossils would look weird and sometimes they might not be the exact shape as before because they've grown with the earth meaning they're going to come out of the ground go back under and what not, Its hard to tell how deep a fossil can be in the ground because of how many years ago it was because how much the earth has grown.

Step-by-step explanation:

Angle ADB is a right angle --- Given

Angle ADB is 90 degrees --- Definition of a Right Angle

Angle CDB is 90 degrees --- Definition of Supplementary Angles

Angle ADB = Angle CDB --- Definition of Congruent Angles

Proofs can be tricky! What helps me is thinking through them step by step and how I would prove I did something. While I'm not entirely sure what options you have for this proof, I've given my best guess.

Hope this helps!! :)

Answer:

You will pay $3.78 in tax. And you would pay a total of $66.78

Step-by-step explanation:

Answer: $3.78 or $66.78 if you are looking for the total amount including tax.

Step-by-step explanation:

6% can be represented by 0.06 so multiply that by 63

63*0.06=3.78

You will pay $3.78 in taxes

The total is 66.78 but I think you are asking for the tax.

Answer:

[tex] \frac{15}{13} = 1 \frac{2}{13} [/tex]

Step-by-step explanation:

[tex]2 \frac{1}{2} \div 2 \frac{1}{6} \\ \\ \\ \frac{5}{2} \div \frac{13}{6} \\ \\ \\ \frac{5}{2} \times \frac{6}{13} \\ \\ \\ \frac{5}{1} \times \frac{3}{13} \\ \\ \\ = \frac{15}{13} \\ \\ \\ = 1\frac{2}{13} [/tex]

I hope I helped you^_^

Answer:

[tex]2 \frac{1}{2} /2 \frac{1}{6} = \frac{5}{2} / \frac{13}{6} [/tex]

[tex] = \frac{5}{2} \times \frac{6}{13 } = \frac{5 \times 6}{2 \times 13} [/tex]

[tex] = \frac{5 \times 3}{1 \times 13} [/tex]

[tex] = \frac{15}{13} [/tex]

[tex] = 1 \frac{2}{13} [/tex]

Step-by-step explanation:

Thank you!!!!!!!!!!!

The full price of a rashguard is $25 and the expression for the full price is 3 (x - 5) = 60.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the full price of each rashguard be x,
Rashguards sell for $5 less than full price.
x - 5
Miguel purchases 3 rashguards and pays a total of $60.
3 (x - 5) = 60
Simplifying,
x - 5 = 60 / 3
x - 5 = 20
x = 20 + 5
x = 25

Thus, the full price of a rashguard is $25 and the expression for the full price is 3 (x - 5) = 60.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ6

Answer:3.33%

easy

Step-by-step explanation:

A = true value = 60

B = estimated or measured value = 62

C = percent error

C = ( |A-B|/A ) * 100%

C = ( |60-62|/60 ) * 100%

C = (2/60)*100%

C = 0.0333*100%

C = 3.33%

Answer:

1) 1085 ÷ 7

7 )1085(155

- 7

38

- 35

× 35

- 35

0

1085 ÷ 7 = 155

2) 7104 ÷ 32

32 )7104(222

- 64

× 70

- 64

×64

- 64

××

7104 ÷ 32 = 222

3) 2244 ÷ 51

51)2244(44

- 204

×244

- 244

×××

2244 ÷ 51 = 33

4) 1584 ÷ 12

12)1584(132

- 12

×38

- 36

×24

- 24

××

1584 ÷ 12 = 132

5) 1467 ÷ 9

9)1467(163

- 9

56

- 54

27

- 27

××

1467 ÷ 9 = 163

6) 2830 ÷ 28

28)2830(101

- 28

××3

- 0

30

- 28

×2

2830 ÷ 28 = 101 with the remainder 2

7) 9090 ÷ 45

45)9090(202

- 90

××9

- 0

90

- 90

××

9090 ÷ 45 = 202

8) 7000 ÷ 62

62)7000(112

- 62

×80

- 62

180

- 125

×55

7000 ÷ 62 = 112 with the remainder 55

9) 1150 ÷ 15

15)1150(76

- 105

×100

- 90

10

1150 ÷ 15 = 76 with the remainder 10

Hope that my answer is right and helpful to you

Answer:  The Van needs 18 gallons of gas to travel 360 miles.

Answer: 2 hours 25 minutes

Step-by-step explanation:

Answer:

2 hours 25 minutes.

Step-by-step explanation:

12:15pm-9:50am=2:25.

Pretty much it, hope this helps!

Answer:

2.4hrs or 2hrs 24 minutes

Step-by-step explanation:

3/5 × 4/1 = 12/5

60÷5=12

12×12=144

144÷60=2.4hrs

Answer:

11/4 The reciprocal will be 4/11

[tex]4y ^{2} = 49 \\ = > {y}^{2} = \frac{49}{4} \\ = > {y} = \sqrt{ \frac{49}{4} } \\ = > y = \frac{ \sqrt{49} }{ \sqrt{4} } \\ = > y = \frac{7}{2} \\ = > y = 3.5[/tex]

y = 3.5

Answer:

-6/7

Step-by-step explanation:

maf

Answer:

As it gets closer to the sun

Step-by-step explanation:

just trust me

The tail of comet will appear to become longer : (c) as it gets closer to sun.

The tail of a comet becomes longer and more pronounced as it gets closer to sun. Comets are made up of ice, dust, and volatile gases. As a comet approaches the sun, the sun's heat causes the ices within the comet to vaporize, creating a glowing coma (a cloud of gas and dust) around the nucleus.

The solar wind and radiation pressure then push the gas and dust particles away from the coma, forming the tail that points away from the sun due to the solar wind's influence. This tail becomes more visible and elongated as the comet gets closer to the sun, making it a sight in night sky.

Therefore, the correct option is (c).

Learn more about Comet here

https://brainly.com/question/29913698

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The given question is incomplete, the complete question is

When would the tail of a comet appear to become longer?

(a) as it gets farther from Earth

(b) as it gets closer to Earth

(c) as it gets closer to the sun

(d) as it gets farther from the sun

x=5.....................

Step-by-step explanation:

[tex] { - 100}^{1} [/tex]